[ { "id": "Arithmetic_0000", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Interpreting integers", "level": "3", "keywords": [ "distributive", "expression", "linear", "negative" ], "problem_v1": "The additive inverse of $5$ is [ANS]", "answer_v1": [ "-5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The additive inverse of $-9$ is [ANS]", "answer_v2": [ "9" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The additive inverse of $-4$ is [ANS]", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0001", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Interpreting integers", "level": "2", "keywords": [ "real numbers" ], "problem_v1": "Which of the following are integers? There may be more than one correct answer. [ANS] A. $\\sqrt{3}$ B. $-2.101001000100001\\ldots$ C. $58$ D. $-43261$ E. ${\\textstyle\\frac{3}{28}}$ F. $62120$ G. $-2.063$ H. $-7$", "answer_v1": [ "CDFH" ], "answer_type_v1": [ "MCM" ], "options_v1": [ [ "A", "B", "C", "D", "E", "F", "G", "H" ] ], "problem_v2": "Which of the following are integers? There may be more than one correct answer. [ANS] A. $-{\\textstyle\\frac{9}{65}}$ B. $-81699$ C. $-6.143$ D. $\\sqrt{4}$ E. $93$ F. $\\pi$ G. $\\sqrt{3}$ H. $-7$", "answer_v2": [ "BDEH" ], "answer_type_v2": [ "MCM" ], "options_v2": [ [ "A", "B", "C", "D", "E", "F", "G", "H" ] ], "problem_v3": "Which of the following are integers? There may be more than one correct answer. [ANS] A. $9.101001000100001\\ldots$ B. $-1.613$ C. $3.7\\overline{52}$ D. $0$ E. $-6$ F. $27933$ G. $-19139$ H. $\\pi$", "answer_v3": [ "DEFG" ], "answer_type_v3": [ "MCM" ], "options_v3": [ [ "A", "B", "C", "D", "E", "F", "G", "H" ] ] }, { "id": "Arithmetic_0003", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "4", "keywords": [ "financial mathematics", "algebra" ], "problem_v1": "Suppose that Alice has 10000 dollars and Bill has 3000 dollars. How much more money does Alice have than Bill? Answer=[ANS]", "answer_v1": [ "7000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Suppose that Alice has 7000 dollars and Bill has 4000 dollars. How much more money does Alice have than Bill? Answer=[ANS]", "answer_v2": [ "3000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Suppose that Alice has 8000 dollars and Bill has 3000 dollars. How much more money does Alice have than Bill? Answer=[ANS]", "answer_v3": [ "5000" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0004", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "integer", "negative", "subtract" ], "problem_v1": "Subtract the following integers:\n${4-8=}$ [ANS]\n${8-3=}$ [ANS]\n${3-14=}$ [ANS]", "answer_v1": [ "-4", "5", "-11" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Subtract the following integers:\n${1-10=}$ [ANS]\n${5-2=}$ [ANS]\n${6-14=}$ [ANS]", "answer_v2": [ "-9", "3", "-8" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Subtract the following integers:\n${2-9=}$ [ANS]\n${6-3=}$ [ANS]\n${3-14=}$ [ANS]", "answer_v3": [ "-7", "3", "-11" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0005", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [ "integer", "negative", "add", "subtract", "absolute value" ], "problem_v1": "Consider the following situation in which you borrow money from your cousin:\nOn June 1st, you borrowed $1400$ dollars from your cousin.\nOn July 1st, you borrowed $420$ more dollars from your cousin.\nOn August 1st, you paid back $630$ dollars to your cousin.\nOn September 1st, you borrowed another $950$ dollars from your cousin. How much money do you owe your cousin now? [ANS]", "answer_v1": [ "2140" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Consider the following situation in which you borrow money from your cousin:\nOn June 1st, you borrowed $1000$ dollars from your cousin.\nOn July 1st, you borrowed $490$ more dollars from your cousin.\nOn August 1st, you paid back $530$ dollars to your cousin.\nOn September 1st, you borrowed another $870$ dollars from your cousin. How much money do you owe your cousin now? [ANS]", "answer_v2": [ "1830" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Consider the following situation in which you borrow money from your cousin:\nOn June 1st, you borrowed $1100$ dollars from your cousin.\nOn July 1st, you borrowed $420$ more dollars from your cousin.\nOn August 1st, you paid back $550$ dollars to your cousin.\nOn September 1st, you borrowed another $910$ dollars from your cousin. How much money do you owe your cousin now? [ANS]", "answer_v3": [ "1880" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0006", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "integer", "negative", "add", "subtract" ], "problem_v1": "Perform the given addition and subtraction:\n${{-12-6+\\left(-4\\right)}=}$ [ANS]\n${{8-\\left(-17\\right)+\\left(-17\\right)}=}$ [ANS]", "answer_v1": [ "-22", "8" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Perform the given addition and subtraction:\n${{-20-10+\\left(-9\\right)}=}$ [ANS]\n${{4-\\left(-10\\right)+\\left(-17\\right)}=}$ [ANS]", "answer_v2": [ "-39", "-3" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Perform the given addition and subtraction:\n${{-17-7+\\left(-8\\right)}=}$ [ANS]\n${{6-\\left(-18\\right)+\\left(-17\\right)}=}$ [ANS]", "answer_v3": [ "-32", "7" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0007", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [ "integer", "negative", "add", "subtract", "absolute value" ], "problem_v1": "Consider the following scenario in which you study your bank account.\nOn Jan. 1, you had a balance of $-400$ dollars in your bank account.\nOn Jan. 2, your bank charged $40$ dollar overdraft fee.\nOn Jan. 3, you deposited $930$ dollars.\nOn Jan. 10, you withdrew $720$ dollars. What is your balance on Jan. 11? [ANS]", "answer_v1": [ "-230" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Consider the following scenario in which you study your bank account.\nOn Jan. 1, you had a balance of $-130$ dollars in your bank account.\nOn Jan. 2, your bank charged $50$ dollar overdraft fee.\nOn Jan. 3, you deposited $830$ dollars.\nOn Jan. 10, you withdrew $600$ dollars. What is your balance on Jan. 11? [ANS]", "answer_v2": [ "50" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Consider the following scenario in which you study your bank account.\nOn Jan. 1, you had a balance of $-220$ dollars in your bank account.\nOn Jan. 2, your bank charged $45$ dollar overdraft fee.\nOn Jan. 3, you deposited $850$ dollars.\nOn Jan. 10, you withdrew $670$ dollars. What is your balance on Jan. 11? [ANS]", "answer_v3": [ "-85" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0008", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "real numbers", "operations with signed numbers" ], "problem_v1": "Add as indicated: a) $-4+(-6)=$ [ANS]\nb) $-6+9=$ [ANS]", "answer_v1": [ "-10", "3" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Add as indicated: a) $-12+(-2)=$ [ANS]\nb) $-11+5=$ [ANS]", "answer_v2": [ "-14", "-6" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Add as indicated: a) $-9+(-6)=$ [ANS]\nb) $-9+8=$ [ANS]", "answer_v3": [ "-15", "-1" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0009", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [], "problem_v1": "Ms. Jaffe solved this problem. $39+48=87$ Which number sentence could Ms. Jaffe use to check her work? [ANS] A. $65+27=\\square$ B. $39+87=\\square$ C. $87-39=\\square$ D. $48-39=\\square$", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Ms. Jaffe solved this problem. $36+49=85$ Which number sentence could Ms. Jaffe use to check her work? [ANS] A. $65+27=\\square$ B. $36+85=\\square$ C. $49-36=\\square$ D. $85-36=\\square$", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Ms. Jaffe solved this problem. $37+48=85$ Which number sentence could Ms. Jaffe use to check her work? [ANS] A. $65+27=\\square$ B. $85-37=\\square$ C. $48-37=\\square$ D. $37+85=\\square$", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0010", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "4", "keywords": [], "problem_v1": "Kim scored $28$ points in a basketball game. Adam scored $8$ fewer points than Kim. How many point did Adam score? [ANS] A. $24$ B. $36$ C. $20$ D. $32$", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Kim scored $16$ points in a basketball game. Adam scored $10$ fewer points than Kim. How many point did Adam score? [ANS] A. $11$ B. $26$ C. $21$ D. $6$", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Kim scored $20$ points in a basketball game. Adam scored $8$ fewer points than Kim. How many point did Adam score? [ANS] A. $16$ B. $12$ C. $24$ D. $28$", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0011", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [], "problem_v1": "Write a number in the box to make this number sentence true. $5+8=$ [ANS] $+4$", "answer_v1": [ "9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Write a number in the box to make this number sentence true. $3+7=$ [ANS] $+2$", "answer_v2": [ "8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Write a number in the box to make this number sentence true. $3+6=$ [ANS] $+2$", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0012", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "4", "keywords": [], "problem_v1": "Mrs. Thompson has some puzzles. She gave $24$ puzzles to her students. Now she has $22$ puzzles left. Mrs. Thompson started with [ANS] puzzles.", "answer_v1": [ "46" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Mrs. Thompson has some puzzles. She gave $29$ puzzles to her students. Now she has $16$ puzzles left. Mrs. Thompson started with [ANS] puzzles.", "answer_v2": [ "45" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Mrs. Thompson has some puzzles. She gave $25$ puzzles to her students. Now she has $18$ puzzles left. Mrs. Thompson started with [ANS] puzzles.", "answer_v3": [ "43" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0013", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "The smallest sum one could get by adding three different numbers from the set {-1, 20, 24, 13,-4, 17} is [ANS].", "answer_v1": [ "8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The smallest sum one could get by adding three different numbers from the set {-3, 22, 24, 14,-5, 15} is [ANS].", "answer_v2": [ "6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The smallest sum one could get by adding three different numbers from the set {-3, 19, 24, 13,-5, 16} is [ANS].", "answer_v3": [ "5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0014", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "Compute:\n9+17=[ANS]\n8+8=[ANS]\n14+9=[ANS]\n7+18=[ANS]\n14+15=[ANS]\n17+21=[ANS]\n12+13=[ANS]\n19+19=[ANS]", "answer_v1": [ "26", "16", "23", "25", "29", "38", "25", "38" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "Compute:\n6+19=[ANS]\n6+6=[ANS]\n19+9=[ANS]\n5+17=[ANS]\n16+12=[ANS]\n17+23=[ANS]\n16+11=[ANS]\n15+16=[ANS]", "answer_v2": [ "25", "12", "28", "22", "28", "40", "27", "31" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "Compute:\n7+17=[ANS]\n7+7=[ANS]\n13+9=[ANS]\n8+19=[ANS]\n18+13=[ANS]\n14+21=[ANS]\n8+15=[ANS]\n29+25=[ANS]", "answer_v3": [ "24", "14", "22", "27", "31", "35", "23", "54" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0015", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [], "problem_v1": "For the problems below add or subtract as indicated. $7506$ $+9911$=[ANS]\n$64784$ $-33928$=[ANS]\n$835026$ $-26332$=[ANS]\n$85926$ $+17937$=[ANS]\n$734584$ $+141675$=[ANS]\n$901638$ $+22457$=[ANS]\nMyronville School District has 23083 students, and Saddelton School District has 44191 students. That means that there are [ANS] more students in Saddelton than in Myronville.", "answer_v1": [ "17417", "30856", "808694", "103863", "876259", "924095", "21108" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [] ], "problem_v2": "For the problems below add or subtract as indicated. $7502$ $+9912$=[ANS]\n$64782$ $-33927$=[ANS]\n$835029$ $-26332$=[ANS]\n$85924$ $+17935$=[ANS]\n$734586$ $+141671$=[ANS]\n$901638$ $+22457$=[ANS]\nMyronville School District has 23084 students, and Saddelton School District has 44655 students. That means that there are [ANS] more students in Saddelton than in Myronville.", "answer_v2": [ "17414", "30855", "808697", "103859", "876257", "924095", "21571" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [] ], "problem_v3": "For the problems below add or subtract as indicated. $7503$ $+9911$=[ANS]\n$64783$ $-33928$=[ANS]\n$835026$ $-26332$=[ANS]\n$85927$ $+17939$=[ANS]\n$734588$ $+141672$=[ANS]\n$901636$ $+22457$=[ANS]\nMyronville School District has 23081 students, and Saddelton School District has 43904 students. That means that there are [ANS] more students in Saddelton than in Myronville.", "answer_v3": [ "17414", "30855", "808694", "103866", "876260", "924093", "20823" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0016", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "Add:\n$\\begin{array}{ccccccc}\\hline 788 & & 872 & & 467 & & 448 \\\\ \\hline+669 & &+715 & &+675 & &+928 \\\\ \\hline & & & & & & \\\\ \\hline [ANS] & & [ANS] & & [ANS] & & [ANS] \\\\ \\hline \\end{array}$", "answer_v1": [ "1457", "1587", "1142", "1376" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Add:\n$\\begin{array}{ccccccc}\\hline 758 & & 892 & & 427 & & 428 \\\\ \\hline+699 & &+715 & &+655 & &+918 \\\\ \\hline & & & & & & \\\\ \\hline [ANS] & & [ANS] & & [ANS] & & [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "1457", "1607", "1082", "1346" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Add:\n$\\begin{array}{ccccccc}\\hline 768 & & 882 & & 437 & & 438 \\\\ \\hline+669 & &+725 & &+695 & &+938 \\\\ \\hline & & & & & & \\\\ \\hline [ANS] & & [ANS] & & [ANS] & & [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "1437", "1607", "1132", "1376" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0017", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "6-10=[ANS].-6-5=[ANS].-9-(-12)=[ANS]. 20-(-13)=[ANS].-18-14=[ANS].-18-(-27)=[ANS]. 15-29=[ANS].-26-(-13)=[ANS].", "answer_v1": [ "-4", "-11", "3", "33", "-32", "9", "-14", "-13" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "3-12=[ANS].-9-4=[ANS].-5-(-12)=[ANS]. 18-(-15)=[ANS].-17-12=[ANS].-18-(-26)=[ANS]. 19-27=[ANS].-27-(-14)=[ANS].", "answer_v2": [ "-9", "-13", "7", "33", "-29", "8", "-8", "-13" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "4-11=[ANS].-9-5=[ANS].-9-(-10)=[ANS]. 21-(-11)=[ANS].-15-13=[ANS].-20-(-27)=[ANS]. 9-31=[ANS].-22-(-12)=[ANS].", "answer_v3": [ "-7", "-14", "1", "32", "-28", "7", "-22", "-10" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0018", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "Show how you can add and subtract mentally. Try to do these problems. 1) 70+90+30=[ANS]\n2) 360-110=[ANS]", "answer_v1": [ "190", "250" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Show how you can add and subtract mentally. Try to do these problems. 1) 50+90+20=[ANS]\n2) 350-130=[ANS]", "answer_v2": [ "160", "220" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Show how you can add and subtract mentally. Try to do these problems. 1) 50+90+20=[ANS]\n2) 360-110=[ANS]", "answer_v3": [ "160", "250" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0019", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [], "problem_v1": "Evaluate: $(6-7)-(5+6)=$ [ANS]\nNote: Your answer should be completely simplified. Unsimplified answers will not be accepted.", "answer_v1": [ "-12" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate: $(3-4)-(2+3)=$ [ANS]\nNote: Your answer should be completely simplified. Unsimplified answers will not be accepted.", "answer_v2": [ "-6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate: $(4-5)-(3+4)=$ [ANS]\nNote: Your answer should be completely simplified. Unsimplified answers will not be accepted.", "answer_v3": [ "-8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0020", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Use rules to find the sum\n$37-(-31)-(-13)$ [ANS]", "answer_v1": [ "37+31+13" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use rules to find the sum\n$28-(-28)-(-16)$ [ANS]", "answer_v2": [ "28+28+16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use rules to find the sum\n$31-(-31)-(-16)$ [ANS]", "answer_v3": [ "31+31+16" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0021", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "2", "keywords": [ "integer", "negative", "operation", "multiply" ], "problem_v1": "Multiply the following integers.\n${(-1)\\cdot(-5)\\cdot(-3)=}$ [ANS]\n${6\\cdot(-8)\\cdot(-4)=}$ [ANS]\n${(-89)\\cdot(-62)\\cdot0=}$ [ANS]", "answer_v1": [ "-15", "192", "0" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Multiply the following integers.\n${(-3)\\cdot(-4)\\cdot(-5)=}$ [ANS]\n${4\\cdot(-6)\\cdot(-4)=}$ [ANS]\n${(-97)\\cdot(-70)\\cdot0=}$ [ANS]", "answer_v2": [ "-60", "96", "0" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Multiply the following integers.\n${(-3)\\cdot(-5)\\cdot(-4)=}$ [ANS]\n${5\\cdot(-9)\\cdot(-4)=}$ [ANS]\n${(-84)\\cdot(-52)\\cdot0=}$ [ANS]", "answer_v3": [ "-60", "180", "0" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0022", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "2", "keywords": [ "integer", "order of operations", "multiply", "subtract", "negative", "evaluate" ], "problem_v1": "Evaluate this expression:\n${8-4(-4)4=}$ [ANS]", "answer_v1": [ "72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${2-5(-2)3=}$ [ANS]", "answer_v2": [ "32" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${4-4(-3)4=}$ [ANS]", "answer_v3": [ "52" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0023", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "2", "keywords": [ "decimal", "multiply" ], "problem_v1": "Calculate the following:\n${8 \\cdot 60=}$ [ANS]\n${8 \\cdot 600=}$ [ANS]\n${8 \\cdot 6000=}$ [ANS]", "answer_v1": [ "480", "4800", "48000" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Calculate the following:\n${2 \\cdot 90=}$ [ANS]\n${2 \\cdot 900=}$ [ANS]\n${2 \\cdot 9000=}$ [ANS]", "answer_v2": [ "180", "1800", "18000" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Calculate the following:\n${4 \\cdot 60=}$ [ANS]\n${4 \\cdot 600=}$ [ANS]\n${4 \\cdot 6000=}$ [ANS]", "answer_v3": [ "240", "2400", "24000" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0024", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "2", "keywords": [ "decimal", "multiply" ], "problem_v1": "Calculate the following. Don\u2019t use commas in your answer. $8 \\cdot 10$=[ANS]\n$8 \\cdot 100$=[ANS]\n$8 \\cdot 1000$=[ANS]", "answer_v1": [ " 80", " 800", " 8000" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Calculate the following. Don\u2019t use commas in your answer. $2 \\cdot 10$=[ANS]\n$2 \\cdot 100$=[ANS]\n$2 \\cdot 1000$=[ANS]", "answer_v2": [ " 20", " 200", " 2000" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Calculate the following. Don\u2019t use commas in your answer. $4 \\cdot 10$=[ANS]\n$4 \\cdot 100$=[ANS]\n$4 \\cdot 1000$=[ANS]", "answer_v3": [ " 40", " 400", " 4000" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0025", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "4", "keywords": [], "problem_v1": "What number is 13 tens more than 30552 [ANS] A. 30752 B. 30565 C. 30682 D. 43552", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "What number is 14 tens more than 30512 [ANS] A. 30712 B. 30526 C. 44512 D. 30652", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "What number is 13 tens more than 30527 [ANS] A. 30727 B. 30657 C. 43527 D. 30540", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0026", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiplication", "level": "2", "keywords": [], "problem_v1": "Compute:\n$2\\times 46$=[ANS]\n$2\\times 63$=[ANS]\n$2\\times 73$=[ANS]\n$2\\times 36$=[ANS]\n$2\\times 86$=[ANS]", "answer_v1": [ "92", "126", "146", "72", "172" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [] ], "problem_v2": "Compute:\n$2\\times 69$=[ANS]\n$2\\times 21$=[ANS]\n$2\\times 73$=[ANS]\n$2\\times 54$=[ANS]\n$2\\times 93$=[ANS]", "answer_v2": [ "138", "42", "146", "108", "186" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [] ], "problem_v3": "Compute:\n$2\\times 88$=[ANS]\n$2\\times 36$=[ANS]\n$2\\times 43$=[ANS]\n$2\\times 55$=[ANS]\n$2\\times 23$=[ANS]", "answer_v3": [ "176", "72", "86", "110", "46" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [] ] }, { "id": "Arithmetic_0027", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "2", "keywords": [ "decimal", "divide" ], "problem_v1": "Write the following as decimal numbers. $7 \\div 10$=[ANS]\n$7 \\div 100$=[ANS]\n$7 \\div 1000$=[ANS]", "answer_v1": [ "0.7", "0.07", "0.007" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Write the following as decimal numbers. $1 \\div 10$=[ANS]\n$1 \\div 100$=[ANS]\n$1 \\div 1000$=[ANS]", "answer_v2": [ "0.1", "0.01", "0.001" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Write the following as decimal numbers. $3 \\div 10$=[ANS]\n$3 \\div 100$=[ANS]\n$3 \\div 1000$=[ANS]", "answer_v3": [ "0.3", "0.03", "0.003" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0028", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "2", "keywords": [ "real numbers", "operations with signed numbers" ], "problem_v1": "Divide or state that the division is undefined. (In this case, enter undefined.) a) $ \\frac{6}{-2}=$ [ANS]\nb) $ \\frac{-126}{-3}=$ [ANS]", "answer_v1": [ "-3", "42" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Divide or state that the division is undefined. (In this case, enter undefined.) a) $ \\frac{10}{-5}=$ [ANS]\nb) $ \\frac{-150}{-5}=$ [ANS]", "answer_v2": [ "-2", "30" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Divide or state that the division is undefined. (In this case, enter undefined.) a) $ \\frac{12}{-4}=$ [ANS]\nb) $ \\frac{-148}{-4}=$ [ANS]", "answer_v3": [ "-3", "37" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0029", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "3", "keywords": [], "problem_v1": "Reggie received a free movie ticket for every 15 movies he rented at Sky Videos. Reggie rented 92 movies at Sky Videos. What is he total number of free movie tickets that Reggie received? [ANS] A. 6 B. 8 C. 7 D. 5", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Reggie received a free movie ticket for every 15 movies he rented at Sky Videos. Reggie rented 71 movies at Sky Videos. What is he total number of free movie tickets that Reggie received? [ANS] A. 5 B. 6 C. 3 D. 4", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Reggie received a free movie ticket for every 15 movies he rented at Sky Videos. Reggie rented 80 movies at Sky Videos. What is he total number of free movie tickets that Reggie received? [ANS] A. 6 B. 5 C. 7 D. 4", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0030", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "2", "keywords": [], "problem_v1": "125 $\\div$ 5=[ANS]\n138 $\\div$ 6=[ANS]\n119 $\\div$ 7=[ANS]\n184 $\\div$ 8=[ANS]\n152 $\\div$ 8=[ANS]", "answer_v1": [ "25", "23", "17", "23", "19" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [] ], "problem_v2": "78 $\\div$ 6=[ANS]\n60 $\\div$ 4=[ANS]\n203 $\\div$ 7=[ANS]\n105 $\\div$ 7=[ANS]\n161 $\\div$ 7=[ANS]", "answer_v2": [ "13", "15", "29", "15", "23" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [] ], "problem_v3": "85 $\\div$ 5=[ANS]\n85 $\\div$ 5=[ANS]\n105 $\\div$ 7=[ANS]\n243 $\\div$ 9=[ANS]\n189 $\\div$ 7=[ANS]", "answer_v3": [ "17", "17", "15", "27", "27" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [] ] }, { "id": "Arithmetic_0031", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "2", "keywords": [], "problem_v1": "When you divide 177 by 6 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 127 by 6 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 151 by 7 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 137 by 7 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 187 by 8 the quotient is [ANS] and the remainder is [ANS]", "answer_v1": [ "29", "3", "21", "1", "21", "4", "19", "4", "23", "3" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [], [], [] ], "problem_v2": "When you divide 47 by 3 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 106 by 5 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 137 by 5 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 142 by 6 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 155 by 9 the quotient is [ANS] and the remainder is [ANS]", "answer_v2": [ "15", "2", "21", "1", "27", "2", "23", "4", "17", "2" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [], [], [] ], "problem_v3": "When you divide 78 by 4 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 127 by 6 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 287 by 8 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 116 by 6 the quotient is [ANS] and the remainder is [ANS]\nWhen you divide 263 by 7 the quotient is [ANS] and the remainder is [ANS]", "answer_v3": [ "19", "2", "21", "1", "35", "7", "19", "2", "37", "4" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0032", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Integer division", "level": "2", "keywords": [], "problem_v1": "Find the quotient and remainder in each of the following. $80\\vert\\overline{9075}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$77\\vert\\overline{8685}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$56\\vert\\overline{8331}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]", "answer_v1": [ "113", "35", "112", "61", "148", "43" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Find the quotient and remainder in each of the following. $94\\vert\\overline{9009}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$56\\vert\\overline{8163}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$56\\vert\\overline{9045}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]", "answer_v2": [ "95", "79", "145", "43", "161", "29" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Find the quotient and remainder in each of the following. $80\\vert\\overline{9033}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$70\\vert\\overline{8307}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]\n$56\\vert\\overline{8223}\\ \\ \\ \\ \\ $ quotient=[ANS] remainder=[ANS]", "answer_v3": [ "112", "73", "118", "47", "146", "47" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0033", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "multiply", "exponent", "simplify" ], "problem_v1": "Use the properties of exponents to simplify the following\n${8^{7}}\\cdot{8^{7}}=$ [ANS]", "answer_v1": [ "8^14" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use the properties of exponents to simplify the following\n${2^{10}}\\cdot{2^{3}}=$ [ANS]", "answer_v2": [ "2^13" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use the properties of exponents to simplify the following\n${4^{7}}\\cdot{4^{4}}=$ [ANS]", "answer_v3": [ "4^11" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0034", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "integer", "negative", "operation", "integer exponent", "evaluate" ], "problem_v1": "Evaluate the following expressions that have integer exponents:\n${5^{2}=}$ [ANS]\n${4^{3}=}$ [ANS]\n${(-3)^{2}=}$ [ANS]\n${(-4)^{3}=}$ [ANS]", "answer_v1": [ "25", "64", "9", "-64" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Evaluate the following expressions that have integer exponents:\n${2^{2}=}$ [ANS]\n${5^{3}=}$ [ANS]\n${(-5)^{2}=}$ [ANS]\n${(-4)^{3}=}$ [ANS]", "answer_v2": [ "4", "125", "25", "-64" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Evaluate the following expressions that have integer exponents:\n${3^{2}=}$ [ANS]\n${4^{3}=}$ [ANS]\n${(-4)^{2}=}$ [ANS]\n${(-3)^{3}=}$ [ANS]", "answer_v3": [ "9", "64", "16", "-27" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0035", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponent", "simplify", "zero" ], "problem_v1": "Use the properties of exponents to simplify the following\n$-38\\cdot\\left(-293^{7}\\right)^0=$ [ANS]", "answer_v1": [ "-38" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use the properties of exponents to simplify the following\n$-6\\cdot\\left(-467^{3}\\right)^0=$ [ANS]", "answer_v2": [ "-6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use the properties of exponents to simplify the following\n$-17\\cdot\\left(-305^{4}\\right)^0=$ [ANS]", "answer_v3": [ "-17" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0036", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponent", "negative", "fraction", "evaluate", "simplify" ], "problem_v1": "Here is an expression with negative exponents.\n$\\frac{1}{(-8)^{-3}}=$ [ANS]\nEvaluate the expression; in other words, write the answer without using exponents.", "answer_v1": [ "-512" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Here is an expression with negative exponents.\n$\\frac{1}{(-2)^{-3}}=$ [ANS]\nEvaluate the expression; in other words, write the answer without using exponents.", "answer_v2": [ "-8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Here is an expression with negative exponents.\n$\\frac{1}{(-4)^{-3}}=$ [ANS]\nEvaluate the expression; in other words, write the answer without using exponents.", "answer_v3": [ "-64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0037", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponent", "simplify", "fraction", "divide" ], "problem_v1": "Use the properties of exponents to simplify the following\n$\\frac{{18^{16}}}{{18^{10}}}=$ [ANS]", "answer_v1": [ "18^6" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use the properties of exponents to simplify the following\n$\\frac{{9^{20}}}{{9^{4}}}=$ [ANS]", "answer_v2": [ "9^16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use the properties of exponents to simplify the following\n$\\frac{{12^{16}}}{{12^{5}}}=$ [ANS]", "answer_v3": [ "12^11" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0038", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponents" ], "problem_v1": "Simplify your answers as much as possible.\n(a) $ \\frac{13^{5}}{13^{4}}=$ [ANS]\n(b) $ \\frac{7^{3}}{7}=$ [ANS]\n(c) $ \\frac{10^{9}}{10^{3}}=$ [ANS]\n(d) $ \\frac{5^{6}}{5^{6}}=$ [ANS]", "answer_v1": [ "13", "49", "1E+06", "1" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Simplify your answers as much as possible.\n(a) $ \\frac{5^{7}}{5^{6}}=$ [ANS]\n(b) $ \\frac{4^{3}}{4}=$ [ANS]\n(c) $ \\frac{10^{8}}{10^{5}}=$ [ANS]\n(d) $ \\frac{5^{4}}{5^{4}}=$ [ANS]", "answer_v2": [ "5", "16", "1000", "1" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Simplify your answers as much as possible.\n(a) $ \\frac{8^{6}}{8^{5}}=$ [ANS]\n(b) $ \\frac{5^{3}}{5}=$ [ANS]\n(c) $ \\frac{10^{8}}{10^{2}}=$ [ANS]\n(d) $ \\frac{6^{8}}{6^{8}}=$ [ANS]", "answer_v3": [ "8", "25", "1E+06", "1" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0039", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "algebra" ], "problem_v1": "Evaluate the expression $ \\frac{4^{3}}{3^{-2}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v1": [ "576" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression $ \\frac{1^{3}}{1^{-3}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v2": [ "1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression $ \\frac{2^{3}}{2^{-3}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v3": [ "64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0040", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "real numbers", "algebraic expressions" ], "problem_v1": "Write the expression with positive exponents and simplify. $ \\frac{1}{5^{-1}}$=[ANS]", "answer_v1": [ "5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Write the expression with positive exponents and simplify. $ \\frac{1}{7^{-4}}$=[ANS]", "answer_v2": [ "2401" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Write the expression with positive exponents and simplify. $ \\frac{1}{5^{-3}}$=[ANS]", "answer_v3": [ "125" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0041", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "algebra", "exponent" ], "problem_v1": "The expression $6^45^{-2}$ equals $n/d$ where the integer numerator $n$ is [ANS]\nthe integer denorminator $d$ is [ANS].", "answer_v1": [ "1296", "25" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "The expression $2^47^{-2}$ equals $n/d$ where the integer numerator $n$ is [ANS]\nthe integer denorminator $d$ is [ANS].", "answer_v2": [ "16", "49" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "The expression $2^45^{-2}$ equals $n/d$ where the integer numerator $n$ is [ANS]\nthe integer denorminator $d$ is [ANS].", "answer_v3": [ "16", "25" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0042", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponents" ], "problem_v1": "determine whether the following quantities are positive or negative.\n[ANS] 1. $(-37)^{-65}$ [ANS] 2. $(-57)^0$ [ANS] 3. $-31^{-72}$ [ANS] 4. $63^{-1}$ [ANS] 5. $(-75)^{58}$", "answer_v1": [ "NEGATIVE", "POSITIVE", "NEGATIVE", "Positive", "Positive" ], "answer_type_v1": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v1": [ [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ] ], "problem_v2": "determine whether the following quantities are positive or negative.\n[ANS] 1. $(-9)^{92}$ [ANS] 2. $(-19)^0$ [ANS] 3. $(-57)^{-65}$ [ANS] 4. $-95^{-34}$ [ANS] 5. $15^{-1}$", "answer_v2": [ "POSITIVE", "POSITIVE", "NEGATIVE", "Negative", "Positive" ], "answer_type_v2": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v2": [ [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ] ], "problem_v3": "determine whether the following quantities are positive or negative.\n[ANS] 1. $27^{-1}$ [ANS] 2. $-21^{-54}$ [ANS] 3. $(-81)^0$ [ANS] 4. $(-87)^{-29}$ [ANS] 5. $(-31)^{60}$", "answer_v3": [ "POSITIVE", "NEGATIVE", "POSITIVE", "Negative", "Positive" ], "answer_type_v3": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v3": [ [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ], [ "Positive", "Negative" ] ] }, { "id": "Arithmetic_0043", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "exponents" ], "problem_v1": "Using laws of exponents, rewrite the following expression as a product.\n$3^{5+4}$=[ANS] $\\cdot$ [ANS]", "answer_v1": [ "243", "81" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Using laws of exponents, rewrite the following expression as a product.\n$2^{3+5}$=[ANS] $\\cdot$ [ANS]", "answer_v2": [ "8", "32" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Using laws of exponents, rewrite the following expression as a product.\n$2^{3+4}$=[ANS] $\\cdot$ [ANS]", "answer_v3": [ "8", "16" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0044", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Exponentiation", "level": "2", "keywords": [ "algebra", "radicals", "exponents" ], "problem_v1": "Evaluate the numerical expression $343^\\frac{2}{3}.$ Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v1": [ "49" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the numerical expression $64^\\frac{2}{3}.$ Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v2": [ "16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the numerical expression $125^\\frac{2}{3}.$ Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v3": [ "25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0045", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "integer", "operation", "multiply", "divide", "evaluate" ], "problem_v1": "Evaluate these expressions:\n${20\\cdot5\\div4=}$ [ANS]\n${20\\div5\\cdot4=}$ [ANS]", "answer_v1": [ "25", "16" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Evaluate these expressions:\n${12\\cdot2\\div6=}$ [ANS]\n${12\\div2\\cdot6=}$ [ANS]", "answer_v2": [ "4", "36" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Evaluate these expressions:\n${15\\cdot3\\div5=}$ [ANS]\n${15\\div3\\cdot5=}$ [ANS]", "answer_v3": [ "9", "25" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0046", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "integer", "order of operations", "add", "subtract", "multiply", "evaluate" ], "problem_v1": "Evaluate this expression:\n${6[18-5(5+4)]=}$ [ANS]", "answer_v1": [ "-162" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${2[20-3(3+8)]=}$ [ANS]", "answer_v2": [ "-26" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${2[18-3(5+2)]=}$ [ANS]", "answer_v3": [ "-6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0047", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "integer", "order of operations", "integer exponent", "add", "subtract", "divide", "evaluate" ], "problem_v1": "Evaluate this expression:\n${\\frac{9^{2}-4^{2}}{5+8}=}$ [ANS]", "answer_v1": [ "5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${\\frac{6^{2}-5^{2}}{1+10}=}$ [ANS]", "answer_v2": [ "1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${\\frac{7^{2}-4^{2}}{3+8}=}$ [ANS]", "answer_v3": [ "3" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0048", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "integer", "order of operations", "evaluate" ], "problem_v1": "Evaluate this expression:\n${3+4(113-4\\cdot3^{3})=}$ [ANS]", "answer_v1": [ "23" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${9+3(42-5\\cdot2^{3})=}$ [ANS]", "answer_v2": [ "15" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${2+3(35-4\\cdot2^{3})=}$ [ANS]", "answer_v3": [ "11" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0049", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "integer", "operation", "multiply", "divide", "evaluate" ], "problem_v1": "Evaluate the expression:\n${48\\div(8)6=}$ [ANS]", "answer_v1": [ "36" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression:\n${18\\div(2)3=}$ [ANS]", "answer_v2": [ "27" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression:\n${24\\div(4)4=}$ [ANS]", "answer_v3": [ "24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0050", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "integer", "order of operations", "evaluate" ], "problem_v1": "Evaluate this expression:\n${(19-4)^{2}+4(19-4^{2})}$ [ANS]", "answer_v1": [ "237" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${(9-2)^{2}+2(9-2^{2})}$ [ANS]", "answer_v2": [ "59" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${(8-2)^{2}+3(8-2^{2})}$ [ANS]", "answer_v3": [ "48" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0051", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "algebra", "powers" ], "problem_v1": "Evaluate the expression $6^3+6^5$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v1": [ "7992" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression $3^3+3^4$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v2": [ "108" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression $4^3+4^4$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v3": [ "320" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0052", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "real numbers", "operations with signed numbers", "order of operations" ], "problem_v1": "Use the order of operations to simplify: a) $4(4-7)^2+15 \\div (-3)=$ [ANS]", "answer_v1": [ "31" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use the order of operations to simplify: a) $2(5-7)^2+36 \\div (-4)=$ [ANS]", "answer_v2": [ "-1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use the order of operations to simplify: a) $2(4-6)^2+12 \\div (-3)=$ [ANS]", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0053", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "real numbers", "operations with signed numbers", "order of operations" ], "problem_v1": "Simplify 7-6(-3(4-3)-3(4-4)) Answer: [ANS]", "answer_v1": [ "25" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify 1-9(-5(3-5)-3(2-3)) Answer: [ANS]", "answer_v2": [ "-116" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify 3-6(-4(4-2)-3(5-5)) Answer: [ANS]", "answer_v3": [ "51" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0054", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "real numbers", "operations with signed numbers", "order of operations" ], "problem_v1": "Use the order of operations to simplify: a) $[13-(11-11)]-[8-(5-6)]=$ [ANS]\nb) $4 \\cdot 3-2+2 \\cdot 3=$ [ANS]", "answer_v1": [ "4", "16" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Use the order of operations to simplify: a) $[5-(15-6)]-[5-(9-6)]=$ [ANS]\nb) $2 \\cdot 2-3+2 \\cdot 3=$ [ANS]", "answer_v2": [ "-6", "7" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Use the order of operations to simplify: a) $[8-(11-8)]-[6-(4-6)]=$ [ANS]\nb) $5 \\cdot 4-3+2 \\cdot 2=$ [ANS]", "answer_v3": [ "-3", "21" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0055", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [], "problem_v1": "Compute: $16 \\div 4-5\\times 3+4\\div 2=$ [ANS].", "answer_v1": [ "-9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Compute: $10 \\div 2-3\\times 2+8\\div 4=$ [ANS].", "answer_v2": [ "1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Compute: $8 \\div 2-4\\times 3+6\\div 2=$ [ANS].", "answer_v3": [ "-5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0056", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [], "problem_v1": "$8+9$=[ANS]\n$8-4$=[ANS]\n$5 \\times 5$=[ANS]\n$20 \\div 5$=[ANS]", "answer_v1": [ "17", "4", "25", "4" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "$3+4$=[ANS]\n$9-3$=[ANS]\n$4 \\times 8$=[ANS]\n$15 \\div 5$=[ANS]", "answer_v2": [ "7", "6", "32", "3" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "$5+6$=[ANS]\n$8-3$=[ANS]\n$5 \\times 5$=[ANS]\n$25 \\div 5$=[ANS]", "answer_v3": [ "11", "5", "25", "5" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0057", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "4", "keywords": [], "problem_v1": "Write a numerical expression for each verbal phrase. nine added to four [ANS]\neight divided by three [ANS]", "answer_v1": [ "9+4", "8/3" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Write a numerical expression for each verbal phrase. six multiplied by five [ANS]\nseven divided by five [ANS]", "answer_v2": [ "6*5", "7/5" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Write a numerical expression for each verbal phrase. seven divided by four [ANS]\neight divided by two [ANS]", "answer_v3": [ "7/4", "8/2" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0058", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "algebra" ], "problem_v1": "Evaluate the expression $7 \\times 6-6 \\times 7$=[ANS]\nEvaluate the expression $7 \\times (6-6) \\times 7$=[ANS]\nEvaluate the expression $7 \\times (6-6 \\times 7)$=[ANS]", "answer_v1": [ "0", "0", "-252" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Evaluate the expression $1 \\times 9-2 \\times 4$=[ANS]\nEvaluate the expression $1 \\times (9-2) \\times 4$=[ANS]\nEvaluate the expression $1 \\times (9-2 \\times 4)$=[ANS]", "answer_v2": [ "1", "28", "1" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Evaluate the expression $3 \\times 6-3 \\times 5$=[ANS]\nEvaluate the expression $3 \\times (6-3) \\times 5$=[ANS]\nEvaluate the expression $3 \\times (6-3 \\times 5)$=[ANS]", "answer_v3": [ "3", "45", "-27" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0059", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "calculus", "algebra", "financial mathematics", "algebra" ], "problem_v1": "Evaluate the expression $3(-3)(7-7-2(8))$. [ANS]\n(Your answer cannot be an algebraic expression.)", "answer_v1": [ "144" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression $3(-10)(11-2-2(4))$. [ANS]\n(Your answer cannot be an algebraic expression.)", "answer_v2": [ "-30" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression $3(-7)(7-4-2(7))$. [ANS]\n(Your answer cannot be an algebraic expression.)", "answer_v3": [ "231" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0060", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "exponents" ], "problem_v1": "Evaluate the following expressions. Simplify your answers as much as possible.\n$\\begin{array}{ccc}\\hline-8^2 &=& [ANS] \\\\ \\hline 4^1 \\cdot 1^7 \\cdot 3^2 &=& [ANS] \\\\ \\hline \\frac{-1^{5} \\cdot (-3)^4}{9^2} &=& [ANS] \\\\ \\hline \\end{array}$", "answer_v1": [ "-64", "36", "-1" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Evaluate the following expressions. Simplify your answers as much as possible.\n$\\begin{array}{ccc}\\hline-3^2 &=& [ANS] \\\\ \\hline 5^1 \\cdot 1^7 \\cdot 3^2 &=& [ANS] \\\\ \\hline \\frac{-1^{3} \\cdot (-2)^4}{4^2} &=& [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "-9", "45", "-1" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Evaluate the following expressions. Simplify your answers as much as possible.\n$\\begin{array}{ccc}\\hline-5^2 &=& [ANS] \\\\ \\hline 4^1 \\cdot 1^7 \\cdot 3^2 &=& [ANS] \\\\ \\hline \\frac{-1^{3} \\cdot (-3)^4}{9^2} &=& [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "-25", "36", "-1" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0061", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "order of operations" ], "problem_v1": "Use order of operations to simplify: $ \\frac{-6\\sqrt{41+8}+(-6)^2}{3^3+|-3(5)|}=$ [ANS]", "answer_v1": [ "-1/7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Use order of operations to simplify: $ \\frac{-2\\sqrt{15+10}+(-7)^2}{3^3+|-3(3)|}=$ [ANS]", "answer_v2": [ "13/12" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Use order of operations to simplify: $ \\frac{(-4)^4+7\\sqrt{32-16}}{3^3+|2(-5)|}=$ [ANS]", "answer_v3": [ "284/37" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0062", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "order of operations" ], "problem_v1": "Evaluate: $\\frac{2(4-(-3))^2-4 \\cdot 5+6 \\cdot 3}{2(3^2+1)^2}$ Give your answer as a fraction. Answer: [ANS]", "answer_v1": [ "12/25" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate: $\\frac{-2(5-(-1))^2+4 \\cdot 4-6 \\cdot 5}{-2(3^2+1)^2}$ Give your answer as a fraction. Answer: [ANS]", "answer_v2": [ "43/100" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate: $\\frac{-2(4-(-2))^2+4 \\cdot 5-6 \\cdot 2}{-2(3^2+1)^2}$ Give your answer as a fraction. Answer: [ANS]", "answer_v3": [ "8/25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0063", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "algebra", "fraction", "exponents" ], "problem_v1": "Express the number 2^{-5}+5^{-1} as a reduced fraction. Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v1": [ "37/160" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Express the number 2^{-2}+7^{-1} as a reduced fraction. Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v2": [ "11/28" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Express the number 2^{-3}+5^{-1} as a reduced fraction. Answer: [ANS]\nNote: You cannot use any operations except division (/) and negation (-). You cannot use any operations except division (/) and negation (-).", "answer_v3": [ "13/40" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0064", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Simplify the expression:\n$18-6 \\div 2$ [ANS]", "answer_v1": [ "18-6/2" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the expression:\n$12-8 \\div 2$ [ANS]", "answer_v2": [ "12-8/2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the expression:\n$14-6 \\div 2$ [ANS]", "answer_v3": [ "14-6/2" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0065", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Simplify the expression:\n$8\\times 6+0 \\times 7$ [ANS]", "answer_v1": [ "8*6+0*7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the expression:\n$2\\times 8+0 \\times 4$ [ANS]", "answer_v2": [ "2*8+0*4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the expression:\n$4\\times 7+0 \\times 4$ [ANS]", "answer_v3": [ "4*7+0*4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0066", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Use repeated addition, patterns, or rules to find:\n$(12)(-12)(8)$=[ANS]\n$\\frac{(12)(-12)}{(8)}$=[ANS]", "answer_v1": [ "12*-12*8", "12*-12/8" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Use repeated addition, patterns, or rules to find:\n$(-20)(-4)(-16)$=[ANS]\n$\\frac{(-20)(-4)}{(-16)}$=[ANS]", "answer_v2": [ "-20*-4*-16", "-20*-4/-16" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Use repeated addition, patterns, or rules to find:\n$(-8)(-8)(-8)$=[ANS]\n$\\frac{(-8)(-8)}{(-8)}$=[ANS]", "answer_v3": [ "-8*-8*-8", "-8*-8/-8" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0067", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Evaluate the expressions for $x=7$, $y=9$ and $z=3$:\n$x+7$=[ANS]\n$2 z-7$=[ANS]\n$x y z$=[ANS]\n$y+z$=[ANS]", "answer_v1": [ "7+7", "2*3-7", "7*9*3", "9+3" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Evaluate the expressions for $x=4$, $y=7$ and $z=5$:\n$x+5$=[ANS]\n$2 z-5$=[ANS]\n$x y z$=[ANS]\n$y+z$=[ANS]", "answer_v2": [ "4+5", "2*5-5", "4*7*5", "7+5" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Evaluate the expressions for $x=5$, $y=7$ and $z=4$:\n$x+6$=[ANS]\n$2 z-6$=[ANS]\n$x y z$=[ANS]\n$y+z$=[ANS]", "answer_v3": [ "5+6", "2*4-6", "5*7*4", "7+4" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0069", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Inequalities", "level": "2", "keywords": [], "problem_v1": "2. Order the numbers from least to greatest 7957, 7597, 7795 [ANS] [ANS] [ANS]", "answer_v1": [ "7597", "7795", "7957" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "2. Order the numbers from least to greatest 1877, 1787, 1787 [ANS] [ANS] [ANS]", "answer_v2": [ "1787", "1787", "1877" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "2. Order the numbers from least to greatest 3856, 3586, 3685 [ANS] [ANS] [ANS]", "answer_v3": [ "3586", "3685", "3856" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0070", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Inequalities", "level": "1", "keywords": [ "true-false" ], "problem_v1": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. $5 > 5$ [ANS] 2. $5=5$ [ANS] 3. $5 \\geq 5$ [ANS] 4. $5 \\neq 5$ [ANS] 5. $5 < 5$ [ANS] 6. $5 \\leq 5$", "answer_v1": [ "F", "T", "T", "F", "F", "T" ], "answer_type_v1": [ "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. $5 < 5$ [ANS] 2. $5 \\neq 5$ [ANS] 3. $5 \\leq 5$ [ANS] 4. $5 \\geq 5$ [ANS] 5. $5 > 5$ [ANS] 6. $5=5$", "answer_v2": [ "F", "F", "T", "T", "F", "T" ], "answer_type_v2": [ "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. $5 \\leq 5$ [ANS] 2. $5 > 5$ [ANS] 3. $5=5$ [ANS] 4. $5 \\geq 5$ [ANS] 5. $5 < 5$ [ANS] 6. $5 \\neq 5$", "answer_v3": [ "T", "F", "T", "T", "F", "F" ], "answer_type_v3": [ "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0071", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Inequalities", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Simplify each side and identify the correct $<$, $=$ or $>$\n$12+20 \\div 4 \\; \\;?? \\; \\; (12+20) \\div 4$ [ANS] [ANS]:>> [ANS]", "answer_v1": [ "12+20/4", ">", "(12+20)/4" ], "answer_type_v1": [ "NV", "MCS", "NV" ], "options_v1": [ [], [ "<", "=", ">" ], [] ], "problem_v2": "Simplify each side and identify the correct $<$, $=$ or $>$\n$4+24 \\div 4 \\; \\;?? \\; \\; (4+24) \\div 4$ [ANS] [ANS]:>> [ANS]", "answer_v2": [ "4+24/4", ">", "(4+24)/4" ], "answer_type_v2": [ "NV", "MCS", "NV" ], "options_v2": [ [], [ "<", "=", ">" ], [] ], "problem_v3": "Simplify each side and identify the correct $<$, $=$ or $>$\n$4+20 \\div 4 \\; \\;?? \\; \\; (4+20) \\div 4$ [ANS] [ANS]:>> [ANS]", "answer_v3": [ "4+20/4", ">", "(4+20)/4" ], "answer_type_v3": [ "NV", "MCS", "NV" ], "options_v3": [ [], [ "<", "=", ">" ], [] ] }, { "id": "Arithmetic_0073", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Inequalities", "level": "2", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Order $-8$, $19$, $1$, $12$ from least to greatest. (Separate your answers by commas.) [ANS]", "answer_v1": [ "(-8, 1, 12, 19)" ], "answer_type_v1": [ "OL" ], "options_v1": [ [] ], "problem_v2": "Order $7$, $17$, $-15$, $5$ from least to greatest. (Separate your answers by commas.) [ANS]", "answer_v2": [ "(-15, 5, 7, 17)" ], "answer_type_v2": [ "OL" ], "options_v2": [ [] ], "problem_v3": "Order $-12$, $18$, $1$, $8$ from least to greatest. (Separate your answers by commas.) [ANS]", "answer_v3": [ "(-12, 1, 8, 18)" ], "answer_type_v3": [ "OL" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0074", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "3", "keywords": [ "integer", "order of operations", "integer exponent", "subtract", "evaluate", "absolute value" ], "problem_v1": "Evaluate these expressions:\n${|8-7|^{2}-|8-7^{2}|=}$ [ANS]\n${(8-7)^{2}-(8-7^{2})=}$ [ANS]", "answer_v1": [ "-40", "42" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Evaluate these expressions:\n${|2-9|^{2}-|2-9^{2}|=}$ [ANS]\n${(2-9)^{2}-(2-9^{2})=}$ [ANS]", "answer_v2": [ "-30", "128" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Evaluate these expressions:\n${|4-7|^{2}-|4-7^{2}|=}$ [ANS]\n${(4-7)^{2}-(4-7^{2})=}$ [ANS]", "answer_v3": [ "-36", "54" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0075", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "3", "keywords": [ "integer", "order of operations", "integer exponent", "subtract", "evaluate", "absolute value" ], "problem_v1": "Evaluate this expression:\n${-3^{2}-|6\\cdot(-5)|=}$ [ANS]", "answer_v1": [ "-39" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${-9^{2}-|8\\cdot(-9)|=}$ [ANS]", "answer_v2": [ "-153" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${-7^{2}-|6\\cdot(-7)|=}$ [ANS]", "answer_v3": [ "-91" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0076", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "3", "keywords": [ "integer", "negative", "add", "subtract", "absolute value" ], "problem_v1": "Evaluate the following expressions which involve the absolute value:\n${-\\lvert 3-9 \\rvert=}$ [ANS]\n${\\lvert-3-9 \\rvert=}$ [ANS]\n${-1 \\lvert 9-3 \\rvert=}$ [ANS]", "answer_v1": [ "-6", "12", "-6" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Evaluate the following expressions which involve the absolute value:\n${-\\lvert 5-6 \\rvert=}$ [ANS]\n${\\lvert-5-6 \\rvert=}$ [ANS]\n${-4 \\lvert 6-5 \\rvert=}$ [ANS]", "answer_v2": [ "-1", "11", "-4" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Evaluate the following expressions which involve the absolute value:\n${-\\lvert 4-7 \\rvert=}$ [ANS]\n${\\lvert-4-7 \\rvert=}$ [ANS]\n${-3 \\lvert 7-4 \\rvert=}$ [ANS]", "answer_v3": [ "-3", "11", "-9" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0077", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "2", "keywords": [ "absolute value" ], "problem_v1": "Find the absolute value of this number.\n${|{5}|=}$ [ANS]", "answer_v1": [ "5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the absolute value of this number.\n${|{-9}|=}$ [ANS]", "answer_v2": [ "9" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the absolute value of this number.\n${|{-4}|=}$ [ANS]", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0078", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "2", "keywords": [ "real numbers", "algebraic expressions" ], "problem_v1": "Simplify: a) $|8|=$ [ANS]\nb) $|-4|=$ [ANS]", "answer_v1": [ "8", "4" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Simplify: a) $|-12|=$ [ANS]\nb) $|12|=$ [ANS]", "answer_v2": [ "12", "12" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Simplify: a) $|-9|=$ [ANS]\nb) $|8|=$ [ANS]", "answer_v3": [ "9", "8" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0079", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "2", "keywords": [ "absolute value" ], "problem_v1": "Simplify: $|-76|-|-59|+|24|$ Answer: [ANS]", "answer_v1": [ "41" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify: $|-9|-|-94|+|-70|$ Answer: [ANS]", "answer_v2": [ "-15" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify: $|-32|-|-61|+|-44|$ Answer: [ANS]", "answer_v3": [ "15" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0080", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Absolute value", "level": "2", "keywords": [ "absolute value", "distance" ], "problem_v1": "Find the distance between the pair of real numbers: $51$, $-59$. Answer: [ANS]", "answer_v1": [ "110" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the distance between the pair of real numbers: $-84$, $-94$. Answer: [ANS]", "answer_v2": [ "10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the distance between the pair of real numbers: $-37$, $-61$. Answer: [ANS]", "answer_v3": [ "24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0081", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Estimation", "level": "4", "keywords": [ "division", "application" ], "problem_v1": "Do the following problem. Round numbers to the thousands place first, and then do addition or subtraction. Eric purchased a used car with $7134$ miles on its odometer. After a few years, he sold the car with $90073$ miles on its odometer. Approximately how many miles did Eric drive with this car? Eric drove approximately [ANS] miles with this car.", "answer_v1": [ "83000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Do the following problem. Round numbers to the thousands place first, and then do addition or subtraction. Hannah purchased a used car with $8900$ miles on its odometer. After a few years, she sold the car with $62789$ miles on its odometer. Approximately how many miles did Hannah drive with this car? Hannah drove approximately [ANS] miles with this car.", "answer_v2": [ "54000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Do the following problem. Round numbers to the thousands place first, and then do addition or subtraction. Evan purchased a used car with $8029$ miles on its odometer. After a few years, he sold the car with $71867$ miles on its odometer. Approximately how many miles did Evan drive with this car? Evan drove approximately [ANS] miles with this car.", "answer_v3": [ "64000" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0082", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Estimation", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "The following table shows the number of canned food collected by a non-profit organization last year.\n$\\begin{array}{cc}\\hline MonthMonth & Number of CansNumber of Cans \\\\ \\hline JanuaryJanuary & 7022 \\\\ \\hline FebruaryFebruary & 5653 \\\\ \\hline MarchMarch & 6780 \\\\ \\hline AprilApril & 3413 \\\\ \\hline MayMay & 5539 \\\\ \\hline JuneJune & 3968 \\\\ \\hline JulyJuly & 6222 \\\\ \\hline AugustAugust & 3158 \\\\ \\hline SeptemberSeptember & 5058 \\\\ \\hline OctoberOctober & 2075 \\\\ \\hline NovemberNovember & 4154 \\\\ \\hline DecemberDecember & 7292 \\\\ \\hline \\end{array}$\nAnswer the following questions. Round numbers to the thousands place first, and then do addition or subtraction. 1) Approximately how many cans were collected in the first quarter (January, February and March)? Approximately [ANS] cans were collected in the first quarter. 2) Approximately how many more cans were collected in July than in June? Approximately [ANS] more cans were collected in July than in June.", "answer_v1": [ "20000", "2000" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "The following table shows the number of canned food collected by a non-profit organization last year.\n$\\begin{array}{cc}\\hline MonthMonth & Number of CansNumber of Cans \\\\ \\hline JanuaryJanuary & 1664 \\\\ \\hline FebruaryFebruary & 8454 \\\\ \\hline MarchMarch & 2196 \\\\ \\hline AprilApril & 3673 \\\\ \\hline MayMay & 8575 \\\\ \\hline JuneJune & 3533 \\\\ \\hline JulyJuly & 2464 \\\\ \\hline AugustAugust & 3626 \\\\ \\hline SeptemberSeptember & 5514 \\\\ \\hline OctoberOctober & 1547 \\\\ \\hline NovemberNovember & 6127 \\\\ \\hline DecemberDecember & 4528 \\\\ \\hline \\end{array}$\nAnswer the following questions. Round numbers to the thousands place first, and then do addition or subtraction. 1) Approximately how many cans were collected in the first quarter (January, February and March)? Approximately [ANS] cans were collected in the first quarter. 2) Approximately how many more cans were collected in May than in April? Approximately [ANS] more cans were collected in May than in April.", "answer_v2": [ "12000", "5000" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "The following table shows the number of canned food collected by a non-profit organization last year.\n$\\begin{array}{cc}\\hline MonthMonth & Number of CansNumber of Cans \\\\ \\hline JanuaryJanuary & 3507 \\\\ \\hline FebruaryFebruary & 5844 \\\\ \\hline MarchMarch & 3229 \\\\ \\hline AprilApril & 5389 \\\\ \\hline MayMay & 2649 \\\\ \\hline JuneJune & 3769 \\\\ \\hline JulyJuly & 7469 \\\\ \\hline AugustAugust & 2602 \\\\ \\hline SeptemberSeptember & 1343 \\\\ \\hline OctoberOctober & 5581 \\\\ \\hline NovemberNovember & 8837 \\\\ \\hline DecemberDecember & 7337 \\\\ \\hline \\end{array}$\nAnswer the following questions. Round numbers to the thousands place first, and then do addition or subtraction. 1) Approximately how many cans were collected in the first quarter (January, February and March)? Approximately [ANS] cans were collected in the first quarter. 2) Approximately how many more cans were collected in July than in June? Approximately [ANS] more cans were collected in July than in June.", "answer_v3": [ "13000", "3000" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0083", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Rounding", "level": "3", "keywords": [ "round", "whole number" ], "problem_v1": "Round the following numbers to the nearest ten thousand. (Don\u2019t use commas in your answer.)\n${5853722=}$ [ANS]\n${5856722=}$ [ANS]", "answer_v1": [ "5850000", "5860000" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Round the following numbers to the nearest ten. (Don\u2019t use commas in your answer.)\n${9323626=}$ [ANS]\n${9323620=}$ [ANS]", "answer_v2": [ "9323630", "9323620" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Round the following numbers to the nearest hundred. (Don\u2019t use commas in your answer.)\n${6093715=}$ [ANS]\n${6093765=}$ [ANS]", "answer_v3": [ "6093700", "6093800" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0084", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "rate" ], "problem_v1": "According to a salad recipe, each teaspoon of vinegar should be mixed with $6$ teaspoons of vegetable oil. Fill in the blanks. Question 1: By this recipe, [ANS] teaspoons of vinegar should be mixed with $42$ teaspoons of vegetable oil.\nQuestion 2: By this recipe, [ANS] teaspoons of vegetable oil should be mixed with $8$ teaspoons of vinegar.", "answer_v1": [ "7", "48" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "According to a salad recipe, each teaspoon of vinegar should be mixed with $3$ teaspoons of vegetable oil. Fill in the blanks. Question 1: By this recipe, [ANS] teaspoons of vinegar should be mixed with $30$ teaspoons of vegetable oil.\nQuestion 2: By this recipe, [ANS] teaspoons of vegetable oil should be mixed with $4$ teaspoons of vinegar.", "answer_v2": [ "10", "12" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "According to a salad recipe, each teaspoon of vinegar should be mixed with $4$ teaspoons of vegetable oil. Fill in the blanks. Question 1: By this recipe, [ANS] teaspoons of vinegar should be mixed with $28$ teaspoons of vegetable oil.\nQuestion 2: By this recipe, [ANS] teaspoons of vegetable oil should be mixed with $5$ teaspoons of vinegar.", "answer_v3": [ "7", "20" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0085", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "rate" ], "problem_v1": "On average, Fabrienne collects $126$ stamps every year. Fill in blanks: Question 1: At this rate, Fabrienne would collect [ANS] stamps in $9$ years.\nQuestion 2: At this rate, Fabrienne would collect $2016$ stamps in [ANS] years.", "answer_v1": [ "1134", "16" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "On average, Tien collects $58$ stamps every year. Fill in blanks: Question 1: At this rate, Tien would collect [ANS] stamps in $11$ years.\nQuestion 2: At this rate, Tien would collect $754$ stamps in [ANS] years.", "answer_v2": [ "638", "13" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "On average, Dawn collects $81$ stamps every year. Fill in blanks: Question 1: At this rate, Dawn would collect [ANS] stamps in $9$ years.\nQuestion 2: At this rate, Dawn would collect $1053$ stamps in [ANS] years.", "answer_v3": [ "729", "13" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0086", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "rate" ], "problem_v1": "Penelope collected a total of $2016$ stamps over the past $16$ years. On average, how many stamps did Penelope collect each year? Solution: On average, Penelope collected [ANS] stamps each year.", "answer_v1": [ "126" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evan collected a total of $1102$ stamps over the past $19$ years. On average, how many stamps did Evan collect each year? Solution: On average, Evan collected [ANS] stamps each year.", "answer_v2": [ "58" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jon collected a total of $1296$ stamps over the past $16$ years. On average, how many stamps did Jon collect each year? Solution: On average, Jon collected [ANS] stamps each year.", "answer_v3": [ "81" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0087", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application", "remainder" ], "problem_v1": "Fabrienne saved ${\\$216.00}$, and will start spending her money on Lego figures. Each week, Fabrienne will spend ${\\$13.00}$ to buy a Lego figure. For how many weeks can Fabrienne spend her money this way? How much left-over money will she have? Solution: Fabrienne can spend her money this way for [ANS] weeks. There will be [ANS] of left-over money.", "answer_v1": [ "16", "8.00" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Tien saved ${\\$101.00}$, and will start spending his money on Lego figures. Each week, Tien will spend ${\\$5.00}$ to buy a Lego figure. For how many weeks can Tien spend his money this way? How much left-over money will he have? Solution: Tien can spend his money this way for [ANS] weeks. There will be [ANS] of left-over money.", "answer_v2": [ "20", "1.00" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Dawn saved ${\\$130.00}$, and will start spending her money on Lego figures. Each week, Dawn will spend ${\\$8.00}$ to buy a Lego figure. For how many weeks can Dawn spend her money this way? How much left-over money will she have? Solution: Dawn can spend her money this way for [ANS] weeks. There will be [ANS] of left-over money.", "answer_v3": [ "16", "2.00" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0088", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "One piece of paper is approximately $17$ millimeters in thickness. A stack of paper is $8075$ millimeters tall. About how many pieces of paper are there in the stack? Solution: There are about [ANS] pieces of paper in the stack.", "answer_v1": [ "475" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "One piece of paper is approximately $6$ millimeters in thickness. A stack of paper is $3480$ millimeters tall. About how many pieces of paper are there in the stack? Solution: There are about [ANS] pieces of paper in the stack.", "answer_v2": [ "580" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "One piece of paper is approximately $10$ millimeters in thickness. A stack of paper is $4820$ millimeters tall. About how many pieces of paper are there in the stack? Solution: There are about [ANS] pieces of paper in the stack.", "answer_v3": [ "482" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0089", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "multiplication", "application" ], "problem_v1": "Lily loves sports. Every week, she practices $70$ minutes of basketball, $75$ minutes of volleyball, and $55$ minutes of soccer. In total, how many minutes of basketball will Lily play in $14$ weeks? Solution: Lily will play [ANS] minutes of basketball in $14$ weeks.", "answer_v1": [ "980" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Connor loves sports. Every week, he practices $90$ minutes of basketball, $45$ minutes of volleyball, and $55$ minutes of soccer. In total, how many minutes of soccer will Connor play in $9$ weeks? Solution: Connor will play [ANS] minutes of soccer in $9$ weeks.", "answer_v2": [ "495" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sydney loves sports. Every week, she practices $70$ minutes of basketball, $55$ minutes of volleyball, and $50$ minutes of soccer. In total, how many minutes of volleyball will Sydney play in $11$ weeks? Solution: Sydney will play [ANS] minutes of volleyball in $11$ weeks.", "answer_v3": [ "605" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0090", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "multiplication", "application" ], "problem_v1": "Fabrienne is a star player in her basketball team. Last season, Fabrienne scored an average of $17$ points per game. The season had a total of $62$ games, but Fabrienne missed $8$ games. How many points did Fabrienne score in total last season? Solution: Fabrienne scored a total of [ANS] points last season.", "answer_v1": [ "918" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tien is a star player in his basketball team. Last season, Tien scored an average of $6$ points per game. The season had a total of $69$ games, but Tien missed $5$ games. How many points did Tien score in total last season? Solution: Tien scored a total of [ANS] points last season.", "answer_v2": [ "384" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dawn is a star player in her basketball team. Last season, Dawn scored an average of $10$ points per game. The season had a total of $62$ games, but Dawn missed $6$ games. How many points did Dawn score in total last season? Solution: Dawn scored a total of [ANS] points last season.", "answer_v3": [ "560" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0091", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "For an activity in a class, each student will use $16$ marbles. The teacher purchased a total of $432$ marbles for his class. How many students are there in this class? Solution: There are [ANS] students in this class.", "answer_v1": [ "27" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "For an activity in a class, each student will use $20$ marbles. The teacher purchased a total of $320$ marbles for his class. How many students are there in this class? Solution: There are [ANS] students in this class.", "answer_v2": [ "16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "For an activity in a class, each student will use $16$ marbles. The teacher purchased a total of $320$ marbles for his class. How many students are there in this class? Solution: There are [ANS] students in this class.", "answer_v3": [ "20" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0092", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "An archeology team is studying a buried city. The team can cover $45$ square meters every day. The whole area covers about $1935$ square meters. How many days will it take the team to complete studying the whole area? Solution: It would take the team [ANS] days to cover the whole area.", "answer_v1": [ "43" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An archeology team is studying a buried city. The team can cover $31$ square meters every day. The whole area covers about $1798$ square meters. How many days will it take the team to complete studying the whole area? Solution: It would take the team [ANS] days to cover the whole area.", "answer_v2": [ "58" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An archeology team is studying a buried city. The team can cover $36$ square meters every day. The whole area covers about $1584$ square meters. How many days will it take the team to complete studying the whole area? Solution: It would take the team [ANS] days to cover the whole area.", "answer_v3": [ "44" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0093", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "multiplication", "application" ], "problem_v1": "Gregory and Lesley are participating in a summer reading program. Gregory reads $45$ pages every day, and Lesley reads $11$ more pages than Gregory every day. How many pages will Lesley read in $49$ days? Solution: Lesley will read [ANS] pages in $49$ days.", "answer_v1": [ "2744" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Martha and Sebastian are participating in a summer reading program. Martha reads $31$ pages every day, and Sebastian reads $15$ more pages than Martha every day. How many pages will Sebastian read in $34$ days? Solution: Sebastian will read [ANS] pages in $34$ days.", "answer_v2": [ "1564" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Aaron and Izabelle are participating in a summer reading program. Aaron reads $36$ pages every day, and Izabelle reads $11$ more pages than Aaron every day. How many pages will Izabelle read in $38$ days? Solution: Izabelle will read [ANS] pages in $38$ days.", "answer_v3": [ "1786" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0094", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "A tank can drain ${1710\\ {\\rm L}}$ (liters) of water in ${38\\ {\\rm min}}$ minutes. How many liters of water does the tank drain per minute? Solution: The tank drains water at the rate of [ANS]. Use L for liters, min for minutes, and L/min for liters per minute.", "answer_v1": [ "45" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A tank can drain ${1488\\ {\\rm L}}$ (liters) of water in ${48\\ {\\rm min}}$ minutes. How many liters of water does the tank drain per minute? Solution: The tank drains water at the rate of [ANS]. Use L for liters, min for minutes, and L/min for liters per minute.", "answer_v2": [ "31" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A tank can drain ${1368\\ {\\rm L}}$ (liters) of water in ${38\\ {\\rm min}}$ minutes. How many liters of water does the tank drain per minute? Solution: The tank drains water at the rate of [ANS]. Use L for liters, min for minutes, and L/min for liters per minute.", "answer_v3": [ "36" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0095", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "A queen termite produces $80640$ eggs every week. How many eggs does the queen produce every minute? Solution: The queen termite produces [ANS] eggs every minute.", "answer_v1": [ "8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A queen termite produces $20160$ eggs every week. How many eggs does the queen produce every minute? Solution: The queen termite produces [ANS] eggs every minute.", "answer_v2": [ "2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A queen termite produces $40320$ eggs every week. How many eggs does the queen produce every minute? Solution: The queen termite produces [ANS] eggs every minute.", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0096", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application", "remainder" ], "problem_v1": "A school is planning for a field trip for $812$ students and staff. Each school bus can hold $46$ people. How many school buses are needed? Solution: [ANS] school buses are needed.", "answer_v1": [ "18" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A school is planning for a field trip for $561$ students and staff. Each school bus can hold $50$ people. How many school buses are needed? Solution: [ANS] school buses are needed.", "answer_v2": [ "12" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A school is planning for a field trip for $614$ students and staff. Each school bus can hold $46$ people. How many school buses are needed? Solution: [ANS] school buses are needed.", "answer_v3": [ "14" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0097", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "Penelope drove a total of ${540\\ {\\rm mi}}$ in ${9\\ {\\rm hr}}$ at a constant speed. What was Penelope\u2019s speed in miles per hour? Solution: Penelope drove at the speed of [ANS]. Use mi for miles, hr for hours, and mi/hr for miles per hour.", "answer_v1": [ "60" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evan drove a total of ${396\\ {\\rm mi}}$ in ${12\\ {\\rm hr}}$ at a constant speed. What was Evan\u2019s speed in miles per hour? Solution: Evan drove at the speed of [ANS]. Use mi for miles, hr for hours, and mi/hr for miles per hour.", "answer_v2": [ "33" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jon drove a total of ${378\\ {\\rm mi}}$ in ${9\\ {\\rm hr}}$ at a constant speed. What was Jon\u2019s speed in miles per hour? Solution: Jon drove at the speed of [ANS]. Use mi for miles, hr for hours, and mi/hr for miles per hour.", "answer_v3": [ "42" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0098", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "Fabrienne is working to pass a local measure, and she needs to collect a total of $108$ signatures in three days. On the first day, she collected $40$ signatures; on the second day, she collected $33$. To complete her job, how many more signatures does she need to collect on the third day? Fabrienne needs to collect [ANS] more signatures on the third day.", "answer_v1": [ "35" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tien is working to pass a local measure, and he needs to collect a total of $77$ signatures in three days. On the first day, he collected $13$ signatures; on the second day, he collected $48$. To complete her job, how many more signatures does he need to collect on the third day? Tien needs to collect [ANS] more signatures on the third day.", "answer_v2": [ "16" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dawn is working to pass a local measure, and she needs to collect a total of $77$ signatures in three days. On the first day, she collected $22$ signatures; on the second day, she collected $34$. To complete her job, how many more signatures does she need to collect on the third day? Dawn needs to collect [ANS] more signatures on the third day.", "answer_v3": [ "21" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0099", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "Julie collects Pokemon cards. This table records the number of cards she collected last year: Julie collects Pokemon cards. This table records the number of cards she collected last year:\n$\\begin{array}{cc}\\hline Months & Number of cards collected \\\\ \\hline January & 40 \\\\ \\hline February & 33 \\\\ \\hline March & 35 \\\\ \\hline April & 39 \\\\ \\hline May & 22 \\\\ \\hline June & 23 \\\\ \\hline July & 33 \\\\ \\hline August & 33 \\\\ \\hline September & 25 \\\\ \\hline October & 30 \\\\ \\hline November & 36 \\\\ \\hline December & 21 \\\\ \\hline \\end{array}$ 21\nAnswer the following questions:\nIn the first quarter (January, February and March), how many Pokemon cards did Julie collect in all? [ANS]\nIn the first half of the year, how many more cards did Julie collect than in the second half? [ANS]", "answer_v1": [ "108", "14" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Cheryl collects Pokemon cards. This table records the number of cards she collected last year: Cheryl collects Pokemon cards. This table records the number of cards she collected last year:\n$\\begin{array}{cc}\\hline Months & Number of cards collected \\\\ \\hline January & 13 \\\\ \\hline February & 48 \\\\ \\hline March & 16 \\\\ \\hline April & 23 \\\\ \\hline May & 48 \\\\ \\hline June & 22 \\\\ \\hline July & 17 \\\\ \\hline August & 23 \\\\ \\hline September & 33 \\\\ \\hline October & 12 \\\\ \\hline November & 36 \\\\ \\hline December & 28 \\\\ \\hline \\end{array}$ 28\nAnswer the following questions:\nIn the first quarter (January, February and March), how many Pokemon cards did Cheryl collect in all? [ANS]\nIn the first half of the year, how many more cards did Cheryl collect than in the second half? [ANS]", "answer_v2": [ "77", "21" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Chris collects Pokemon cards. This table records the number of cards he collected last year: Chris collects Pokemon cards. This table records the number of cards he collected last year:\n$\\begin{array}{cc}\\hline Months & Number of cards collected \\\\ \\hline January & 42 \\\\ \\hline February & 44 \\\\ \\hline March & 33 \\\\ \\hline April & 33 \\\\ \\hline May & 49 \\\\ \\hline June & 41 \\\\ \\hline July & 16 \\\\ \\hline August & 32 \\\\ \\hline September & 48 \\\\ \\hline October & 40 \\\\ \\hline November & 18 \\\\ \\hline December & 36 \\\\ \\hline \\end{array}$ 36\nAnswer the following questions:\nIn the first quarter (January, February and March), how many Pokemon cards did Chris collect in all? [ANS]\nIn the first half of the year, how many more cards did Chris collect than in the second half? [ANS]", "answer_v3": [ "119", "52" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0100", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "rate", "ratio", "proportion", "solve", "word problem" ], "problem_v1": "A biologist wants to estimate the number of fish living in a lake. She caught $175$ fish, tagged each one, and then released them back into the lake. After a few days, she caught $258$ fish, and found that $22$ of them were tagged. Use a proportion to estimate the number of fish living in this lake.\nThere are approximately [ANS] fish living in the lake.", "answer_v1": [ "2052" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A biologist wants to estimate the number of fish living in a lake. She caught $109$ fish, tagged each one, and then released them back into the lake. After a few days, she caught $293$ fish, and found that $13$ of them were tagged. Use a proportion to estimate the number of fish living in this lake.\nThere are approximately [ANS] fish living in the lake.", "answer_v2": [ "2457" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A biologist wants to estimate the number of fish living in a lake. She caught $132$ fish, tagged each one, and then released them back into the lake. After a few days, she caught $260$ fish, and found that $21$ of them were tagged. Use a proportion to estimate the number of fish living in this lake.\nThere are approximately [ANS] fish living in the lake.", "answer_v3": [ "1634" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0101", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "rate", "proportion" ], "problem_v1": "A mutual fund consists of $70$ \\% stock and $30$ \\% bond. In other words, for each $70$ of stock, there are $30$ dollars of bond. For a mutual fund with ${\\$2{,}580.00}$ of bond, how many dollars of stock are there? Fill in the blank with decimal rounded to the hundredth place. For a mutual fund with ${\\$2{,}580.00}$ of bond, there are approximately [ANS] of stock.", "answer_v1": [ "6020.00" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A mutual fund consists of $17$ \\% stock and $83$ \\% bond. In other words, for each $17$ of stock, there are $83$ dollars of bond. For a mutual fund with ${\\$2{,}930.00}$ of bond, how many dollars of stock are there? Fill in the blank with decimal rounded to the hundredth place. For a mutual fund with ${\\$2{,}930.00}$ of bond, there are approximately [ANS] of stock.", "answer_v2": [ "600.12" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A mutual fund consists of $35$ \\% stock and $65$ \\% bond. In other words, for each $35$ of stock, there are $65$ dollars of bond. For a mutual fund with ${\\$2{,}600.00}$ of bond, how many dollars of stock are there? Fill in the blank with decimal rounded to the hundredth place. For a mutual fund with ${\\$2{,}600.00}$ of bond, there are approximately [ANS] of stock.", "answer_v3": [ "1400.0" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0102", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "3", "keywords": [], "problem_v1": "Hannah is stenciling a border on a wall. She plans to repeat picture a tulib, a daisy, a rose, and a lily in that order, as shown below tulip, daisy, rose, lily, tulip, daisy, rose, lily,... The first flower Hannah stencils is a tulip. What will be the 30th flower she stencils? [ANS] A. rose B. tulip C. daisy D. lily", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Hannah is stenciling a border on a wall. She plans to repeat picture a tulib, a daisy, a rose, and a lily in that order, as shown below tulip, daisy, rose, lily, tulip, daisy, rose, lily,... The first flower Hannah stencils is a tulip. What will be the 30th flower she stencils? [ANS] A. daisy B. tulip C. rose D. lily", "answer_v2": [ "A" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Hannah is stenciling a border on a wall. She plans to repeat picture a tulib, a daisy, a rose, and a lily in that order, as shown below tulip, daisy, rose, lily, tulip, daisy, rose, lily,... The first flower Hannah stencils is a tulip. What will be the 30th flower she stencils? [ANS] A. rose B. daisy C. tulip D. lily", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0103", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "4", "keywords": [], "problem_v1": "One cup of milk has the same amount of calcium as 6 oranges One orange has the same amount of calcium as 2 eggs. How many eggs have the same amount of calcium as one cup of milk [ANS] A. 4 B. 3 C. 12 D. 8", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "One cup of milk has the same amount of calcium as 6 oranges One orange has the same amount of calcium as 2 eggs. How many eggs have the same amount of calcium as one cup of milk [ANS] A. 12 B. 3 C. 4 D. 8", "answer_v2": [ "A" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "One cup of milk has the same amount of calcium as 6 oranges One orange has the same amount of calcium as 2 eggs. How many eggs have the same amount of calcium as one cup of milk [ANS] A. 4 B. 12 C. 3 D. 8", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0104", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [], "problem_v1": "Keesha's computer can receive information at a rate of 56 megabits per second\nAt this rate, how many megabits of information can her computer receive in one minute? [ANS] A. 3360 B. 5640 C. 5600 D. 3260", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Keesha's computer can receive information at a rate of 48 megabits per second\nAt this rate, how many megabits of information can her computer receive in one minute? [ANS] A. 4800 B. 4840 C. 2780 D. 2880", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Keesha's computer can receive information at a rate of 50 megabits per second\nAt this rate, how many megabits of information can her computer receive in one minute? [ANS] A. 5000 B. 3000 C. 5040 D. 2900", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0105", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "In a group of healthy cows and chickens, the number of legs is 22 more than twice the number of heads. The number of the cows in the group is [ANS].", "answer_v1": [ "11" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In a group of healthy cows and chickens, the number of legs is 16 more than twice the number of heads. The number of the cows in the group is [ANS].", "answer_v2": [ "8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In a group of healthy cows and chickens, the number of legs is 18 more than twice the number of heads. The number of the cows in the group is [ANS].", "answer_v3": [ "9" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0106", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [], "problem_v1": "If the positive numbers from 1 to 79, inclusive, are written on a piece of paper, then the sum of all of the digits that are written on the paper is [ANS].", "answer_v1": [ "640" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "If the positive numbers from 1 to 29, inclusive, are written on a piece of paper, then the sum of all of the digits that are written on the paper is [ANS].", "answer_v2": [ "165" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "If the positive numbers from 1 to 49, inclusive, are written on a piece of paper, then the sum of all of the digits that are written on the paper is [ANS].", "answer_v3": [ "325" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0107", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "a) In a dictionary 16 pages are 1 millimeter thick. To find the thickness of 1120 pages we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The thickness is [ANS] mm. b) A book contains 12 sections with 64 pages each. To find the total number of pages in the book we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The book has [ANS] pages. c) A book company has received an order for 3920 books. If there are 28 books in each box, to find out how many boxes are needed \nwe must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The company needs [ANS] boxes.", "answer_v1": [ "2", "70", "1", "768", "2", "140" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "a) In a dictionary 14 pages are 1 millimeter thick. To find the thickness of 1120 pages we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The thickness is [ANS] mm. b) A book contains 11 sections with 60 pages each. To find the total number of pages in the book we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The book has [ANS] pages. c) A book company has received an order for 5040 books. If there are 36 books in each box, to find out how many boxes are needed \nwe must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The company needs [ANS] boxes.", "answer_v2": [ "2", "80", "1", "660", "2", "140" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "a) In a dictionary 14 pages are 1 millimeter thick. To find the thickness of 980 pages we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The thickness is [ANS] mm. b) A book contains 11 sections with 64 pages each. To find the total number of pages in the book we must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The book has [ANS] pages. c) A book company has received an order for 4200 books. If there are 28 books in each box, to find out how many boxes are needed \nwe must (1) multiply or (2) divide Answer 1 or 2. [ANS]. The company needs [ANS] boxes.", "answer_v3": [ "2", "70", "1", "704", "2", "150" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0108", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "a) Charles has 133 cookies and wants to share them with his 8 friends. He wants to give each friend the same number of cookies and make sure that he has given away as many as he can in that way. He will eat any that are left over. Charles will give each friend [ANS] cookies and eat [ANS] himself. b) There are 8 big fish in Lake Hiawatha. Each morning 115 small fish swim into the lake from the Hiawatha river. For as long as there are enough small fish for each large fish to get at least one, the large fish eat one small fish per minute. But when there are not enough left to go around, the large fish start fighting and the remaining small fish all escape. This means that each large fish eats [ANS] small fish and [ANS] escape. c) Max has a birdhouse with 8 feedholes through which a birdfeed pellet can be made to fall into a tray for a hungry bird. In order for any bird to be fed there must be a bird at each feedhole and each bird must peck at a button above its feed hole within 5 seconds of hearing a bell ring. If they do that, and there are at least 8 pellets in the food bin, one pellet will fall from a central food bin into each feedhole. A group of 8 sparrows have learned how to use this feeding device. When Max puts pellets in the food bin the bell rings once a minute and the birds eat until they cannot get any more food. If Max puts 211 pellets into the food bin each bird can eat [ANS] pellets and [ANS] pellets are left in the bin (because there are not enough left to provide one for each bird).", "answer_v1": [ "16", "5", "14", "3", "26", "3" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "a) Charles has 55 cookies and wants to share them with his 3 friends. He wants to give each friend the same number of cookies and make sure that he has given away as many as he can in that way. He will eat any that are left over. Charles will give each friend [ANS] cookies and eat [ANS] himself. b) There are 5 big fish in Lake Hiawatha. Each morning 92 small fish swim into the lake from the Hiawatha river. For as long as there are enough small fish for each large fish to get at least one, the large fish eat one small fish per minute. But when there are not enough left to go around, the large fish start fighting and the remaining small fish all escape. This means that each large fish eats [ANS] small fish and [ANS] escape. c) Max has a birdhouse with 7 feedholes through which a birdfeed pellet can be made to fall into a tray for a hungry bird. In order for any bird to be fed there must be a bird at each feedhole and each bird must peck at a button above its feed hole within 5 seconds of hearing a bell ring. If they do that, and there are at least 7 pellets in the food bin, one pellet will fall from a central food bin into each feedhole. A group of 7 sparrows have learned how to use this feeding device. When Max puts pellets in the food bin the bell rings once a minute and the birds eat until they cannot get any more food. If Max puts 172 pellets into the food bin each bird can eat [ANS] pellets and [ANS] pellets are left in the bin (because there are not enough left to provide one for each bird).", "answer_v2": [ "18", "1", "18", "2", "24", "4" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "a) Charles has 82 cookies and wants to share them with his 5 friends. He wants to give each friend the same number of cookies and make sure that he has given away as many as he can in that way. He will eat any that are left over. Charles will give each friend [ANS] cookies and eat [ANS] himself. b) There are 6 big fish in Lake Hiawatha. Each morning 80 small fish swim into the lake from the Hiawatha river. For as long as there are enough small fish for each large fish to get at least one, the large fish eat one small fish per minute. But when there are not enough left to go around, the large fish start fighting and the remaining small fish all escape. This means that each large fish eats [ANS] small fish and [ANS] escape. c) Max has a birdhouse with 9 feedholes through which a birdfeed pellet can be made to fall into a tray for a hungry bird. In order for any bird to be fed there must be a bird at each feedhole and each bird must peck at a button above its feed hole within 5 seconds of hearing a bell ring. If they do that, and there are at least 9 pellets in the food bin, one pellet will fall from a central food bin into each feedhole. A group of 9 sparrows have learned how to use this feeding device. When Max puts pellets in the food bin the bell rings once a minute and the birds eat until they cannot get any more food. If Max puts 259 pellets into the food bin each bird can eat [ANS] pellets and [ANS] pellets are left in the bin (because there are not enough left to provide one for each bird).", "answer_v3": [ "16", "2", "13", "2", "28", "7" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0109", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "a) John has 136 marbles. If he gives all of his marbles to each of his 8 friends and gives the same number to each friend then each friend will receive [ANS] marbles. b) Mary's Bakery delivers a selection of cakes to its 7 customers. Each customer receives the name number of cakes. She loads the delivery truck with 126 cakes so that each customer will receive [ANS] cakes. c) Jesse's zoo has 5 monkeys. Each morning he brings a total of 80 bananas which are shared equally by his monkeys. Each monkey gets [ANS] of the bananas. d) Oswald mother gave him 6 anteaters. Each day exactly 102 ants try to eat the crumbs on Oswalds floor. The anteaters eat all of those ants, being very careful to share equally. So each anteater eats exactly [ANS] ants.", "answer_v1": [ "17", "18", "16", "17" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "a) John has 57 marbles. If he gives all of his marbles to each of his 3 friends and gives the same number to each friend then each friend will receive [ANS] marbles. b) Mary's Bakery delivers a selection of cakes to its 4 customers. Each customer receives the name number of cakes. She loads the delivery truck with 64 cakes so that each customer will receive [ANS] cakes. c) Jesse's zoo has 9 monkeys. Each morning he brings a total of 144 bananas which are shared equally by his monkeys. Each monkey gets [ANS] of the bananas. d) Oswald mother gave him 4 anteaters. Each day exactly 64 ants try to eat the crumbs on Oswalds floor. The anteaters eat all of those ants, being very careful to share equally. So each anteater eats exactly [ANS] ants.", "answer_v2": [ "19", "16", "16", "16" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "a) John has 90 marbles. If he gives all of his marbles to each of his 5 friends and gives the same number to each friend then each friend will receive [ANS] marbles. b) Mary's Bakery delivers a selection of cakes to its 4 customers. Each customer receives the name number of cakes. She loads the delivery truck with 68 cakes so that each customer will receive [ANS] cakes. c) Jesse's zoo has 4 monkeys. Each morning he brings a total of 64 bananas which are shared equally by his monkeys. Each monkey gets [ANS] of the bananas. d) Oswald mother gave him 8 anteaters. Each day exactly 152 ants try to eat the crumbs on Oswalds floor. The anteaters eat all of those ants, being very careful to share equally. So each anteater eats exactly [ANS] ants.", "answer_v3": [ "18", "17", "16", "19" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0110", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "4", "keywords": [], "problem_v1": "Show how you can add and subtract mentally. Try to do this problem. Fresh Market bought 58 lb of apples in August from a local orchard. In September, the market purchased an additional 52 lb of apples and 34 lb of strawberries. How many pounds did the market buy? [ANS] pounds.", "answer_v1": [ "144" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Show how you can add and subtract mentally. Try to do this problem. Fresh Market bought 54 lb of apples in August from a local orchard. In September, the market purchased an additional 53 lb of apples and 31 lb of strawberries. How many pounds did the market buy? [ANS] pounds.", "answer_v2": [ "138" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Show how you can add and subtract mentally. Try to do this problem. Fresh Market bought 55 lb of apples in August from a local orchard. In September, the market purchased an additional 52 lb of apples and 32 lb of strawberries. How many pounds did the market buy? [ANS] pounds.", "answer_v3": [ "139" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0111", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "1) The cafeteria workers keep small milk cartons in the refrigerator in stacks of 7. If each worker carries no more than one stack then at least [ANS] cafeteria workers needed to carry small milk cartons for a class of 60. 2) In the teacher's lunchroom, teachers sit at tables for 6. There are 49 teachers eating lunch, so [ANS] tables must be set up. 3) A truck is loaded with 9801 kilograms of food. Each box of food weighs 27 kilograms. That means that there are [ANS] boxes on the truck. 4) There are 5249 auto parts to be packed for a shipment with as many boxes full as possible. The parts are to be packed 24 to a box. There will be [ANS] full boxes and [ANS] parts left over.", "answer_v1": [ "9", "9", "363", "218", "17" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [] ], "problem_v2": "1) The cafeteria workers keep small milk cartons in the refrigerator in stacks of 8. If each worker carries no more than one stack then at least [ANS] cafeteria workers needed to carry small milk cartons for a class of 52. 2) In the teacher's lunchroom, teachers sit at tables for 8. There are 59 teachers eating lunch, so [ANS] tables must be set up. 3) A truck is loaded with 8165 kilograms of food. Each box of food weighs 23 kilograms. That means that there are [ANS] boxes on the truck. 4) There are 5129 auto parts to be packed for a shipment with as many boxes full as possible. The parts are to be packed 24 to a box. There will be [ANS] full boxes and [ANS] parts left over.", "answer_v2": [ "7", "8", "355", "213", "17" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [] ], "problem_v3": "1) The cafeteria workers keep small milk cartons in the refrigerator in stacks of 7. If each worker carries no more than one stack then at least [ANS] cafeteria workers needed to carry small milk cartons for a class of 45. 2) In the teacher's lunchroom, teachers sit at tables for 6. There are 45 teachers eating lunch, so [ANS] tables must be set up. 3) A truck is loaded with 11439 kilograms of food. Each box of food weighs 31 kilograms. That means that there are [ANS] boxes on the truck. 4) There are 6036 auto parts to be packed for a shipment with as many boxes full as possible. The parts are to be packed 28 to a box. There will be [ANS] full boxes and [ANS] parts left over.", "answer_v3": [ "7", "8", "369", "215", "16" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [] ] }, { "id": "Arithmetic_0112", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "Angelina's goal for each five-day work week is to have average total sales of \\$ 245 per day. For the first four days of this week her average total sales was \\$ 210 per day. In order for her to meet her goal for the week her average total sales for the fifth day must be [ANS]", "answer_v1": [ "385" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Angelina's goal for each five-day work week is to have average total sales of \\$ 210 per day. For the first four days of this week her average total sales was \\$ 185 per day. In order for her to meet her goal for the week her average total sales for the fifth day must be [ANS]", "answer_v2": [ "310" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Angelina's goal for each five-day work week is to have average total sales of \\$ 225 per day. For the first four days of this week her average total sales was \\$ 190 per day. In order for her to meet her goal for the week her average total sales for the fifth day must be [ANS]", "answer_v3": [ "365" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0113", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "John's room is shaped like a box. It has a flat ceiling that is a rectangle that is 14 feet long and 10 feet wide and the walls are 8 feet high. It has one door that is 7 feet high and 3 feet wide. It has two windows that are each 3 feet high and 30 inches wide. John wants to paint the walls and ceiling, but not the door or windows. He can paint 100 square feet with a quart of paint and paint costs \\$3.75 per quart. He has to buy whole quarts and may have some paint left over. It will cost John [ANS] to paint his room.", "answer_v1": [ "18.75" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "John's room is shaped like a box. It has a flat ceiling that is a rectangle that is 11 feet long and 12 feet wide and the walls are 7 feet high. It has one door that is 6 feet high and 3 feet wide. It has two windows that are each 5 feet high and 30 inches wide. John wants to paint the walls and ceiling, but not the door or windows. He can paint 100 square feet with a quart of paint and paint costs \\$3.25 per quart. He has to buy whole quarts and may have some paint left over. It will cost John [ANS] to paint his room.", "answer_v2": [ "16.25" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "John's room is shaped like a box. It has a flat ceiling that is a rectangle that is 12 feet long and 11 feet wide and the walls are 7 feet high. It has one door that is 6 feet high and 3 feet wide. It has two windows that are each 3 feet high and 30 inches wide. John wants to paint the walls and ceiling, but not the door or windows. He can paint 100 square feet with a quart of paint and paint costs \\$4.25 per quart. He has to buy whole quarts and may have some paint left over. It will cost John [ANS] to paint his room.", "answer_v3": [ "21.25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0114", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "1) Sadee has 196 quarters. She wants to put them in paper rolls. Each roll holds 20 quarters. a) The number of rolls that will be completely filled is [ANS]. b) The number of quarters in the unfilled roll is [ANS]. 2) Bukka has 1376 paperback books. He wants to put his paperback books on storage shelves. Each shelf can hold 50 paperback books. a) The number of shelves that will be completely filled is [ANS]. b) The number of paperback books that will be on the shelf that is not completely filled is [ANS].", "answer_v1": [ "9", "16", "27", "26" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "1) Sadee has 139 quarters. She wants to put them in paper rolls. Each roll holds 20 quarters. a) The number of rolls that will be completely filled is [ANS]. b) The number of quarters in the unfilled roll is [ANS]. 2) Bukka has 998 paperback books. He wants to put his paperback books on storage shelves. Each shelf can hold 40 paperback books. a) The number of shelves that will be completely filled is [ANS]. b) The number of paperback books that will be on the shelf that is not completely filled is [ANS].", "answer_v2": [ "6", "19", "24", "38" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "1) Sadee has 156 quarters. She wants to put them in paper rolls. Each roll holds 20 quarters. a) The number of rolls that will be completely filled is [ANS]. b) The number of quarters in the unfilled roll is [ANS]. 2) Bukka has 1020 paperback books. He wants to put his paperback books on storage shelves. Each shelf can hold 40 paperback books. a) The number of shelves that will be completely filled is [ANS]. b) The number of paperback books that will be on the shelf that is not completely filled is [ANS].", "answer_v3": [ "7", "16", "25", "20" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0115", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "2", "keywords": [ "animals", "legs" ], "problem_v1": "There are 3 cows and 2 ducks in the garden. How many legs do the animals have together? They have [ANS] legs.", "answer_v1": [ "16" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "There are 1 cow and 3 ducks in the garden. How many legs do the animals have together? They have [ANS] legs.", "answer_v2": [ "10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "There are 1 cow and 2 ducks in the garden. How many legs do the animals have together? They have [ANS] legs.", "answer_v3": [ "8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0116", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "linear", "inequalities", "applications" ], "problem_v1": "A bridge can support a maximum weight of 7200 lb. A delivery truck carrying metal beams for construction has a weight of 4300 lb when it is carrying nothing but its driver. Determine the maximum number of beams that can be carried on the truck for a single trip across the bridge given that each beam weighs 315 lb. Answer: [ANS] beams", "answer_v1": [ "9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A bridge can support a maximum weight of 5700 lb. A delivery truck carrying metal beams for construction has a weight of 3500 lb when it is carrying nothing but its driver. Determine the maximum number of beams that can be carried on the truck for a single trip across the bridge given that each beam weighs 390 lb. Answer: [ANS] beams", "answer_v2": [ "5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A bridge can support a maximum weight of 6200 lb. A delivery truck carrying metal beams for construction has a weight of 3800 lb when it is carrying nothing but its driver. Determine the maximum number of beams that can be carried on the truck for a single trip across the bridge given that each beam weighs 320 lb. Answer: [ANS] beams", "answer_v3": [ "7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0117", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "equations" ], "problem_v1": "Rosette just moved and now lives roughly 90 miles away from her hometown. She has to return to her hometown to give a document by hand to her old employer. Find how long in hours it takes her to drive round-trip if she averages 60 mph. Answer: [ANS] hours", "answer_v1": [ "3" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Rosette just moved and now lives roughly 60 miles away from her hometown. She had to return to her hometown to give a document by hand to her old employer. The entire round-trip took 2.5 hours. Find her average speed in mph for the trip. Answer: [ANS] mph", "answer_v2": [ "48" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Rosette just moved and now lives roughly 170 miles away from her hometown. She has to return to her hometown to give a document by hand to her old employer. Find how long in hours it takes her to drive round-trip if she averages 50 mph. Answer: [ANS] hours", "answer_v3": [ "6.8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0118", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "equations" ], "problem_v1": "A package of floor tiles contains 14 one-foot square tiles. Find how many packages should be bought to cover a square room whose sides measure 8 feet. Answer: [ANS] packages", "answer_v1": [ "5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "One-foot-square ceiling tiles are sold in packages of 30. Find how many packages must be bought for a rectangular ceiling that is 12 feet by 6 feet. Answer: [ANS] packages", "answer_v2": [ "3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A package of floor tiles contains 14 one-foot square tiles. Find how many packages should be bought to cover a square room whose sides measure 10 feet. Answer: [ANS] packages", "answer_v3": [ "8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0119", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "4", "keywords": [ "prealgebra", "common core" ], "problem_v1": "A football team gains 8 yards on first down, loses 6 on second down and then gains 6 on third down. An appropriate expression describing this result is [ANS] $+$ [ANS] $+$ [ANS]\nand the result of the three plays is a total of [ANS] yards. (It is possible for the answer to be a negative number.)", "answer_v1": [ "8", "-6", "6", "8-6+6" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "A football team gains 2 yards on first down, loses 9 on second down and then gains 3 on third down. An appropriate expression describing this result is [ANS] $+$ [ANS] $+$ [ANS]\nand the result of the three plays is a total of [ANS] yards. (It is possible for the answer to be a negative number.)", "answer_v2": [ "2", "-9", "3", "2-9+3" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "A football team gains 4 yards on first down, loses 6 on second down and then gains 4 on third down. An appropriate expression describing this result is [ANS] $+$ [ANS] $+$ [ANS]\nand the result of the three plays is a total of [ANS] yards. (It is possible for the answer to be a negative number.)", "answer_v3": [ "4", "-6", "4", "4-6+4" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0120", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "prealgebra", "common core" ], "problem_v1": "Your school creates student IDs by putting stick-on numbers from 0 to 9 onto a badge. Suppose you have to make $877$ tags with the first tag starting at $101$. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the badges, determine the number of $7$ stickers you will use.\nThe number of $7$ s used up=[ANS]", "answer_v1": [ "256" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Your school creates student IDs by putting stick-on numbers from 0 to 9 onto a badge. Suppose you have to make $817$ tags with the first tag starting at $101$. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the badges, determine the number of $7$ stickers you will use.\nThe number of $7$ s used up=[ANS]", "answer_v2": [ "242" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Your school creates student IDs by putting stick-on numbers from 0 to 9 onto a badge. Suppose you have to make $837$ tags with the first tag starting at $101$. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the badges, determine the number of $7$ stickers you will use.\nThe number of $7$ s used up=[ANS]", "answer_v3": [ "244" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0121", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "prealgebra", "common core" ], "problem_v1": "It is your job to make numbered tags for placing on $372$ bicycles in your city. Tags are created by using stickers from 0 to 9 and placing them on a plastic surface. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the tags, determine the number of $2$ stickers you will use.\nThe number of $2$ s used up=[ANS]", "answer_v1": [ "178" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It is your job to make numbered tags for placing on $312$ bicycles in your city. Tags are created by using stickers from 0 to 9 and placing them on a plastic surface. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the tags, determine the number of $2$ stickers you will use.\nThe number of $2$ s used up=[ANS]", "answer_v2": [ "162" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It is your job to make numbered tags for placing on $332$ bicycles in your city. Tags are created by using stickers from 0 to 9 and placing them on a plastic surface. For example, you would create the tag number 313 by using a 3 sticker, a 1 sticker and then another 3 sticker. In creating all of the tags, determine the number of $2$ stickers you will use.\nThe number of $2$ s used up=[ANS]", "answer_v3": [ "174" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0122", "subject": "Arithmetic", "topic": "Integers", "subtopic": "Applications", "level": "5", "keywords": [ "prealgebra", "common core" ], "problem_v1": "You have a job raking leaves and have been able to save \\$93. You decide to use the money to hit balls in the batting cages. If it costs \\$7 for each 10 minute period and you use the batting cage for 7 periods, the amount of money you will have left is \\$ [ANS].", "answer_v1": [ "93-7*7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You have a job raking leaves and have been able to save \\$76. You decide to use the money to hit balls in the batting cages. If it costs \\$9 for each 10 minute period and you use the batting cage for 4 periods, the amount of money you will have left is \\$ [ANS].", "answer_v2": [ "76-9*4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You have a job raking leaves and have been able to save \\$82. You decide to use the money to hit balls in the batting cages. If it costs \\$8 for each 10 minute period and you use the batting cage for 5 periods, the amount of money you will have left is \\$ [ANS].", "answer_v3": [ "82-8*5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0123", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Properties", "level": "1", "keywords": [ "true-false", "algebra", "calculus" ], "problem_v1": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. The difference of two integers is always a natural number. [ANS] 2. The quotient of two integers is always an integer (provided the denominator is non-zero). [ANS] 3. The quotient of two integers is always a rational number (provided the denominator is non-zero). [ANS] 4. The product of two integers is always an integer. [ANS] 5. The sum of two integers is always an integer. [ANS] 6. The difference of two integers is always an integer. [ANS] 7. The ratio of two integers is always positive", "answer_v1": [ "F", "F", "T", "T", "T", "T", "F" ], "answer_type_v1": [ "TF", "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v1": [ [], [], [], [], [], [], [] ], "problem_v2": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. The sum of two integers is always an integer. [ANS] 2. The ratio of two integers is always positive [ANS] 3. The difference of two integers is always an integer. [ANS] 4. The quotient of two integers is always an integer (provided the denominator is non-zero). [ANS] 5. The difference of two integers is always a natural number. [ANS] 6. The product of two integers is always an integer. [ANS] 7. The quotient of two integers is always a rational number (provided the denominator is non-zero).", "answer_v2": [ "T", "F", "T", "F", "F", "T", "T" ], "answer_type_v2": [ "TF", "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v2": [ [], [], [], [], [], [], [] ], "problem_v3": "Indicate whether the following statements are True (T) or False (F). You must get all answers correct in order to receive credit. [ANS] 1. The product of two integers is always an integer. [ANS] 2. The quotient of two integers is always a rational number (provided the denominator is non-zero). [ANS] 3. The difference of two integers is always an integer. [ANS] 4. The difference of two integers is always a natural number. [ANS] 5. The sum of two integers is always an integer. [ANS] 6. The quotient of two integers is always an integer (provided the denominator is non-zero). [ANS] 7. The ratio of two integers is always positive", "answer_v3": [ "T", "T", "T", "F", "T", "F", "F" ], "answer_type_v3": [ "TF", "TF", "TF", "TF", "TF", "TF", "TF" ], "options_v3": [ [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0124", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Properties", "level": "2", "keywords": [ "real numbers" ], "problem_v1": "Given that ${\\textstyle\\frac{15}{13}}$ is the opposite of a number, find the number and that number's reciprocal:\n(a) Number: [ANS]\n(b) Number's reciprocal [ANS]", "answer_v1": [ "-15/13", "-13/15" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Given that $3$ is the opposite of a number, find the number and that number's reciprocal:\n(a) Number: [ANS]\n(b) Number's reciprocal [ANS]", "answer_v2": [ "-3", "-1/3" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Given that $7$ is the opposite of a number, find the number and that number's reciprocal:\n(a) Number: [ANS]\n(b) Number's reciprocal [ANS]", "answer_v3": [ "-7", "-1/7" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0125", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Properties", "level": "2", "keywords": [ "real numbers" ], "problem_v1": "Complete the table below.\n$\\begin{array}{ccc}\\hline Number & Opposite & Reciprocal \\\\ \\hline {\\textstyle\\frac{15}{13}}{\\textstyle\\frac{15}{13}} & [ANS] & [ANS] \\\\ \\hline [ANS] & {\\textstyle\\frac{15}{13}}{\\textstyle\\frac{15}{13}} & [ANS] \\\\ \\hline [ANS] & [ANS] & {\\textstyle\\frac{15}{13}}{\\textstyle\\frac{15}{13}} \\\\ \\hline \\end{array}$", "answer_v1": [ "-15/13", "13/15", "-15/13", "-13/15", "13/15", "-13/15" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Complete the table below.\n$\\begin{array}{ccc}\\hline Number & Opposite & Reciprocal \\\\ \\hline [ANS] & [ANS] & 33 \\\\ \\hline 33 & [ANS] & [ANS] \\\\ \\hline [ANS] & 33 & [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "1/3", "-1/3", "-3", "1/3", "-3", "-1/3" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Complete the table below.\n$\\begin{array}{ccc}\\hline Number & Opposite & Reciprocal \\\\ \\hline [ANS] & 77 & [ANS] \\\\ \\hline [ANS] & [ANS] & 77 \\\\ \\hline 77 & [ANS] & [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "-7", "-1/7", "1/7", "-1/7", "-7", "1/7" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0126", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Interpreting fractions", "level": "2", "keywords": [ "fraction", "decimal" ], "problem_v1": "Change the fraction ${{\\textstyle\\frac{7}{10}}}$ into a decimal.\n${{{\\textstyle\\frac{7}{10}}}=}$ [ANS]", "answer_v1": [ "0.7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Change the fraction ${{\\textstyle\\frac{3}{4}}}$ into a decimal.\n${{{\\textstyle\\frac{3}{4}}}=}$ [ANS]", "answer_v2": [ "0.75" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Change the fraction ${{\\textstyle\\frac{3}{5}}}$ into a decimal.\n${{{\\textstyle\\frac{3}{5}}}=}$ [ANS]", "answer_v3": [ "0.6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0127", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Interpreting fractions", "level": "2", "keywords": [ "fraction", "decimal" ], "problem_v1": "Change the fraction ${-{\\textstyle\\frac{13}{20}}}$ into a decimal.\n${{-{\\textstyle\\frac{13}{20}}}=}$ [ANS]", "answer_v1": [ "-0.65" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Change the fraction ${-{\\textstyle\\frac{3}{4}}}$ into a decimal.\n${{-{\\textstyle\\frac{3}{4}}}=}$ [ANS]", "answer_v2": [ "-0.75" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Change the fraction ${-{\\textstyle\\frac{3}{5}}}$ into a decimal.\n${{-{\\textstyle\\frac{3}{5}}}=}$ [ANS]", "answer_v3": [ "-0.6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0130", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "3", "keywords": [ "divide", "mixed number" ], "problem_v1": "Divide the following: ${{2 {\\textstyle\\frac{1}{12}}} \\div {2 {\\textstyle\\frac{11}{12}}}}$ [ANS]\nBe certain to express your answer in simplest form.", "answer_v1": [ "5/7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide the following: ${{2 {\\textstyle\\frac{1}{10}}} \\div {1 {\\textstyle\\frac{1}{20}}}}$ [ANS]\nBe certain to express your answer in simplest form.", "answer_v2": [ "2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide the following: ${{1 {\\textstyle\\frac{19}{21}}} \\div {2 {\\textstyle\\frac{11}{12}}}}$ [ANS]\nBe certain to express your answer in simplest form.", "answer_v3": [ "32/49" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0131", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "2", "keywords": [ "improper", "fraction", "mixed number" ], "problem_v1": "Change the improper fraction ${{\\textstyle\\frac{44}{7}}}$ into a mixed number. [ANS]", "answer_v1": [ "44/7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Change the improper fraction ${{\\textstyle\\frac{54}{19}}}$ into a mixed number. [ANS]", "answer_v2": [ "54/19" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Change the improper fraction ${{\\textstyle\\frac{65}{14}}}$ into a mixed number. [ANS]", "answer_v3": [ "65/14" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0132", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "2", "keywords": [ "improper", "fraction", "mixed number" ], "problem_v1": "Change the mixed number ${14 {\\textstyle\\frac{5}{8}}}$ into an improper fraction. [ANS]", "answer_v1": [ "117/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Change the mixed number ${2 {\\textstyle\\frac{13}{20}}}$ into an improper fraction. [ANS]", "answer_v2": [ "53/20" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Change the mixed number ${7 {\\textstyle\\frac{3}{16}}}$ into an improper fraction. [ANS]", "answer_v3": [ "115/16" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0135", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "2", "keywords": [ "divide", "mixed number" ], "problem_v1": "Multiply the following: ${{1 {\\textstyle\\frac{1}{20}}} \\div {15}}$ [ANS]", "answer_v1": [ "7/100" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply the following: ${{1 {\\textstyle\\frac{5}{9}}} \\div {10}}$ [ANS]", "answer_v2": [ "7/45" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply the following: ${{2 {\\textstyle\\frac{4}{25}}} \\div {18}}$ [ANS]", "answer_v3": [ "3/25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0136", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "2", "keywords": [ "multiply", "mixed number" ], "problem_v1": "Multiply the following: ${-{8 {\\textstyle\\frac{3}{4}}} \\cdot {32}}$ [ANS]", "answer_v1": [ "-280" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply the following: ${-{7 {\\textstyle\\frac{1}{2}}} \\cdot {8}}$ [ANS]", "answer_v2": [ "-60" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply the following: ${-{2 {\\textstyle\\frac{2}{5}}} \\cdot {30}}$ [ANS]", "answer_v3": [ "-72" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0138", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Mixed/improper fractions", "level": "2", "keywords": [], "problem_v1": "Change to improper fractions. To enter a fraction $\\frac{a}{b}$ in an answer box, type a/b. 1) $8 \\frac{1}{2}$=[ANS]\n2) $8 \\frac{1}{3}$=[ANS]", "answer_v1": [ "17/2", "25/3" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Change to improper fractions. To enter a fraction $\\frac{a}{b}$ in an answer box, type a/b. 1) $5 \\frac{1}{2}$=[ANS]\n2) $9 \\frac{1}{3}$=[ANS]", "answer_v2": [ "11/2", "28/3" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Change to improper fractions. To enter a fraction $\\frac{a}{b}$ in an answer box, type a/b. 1) $6 \\frac{1}{2}$=[ANS]\n2) $8 \\frac{1}{3}$=[ANS]", "answer_v3": [ "13/2", "25/3" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0140", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "integer", "negative", "operation", "divide" ], "problem_v1": "Evaluate the following.\n${\\frac{-28}{-4}=}$ [ANS]\n${\\frac{40}{-5}=}$ [ANS]\n${\\frac{-24}{6}=}$ [ANS]", "answer_v1": [ "7", "-8", "-4" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Evaluate the following.\n${\\frac{-100}{-10}=}$ [ANS]\n${\\frac{35}{-7}=}$ [ANS]\n${\\frac{-36}{9}=}$ [ANS]", "answer_v2": [ "10", "-5", "-4" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Evaluate the following.\n${\\frac{-56}{-8}=}$ [ANS]\n${\\frac{36}{-6}=}$ [ANS]\n${\\frac{-30}{6}=}$ [ANS]", "answer_v3": [ "7", "-6", "-5" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0141", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "fraction", "reduce" ], "problem_v1": "Reduce the fraction ${\\frac{60}{135}}$. [ANS]", "answer_v1": [ "4/9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Reduce the fraction ${\\frac{6}{60}}$. [ANS]", "answer_v2": [ "1/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Reduce the fraction ${\\frac{28}{98}}$. [ANS]", "answer_v3": [ "2/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0142", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "fraction", "reduce" ], "problem_v1": "Reduce the fraction ${\\frac{25}{40}}$. [ANS]", "answer_v1": [ "5/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Reduce the fraction ${\\frac{14}{49}}$. [ANS]", "answer_v2": [ "2/7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Reduce the fraction ${\\frac{15}{35}}$. [ANS]", "answer_v3": [ "3/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0143", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "improper", "fraction", "reduce" ], "problem_v1": "Reduce the fraction ${\\frac{165}{75}}$. Leave the result as an improper fraction, not a mixed number. [ANS]", "answer_v1": [ "11/5" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Reduce the fraction ${\\frac{48}{42}}$. Leave the result as an improper fraction, not a mixed number. [ANS]", "answer_v2": [ "8/7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Reduce the fraction ${\\frac{135}{75}}$. Leave the result as an improper fraction, not a mixed number. [ANS]", "answer_v3": [ "9/5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0144", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "fraction", "reduce" ], "problem_v1": "Reduce the following fractions:\n${\\frac{401}{401}=}$ [ANS]\n${\\frac{333}{1}=}$ [ANS]", "answer_v1": [ "1", "333" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Reduce the following fractions:\n${\\frac{473}{1}=}$ [ANS]\n${\\frac{133}{133}=}$ [ANS]", "answer_v2": [ "473", "1" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Reduce the following fractions:\n${\\frac{342}{1}=}$ [ANS]\n${\\frac{225}{225}=}$ [ANS]", "answer_v3": [ "342", "1" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0145", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [], "problem_v1": "Put in simplest form. For example if $\\frac{3}{7}$ were the answer you would put 3/7 in the answer box. 1) $\\frac{16}{18}$=[ANS]\n2) $\\frac{28}{36}$=[ANS]\n2) $\\frac{40}{8}$=[ANS]", "answer_v1": [ "8/9", "7/9", "5" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Put in simplest form. For example if $\\frac{3}{7}$ were the answer you would put 3/7 in the answer box. 1) $\\frac{12}{14}$=[ANS]\n2) $\\frac{32}{36}$=[ANS]\n2) $\\frac{35}{5}$=[ANS]", "answer_v2": [ "6/7", "8/9", "7" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Put in simplest form. For example if $\\frac{3}{7}$ were the answer you would put 3/7 in the answer box. 1) $\\frac{12}{14}$=[ANS]\n2) $\\frac{28}{32}$=[ANS]\n2) $\\frac{32}{8}$=[ANS]", "answer_v3": [ "6/7", "7/8", "4" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0146", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "prealgebra", "common core", "rational" ], "problem_v1": "Write the rational number in simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {378}{504}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v1": [ "3", "4" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Write the rational number in simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {18}{48}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "3", "8" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Write the rational number in simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {60}{120}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "1", "2" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0147", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "prealgebra", "common core", "greatest common factor", "rational" ], "problem_v1": "Write the following rational number in simplest form:\n$\\frac{24560172}{29255499}=$ [ANS]/[ANS]\nHint: $24560172=$ $3^4 \\cdot 17 \\cdot 4^1 \\cdot 7^3 \\cdot 13$ $29255499=$ $7^3 \\cdot 13 \\cdot 3^4 \\cdot 9^2$", "answer_v1": [ "68", "81" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Write the following rational number in simplest form:\n$\\frac{307635328}{10353112}=$ [ANS]/[ANS]\nHint: $307635328=$ $2^3 \\cdot 13 \\cdot 4^2 \\cdot 7^5 \\cdot 11$ $10353112=$ $7^5 \\cdot 11 \\cdot 2^3 \\cdot 7^1$", "answer_v2": [ "208", "7" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Write the following rational number in simplest form:\n$\\frac{2345728}{77616}=$ [ANS]/[ANS]\nHint: $2345728=$ $2^4 \\cdot 17 \\cdot 4^2 \\cdot 7^2 \\cdot 11$ $77616=$ $7^2 \\cdot 11 \\cdot 2^4 \\cdot 9^1$", "answer_v3": [ "272", "9" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0148", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Reducing fractions", "level": "2", "keywords": [ "prealgebra", "common core", "reduced fraction" ], "problem_v1": "In simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {462}{672}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v1": [ "11", "16" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "In simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {42}{60}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "7", "10" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "In simplest form:\n$\\begin{array}{cccc}\\hline & \\frac {108}{120}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "9", "10" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0149", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "add", "fraction" ], "problem_v1": "Add these two fractions: ${-\\frac{10}{13}+\\frac{6}{13}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "-4/13" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Add these two fractions: ${-\\frac{4}{5}+\\frac{1}{5}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "-3/5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Add these two fractions: ${-\\frac{5}{7}+\\frac{2}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "-3/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0150", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "subtract", "fraction" ], "problem_v1": "Subtract one fraction from the other: ${\\frac{14}{45}-\\frac{4}{9}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "-2/15" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Subtract one fraction from the other: ${\\frac{7}{20}-\\frac{1}{10}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "1/4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Subtract one fraction from the other: ${\\frac{1}{21}-\\frac{5}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "-2/3" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0151", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "subtract", "fraction" ], "problem_v1": "Carry out the subtraction: ${5-\\frac{4}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "31/7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Carry out the subtraction: ${2-\\frac{9}{10}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "11/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Carry out the subtraction: ${3-\\frac{2}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "19/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0152", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "add", "fraction" ], "problem_v1": "Add these together: ${3+\\frac{4}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "25/7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Add these together: ${-5+\\frac{9}{10}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "-41/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Add these together: ${-2+\\frac{2}{7}}$ When needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "-12/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0154", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "algebra", "fraction" ], "problem_v1": "Add the fractions, and reduce your answer. \\frac{14}{6}+\\frac{14}{6} The reduced answer is [ANS]", "answer_v1": [ "14/6+14/6" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Add the fractions, and reduce your answer. \\frac{3}{2}+\\frac{20}{2} The reduced answer is [ANS]", "answer_v2": [ "3/2+20/2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Add the fractions, and reduce your answer. \\frac{7}{4}+\\frac{14}{4} The reduced answer is [ANS]", "answer_v3": [ "7/4+14/4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0155", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "real numbers", "operations with signed numbers" ], "problem_v1": "Add as indicated: (Note: Your answer must be a fraction.) a) $\\frac{2}{5}+(-\\frac{7}{25})=$ [ANS]\nb) $-\\frac{1}{2}+(-\\frac{4}{7})=$ [ANS]", "answer_v1": [ "3/25", "-15/14" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Add as indicated: (Note: Your answer must be a fraction.) a) $\\frac{1}{2}+(-\\frac{1}{4})=$ [ANS]\nb) $-\\frac{4}{5}+(-\\frac{3}{7})=$ [ANS]", "answer_v2": [ "1/4", "-43/35" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Add as indicated: (Note: Your answer must be a fraction.) a) $\\frac{1}{2}+(-\\frac{2}{3})=$ [ANS]\nb) $-\\frac{1}{5}+(-\\frac{2}{11})=$ [ANS]", "answer_v3": [ "-1/6", "-21/55" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0156", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "3", "keywords": [], "problem_v1": "i) $\\frac{1}{4}-\\frac{1}{5}$=[ANS]. ii) $\\frac{1}{5}-\\frac{1}{6}$=[ANS]. iii) $\\frac{1}{7}-\\frac{1}{8}$=[ANS]. The three problems above all satisfy a rule. It is [ANS] A. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{a(a+1)}$ B. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{2a+1}{a (a+1)}$ C. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{a}{2a+1}$ D. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{2a+1}$", "answer_v1": [ "1/20", "1/30", "1/56", "A" ], "answer_type_v1": [ "NV", "NV", "NV", "MCS" ], "options_v1": [ [], [], [], [ "A", "B", "C", "D" ] ], "problem_v2": "i) $\\frac{1}{2}-\\frac{1}{3}$=[ANS]. ii) $\\frac{1}{5}-\\frac{1}{6}$=[ANS]. iii) $\\frac{1}{6}-\\frac{1}{7}$=[ANS]. The three problems above all satisfy a rule. It is [ANS] A. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{a}{2a+1}$ B. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{2a+1}{a (a+1)}$ C. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{2a+1}$ D. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{a(a+1)}$", "answer_v2": [ "1/6", "1/30", "1/42", "D" ], "answer_type_v2": [ "NV", "NV", "NV", "MCS" ], "options_v2": [ [], [], [], [ "A", "B", "C", "D" ] ], "problem_v3": "i) $\\frac{1}{2}-\\frac{1}{3}$=[ANS]. ii) $\\frac{1}{5}-\\frac{1}{6}$=[ANS]. iii) $\\frac{1}{6}-\\frac{1}{7}$=[ANS]. The three problems above all satisfy a rule. It is [ANS] A. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{a(a+1)}$ B. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{1}{2a+1}$ C. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{a}{2a+1}$ D. $\\frac{1}{a}-\\frac{1}{a+1}=\\frac{2a+1}{a (a+1)}$", "answer_v3": [ "1/6", "1/30", "1/42", "A" ], "answer_type_v3": [ "NV", "NV", "NV", "MCS" ], "options_v3": [ [], [], [], [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0161", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "algebra" ], "problem_v1": "The expression\n\\frac{10}{7}+\\frac{9}{10} can be written as a fraction \\frac{a}{b} where the integers $a$ and $b$ have no factor in common, and $b$ is positive. Enter a=[ANS] and b=[ANS]\nHint: Find a common denominator and cancel any common factors in numerator and denominator.", "answer_v1": [ "163", "70" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "The expression\n\\frac{2}{11}+\\frac{3}{6} can be written as a fraction \\frac{a}{b} where the integers $a$ and $b$ have no factor in common, and $b$ is positive. Enter a=[ANS] and b=[ANS]\nHint: Find a common denominator and cancel any common factors in numerator and denominator.", "answer_v2": [ "15", "22" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "The expression\n\\frac{4}{9}+\\frac{5}{8} can be written as a fraction \\frac{a}{b} where the integers $a$ and $b$ have no factor in common, and $b$ is positive. Enter a=[ANS] and b=[ANS]\nHint: Find a common denominator and cancel any common factors in numerator and denominator.", "answer_v3": [ "77", "72" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0162", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "prealgebra", "common core", "fractions" ], "problem_v1": "Add the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{24}{8}-\\frac{15}{9}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v1": [ "(24*9-15*8)/(8*9)" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Add the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{19}{9}-\\frac{12}{8}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v2": [ "(19*8-12*9)/(9*8)" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Add the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{21}{8}-\\frac{13}{9}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v3": [ "(21*9-13*8)/(8*9)" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0163", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "multiply", "fraction" ], "problem_v1": "Do the following multiplications:\n${24 \\cdot \\frac{5}{8}=}$ [ANS]\n${32 \\cdot \\frac{5}{8}=}$ [ANS]\n${40 \\cdot \\frac{5}{8}=}$ [ANS]", "answer_v1": [ "15", "20", "25" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Do the following multiplications:\n${18 \\cdot \\frac{2}{9}=}$ [ANS]\n${27 \\cdot \\frac{2}{9}=}$ [ANS]\n${36 \\cdot \\frac{2}{9}=}$ [ANS]", "answer_v2": [ "4", "6", "8" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Do the following multiplications:\n${14 \\cdot \\frac{3}{7}=}$ [ANS]\n${21 \\cdot \\frac{3}{7}=}$ [ANS]\n${28 \\cdot \\frac{3}{7}=}$ [ANS]", "answer_v3": [ "6", "9", "12" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0164", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "multiply", "fraction" ], "problem_v1": "Multiply these two fractions: ${\\frac{12}{7} \\cdot \\frac{9}{10}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "54/35" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply these two fractions: ${\\frac{3}{2} \\cdot \\frac{13}{15}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "13/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply these two fractions: ${\\frac{6}{5} \\cdot \\frac{13}{10}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "39/25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0165", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "multiply", "fraction" ], "problem_v1": "Multiply the integer with the fraction: ${-15\\cdot \\frac{7}{40}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "-21/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply the integer with the fraction: ${-10\\cdot \\frac{9}{4}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "-45/2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply the integer with the fraction: ${-9\\cdot \\frac{7}{12}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "-21/4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0166", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "multiply", "fraction" ], "problem_v1": "Multiply the integer with the fraction: ${4\\cdot \\frac{4}{9}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "16/9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply the integer with the fraction: ${3\\cdot \\frac{1}{10}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "3/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply the integer with the fraction: ${4\\cdot \\frac{2}{7}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "8/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0167", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "3", "keywords": [ "multiply", "fraction", "negative" ], "problem_v1": "Multiply these fractions: ${\\left(-{{\\textstyle\\frac{3}{7}}} \\right) \\cdot {35} \\cdot \\left(-{{\\textstyle\\frac{2}{9}}} \\right)}$ [ANS]", "answer_v1": [ "10/3" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply these fractions: ${\\left(-{{\\textstyle\\frac{35}{2}}} \\right) \\cdot {6} \\cdot \\left(-{{\\textstyle\\frac{1}{49}}} \\right)}$ [ANS]", "answer_v2": [ "15/7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply these fractions: ${\\left(-{{\\textstyle\\frac{5}{3}}} \\right) \\cdot {6} \\cdot \\left(-{{\\textstyle\\frac{7}{25}}} \\right)}$ [ANS]", "answer_v3": [ "14/5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0168", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "real numbers", "operations with signed numbers" ], "problem_v1": "Multiply: (Note: If necessary, use fractions not decimals.) a) $\\frac{3}{7}(-2)=$ [ANS]\nb) $\\frac{2}{3}(\\frac{3}{7})=$ [ANS]", "answer_v1": [ "-6/7", "2/7" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Multiply: (Note: If necessary, use fractions not decimals.) a) $\\frac{1}{2}(-3)=$ [ANS]\nb) $\\frac{1}{5}(\\frac{5}{7})=$ [ANS]", "answer_v2": [ "-3/2", "1/7" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Multiply: (Note: If necessary, use fractions not decimals.) a) $\\frac{1}{3}(-3)=$ [ANS]\nb) $\\frac{2}{3}(\\frac{2}{7})=$ [ANS]", "answer_v3": [ "-1", "4/21" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0169", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "3", "keywords": [], "problem_v1": "The value of $(1-\\frac{1}{2})(1-\\frac{1}{3})(1-\\frac{1}{4})(1-\\frac{1}{5})\\cdots (1-\\frac{1}{80})$ expressed as a common fraction is [ANS]", "answer_v1": [ "0.0125" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The value of $(1-\\frac{1}{2})(1-\\frac{1}{3})(1-\\frac{1}{4})(1-\\frac{1}{5})\\cdots (1-\\frac{1}{53})$ expressed as a common fraction is [ANS]", "answer_v2": [ "0.0188679" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The value of $(1-\\frac{1}{2})(1-\\frac{1}{3})(1-\\frac{1}{4})(1-\\frac{1}{5})\\cdots (1-\\frac{1}{62})$ expressed as a common fraction is [ANS]", "answer_v3": [ "0.016129" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0170", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiplication", "level": "2", "keywords": [ "prealgebra", "common core", "fractions" ], "problem_v1": "Simplify the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{12}{6} \\times \\frac{13}{7}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v1": [ "12*13/(6*7)" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{9}{7} \\times \\frac{10}{8}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v2": [ "9*10/(7*8)" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the following and express your answer as a single fraction. No decimals or mixed fractions.\n$\\frac{10}{6} \\times \\frac{10}{7}=$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v3": [ "10*10/(6*7)" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0171", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "divide", "fraction" ], "problem_v1": "Divide one fraction into the other: ${\\frac{3}{10} \\div \\left(-\\frac{4}{15}\\right)}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "-9/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide one fraction into the other: ${\\frac{1}{4} \\div \\left(-\\frac{3}{10}\\right)}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "-5/6" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide one fraction into the other: ${\\frac{8}{15} \\div \\left(-\\frac{7}{6}\\right)}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "-16/35" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0172", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "divide", "fraction" ], "problem_v1": "Divide the integer by the fraction: ${28 \\div \\frac{7}{5}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v1": [ "20" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide the integer by the fraction: ${6 \\div \\frac{3}{2}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v2": [ "4" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide the integer by the fraction: ${14 \\div \\frac{7}{3}}$ If needed, use an improper fraction in your answer. Don\u2019t use a mixed number. [ANS]", "answer_v3": [ "6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0173", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "divide", "fraction" ], "problem_v1": "Divide the fraction by the integer:\n${-{\\frac{12}{19}} \\div (-9)}$=[ANS]", "answer_v1": [ "4/57" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide the fraction by the integer:\n${-{\\frac{3}{29}} \\div (-6)}$=[ANS]", "answer_v2": [ "1/58" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide the fraction by the integer:\n${-{\\frac{8}{19}} \\div (-12)}$=[ANS]", "answer_v3": [ "2/57" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0174", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "divide", "fraction" ], "problem_v1": "Divide the integer by the fraction:\n${15 \\div \\frac{5}{8}}$=[ANS]", "answer_v1": [ "24" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide the integer by the fraction:\n${8 \\div \\frac{2}{5}}$=[ANS]", "answer_v2": [ "20" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide the integer by the fraction:\n${6 \\div \\frac{3}{8}}$=[ANS]", "answer_v3": [ "16" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0175", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "divide", "fraction", "reduce" ], "problem_v1": "Divide these two fractions: ${\\frac{3}{14} \\div \\frac{2}{7}}$ [ANS]", "answer_v1": [ "3/4" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Divide these two fractions: ${\\frac{7}{15} \\div \\frac{4}{5}}$ [ANS]", "answer_v2": [ "7/12" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Divide these two fractions: ${\\frac{4}{15} \\div \\frac{5}{12}}$ [ANS]", "answer_v3": [ "16/25" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0176", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Division", "level": "2", "keywords": [ "algebra", "fraction" ], "problem_v1": "Divide the fractions, and reduce your answer. \\frac{8}{55}\\div\\frac{8}{43} The reduced answer is [ANS]/[ANS]", "answer_v1": [ "43", "55" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Divide the fractions, and reduce your answer. \\frac{2}{37}\\div\\frac{11}{33} The reduced answer is [ANS]/[ANS]", "answer_v2": [ "6", "37" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Divide the fractions, and reduce your answer. \\frac{4}{42}\\div\\frac{8}{38} The reduced answer is [ANS]/[ANS]", "answer_v3": [ "19", "42" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0178", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "fraction", "order of operations" ], "problem_v1": "Simplify the following fraction.\n${{\\textstyle\\frac{4}{3}}}+{{\\textstyle\\frac{2}{3}}} \\div {{\\textstyle\\frac{3}{4}}}-{{\\textstyle\\frac{2}{3}}}$ ${}={}$ [ANS]", "answer_v1": [ "14/9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the following fraction.\n${{\\textstyle\\frac{1}{5}}}+{{\\textstyle\\frac{1}{3}}} \\div {{\\textstyle\\frac{5}{3}}}-{{\\textstyle\\frac{1}{3}}}$ ${}={}$ [ANS]", "answer_v2": [ "1/15" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the following fraction.\n${{\\textstyle\\frac{2}{3}}}+{{\\textstyle\\frac{3}{2}}} \\div {{\\textstyle\\frac{2}{5}}}-{{\\textstyle\\frac{5}{2}}}$ ${}={}$ [ANS]", "answer_v3": [ "23/12" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0179", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiple operations", "level": "3", "keywords": [ "fraction", "order of operations", "add", "evaluate", "multiply" ], "problem_v1": "Evaluate this expression:\n${{{\\textstyle\\frac{8}{7}}}+8\\cdot{{\\textstyle\\frac{8}{21}}}=}$ [ANS]", "answer_v1": [ "88/21" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate this expression:\n${{{\\textstyle\\frac{2}{9}}}+2\\cdot{{\\textstyle\\frac{4}{45}}}=}$ [ANS]", "answer_v2": [ "2/5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate this expression:\n${{{\\textstyle\\frac{4}{7}}}+4\\cdot{{\\textstyle\\frac{3}{7}}}=}$ [ANS]", "answer_v3": [ "16/7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0180", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "algebra", "rational powers" ], "problem_v1": "Evaluate the expression \\frac{1}{8} (2+2/4^2) You may express your answer as a fraction or as a decimal.\nAnswer=[ANS]", "answer_v1": [ "0.265625" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression \\frac{1}{2} (8-7/3^2) You may express your answer as a fraction or as a decimal.\nAnswer=[ANS]", "answer_v2": [ "3.61111" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression \\frac{1}{4} (2-4/4^2) You may express your answer as a fraction or as a decimal.\nAnswer=[ANS]", "answer_v3": [ "0.4375" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0181", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Multiple operations", "level": "2", "keywords": [ "algebra", "powers" ], "problem_v1": "Write the following as a simple fraction in lowest terms. \\frac{(-3)^{-4}+(-3)^{-2}}{-3^{-3}} [ANS]", "answer_v1": [ "-3.33333333333333" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Write the following as a simple fraction in lowest terms. \\frac{(-6)^{-4}+(-6)^{-2}}{-6^{-3}} [ANS]", "answer_v2": [ "-6.16666666666667" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Write the following as a simple fraction in lowest terms. \\frac{(-5)^{-4}+(-5)^{-2}}{-5^{-3}} [ANS]", "answer_v3": [ "-5.2" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0187", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Inequalities", "level": "3", "keywords": [ "prealgebra", "common core", "fractions", "ordering" ], "problem_v1": "Enter the following rational numbers from least to greatest. Separate your answers by commas. No decimals or mixed fractions.\n$\\frac{3}{4}$, $\\frac{48}{6}$, $\\frac{40}{3}$, $\\frac{-19}{3}$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v1": [ "(-19/3, 3/4, 48/6, 40/3)" ], "answer_type_v1": [ "OL" ], "options_v1": [ [] ], "problem_v2": "Enter the following rational numbers from least to greatest. Separate your answers by commas. No decimals or mixed fractions.\n$\\frac{55}{6}$, $\\frac{-25}{3}$, $\\frac{36}{2}$, $\\frac{-7}{3}$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v2": [ "(-25/3, -7/3, 55/6, 36/2)" ], "answer_type_v2": [ "OL" ], "options_v2": [ [] ], "problem_v3": "Enter the following rational numbers from least to greatest. Separate your answers by commas. No decimals or mixed fractions.\n$\\frac{42}{3}$, $\\frac{-23}{3}$, $\\frac{-5}{3}$, $\\frac{47}{6}$ [ANS]\nRemember, to enter a fraction of the form $\\frac{a}{b}$, type a/b.", "answer_v3": [ "(-23/3, -5/3, 47/6, 42/3)" ], "answer_type_v3": [ "OL" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0188", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Absolute value", "level": "2", "keywords": [ "absolute value", "distance" ], "problem_v1": "Find the distance between the pair of real numbers: ${\\textstyle\\frac{7}{12}}$, ${\\textstyle\\frac{3}{10}}$. Answer: [ANS]", "answer_v1": [ "17/60" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find the distance between the pair of real numbers: $-{\\textstyle\\frac{2}{3}}$, ${\\textstyle\\frac{2}{15}}$. Answer: [ANS]", "answer_v2": [ "4/5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find the distance between the pair of real numbers: ${\\textstyle\\frac{5}{6}}$, $-{\\textstyle\\frac{7}{10}}$. Answer: [ANS]", "answer_v3": [ "23/15" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0189", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "3", "keywords": [ "rate", "ratio", "proportion", "solve", "word problem" ], "problem_v1": "In your Grandpa Neil\u2019s recipe for a marinade, each serving uses $7.5$ tablespoons of ketchup and $6$ tablespoons of vinegar. If $52.5$ tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? [ANS] tablespoons of vinegar are needed.", "answer_v1": [ "42" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In your Grandpa Evan\u2019s recipe for a marinade, each serving uses $3.5$ tablespoons of ketchup and $3$ tablespoons of vinegar. If $31.5$ tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? [ANS] tablespoons of vinegar are needed.", "answer_v2": [ "27" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In your Grandpa Jon\u2019s recipe for a marinade, each serving uses $4.5$ tablespoons of ketchup and $4$ tablespoons of vinegar. If $31.5$ tablespoons of ketchup will be used for a larger batch of marinade, how much vinegar is needed? [ANS] tablespoons of vinegar are needed.", "answer_v3": [ "28" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0192", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "2", "keywords": [ "ratio", "application" ], "problem_v1": "The ratio of a school\u2019s male students to female students is $8:7$. If the school has $910$ female students, how many male students are there? Solution: If the school has $910$ female students, the school has [ANS] male students.", "answer_v1": [ "1040" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The ratio of a school\u2019s male students to female students is $2:9$. If the school has $990$ female students, how many male students are there? Solution: If the school has $990$ female students, the school has [ANS] male students.", "answer_v2": [ "220" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The ratio of a school\u2019s male students to female students is $4:3$. If the school has $390$ female students, how many male students are there? Solution: If the school has $390$ female students, the school has [ANS] male students.", "answer_v3": [ "520" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0194", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "2", "keywords": [ "equivalent", "fraction" ], "problem_v1": "Find an equivalent fraction to $\\frac{5}{8}$:\n${\\frac{5}{8}=\\frac{?}{32}}$ The question mark should be the number [ANS].", "answer_v1": [ "20" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find an equivalent fraction to $\\frac{1}{2}$:\n${\\frac{1}{2}=\\frac{?}{4}}$ The question mark should be the number [ANS].", "answer_v2": [ "2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find an equivalent fraction to $\\frac{1}{4}$:\n${\\frac{1}{4}=\\frac{?}{16}}$ The question mark should be the number [ANS].", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0195", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "3", "keywords": [], "problem_v1": "Express each ratio as a fraction in lowest terms. 1) 3 goals in 6 attempts: [ANS]\n2) 11 quarters out of 55 coins: [ANS]\nExpress each rate as a unit rate. If the answer is in dollars and cents it must begin with a dollar sign (\\$). 3) \\$221 for 4 theater tickets: [ANS] (Price per ticket in dollars and cents) 4) 112.7 miles in 8.5 hours: [ANS] (Answer rounded to 2 decimal places)", "answer_v1": [ "3/6", "11/55", "55.25", "13.26" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Express each ratio as a fraction in lowest terms. 1) 7 goals in 14 attempts: [ANS]\n2) 7 quarters out of 21 coins: [ANS]\nExpress each rate as a unit rate. If the answer is in dollars and cents it must begin with a dollar sign (\\$). 3) \\$173 for 4 theater tickets: [ANS] (Price per ticket in dollars and cents) 4) 118.7 miles in 8.4 hours: [ANS] (Answer rounded to 2 decimal places)", "answer_v2": [ "7/14", "7/21", "43.25", "14.13" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Express each ratio as a fraction in lowest terms. 1) 7 goals in 14 attempts: [ANS]\n2) 7 quarters out of 21 coins: [ANS]\nExpress each rate as a unit rate. If the answer is in dollars and cents it must begin with a dollar sign (\\$). 3) \\$241 for 4 theater tickets: [ANS] (Price per ticket in dollars and cents) 4) 111.2 miles in 8.4 hours: [ANS] (Answer rounded to 2 decimal places)", "answer_v3": [ "7/14", "7/21", "60.25", "13.24" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0196", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "2", "keywords": [ "prealgebra", "common core", "rational" ], "problem_v1": "Write each ratio as a fraction in simplest form:\n$36: 234$ is the fraction [ANS]\n$208: 104$ is the fraction [ANS]\nYour fraction should be entered in the form $a/b$ and needs be reduced.", "answer_v1": [ "36/234", "208/104" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Write each ratio as a fraction in simplest form:\n$27: 84$ is the fraction [ANS]\n$150: 65$ is the fraction [ANS]\nYour fraction should be entered in the form $a/b$ and needs be reduced.", "answer_v2": [ "27/84", "150/65" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Write each ratio as a fraction in simplest form:\n$24: 104$ is the fraction [ANS]\n$144: 78$ is the fraction [ANS]\nYour fraction should be entered in the form $a/b$ and needs be reduced.", "answer_v3": [ "24/104", "144/78" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0197", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Ratio/proportions", "level": "2", "keywords": [ "prealgebra", "common core", "proportions" ], "problem_v1": "Solve the proportion:\n$\\begin{array}{cccc}\\hline & \\frac{53}{55}=& & [ANS] 1100 \\\\ \\hline \\end{array}$", "answer_v1": [ "1060" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Solve the proportion:\n$\\begin{array}{cccc}\\hline & \\frac{36}{48}=& & [ANS] 624 \\\\ \\hline \\end{array}$", "answer_v2": [ "468" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Solve the proportion:\n$\\begin{array}{cccc}\\hline & \\frac{42}{45}=& & [ANS] 675 \\\\ \\hline \\end{array}$", "answer_v3": [ "630" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0200", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "addition", "application" ], "problem_v1": "A room needs to be painted. It would take Fabrienne $9$ hours to paint the whole room, and it would take Haley $8$ hours to paint the whole room. If they work together, what fraction of the room can be painted in one hour?\nIf they work together, they can paint [ANS] of the room in one hour.", "answer_v1": [ "17/72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A room needs to be painted. It would take Tien $5$ hours to paint the whole room, and it would take Emiliano $10$ hours to paint the whole room. If they work together, what fraction of the room can be painted in one hour?\nIf they work together, they can paint [ANS] of the room in one hour.", "answer_v2": [ "3/10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A room needs to be painted. It would take Corey $6$ hours to paint the whole room, and it would take Heather $8$ hours to paint the whole room. If they work together, what fraction of the room can be painted in one hour?\nIf they work together, they can paint [ANS] of the room in one hour.", "answer_v3": [ "7/24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0201", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application" ], "problem_v1": "$288$ moths lived in a lab. Each week, some moths died, and about ${{\\textstyle\\frac{1}{6}}}$ survived. How many moths were still alive after $2$ weeks? About [ANS] moths were still alive after $2$ weeks.", "answer_v1": [ "8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "$45$ moths lived in a lab. Each week, some moths died, and about ${{\\textstyle\\frac{1}{3}}}$ survived. How many moths were still alive after $2$ weeks? About [ANS] moths were still alive after $2$ weeks.", "answer_v2": [ "5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "$96$ moths lived in a lab. Each week, some moths died, and about ${{\\textstyle\\frac{1}{4}}}$ survived. How many moths were still alive after $2$ weeks? About [ANS] moths were still alive after $2$ weeks.", "answer_v3": [ "6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0203", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "subtraction", "application" ], "problem_v1": "Eric is participating in a running event. In the first hour, he completed ${{\\textstyle\\frac{3}{8}}}$ of the total distance. After another hour, in total he had completed ${{\\textstyle\\frac{43}{72}}}$ of the total distance. What fraction of the total distance did Eric complete during the second hour? Eric completed [ANS] of the distance during the second hour.", "answer_v1": [ "2/9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Connor is participating in a running event. In the first hour, he completed ${{\\textstyle\\frac{2}{7}}}$ of the total distance. After another hour, in total he had completed ${{\\textstyle\\frac{17}{35}}}$ of the total distance. What fraction of the total distance did Connor complete during the second hour? Connor completed [ANS] of the distance during the second hour.", "answer_v2": [ "1/5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Ravi is participating in a running event. In the first hour, he completed ${{\\textstyle\\frac{1}{8}}}$ of the total distance. After another hour, in total he had completed ${{\\textstyle\\frac{7}{24}}}$ of the total distance. What fraction of the total distance did Ravi complete during the second hour? Ravi completed [ANS] of the distance during the second hour.", "answer_v3": [ "1/6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0204", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "addition", "application" ], "problem_v1": "Joseph walked ${{\\textstyle\\frac{3}{10}}}$ of a mile in the morning, and then walked ${{\\textstyle\\frac{1}{9}}}$ of a mile in the afternoon. How far did Joseph walk altogether?\nJoseph walked a total of [ANS] of a mile.", "answer_v1": [ "37/90" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Hannah walked ${{\\textstyle\\frac{1}{4}}}$ of a mile in the morning, and then walked ${{\\textstyle\\frac{1}{5}}}$ of a mile in the afternoon. How far did Hannah walk altogether?\nHannah walked a total of [ANS] of a mile.", "answer_v2": [ "9/20" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Ravi walked ${{\\textstyle\\frac{1}{6}}}$ of a mile in the morning, and then walked ${{\\textstyle\\frac{1}{8}}}$ of a mile in the afternoon. How far did Ravi walk altogether?\nRavi walked a total of [ANS] of a mile.", "answer_v3": [ "7/24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0205", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application" ], "problem_v1": "A food bank just received $30$ kilograms of pasta. Each family in need is to receive ${{\\textstyle\\frac{3}{8}}}$ kilograms of pasta. How many families can be served with the $30$ kilograms of pasta? [ANS] families can be served with the $30$ kilograms of pasta.", "answer_v1": [ "80" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A food bank just received $14$ kilograms of pasta. Each family in need is to receive ${{\\textstyle\\frac{2}{5}}}$ kilograms of pasta. How many families can be served with the $14$ kilograms of pasta? [ANS] families can be served with the $14$ kilograms of pasta.", "answer_v2": [ "35" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A food bank just received $40$ kilograms of beans. Each family in need is to receive ${{\\textstyle\\frac{2}{5}}}$ kilograms of beans. How many families can be served with the $40$ kilograms of beans? [ANS] families can be served with the $40$ kilograms of beans.", "answer_v3": [ "100" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0206", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "subtraction", "application" ], "problem_v1": "A trail\u2019s total length is ${{\\textstyle\\frac{43}{72}}}$ of a mile. It has two legs. The first leg is ${{\\textstyle\\frac{3}{8}}}$ of a mile long. How long is the second leg? The second leg is [ANS] of a mile in length.", "answer_v1": [ "2/9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A trail\u2019s total length is ${{\\textstyle\\frac{17}{35}}}$ of a mile. It has two legs. The first leg is ${{\\textstyle\\frac{2}{7}}}$ of a mile long. How long is the second leg? The second leg is [ANS] of a mile in length.", "answer_v2": [ "1/5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A trail\u2019s total length is ${{\\textstyle\\frac{7}{24}}}$ of a mile. It has two legs. The first leg is ${{\\textstyle\\frac{1}{8}}}$ of a mile long. How long is the second leg? The second leg is [ANS] of a mile in length.", "answer_v3": [ "1/6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0207", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application" ], "problem_v1": "A company received a grant, and decided to spend ${{\\textstyle\\frac{23}{32}}}$ of this grant in research and development next year. Out of the money set aside for research and development, ${{\\textstyle\\frac{20}{23}}}$ will be used to buy new equipment. What fraction of the grant will be used to buy new equipment? [ANS] of the grant will be used to buy new equipment.", "answer_v1": [ "5/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A company received a grant, and decided to spend ${{\\textstyle\\frac{3}{4}}}$ of this grant in research and development next year. Out of the money set aside for research and development, ${{\\textstyle\\frac{2}{3}}}$ will be used to buy new equipment. What fraction of the grant will be used to buy new equipment? [ANS] of the grant will be used to buy new equipment.", "answer_v2": [ "1/2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A company received a grant, and decided to spend ${{\\textstyle\\frac{7}{27}}}$ of this grant in research and development next year. Out of the money set aside for research and development, ${{\\textstyle\\frac{6}{7}}}$ will be used to buy new equipment. What fraction of the grant will be used to buy new equipment? [ANS] of the grant will be used to buy new equipment.", "answer_v3": [ "2/9" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0208", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application", "mixed number" ], "problem_v1": "A stick is ${2 {\\textstyle\\frac{1}{8}}}$ inches in length. A carpenter will cut off ${{\\textstyle\\frac{1}{4}}}$ of the stick. How long is the part to be cut off? Answer this question with a fraction of an inch. The carpenter will cut off [ANS] inches from the stick.", "answer_v1": [ "17/32" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A stick is ${5 {\\textstyle\\frac{1}{2}}}$ inches in length. A carpenter will cut off ${{\\textstyle\\frac{3}{4}}}$ of the stick. How long is the part to be cut off? Answer this question with a fraction of an inch. The carpenter will cut off [ANS] inches from the stick.", "answer_v2": [ "4 1/8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A stick is ${3 {\\textstyle\\frac{1}{4}}}$ inches in length. A carpenter will cut off ${{\\textstyle\\frac{1}{5}}}$ of the stick. How long is the part to be cut off? Answer this question with a fraction of an inch. The carpenter will cut off [ANS] inches from the stick.", "answer_v3": [ "13/20" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0209", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application", "mixed number" ], "problem_v1": "Company A donated ${129 {\\textstyle\\frac{1}{4}}}$ lb of food to a food bank, and Company B donated ${128 {\\textstyle\\frac{3}{4}}}$ lb. The food bank will hand out these two companies\u2019 donation to families in need. Each family will receive ${4 {\\textstyle\\frac{7}{9}}}$ lb of food. How many families will be fed by the donation? Solution: The donation can be used to feed [ANS] families.", "answer_v1": [ "54" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Company A donated ${31 {\\textstyle\\frac{2}{5}}}$ lb of food to a food bank, and Company B donated ${45 {\\textstyle\\frac{3}{5}}}$ lb. The food bank will hand out these two companies\u2019 donation to families in need. Each family will receive ${3 {\\textstyle\\frac{2}{3}}}$ lb of food. How many families will be fed by the donation? Solution: The donation can be used to feed [ANS] families.", "answer_v2": [ "21" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Company A donated ${98 {\\textstyle\\frac{1}{2}}}$ lb of food to a food bank, and Company B donated ${85 {\\textstyle\\frac{1}{2}}}$ lb. The food bank will hand out these two companies\u2019 donation to families in need. Each family will receive ${4 {\\textstyle\\frac{3}{5}}}$ lb of food. How many families will be fed by the donation? Solution: The donation can be used to feed [ANS] families.", "answer_v3": [ "40" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0210", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application" ], "problem_v1": "A construction team maintains a ${63}$-mile-long sewage pipe. Each day, the team can cover ${{\\textstyle\\frac{7}{9}}}$ of a mile. How many days will it take the team to complete the maintenance of the entire sewage pipe? It will take the team [ANS] days to complete maintaining the entire sewage pipe.", "answer_v1": [ "81" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A construction team maintains a ${14}$-mile-long sewage pipe. Each day, the team can cover ${{\\textstyle\\frac{2}{3}}}$ of a mile. How many days will it take the team to complete the maintenance of the entire sewage pipe? It will take the team [ANS] days to complete maintaining the entire sewage pipe.", "answer_v2": [ "21" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A construction team maintains a ${27}$-mile-long sewage pipe. Each day, the team can cover ${{\\textstyle\\frac{3}{5}}}$ of a mile. How many days will it take the team to complete the maintenance of the entire sewage pipe? It will take the team [ANS] days to complete maintaining the entire sewage pipe.", "answer_v3": [ "45" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0211", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application", "mixed number" ], "problem_v1": "A team of biologists are searching for a new species in a forest, which has ${77}$ square miles. The team can cover ${3 {\\textstyle\\frac{2}{3}}}$ square miles every day. How many days will it take the team to cover the whole forest? Solution: It will take the team [ANS] days to cover the whole forest.", "answer_v1": [ "21" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A team of biologists are searching for a new species in a forest, which has ${50}$ square miles. The team can cover ${1 {\\textstyle\\frac{2}{3}}}$ square miles every day. How many days will it take the team to cover the whole forest? Solution: It will take the team [ANS] days to cover the whole forest.", "answer_v2": [ "30" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A team of biologists are searching for a new species in a forest, which has ${66}$ square miles. The team can cover ${1 {\\textstyle\\frac{5}{6}}}$ square miles every day. How many days will it take the team to cover the whole forest? Solution: It will take the team [ANS] days to cover the whole forest.", "answer_v3": [ "36" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0212", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application" ], "problem_v1": "A committee has $81$ members. A motion can pass if it has support from ${{\\textstyle\\frac{7}{9}}}$ of the committee. At least how many members are needed to pass a motion? Support from at least [ANS] members is needed to pass a motion.", "answer_v1": [ "63" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A committee has $21$ members. A motion can pass if it has support from ${{\\textstyle\\frac{2}{3}}}$ of the committee. At least how many members are needed to pass a motion? Support from at least [ANS] members is needed to pass a motion.", "answer_v2": [ "14" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A committee has $45$ members. A motion can pass if it has support from ${{\\textstyle\\frac{3}{5}}}$ of the committee. At least how many members are needed to pass a motion? Support from at least [ANS] members is needed to pass a motion.", "answer_v3": [ "27" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0213", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application" ], "problem_v1": "A child is stacking up tiles. Each tile\u2019s height is ${{\\textstyle\\frac{2}{3}}}$ of a centimeter. How many layers of tiles are needed to reach ${12}$ centimeters in total height? To reach the total height of ${12}$ centimeters, [ANS] layers of tiles are needed.", "answer_v1": [ "18" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A child is stacking up tiles. Each tile\u2019s height is ${{\\textstyle\\frac{3}{4}}}$ of a centimeter. How many layers of tiles are needed to reach ${15}$ centimeters in total height? To reach the total height of ${15}$ centimeters, [ANS] layers of tiles are needed.", "answer_v2": [ "20" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A child is stacking up tiles. Each tile\u2019s height is ${{\\textstyle\\frac{2}{3}}}$ of a centimeter. How many layers of tiles are needed to reach ${10}$ centimeters in total height? To reach the total height of ${10}$ centimeters, [ANS] layers of tiles are needed.", "answer_v3": [ "15" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0214", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application", "mixed number" ], "problem_v1": "Each big truck can hold ${5 {\\textstyle\\frac{3}{5}}}$ tons of sand, while each small truck can hold ${1 {\\textstyle\\frac{1}{4}}}$ tons of sand. A team of $10$ big trucks and $8$ small trucks will deliver sand to a work site. If each truck has a full load of sand, how many tons of sand in total will be delivered? Solution: In total, [ANS] tons of sand will be delivered.", "answer_v1": [ "66" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Each big truck can hold ${6 {\\textstyle\\frac{1}{2}}}$ tons of sand, while each small truck can hold ${1 {\\textstyle\\frac{3}{8}}}$ tons of sand. A team of $2$ big trucks and $16$ small trucks will deliver sand to a work site. If each truck has a full load of sand, how many tons of sand in total will be delivered? Solution: In total, [ANS] tons of sand will be delivered.", "answer_v2": [ "35" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Each big truck can hold ${5 {\\textstyle\\frac{1}{2}}}$ tons of sand, while each small truck can hold ${2 {\\textstyle\\frac{1}{2}}}$ tons of sand. A team of $4$ big trucks and $4$ small trucks will deliver sand to a work site. If each truck has a full load of sand, how many tons of sand in total will be delivered? Solution: In total, [ANS] tons of sand will be delivered.", "answer_v3": [ "32" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0215", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "addition", "application" ], "problem_v1": "Joseph and Gosheven are sharing a pizza. Joseph ate ${{\\textstyle\\frac{2}{9}}}$ of the pizza, and Gosheven ate ${{\\textstyle\\frac{3}{8}}}$ of the pizza. How much of the pizza was eaten in total? They ate [ANS] of the pizza.", "answer_v1": [ "43/72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Eric and Joseph are sharing a pizza. Eric ate ${{\\textstyle\\frac{1}{5}}}$ of the pizza, and Joseph ate ${{\\textstyle\\frac{2}{7}}}$ of the pizza. How much of the pizza was eaten in total? They ate [ANS] of the pizza.", "answer_v2": [ "17/35" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Stephen and Sherial are sharing a pizza. Stephen ate ${{\\textstyle\\frac{1}{6}}}$ of the pizza, and Sherial ate ${{\\textstyle\\frac{1}{8}}}$ of the pizza. How much of the pizza was eaten in total? They ate [ANS] of the pizza.", "answer_v3": [ "7/24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0216", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "multiplication", "application" ], "problem_v1": "A town has $300$ residents in total, of which ${{\\textstyle\\frac{5}{6}}}$ are Asian Americans. How many Asian Americans reside in this town? There are [ANS] Asian Americans residing in this town.", "answer_v1": [ "250" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A town has $150$ residents in total, of which ${{\\textstyle\\frac{2}{3}}}$ are Asian Americans. How many Asian Americans reside in this town? There are [ANS] Asian Americans residing in this town.", "answer_v2": [ "100" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A town has $200$ residents in total, of which ${{\\textstyle\\frac{3}{4}}}$ are African Americans. How many African Americans reside in this town? There are [ANS] African Americans residing in this town.", "answer_v3": [ "150" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0218", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application" ], "problem_v1": "A restaurant made $400$ cups of pudding for a festival. Customers at the festival will be served ${{\\textstyle\\frac{1}{8}}}$ of a cup of pudding per serving. How many customers can the restaurant serve at the festival with the $400$ cups of pudding? The restaurant can serve [ANS] customers at the festival with the $400$ cups of pudding.", "answer_v1": [ "3200" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A restaurant made $100$ cups of pudding for a festival. Customers at the festival will be served ${{\\textstyle\\frac{1}{10}}}$ of a cup of pudding per serving. How many customers can the restaurant serve at the festival with the $100$ cups of pudding? The restaurant can serve [ANS] customers at the festival with the $100$ cups of pudding.", "answer_v2": [ "1000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A restaurant made $200$ cups of pudding for a festival. Customers at the festival will be served ${{\\textstyle\\frac{1}{8}}}$ of a cup of pudding per serving. How many customers can the restaurant serve at the festival with the $200$ cups of pudding? The restaurant can serve [ANS] customers at the festival with the $200$ cups of pudding.", "answer_v3": [ "1600" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0221", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "subtraction", "application" ], "problem_v1": "A room needs to be painted. It would take Joseph $8$ hours to paint the whole room, but Gosheven will help Joseph. Working together, they can pain ${{\\textstyle\\frac{17}{72}}}$ of the room each hour. If Gosheven works alone, how many hours will it take him to paint the whole room? If Gosheven works alone, it would take him [ANS] hours to paint the whole room.", "answer_v1": [ "9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A room needs to be painted. It would take Tien $5$ hours to paint the whole room, but Emiliano will help Tien. Working together, they can pain ${{\\textstyle\\frac{3}{10}}}$ of the room each hour. If Emiliano works alone, how many hours will it take him to paint the whole room? If Emiliano works alone, it would take him [ANS] hours to paint the whole room.", "answer_v2": [ "10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A room needs to be painted. It would take Corey $6$ hours to paint the whole room, but Heather will help Corey. Working together, they can pain ${{\\textstyle\\frac{7}{24}}}$ of the room each hour. If Heather works alone, how many hours will it take her to paint the whole room? If Heather works alone, it would take her [ANS] hours to paint the whole room.", "answer_v3": [ "8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0222", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [ "fraction", "division", "application" ], "problem_v1": "A school just won a grant, and decided to spend ${{\\textstyle\\frac{5}{8}}}$ of the grant to purchase new equipment. The school administrators decide to spend the new equipment money in $7$ months. Assume every month the same amount of money will be spent on new equipment. What fraction of the grant will be spent to purchase new equipment every month? Every month, [ANS] of the grant will be spent to purchase new equipment.", "answer_v1": [ "5/56" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A school just won a grant, and decided to spend ${{\\textstyle\\frac{1}{2}}}$ of the grant to purchase new equipment. The school administrators decide to spend the new equipment money in $6$ months. Assume every month the same amount of money will be spent on new equipment. What fraction of the grant will be spent to purchase new equipment every month? Every month, [ANS] of the grant will be spent to purchase new equipment.", "answer_v2": [ "1/12" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A school just won a grant, and decided to spend ${{\\textstyle\\frac{2}{3}}}$ of the grant to purchase new equipment. The school administrators decide to spend the new equipment money in $7$ months. Assume every month the same amount of money will be spent on new equipment. What fraction of the grant will be spent to purchase new equipment every month? Every month, [ANS] of the grant will be spent to purchase new equipment.", "answer_v3": [ "2/21" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0225", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "4", "keywords": [], "problem_v1": "Jenn is putting her wrenches away. She is missing a wrench with a size between $\\frac{5}{8}$ inch and $\\frac{3}{4}$ inch. Which size wrench is missing [ANS] A. $\\frac{9}{16}$ inch B. $\\frac{1}{2}$ inch C. $\\frac{11}{16}$ inch D. $\\frac{7}{8}$ inch", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Jenn is putting her wrenches away. She is missing a wrench with a size between $\\frac{5}{8}$ inch and $\\frac{3}{4}$ inch. Which size wrench is missing [ANS] A. $\\frac{11}{16}$ inch B. $\\frac{1}{2}$ inch C. $\\frac{9}{16}$ inch D. $\\frac{7}{8}$ inch", "answer_v2": [ "A" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Jenn is putting her wrenches away. She is missing a wrench with a size between $\\frac{5}{8}$ inch and $\\frac{3}{4}$ inch. Which size wrench is missing [ANS] A. $\\frac{9}{16}$ inch B. $\\frac{11}{16}$ inch C. $\\frac{1}{2}$ inch D. $\\frac{7}{8}$ inch", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0226", "subject": "Arithmetic", "topic": "Fractions/rational numbers", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "Sylvia has a compact car with an 8 gallon tank. If the car can travel 33 miles per gallon then it could travel [ANS] miles on a tank that only $\\frac {3}{4}$ full.", "answer_v1": [ "198" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Sylvia has a compact car with an 8 gallon tank. If the car can travel 27 miles per gallon then it could travel [ANS] miles on a tank that only $\\frac {3}{4}$ full.", "answer_v2": [ "162" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Sylvia has a compact car with an 8 gallon tank. If the car can travel 29 miles per gallon then it could travel [ANS] miles on a tank that only $\\frac {3}{4}$ full.", "answer_v3": [ "174" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0227", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Interpreting decimals", "level": "2", "keywords": [ "decimal", "compare", "negative" ], "problem_v1": "Order these decimals from biggest to smallest:\n${-7.6,-7.006,-7.06}$ [ANS] > [ANS] > [ANS]", "answer_v1": [ "-7.006", "-7.06", "-7.6" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Order these decimals from biggest to smallest:\n${-0.09,-0.009,-0.9}$ [ANS] > [ANS] > [ANS]", "answer_v2": [ "-0.009", "-0.09", "-0.9" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Order these decimals from biggest to smallest:\n${-3.006,-3.06,-3.6}$ [ANS] > [ANS] > [ANS]", "answer_v3": [ "-3.006", "-3.06", "-3.6" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0228", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Interpreting decimals", "level": "2", "keywords": [ "decimal", "compare" ], "problem_v1": "Check all numbers which are equivalent to $7.6$ [ANS] A. $7.600$ B. $7.006$ C. $7.60$ D. $7.06$", "answer_v1": [ "AC" ], "answer_type_v1": [ "MCM" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Check all numbers which are equivalent to $0.9$ [ANS] A. $0.09$ B. $0.009$ C. $0.900$ D. $0.90$", "answer_v2": [ "CD" ], "answer_type_v2": [ "MCM" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Check all numbers which are equivalent to $3.6$ [ANS] A. $3.600$ B. $3.006$ C. $3.06$ D. $3.60$", "answer_v3": [ "AD" ], "answer_type_v3": [ "MCM" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0229", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Addition/subtraction", "level": "2", "keywords": [ "decimal", "add" ], "problem_v1": "Add these two decimals.\n${75+6.73=}$ [ANS]", "answer_v1": [ "81.73" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Add these two decimals.\n${19+2.39=}$ [ANS]", "answer_v2": [ "21.39" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Add these two decimals.\n${36+3.52=}$ [ANS]", "answer_v3": [ "39.52" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0230", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Addition/subtraction", "level": "4", "keywords": [], "problem_v1": "Libby had a ten-dollar bill. Then she spent \\$ 2.95 at a store. How much money does Libby have now? [ANS] A. \\$7.05 B. \\$8.05 C. \\$7.95 D. \\$6.95", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Libby had a ten-dollar bill. Then she spent \\$ 2.65 at a store. How much money does Libby have now? [ANS] A. \\$8.25 B. \\$8.35 C. \\$7.25 D. \\$7.35", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Libby had a ten-dollar bill. Then she spent \\$ 2.75 at a store. How much money does Libby have now? [ANS] A. \\$8.15 B. \\$7.25 C. \\$8.25 D. \\$7.15", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0231", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Addition/subtraction", "level": "2", "keywords": [], "problem_v1": "5.751+66.23=[ANS]\n571.7-7.335=[ANS]", "answer_v1": [ "71.981", "564.365" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "5.081+61.43=[ANS]\n53.37-7.315=[ANS]", "answer_v2": [ "66.511", "46.055" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "5.311+62.73=[ANS]\n554.7-7.345=[ANS]", "answer_v3": [ "68.041", "547.355" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0232", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Multiplication", "level": "2", "keywords": [ "decimal", "multiply", "negative" ], "problem_v1": "It\u2019s give that $76\\cdot67=5092$. Use this fact to calculate the following:\n${7.6(-6.7)=}$ [ANS]", "answer_v1": [ "-50.92" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s give that $19\\cdot24=456$. Use this fact to calculate the following:\n${0.019(-2.4)=}$ [ANS]", "answer_v2": [ "-0.0456" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s give that $36\\cdot35=1260$. Use this fact to calculate the following:\n${3.6(-0.35)=}$ [ANS]", "answer_v3": [ "-1.26" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0233", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Multiplication", "level": "2", "keywords": [ "decimal", "multiply" ], "problem_v1": "It\u2019s given that $756\\cdot73=55188$. Calculate the following.\n$75.6 \\cdot 0.73$=[ANS]\n$7.56 \\cdot 7.3$=[ANS]\n$0.756 \\cdot 0.73$=[ANS]", "answer_v1": [ "55.188", "55.188", "0.55188" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "It\u2019s given that $192\\cdot49=9408$. Calculate the following.\n$19.2 \\cdot 4.9$=[ANS]\n$19.2 \\cdot 0.49$=[ANS]\n$1.92 \\cdot 0.49$=[ANS]", "answer_v2": [ "94.08", "9.408", "0.9408" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "It\u2019s given that $363\\cdot52=18876$. Calculate the following.\n$3.63 \\cdot 0.052$=[ANS]\n$0.363 \\cdot 5.2$=[ANS]\n$36.3 \\cdot 5.2$=[ANS]", "answer_v3": [ "0.18876", "1.8876", "188.76" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0234", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Division", "level": "2", "keywords": [], "problem_v1": "5.7 $\\times$ 0.3=[ANS]\n56.6 $\\div$ 0.5=[ANS]", "answer_v1": [ "1.71", "113.2" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "5.1 $\\times$ 0.3=[ANS]\n52.35 $\\div$ 0.5=[ANS]", "answer_v2": [ "1.53", "104.7" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "5.3 $\\times$ 0.3=[ANS]\n53.5 $\\div$ 0.5=[ANS]", "answer_v3": [ "1.59", "107" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0235", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Division", "level": "2", "keywords": [], "problem_v1": "Find the answer to the nearest cent when you perform each division. Your answer should include a dollar sign and a decimal point. $45 \\; \\begin{array}{|l} \\hline \\$64.13 \\end{array}$=[ANS]\n$\\$49.81 \\div 92=$ [ANS]", "answer_v1": [ "1.43", "0.54" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Find the answer to the nearest cent when you perform each division. Your answer should include a dollar sign and a decimal point. $21 \\; \\begin{array}{|l} \\hline \\$66.65 \\end{array}$=[ANS]\n$\\$48.86 \\div 84=$ [ANS]", "answer_v2": [ "3.17", "0.58" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Find the answer to the nearest cent when you perform each division. Your answer should include a dollar sign and a decimal point. $27 \\; \\begin{array}{|l} \\hline \\$64.34 \\end{array}$=[ANS]\n$\\$49.11 \\div 84=$ [ANS]", "answer_v3": [ "2.38", "0.58" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0236", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Division", "level": "2", "keywords": [], "problem_v1": "Find each quotient. $21 \\; \\begin{array}{|l} \\hline 31.5 \\end{array}$=[ANS]\n$117.23\\div 19$=[ANS]", "answer_v1": [ "1.5", "6.17" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Find each quotient. $12 \\; \\begin{array}{|l} \\hline 22.8 \\end{array}$=[ANS]\n$79.69\\div 13$=[ANS]", "answer_v2": [ "1.9", "6.13" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Find each quotient. $15 \\; \\begin{array}{|l} \\hline 25.5 \\end{array}$=[ANS]\n$92.25\\div 15$=[ANS]", "answer_v3": [ "1.7", "6.15" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0237", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Multiple operations", "level": "3", "keywords": [ "algebra", "solve for variable' 'fraction" ], "problem_v1": "Simplify the following expressions. Give exact answers with the fewest number of $e$ 's possible. Then give a decimal approximation.\na.) e^{5} e^{2} e^{3}=[ANS], which is approximately [ANS].\nb.) \\frac{e^{16}-e^{-16}}{e^{8}-e^{-8}}=[ANS], which is approximately [ANS].\nc.) (e^{4}-4)(e^{6}+2)=[ANS], which is approximately [ANS]", "answer_v1": [ "e**10", "22026.4657948067", "(e**16+1)/(e**8)", "2980.95832250435", "e**(4+6) + 2*e**4 + -4*e**6 +-4*2", "20513.946920902" ], "answer_type_v1": [ "EX", "NV", "EX", "NV", "EX", "NV" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "Simplify the following expressions. Give exact answers with the fewest number of $e$ 's possible. Then give a decimal approximation.\na.) e^{-9} e^{9} e^{-7}=[ANS], which is approximately [ANS].\nb.) \\frac{e^{8}-e^{-8}}{e^{4}-e^{-4}}=[ANS], which is approximately [ANS].\nc.) (e^{10}-4)(e^{2}-4)=[ANS], which is approximately [ANS]", "answer_v2": [ "e**-7", "0.000911881965554517", "(e**8+1)/(e**4)", "54.616465672033", "e**(10+2) + -4*e**10 + -4*e**2 +-4*-4", "74635.3720153813" ], "answer_type_v2": [ "EX", "NV", "EX", "NV", "EX", "NV" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "Simplify the following expressions. Give exact answers with the fewest number of $e$ 's possible. Then give a decimal approximation.\na.) e^{-4} e^{2} e^{-5}=[ANS], which is approximately [ANS].\nb.) \\frac{e^{12}-e^{-12}}{e^{6}-e^{-6}}=[ANS], which is approximately [ANS].\nc.) (e^{3}-3)(e^{9}+9)=[ANS], which is approximately [ANS]", "answer_v3": [ "e**-7", "0.000911881965554517", "(e**12+1)/(e**6)", "403.431272244912", "e**(3+9) + 9*e**3 + -3*e**9 +-3*9", "138599.309468586" ], "answer_type_v3": [ "EX", "NV", "EX", "NV", "EX", "NV" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0238", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [ "calculus", "repeating decimal", "fractions" ], "problem_v1": "Express the repeating decimal $r_{1}=0.\\overline{27}$ as a fraction. Hint: $100r_{1}-r_{1}$ is an integer. $0.\\overline{27}=$ [ANS] $/$ [ANS]. Then express the repeating decimal $r_{2}=0.4\\overline{6}$ as a fraction. $0.4\\overline{6}=$ [ANS] $/$ [ANS]. Note: Enter both fractions in reduced terms. That is, numerator and denominator should have no common factors.", "answer_v1": [ "3", "11", "7", "15" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Express the repeating decimal $r_{1}=0.\\overline{27}$ as a fraction. Hint: $100r_{1}-r_{1}$ is an integer. $0.\\overline{27}=$ [ANS] $/$ [ANS]. Then express the repeating decimal $r_{2}=0.2\\overline{6}$ as a fraction. $0.2\\overline{6}=$ [ANS] $/$ [ANS]. Note: Enter both fractions in reduced terms. That is, numerator and denominator should have no common factors.", "answer_v2": [ "3", "11", "4", "15" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Express the repeating decimal $r_{1}=0.\\overline{27}$ as a fraction. Hint: $100r_{1}-r_{1}$ is an integer. $0.\\overline{27}=$ [ANS] $/$ [ANS]. Then express the repeating decimal $r_{2}=0.\\overline{2}$ as a fraction. $0.\\overline{2}=$ [ANS] $/$ [ANS]. Note: Enter both fractions in reduced terms. That is, numerator and denominator should have no common factors.", "answer_v3": [ "3", "11", "2", "9" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0239", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "1", "keywords": [ "decimal" ], "problem_v1": "Write the following decimals: seventy-seven and six hundred six thousandths=[ANS]", "answer_v1": [ "77.606" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Write the following decimals: seventeen and nine hundred two thousandths=[ANS]", "answer_v2": [ "17.902" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Write the following decimals: thirty-eight and six hundred three thousandths=[ANS]", "answer_v3": [ "38.603" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0240", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "1", "keywords": [ "decimal" ], "problem_v1": "What is the correct way to read $7.765$ [ANS] A. seven and seven hundred sixty-five thousandths B. seven and seven hundred sixty-five tenths C. seven and seven hundred sixty-five hundredths", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C" ] ], "problem_v2": "What is the correct way to read $1.319$ [ANS] A. one and three hundred nineteen hundredths B. one and three hundred nineteen tenths C. one and three hundred nineteen thousandths", "answer_v2": [ "C" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C" ] ], "problem_v3": "What is the correct way to read $3.526$ [ANS] A. three and five hundred twenty-six hundredths B. three and five hundred twenty-six thousandths C. three and five hundred twenty-six tenths", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C" ] ] }, { "id": "Arithmetic_0241", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [], "problem_v1": "Write each as a decimal $\\frac{67}{100}=$ [ANS]\n$\\frac{36}{100}=$ [ANS]\n$\\frac{6}{100}=$ [ANS]", "answer_v1": [ "0.67", "0.36", "0.06" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Write each as a decimal $\\frac{61}{100}=$ [ANS]\n$\\frac{39}{100}=$ [ANS]\n$\\frac{2}{100}=$ [ANS]", "answer_v2": [ "0.61", "0.39", "0.02" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Write each as a decimal $\\frac{63}{100}=$ [ANS]\n$\\frac{36}{100}=$ [ANS]\n$\\frac{3}{100}=$ [ANS]", "answer_v3": [ "0.63", "0.36", "0.03" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0242", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [], "problem_v1": "Express each decimal as a fraction or mixed number in simplest form. 1) 0.83=[ANS]\n2) $0.\\overline{83}$=[ANS]", "answer_v1": [ "83/100", "83/99" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Express each decimal as a fraction or mixed number in simplest form. 1) 0.45=[ANS]\n2) $0.\\overline{45}$=[ANS]", "answer_v2": [ "9/20", "5/11" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Express each decimal as a fraction or mixed number in simplest form. 1) 0.59=[ANS]\n2) $0.\\overline{59}$=[ANS]", "answer_v3": [ "59/100", "59/99" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0243", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [], "problem_v1": "Express each of the following as a fraction in simplest form.\na) 0.75=[ANS]\nb) 0.55=[ANS]", "answer_v1": [ "3/4", "11/20" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Express each of the following as a fraction in simplest form.\na) 0.75=[ANS]\nb) 0.15=[ANS]", "answer_v2": [ "3/4", "3/20" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Express each of the following as a fraction in simplest form.\na) 0.75=[ANS]\nb) 0.3=[ANS]", "answer_v3": [ "3/4", "3/10" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0244", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [], "problem_v1": "Change the following fractions to decimals. If answer is a repeating decimal, round to 3 decimal places. $\\frac{40}{50}$=[ANS]. $\\frac{11}{20}$=[ANS]. $\\frac{5}{6}$=[ANS]. $\\frac{9}{10}$=[ANS]. $\\frac{19}{25}$=[ANS]. $\\frac{33}{50}$=[ANS]. $\\frac{3}{5}$=[ANS]. $\\frac{18}{40}$=[ANS].", "answer_v1": [ "0.8", "0.55", "0.833333", "0.9", "0.76", "0.66", "0.6", "0.45" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "Change the following fractions to decimals. If answer is a repeating decimal, round to 3 decimal places. $\\frac{10}{50}$=[ANS]. $\\frac{13}{20}$=[ANS]. $\\frac{1}{6}$=[ANS]. $\\frac{7}{10}$=[ANS]. $\\frac{23}{25}$=[ANS]. $\\frac{33}{50}$=[ANS]. $\\frac{2}{5}$=[ANS]. $\\frac{14}{40}$=[ANS].", "answer_v2": [ "0.2", "0.65", "0.166667", "0.7", "0.92", "0.66", "0.4", "0.35" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "Change the following fractions to decimals. If answer is a repeating decimal, round to 3 decimal places. $\\frac{20}{50}$=[ANS]. $\\frac{11}{20}$=[ANS]. $\\frac{1}{6}$=[ANS]. $\\frac{9}{10}$=[ANS]. $\\frac{17}{25}$=[ANS]. $\\frac{36}{50}$=[ANS]. $\\frac{4}{5}$=[ANS]. $\\frac{22}{40}$=[ANS].", "answer_v3": [ "0.4", "0.55", "0.166667", "0.9", "0.68", "0.72", "0.8", "0.55" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0245", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "3", "keywords": [ "calculus", "algebra", "rational number", "fraction" ], "problem_v1": "Express $8.765765765...$ as a rational number, in the form $\\frac{p}{q}$ where $p$ and $q$ have no common factors. $p$=[ANS] and $q$=[ANS]", "answer_v1": [ "973", "111" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Express $2.927927927...$ as a rational number, in the form $\\frac{p}{q}$ where $p$ and $q$ have no common factors. $p$=[ANS] and $q$=[ANS]", "answer_v2": [ "325", "111" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Express $4.846846846...$ as a rational number, in the form $\\frac{p}{q}$ where $p$ and $q$ have no common factors. $p$=[ANS] and $q$=[ANS]", "answer_v3": [ "538", "111" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0246", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [ "algebra", "fractions" ], "problem_v1": "For each of the following problems, show that the repeating decimal is a rational number by writing the decimal as a fraction. Make sure that you reduce the factor to the lowest common denominator. For example, 0.33333333...=1/3, not 3/9. 0.581658165816582...=[ANS]\n0.0301730173017302...=[ANS]\n0.574574574574575...=[ANS]\n0.0653653653653654...=[ANS]\n0.428428428428428...=[ANS]", "answer_v1": [ "5816/9999", "3017/99990", "574/999", "653/9990", "428/999" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [] ], "problem_v2": "For each of the following problems, show that the repeating decimal is a rational number by writing the decimal as a fraction. Make sure that you reduce the factor to the lowest common denominator. For example, 0.33333333...=1/3, not 3/9. 0.0939393939393939...=[ANS]\n0.0946946946946947...=[ANS]\n0.333333333333333...=[ANS]\n0.646464646464647...=[ANS]\n0.0192919291929193...=[ANS]", "answer_v2": [ "31/330", "473/4995", "1/3", "64/99", "643/33330" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [] ], "problem_v3": "For each of the following problems, show that the repeating decimal is a rational number by writing the decimal as a fraction. Make sure that you reduce the factor to the lowest common denominator. For example, 0.33333333...=1/3, not 3/9. 0.0606060606060606...=[ANS]\n0.206206206206206...=[ANS]\n9.11291129112911...=[ANS]\n0.0292929292929293...=[ANS]\n5.75757575757576...=[ANS]", "answer_v3": [ "2/33", "206/999", "91120/9999", "29/990", "190/33" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [] ] }, { "id": "Arithmetic_0247", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Converting between fractions and decimals", "level": "2", "keywords": [ "prealgebra", "common core", "fractions", "ordering", "decimals", "mixed fractions" ], "problem_v1": "Convert each mixed fraction to a decimal using at least four decimal places.\n$4 \\frac{3}{8}$=[ANS]\n$7 \\frac{2}{6}$=[ANS]\n$11 \\frac{3}{7}$=[ANS]", "answer_v1": [ "4+3/8", "7+2/6", "11+3/7" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Convert each mixed fraction to a decimal using at least four decimal places.\n$1 \\frac{4}{5}$=[ANS]\n$6 \\frac{4}{6}$=[ANS]\n$9 \\frac{2}{8}$=[ANS]", "answer_v2": [ "1+4/5", "6+4/6", "9+2/8" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Convert each mixed fraction to a decimal using at least four decimal places.\n$2 \\frac{3}{6}$=[ANS]\n$7 \\frac{1}{7}$=[ANS]\n$12 \\frac{4}{10}$=[ANS]", "answer_v3": [ "2+3/6", "7+1/7", "12+4/10" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0248", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Inequalities", "level": "3", "keywords": [], "problem_v1": "The number of integers between $\\sqrt{3}$ and $\\sqrt{32}$ is [ANS].", "answer_v1": [ "4" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The number of integers between $\\sqrt{8}$ and $\\sqrt{28}$ is [ANS].", "answer_v2": [ "3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The number of integers between $\\sqrt{3}$ and $\\sqrt{40}$ is [ANS].", "answer_v3": [ "5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0249", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [], "problem_v1": "Find this expression\u2019s value. Round your answer to two or more decimal places.\n${\\sqrt[4]{78^{7}}}$ [ANS]", "answer_v1": [ "2047.22" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Find this expression\u2019s value. Round your answer to two or more decimal places.\n${\\sqrt[9]{17^{4}}}$ [ANS]", "answer_v2": [ "3.52262" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Find this expression\u2019s value. Round your answer to two or more decimal places.\n${\\sqrt[8]{38^{9}}}$ [ANS]", "answer_v3": [ "59.8765" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0251", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "decimal", "round" ], "problem_v1": "Round the decimal $75.6733$ to the specified places. Round to a whole number: [ANS]\nRound to the tenth place: [ANS]\nRound to the hundredth place: [ANS]\nRound to the thousandth place: [ANS]", "answer_v1": [ "76.000000", "75.700000", "75.670000", "75.673000" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Round the decimal $19.1393$ to the specified places. Round to a whole number: [ANS]\nRound to the tenth place: [ANS]\nRound to the hundredth place: [ANS]\nRound to the thousandth place: [ANS]", "answer_v2": [ "19.000000", "19.100000", "19.140000", "19.139000" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Round the decimal $36.2524$ to the specified places. Round to a whole number: [ANS]\nRound to the tenth place: [ANS]\nRound to the hundredth place: [ANS]\nRound to the thousandth place: [ANS]", "answer_v3": [ "36.000000", "36.300000", "36.250000", "36.252000" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0252", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "prealgebra", "common core", "rounding", "estimating" ], "problem_v1": "Estimate the sum by rounding each of the given data values to the nearest tenth.\n$13.182+11.385$ $\\approx$ [ANS] $+$ $11.4$=[ANS]", "answer_v1": [ "13.2", "24.6" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Estimate the sum by rounding each of the given data values to the nearest tenth.\n$5.841+5.683$ $\\approx$ [ANS] $+$ $5.7$=[ANS]", "answer_v2": [ "5.8", "11.5" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Estimate the sum by rounding each of the given data values to the nearest tenth.\n$8.173+8.086$ $\\approx$ [ANS] $+$ $8.1$=[ANS]", "answer_v3": [ "8.2", "16.3" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0253", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "prealgebra", "common core", "rounding", "estimating" ], "problem_v1": "Estimate the product by rounding each of the given values to the nearest tenth.\n$7.182 \\times 6.385$ $\\approx$ $7.2$ $\\times$ [ANS]=[ANS]", "answer_v1": [ "6.4", "46.08" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Estimate the product by rounding each of the given values to the nearest tenth.\n$3.841 \\times 2.683$ $\\approx$ $3.8$ $\\times$ [ANS]=[ANS]", "answer_v2": [ "2.7", "10.26" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Estimate the product by rounding each of the given values to the nearest tenth.\n$4.173 \\times 4.086$ $\\approx$ $4.2$ $\\times$ [ANS]=[ANS]", "answer_v3": [ "4.1", "17.22" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0254", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "prealgebra", "common core", "rounding", "estimating" ], "problem_v1": "Estimate the quotient by considering close values (say within one tenth) so that the result is a \"nice\" whole number.\n$43.22 \\div 7.182$ $\\approx$ [ANS] $\\div$ [ANS]=[ANS]", "answer_v1": [ "43.2", "7.2", "6" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Estimate the quotient by considering close values (say within one tenth) so that the result is a \"nice\" whole number.\n$11.385 \\div 3.841$ $\\approx$ [ANS] $\\div$ [ANS]=[ANS]", "answer_v2": [ "11.4", "3.8", "3" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Estimate the quotient by considering close values (say within one tenth) so that the result is a \"nice\" whole number.\n$16.804 \\div 4.173$ $\\approx$ [ANS] $\\div$ [ANS]=[ANS]", "answer_v3": [ "16.8", "4.2", "4" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0255", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "prealgebra", "common core", "rounding", "estimating" ], "problem_v1": "Estimate the difference by rounding each of the given values to the nearest integer.\n$40.024-37.045$ $\\approx$ [ANS] $-$ [ANS]=[ANS]", "answer_v1": [ "40", "37", "3" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Estimate the difference by rounding each of the given values to the nearest integer.\n$25.93-43.967$ $\\approx$ [ANS] $-$ [ANS]=[ANS]", "answer_v2": [ "26", "44", "-18" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Estimate the difference by rounding each of the given values to the nearest integer.\n$30.956-37.01$ $\\approx$ [ANS] $-$ [ANS]=[ANS]", "answer_v3": [ "31", "37", "-6" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0256", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Estimation", "level": "2", "keywords": [ "prealgebra", "common core", "rounding", "estimating" ], "problem_v1": "Estimate the sum to one decimal place using front-end estimation. To do this, combine the whole number parts and then combine the tenths digits place separately. Add these two together for the final answer.\n42.605+36.706+20.29 _______________\n$\\begin{array}{cccc}\\hline & integer &+& tenths \\\\ \\hline & [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline & _______ & & _______ \\\\ \\hline & [ANS] &+& 1.6 \\\\ \\hline \\end{array}$\nfor a final total of [ANS]", "answer_v1": [ "42", "10*0.6", "36", "10*0.7", "20", "10*0.3", "42+36+20", "99.6" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "Estimate the sum to one decimal place using front-end estimation. To do this, combine the whole number parts and then combine the tenths digits place separately. Add these two together for the final answer.\n5.874+12.386+53.305 _______________\n$\\begin{array}{cccc}\\hline & integer &+& tenths \\\\ \\hline & [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline & _______ & & _______ \\\\ \\hline & [ANS] &+& 1.6 \\\\ \\hline \\end{array}$\nfor a final total of [ANS]", "answer_v2": [ "5", "10*0.9", "12", "10*0.4", "53", "10*0.3", "5+12+53", "71.6" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "Estimate the sum to one decimal place using front-end estimation. To do this, combine the whole number parts and then combine the tenths digits place separately. Add these two together for the final answer.\n18.625+19.533+15.43 _______________\n$\\begin{array}{cccc}\\hline & integer &+& tenths \\\\ \\hline & [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline+& [ANS] &. & [ANS] \\\\ \\hline & _______ & & _______ \\\\ \\hline & [ANS] &+& 1.5 \\\\ \\hline \\end{array}$\nfor a final total of [ANS]", "answer_v3": [ "18", "10*0.6", "19", "10*0.5", "15", "10*0.4", "18+19+15", "53.5" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0257", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "5", "keywords": [ "rate" ], "problem_v1": "On average, a restaurant uses ${35.6\\ {\\rm lb}}$ of vegetable oil per day. Fill in blanks. Question 1: The restaurant will use [ANS]lb of vegetable oil in $33$ days. Question 2: The restaurant will use ${1958\\ {\\rm lb}}$ of vegetable oil in [ANS] days. Use lb for pounds.", "answer_v1": [ "1174.8", "55" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "On average, a restaurant uses ${21.9\\ {\\rm lb}}$ of vegetable oil per day. Fill in blanks. Question 1: The restaurant will use [ANS]lb of vegetable oil in $23$ days. Question 2: The restaurant will use ${1029.3\\ {\\rm lb}}$ of vegetable oil in [ANS] days. Use lb for pounds.", "answer_v2": [ "503.7", "47" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "On average, a restaurant uses ${26.6\\ {\\rm lb}}$ of vegetable oil per day. Fill in blanks. Question 1: The restaurant will use [ANS]lb of vegetable oil in $25$ days. Question 2: The restaurant will use ${1356.6\\ {\\rm lb}}$ of vegetable oil in [ANS] days. Use lb for pounds.", "answer_v3": [ "665", "51" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0261", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "5", "keywords": [ "rate" ], "problem_v1": "In a city, the property tax rate for per thousand dollars of property value is ${\\$4.66}$. Fill in blanks: Question 1: The owner of a house worth $420$ thousand dollars should pay [ANS] dollars in tax.\nQuestion 2: The owner of a house worth [ANS] thousand dollars should pay ${\\$3{,}075.60}$ in tax.", "answer_v1": [ "1957.2", "660" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "In a city, the property tax rate for per thousand dollars of property value is ${\\$1.92}$. Fill in blanks: Question 1: The owner of a house worth $300$ thousand dollars should pay [ANS] dollars in tax.\nQuestion 2: The owner of a house worth [ANS] thousand dollars should pay ${\\$1{,}516.80}$ in tax.", "answer_v2": [ "576", "790" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "In a city, the property tax rate for per thousand dollars of property value is ${\\$2.63}$. Fill in blanks: Question 1: The owner of a house worth $370$ thousand dollars should pay [ANS] dollars in tax.\nQuestion 2: The owner of a house worth [ANS] thousand dollars should pay ${\\$1{,}683.20}$ in tax.", "answer_v3": [ "973.1", "640" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0265", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "5", "keywords": [ "division", "application" ], "problem_v1": "Fabrienne is gambling. She won ${\\$25.00}$ in the first game, lost ${\\$16.00}$ in the second game, and won ${\\$23.00}$ in the third game. Altogether, how much money did she win? Altogether, Fabrienne won [ANS].", "answer_v1": [ "32.00" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Tien is gambling. He won ${\\$11.00}$ in the first game, lost ${\\$10.00}$ in the second game, and won ${\\$13.00}$ in the third game. Altogether, how much money did he win? Altogether, Tien won [ANS].", "answer_v2": [ "14.00" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Dawn is gambling. She won ${\\$16.00}$ in the first game, lost ${\\$11.00}$ in the second game, and won ${\\$15.00}$ in the third game. Altogether, how much money did she win? Altogether, Dawn won [ANS].", "answer_v3": [ "20.00" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0266", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "3", "keywords": [ "decimal", "money" ], "problem_v1": "If $1$ dollar is represented by the integer $1$, write the following money amount with decimals. There is no need to type the dollar sign.\n$8 \\text{dollars}$=[ANS]\n$8 \\text{cents}$=[ANS]\n$8 \\text{dimes}$=[ANS]", "answer_v1": [ "8", "0.08", "0.8" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "If $1$ dollar is represented by the integer $1$, write the following money amount with decimals. There is no need to type the dollar sign.\n$2 \\text{dollars}$=[ANS]\n$2 \\text{cents}$=[ANS]\n$2 \\text{dimes}$=[ANS]", "answer_v2": [ "2", "0.02", "0.2" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "If $1$ dollar is represented by the integer $1$, write the following money amount with decimals. There is no need to type the dollar sign.\n$4 \\text{dollars}$=[ANS]\n$4 \\text{cents}$=[ANS]\n$4 \\text{dimes}$=[ANS]", "answer_v3": [ "4", "0.04", "0.4" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0267", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "Mr. Mason owes \\$ 21.28 for his groceries. He pays with a twenty-dollar bill and a five dollar bill. What is the correct amount of change Mr. Mason will receive? [ANS] A. \\$ 3.72 B. \\$ 4.28 C. \\$ 3.28 D. \\$ 4.72", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Mr. Mason owes \\$ 21.28 for his groceries. He pays with a twenty-dollar bill and a five dollar bill. What is the correct amount of change Mr. Mason will receive? [ANS] A. \\$ 3.28 B. \\$ 4.28 C. \\$ 4.72 D. \\$ 3.72", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Mr. Mason owes \\$ 21.28 for his groceries. He pays with a twenty-dollar bill and a five dollar bill. What is the correct amount of change Mr. Mason will receive? [ANS] A. \\$ 3.28 B. \\$ 3.72 C. \\$ 4.28 D. \\$ 4.72", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0268", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "4", "keywords": [], "problem_v1": "A model car has a scale factor of $\\frac{1}{64}$ The diameter of a tire on the model is 0.42 inches. So, the diameter of the tire on an actual car must be [ANS] inches. Your answer must be correct to one decimal place.", "answer_v1": [ "26.9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A model car has a scale factor of $\\frac{1}{64}$ The diameter of a tire on the model is 0.39 inches. So, the diameter of the tire on an actual car must be [ANS] inches. Your answer must be correct to one decimal place.", "answer_v2": [ "25" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A model car has a scale factor of $\\frac{1}{64}$ The diameter of a tire on the model is 0.4 inches. So, the diameter of the tire on an actual car must be [ANS] inches. Your answer must be correct to one decimal place.", "answer_v3": [ "25.6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0271", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "2", "keywords": [ "prealgebra", "common core", "rational", "ratios", "unit rate" ], "problem_v1": "Find each unit rate and express your answer as a decimal:\n$75$ miles in $6$ hours is [ANS] miles per hour. $1230$ miles in $24$ hours is [ANS] miles per hour.", "answer_v1": [ "12.5", "51.25" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Find each unit rate and express your answer as a decimal:\n$44$ miles in $8$ hours is [ANS] miles per hour. $744$ miles in $16$ hours is [ANS] miles per hour.", "answer_v2": [ "5.5", "46.5" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Find each unit rate and express your answer as a decimal:\n$48$ miles in $6$ hours is [ANS] miles per hour. $764$ miles in $16$ hours is [ANS] miles per hour.", "answer_v3": [ "8", "47.75" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0272", "subject": "Arithmetic", "topic": "Decimals", "subtopic": "Applications", "level": "4", "keywords": [ "prealgebra", "common core", "proportions" ], "problem_v1": "Your father is planning to cook for 35 people using a recipe that specifies one and three quarter cups of sugar for each four people. For the larger group, your father will require [ANS] cups of sugar. When necessary, round to three decimal places. When necessary, round to three decimal places.", "answer_v1": [ "15.3125" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Your father is planning to cook for 20 people using a recipe that specifies two-thirds cups of sugar for each six people. For the larger group, your father will require [ANS] cups of sugar. When necessary, round to three decimal places. When necessary, round to three decimal places.", "answer_v2": [ "2.22222" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Your father is planning to cook for 25 people using a recipe that specifies three-fourths cups of sugar for each five people. For the larger group, your father will require [ANS] cups of sugar. When necessary, round to three decimal places. When necessary, round to three decimal places.", "answer_v3": [ "3.75" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0273", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "percent", "multiply" ], "problem_v1": "Fill in the blanks: [ANS] is $6\\%$ of $770$? [ANS] is $60\\%$ of $770$? [ANS] is $600\\%$ of $770$?", "answer_v1": [ "46.2", "462", "4620" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Fill in the blanks: [ANS] is $9\\%$ of $180$? [ANS] is $90\\%$ of $180$? [ANS] is $900\\%$ of $180$?", "answer_v2": [ "16.2", "162", "1620" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Fill in the blanks: [ANS] is $6\\%$ of $380$? [ANS] is $60\\%$ of $380$? [ANS] is $600\\%$ of $380$?", "answer_v3": [ "22.8", "228", "2280" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0275", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "percent", "proportion" ], "problem_v1": "$0.6\\%$ of [ANS] is $4.62$.", "answer_v1": [ "770" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "$0.9\\%$ of [ANS] is $1.62$.", "answer_v2": [ "180" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "$0.6\\%$ of [ANS] is $2.28$.", "answer_v3": [ "380" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0276", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "percent", "proportion" ], "problem_v1": "$390\\%$ of [ANS] is $3003$.", "answer_v1": [ "770" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "$560\\%$ of [ANS] is $1008$.", "answer_v2": [ "180" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "$400\\%$ of [ANS] is $1520$.", "answer_v3": [ "380" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0278", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "You start with 800 items. How many do you have after a 90\\% increase?\nYou will have [ANS] items.", "answer_v1": [ "1520" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You start with 200 items. How many do you have after a 100\\% increase?\nYou will have [ANS] items.", "answer_v2": [ "400" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You start with 400 items. How many do you have after a 90\\% increase?\nYou will have [ANS] items.", "answer_v3": [ "760" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0279", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "exponential functions", "growth rate", "growth factor" ], "problem_v1": "An investment decreases by 5\\% per year for 5 years. By what total percent does it decrease after the 5 years? Overall it decreases by [ANS] \\% (round your answer to the nearest 0.01\\%)", "answer_v1": [ "22.6219" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "An investment decreases by 2\\% per year for 6 years. By what total percent does it decrease after the 6 years? Overall it decreases by [ANS] \\% (round your answer to the nearest 0.01\\%)", "answer_v2": [ "11.4158" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "An investment decreases by 3\\% per year for 5 years. By what total percent does it decrease after the 5 years? Overall it decreases by [ANS] \\% (round your answer to the nearest 0.01\\%)", "answer_v3": [ "14.1266" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0280", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "3", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "(a) What percent of 140 is 7? [ANS]\n(b) 12\\% of what number is 40? [ANS]", "answer_v1": [ "5", "333.333333333333" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "(a) What percent of 30 is 1? [ANS]\n(b) 3\\% of what number is 20? [ANS]", "answer_v2": [ "3.33333333333333", "666.666666666667" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "(a) What percent of 60 is 3? [ANS]\n(b) 6\\% of what number is 30? [ANS]", "answer_v3": [ "5", "500" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0281", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Calculations", "level": "2", "keywords": [ "percent", "mathematics for business", "algebraic expression" ], "problem_v1": "Determine the indicated quantity. 75\\% of 60=[ANS]\n260\\% of 70=[ANS]", "answer_v1": [ "45", "182" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Determine the indicated quantity. 9\\% of 90=[ANS]\n220\\% of 40=[ANS]", "answer_v2": [ "8.1", "88" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Determine the indicated quantity. 32\\% of 60=[ANS]\n230\\% of 50=[ANS]", "answer_v3": [ "19.2", "115" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0282", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Conversion between decimals and percents", "level": "2", "keywords": [ "percent", "decimal", "convert" ], "problem_v1": "Change the following percentages into decimals:\n${7\\%=}$ [ANS]\n${0.7\\%=}$ [ANS]\n${0.07\\%=}$ [ANS]", "answer_v1": [ "0.07", "0.007", "0.0007" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "Change the following percentages into decimals:\n${1\\%=}$ [ANS]\n${0.1\\%=}$ [ANS]\n${0.01\\%=}$ [ANS]", "answer_v2": [ "0.01", "0.001", "0.0001" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "Change the following percentages into decimals:\n${3\\%=}$ [ANS]\n${0.3\\%=}$ [ANS]\n${0.03\\%=}$ [ANS]", "answer_v3": [ "0.03", "0.003", "0.0003" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0283", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Conversion between decimals and percents", "level": "4", "keywords": [ "percent", "English to math" ], "problem_v1": "Translate the following phrases into algebraic expressions:\n$7.6\\%$ of $x$ $\\longrightarrow$ [ANS]\n$76.3\\%$ of $y$ $\\longrightarrow$ [ANS]\n$455.4\\%$ of $z$ $\\longrightarrow$ [ANS]", "answer_v1": [ "7.6/100*x", "76.3/100*y", "455.4/100*z" ], "answer_type_v1": [ "EX", "EX", "EX" ], "options_v1": [ [], [], [] ], "problem_v2": "Translate the following phrases into algebraic expressions:\n$1.8\\%$ of $x$ $\\longrightarrow$ [ANS]\n$14.9\\%$ of $y$ $\\longrightarrow$ [ANS]\n$413.6\\%$ of $z$ $\\longrightarrow$ [ANS]", "answer_v2": [ "1.8/100*x", "14.9/100*y", "413.6/100*z" ], "answer_type_v2": [ "EX", "EX", "EX" ], "options_v2": [ [], [], [] ], "problem_v3": "Translate the following phrases into algebraic expressions:\n$3.6\\%$ of $x$ $\\longrightarrow$ [ANS]\n$36.3\\%$ of $y$ $\\longrightarrow$ [ANS]\n$489.8\\%$ of $z$ $\\longrightarrow$ [ANS]", "answer_v3": [ "3.6/100*x", "36.3/100*y", "489.8/100*z" ], "answer_type_v3": [ "EX", "EX", "EX" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0284", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Conversion between decimals and percents", "level": "1", "keywords": [], "problem_v1": "Express each decimal as a percent.\n0.7=[ANS] \\%. 0.02=[ANS] \\%. 0.042=[ANS] \\%. 3.79=[ANS] \\%. 7.03=[ANS] \\%. 0.681=[ANS] \\%. 0.007=[ANS] \\%. 7.1=[ANS] \\%.", "answer_v1": [ "70", "2", "4.2", "379", "703", "68.1", "0.7", "710" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "Express each decimal as a percent.\n0.3=[ANS] \\%. 0.02=[ANS] \\%. 0.012=[ANS] \\%. 3.63=[ANS] \\%. 7.09=[ANS] \\%. 0.681=[ANS] \\%. 0.005=[ANS] \\%. 5.5=[ANS] \\%.", "answer_v2": [ "30", "2", "1.2", "363", "709", "68.1", "0.5", "550" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "Express each decimal as a percent.\n0.4=[ANS] \\%. 0.02=[ANS] \\%. 0.022=[ANS] \\%. 3.71=[ANS] \\%. 7.02=[ANS] \\%. 0.686=[ANS] \\%. 0.009=[ANS] \\%. 9.5=[ANS] \\%.", "answer_v3": [ "40", "2", "2.2", "371", "702", "68.6", "0.9", "950" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0285", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Conversion between decimals and percents", "level": "2", "keywords": [], "problem_v1": "Express each of the following fractions as a percent.\n(87/100)=[ANS] \\%. (6/25)=[ANS] \\%. (26/5)=[ANS] \\%. (17/20)=[ANS] \\%. (37/50)=[ANS] \\%. (7/4)=[ANS] \\%. (8/5)=[ANS] \\%. (5/2)=[ANS] \\%.", "answer_v1": [ "87", "24", "520", "85", "74", "175", "160", "250" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [] ], "problem_v2": "Express each of the following fractions as a percent.\n(27/100)=[ANS] \\%. (8/25)=[ANS] \\%. (16/5)=[ANS] \\%. (13/20)=[ANS] \\%. (9/10)=[ANS] \\%. (7/4)=[ANS] \\%. (6/5)=[ANS] \\%. (3/2)=[ANS] \\%.", "answer_v2": [ "27", "32", "320", "65", "90", "175", "120", "150" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [] ], "problem_v3": "Express each of the following fractions as a percent.\n(47/100)=[ANS] \\%. (6/25)=[ANS] \\%. (21/5)=[ANS] \\%. (13/20)=[ANS] \\%. (33/50)=[ANS] \\%. (7/4)=[ANS] \\%. (9/5)=[ANS] \\%. (7/2)=[ANS] \\%.", "answer_v3": [ "47", "24", "420", "65", "66", "175", "180", "350" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0286", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "4", "keywords": [ "equation", "solve", "word problem", "mixture" ], "problem_v1": "You\u2019ve poured $140$ grams of a $6\\%$ (by mass) alcohol solution into a large glass container. You have plenty of $4\\%$ alcohol solution. You need to make some $4.7\\%$ alcohol solution. How many grams of $4\\%$ solution do you have to add to the glass container to end up with a $4.7\\%$ alcohol solution?\nYou need to add [ANS] grams of $4\\%$ solution to end up with a $4.7\\%$ alcohol solution.", "answer_v1": [ "260" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "You\u2019ve poured $120$ grams of a $2\\%$ (by mass) alcohol solution into a large glass container. You have plenty of $4\\%$ alcohol solution. You need to make some $3.4\\%$ alcohol solution. How many grams of $4\\%$ solution do you have to add to the glass container to end up with a $3.4\\%$ alcohol solution?\nYou need to add [ANS] grams of $4\\%$ solution to end up with a $3.4\\%$ alcohol solution.", "answer_v2": [ "280" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "You\u2019ve poured $200$ grams of a $8\\%$ (by mass) alcohol solution into a large glass container. You have plenty of $6\\%$ alcohol solution. You need to make some $6.8\\%$ alcohol solution. How many grams of $6\\%$ solution do you have to add to the glass container to end up with a $6.8\\%$ alcohol solution?\nYou need to add [ANS] grams of $6\\%$ solution to end up with a $6.8\\%$ alcohol solution.", "answer_v3": [ "300" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0287", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [ "percent", "application", "multiply", "divide" ], "problem_v1": "According to a survey, $6.6\\%$ of a city\u2019s residents are native Americans. The last Census found that there are $9108$ native American residents in this city. If there were no significant population changes since the Census, approximately how many total residents live in the city?\nThe city has approximately [ANS] residents.", "answer_v1": [ "138000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "According to a survey, $8.2\\%$ of a city\u2019s residents are native Americans. The last Census found that there are $8528$ native American residents in this city. If there were no significant population changes since the Census, approximately how many total residents live in the city?\nThe city has approximately [ANS] residents.", "answer_v2": [ "104000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "According to a survey, $6.3\\%$ of a city\u2019s residents are native Americans. The last Census found that there are $7308$ native American residents in this city. If there were no significant population changes since the Census, approximately how many total residents live in the city?\nThe city has approximately [ANS] residents.", "answer_v3": [ "116000" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0288", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [ "percent", "application", "multiply" ], "problem_v1": "A city has $77000$ voters. According to a survey, $56\\%$ of them will vote to support a local measure. How many people will vote for this measure? [ANS] residents will vote for this measure.", "answer_v1": [ "43120" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A city has $17300$ voters. According to a survey, $92\\%$ of them will vote to support a local measure. How many people will vote for this measure? [ANS] residents will vote for this measure.", "answer_v2": [ "15916" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A city has $37900$ voters. According to a survey, $74\\%$ of them will vote to support a local measure. How many people will vote for this measure? [ANS] residents will vote for this measure.", "answer_v3": [ "28046" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0289", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [ "equation", "solve", "word problem", "mixture" ], "problem_v1": "Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with $8\\%$ African Americans. Town B had a population with $12\\%$ African Americans. After the merge, the new city has a total of $4800$ residents, with $11\\%$ African Americans. How many residents did Town A and Town B used to have?\nTown A used to have [ANS] residents, and Town B used to have [ANS] residents.", "answer_v1": [ "1200", "3600" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with $6\\%$ Asians. Town B had a population with $8\\%$ Asians. After the merge, the new city has a total of $4000$ residents, with $7.4\\%$ Asians. How many residents did Town A and Town B used to have?\nTown A used to have [ANS] residents, and Town B used to have [ANS] residents.", "answer_v2": [ "1200", "2800" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with $12\\%$ native Americans. Town B had a population with $6\\%$ native Americans. After the merge, the new city has a total of $4800$ residents, with $7.75\\%$ native Americans. How many residents did Town A and Town B used to have?\nTown A used to have [ANS] residents, and Town B used to have [ANS] residents.", "answer_v3": [ "1400", "3400" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0293", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "In the past few seasons\u2019 basketball games, Penelope attempted $330$ free throws, and made $264$ of them. What percent of free throws did Penelope make? Fill in the blank with a percent. Solution: Penelope made [ANS] of free throws in the past few seasons.", "answer_v1": [ "80%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In the past few seasons\u2019 basketball games, Evan attempted $470$ free throws, and made $94$ of them. What percent of free throws did Evan make? Fill in the blank with a percent. Solution: Evan made [ANS] of free throws in the past few seasons.", "answer_v2": [ "20%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In the past few seasons\u2019 basketball games, Jon attempted $340$ free throws, and made $136$ of them. What percent of free throws did Jon make? Fill in the blank with a percent. Solution: Jon made [ANS] of free throws in the past few seasons.", "answer_v3": [ "40%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0294", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "Among a town\u2019s registered voters, there are $36\\%$ Democrats and $33\\%$ Republicans. The rest are Independents. If there are $1240$ registered Independent voters in this town, how many total registered voters are there? Solution: This town has [ANS] registered Independent voters.", "answer_v1": [ "4000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Among a town\u2019s registered voters, there are $39\\%$ Democrats and $23\\%$ Republicans. The rest are Independents. If there are $494$ registered Independent voters in this town, how many total registered voters are there? Solution: This town has [ANS] registered Independent voters.", "answer_v2": [ "1300" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Among a town\u2019s registered voters, there are $36\\%$ Democrats and $26\\%$ Republicans. The rest are Independents. If there are $836$ registered Independent voters in this town, how many total registered voters are there? Solution: This town has [ANS] registered Independent voters.", "answer_v3": [ "2200" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0295", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "increase", "application" ], "problem_v1": "The population of cats in a shelter increased from $16$ to $80$. What is the percentage increase of the shelter\u2019s cat population? Solution: The percentage increase is [ANS].", "answer_v1": [ "400%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The population of cats in a shelter increased from $6$ to $42$. What is the percentage increase of the shelter\u2019s cat population? Solution: The percentage increase is [ANS].", "answer_v2": [ "600%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The population of cats in a shelter increased from $9$ to $54$. What is the percentage increase of the shelter\u2019s cat population? Solution: The percentage increase is [ANS].", "answer_v3": [ "500%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0298", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "In the last election, $53\\%$ of a county\u2019s residents, or $21253$ people, turned out to vote. How many residents live in this county? Solution: This county has [ANS] residents.", "answer_v1": [ "40100" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "In the last election, $67\\%$ of a county\u2019s residents, or $8911$ people, turned out to vote. How many residents live in this county? Solution: This county has [ANS] residents.", "answer_v2": [ "13300" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "In the last election, $54\\%$ of a county\u2019s residents, or $12150$ people, turned out to vote. How many residents live in this county? Solution: This county has [ANS] residents.", "answer_v3": [ "22500" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0299", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application", "rounding" ], "problem_v1": "Penelope invested ${\\$40{,}100.00}$ in a mutual fund, and earned ${\\$73.00}$ of interest. What percent of interest did Penelope earn? Fill in the blank with a percent. Round your percent to two decimal places, like $1.23\\%$. Solution: Penelope earned approximately [ANS] of interest.", "answer_v1": [ "0.18%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evan invested ${\\$13{,}300.00}$ in a mutual fund, and earned ${\\$88.00}$ of interest. What percent of interest did Evan earn? Fill in the blank with a percent. Round your percent to two decimal places, like $1.23\\%$. Solution: Evan earned approximately [ANS] of interest.", "answer_v2": [ "0.66%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jon invested ${\\$22{,}500.00}$ in a mutual fund, and earned ${\\$74.00}$ of interest. What percent of interest did Jon earn? Fill in the blank with a percent. Round your percent to two decimal places, like $1.23\\%$. Solution: Jon earned approximately [ANS] of interest.", "answer_v3": [ "0.33%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0300", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "Penelope is paying a dinner bill of ${\\$43.00}$. Penelope plans to pay $16\\%$ in tips. How much in total (including bill and tip) will Penelope pay? Solution: Penelope will pay [ANS] in total (including bill and tip).", "answer_v1": [ "$49.88" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evan is paying a dinner bill of ${\\$22.00}$. Evan plans to pay $20\\%$ in tips. How much in total (including bill and tip) will Evan pay? Solution: Evan will pay [ANS] in total (including bill and tip).", "answer_v2": [ "$26.40" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jon is paying a dinner bill of ${\\$29.00}$. Jon plans to pay $16\\%$ in tips. How much in total (including bill and tip) will Jon pay? Solution: Jon will pay [ANS] in total (including bill and tip).", "answer_v3": [ "$33.64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0302", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "A watch\u2019s wholesale price was ${\\$440.00}$. The retailer marked up the price by $30\\%$. What\u2019s the watch\u2019s new price (markup price)?\nThe watch\u2019s markup price is [ANS].", "answer_v1": [ "572.00" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A watch\u2019s wholesale price was ${\\$220.00}$. The retailer marked up the price by $40\\%$. What\u2019s the watch\u2019s new price (markup price)?\nThe watch\u2019s markup price is [ANS].", "answer_v2": [ "308.00" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A watch\u2019s wholesale price was ${\\$300.00}$. The retailer marked up the price by $35\\%$. What\u2019s the watch\u2019s new price (markup price)?\nThe watch\u2019s markup price is [ANS].", "answer_v3": [ "405.00" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0303", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "1", "keywords": [ "percent", "decrease", "application" ], "problem_v1": "A sweater is on sale for $60\\%$ off. The sale price is ${\\$68}$. What is the original price?\nThe original price was [ANS].", "answer_v1": [ "170" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A sweater is on sale for $90\\%$ off. The sale price is ${\\$6}$. What is the original price?\nThe original price was [ANS].", "answer_v2": [ "60" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A sweater is on sale for $60\\%$ off. The sale price is ${\\$40}$. What is the original price?\nThe original price was [ANS].", "answer_v3": [ "100" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0304", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [ "percent", "increase", "application" ], "problem_v1": "Over the course of the last year, Fabrienne\u2019s investment account has grown by $6.7\\%$. Currently, Fabrienne has ${\\$8{,}215.90}$ in this account. What was the balance in her account one year ago, before this gain?\nOne year ago the balance was [ANS].", "answer_v1": [ "7700" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Over the course of the last year, Tien\u2019s investment account has grown by $8.1\\%$. Currently, Tien has ${\\$1{,}945.80}$ in this account. What was the balance in his account one year ago, before this gain?\nOne year ago the balance was [ANS].", "answer_v2": [ "1800" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Over the course of the last year, Dawn\u2019s investment account has grown by $6.3\\%$. Currently, Dawn has ${\\$4{,}039.40}$ in this account. What was the balance in her account one year ago, before this gain?\nOne year ago the balance was [ANS].", "answer_v3": [ "3800" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0306", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "decrease", "application" ], "problem_v1": "A company\u2019s stock value (per share) dropped by ${\\$2.80}$, and its current value is ${\\$2.80}$. What is the percentage decrease of the stock\u2019s value? Solution: The percentage decrease in the stock\u2019s value was [ANS].", "answer_v1": [ "50%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A company\u2019s stock value (per share) dropped by ${\\$0.58}$, and its current value is ${\\$2.32}$. What is the percentage decrease of the stock\u2019s value? Solution: The percentage decrease in the stock\u2019s value was [ANS].", "answer_v2": [ "20%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A company\u2019s stock value (per share) dropped by ${\\$1.08}$, and its current value is ${\\$2.52}$. What is the percentage decrease of the stock\u2019s value? Solution: The percentage decrease in the stock\u2019s value was [ANS].", "answer_v3": [ "30%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0307", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "proportion", "application" ], "problem_v1": "A painting is on sale at ${\\$560.00}$. Its original price was ${\\$700.00}$. What percentage is off its original price? Fill in the blank with a percent. Solution: The painting was [ANS] off its original price.", "answer_v1": [ "20%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A painting is on sale at ${\\$280.00}$. Its original price was ${\\$400.00}$. What percentage is off its original price? Fill in the blank with a percent. Solution: The painting was [ANS] off its original price.", "answer_v2": [ "30%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A painting is on sale at ${\\$375.00}$. Its original price was ${\\$500.00}$. What percentage is off its original price? Fill in the blank with a percent. Solution: The painting was [ANS] off its original price.", "answer_v3": [ "25%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0308", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "increase", "application" ], "problem_v1": "A small town experienced explosive population increase. Originally, the town had $460$ population. Within 3 years, the town\u2019s population increased by $400\\%$. What\u2019s the town\u2019s current population? Solution: The town\u2019s current population is [ANS].", "answer_v1": [ "2300" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A small town experienced explosive population increase. Originally, the town had $190$ population. Within 3 years, the town\u2019s population increased by $200\\%$. What\u2019s the town\u2019s current population? Solution: The town\u2019s current population is [ANS].", "answer_v2": [ "570" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A small town experienced explosive population increase. Originally, the town had $260$ population. Within 3 years, the town\u2019s population increased by $300\\%$. What\u2019s the town\u2019s current population? Solution: The town\u2019s current population is [ANS].", "answer_v3": [ "1040" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0309", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "increase", "application" ], "problem_v1": "After a $35\\%$ increase, a town has $945$ people. What was the population before the increase?\nBefore the increase, the town\u2019s population was [ANS].", "answer_v1": [ "700" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "After a $55\\%$ increase, a town has $155$ people. What was the population before the increase?\nBefore the increase, the town\u2019s population was [ANS].", "answer_v2": [ "100" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "After a $45\\%$ increase, a town has $435$ people. What was the population before the increase?\nBefore the increase, the town\u2019s population was [ANS].", "answer_v3": [ "300" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0310", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [ "percent", "increase", "application", "rounding" ], "problem_v1": "A baby was born $2$ years ago. In these $2$ years, the baby grew $13.6$ pounds. The baby\u2019s current weight is $22.2$ pounds. What\u2019s the percentage increase of the baby\u2019s weight in the past $2$ years? Fill in blank with a percent. Round your answer to a whole percent, like $12\\%$. Solution: The percentage increase of the baby\u2019s weight was approximately [ANS].", "answer_v1": [ "158%" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A baby was born $2$ years ago. In these $2$ years, the baby grew $6.9$ pounds. The baby\u2019s current weight is $12.8$ pounds. What\u2019s the percentage increase of the baby\u2019s weight in the past $2$ years? Fill in blank with a percent. Round your answer to a whole percent, like $12\\%$. Solution: The percentage increase of the baby\u2019s weight was approximately [ANS].", "answer_v2": [ "117%" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A baby was born $2$ years ago. In these $2$ years, the baby grew $8.6$ pounds. The baby\u2019s current weight is $15.2$ pounds. What\u2019s the percentage increase of the baby\u2019s weight in the past $2$ years? Fill in blank with a percent. Round your answer to a whole percent, like $12\\%$. Solution: The percentage increase of the baby\u2019s weight was approximately [ANS].", "answer_v3": [ "130%" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0311", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "2", "keywords": [], "problem_v1": "Jason buys sports equipment worth \\$ \\$80.00 and pays 5\\% sales tax. What is the total amount Jason pays, including sales tax, for the sports equipment [ANS] A. \\$84.00 B. \\$83.00 C. \\$86.00 D. \\$85.00", "answer_v1": [ "A" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C", "D" ] ], "problem_v2": "Jason buys sports equipment worth \\$ \\$50.00 and pays 5\\% sales tax. What is the total amount Jason pays, including sales tax, for the sports equipment [ANS] A. \\$56.00 B. \\$53.00 C. \\$55.00 D. \\$52.50", "answer_v2": [ "D" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C", "D" ] ], "problem_v3": "Jason buys sports equipment worth \\$ \\$60.00 and pays 5\\% sales tax. What is the total amount Jason pays, including sales tax, for the sports equipment [ANS] A. \\$66.00 B. \\$63.00 C. \\$63.00 D. \\$65.00", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C", "D" ] ] }, { "id": "Arithmetic_0312", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "1", "keywords": [], "problem_v1": "Baseball batting averages are somewhat similar to percentages except that they are usually rounded to three decimal places and include the decimal point. That is, if a player got 3 hits in 10 at bats then she had a hit $\\frac {3}{10}=.300$ of the times she was at bat. Her batting average is listed as.300 in the newspapers. a) If Fred got 17 hits in 50 times at bat, his batting average is [ANS]. b) If Mary got 139 hits in 481 times at bat, her batting average is [ANS]. If Mary got 139 hits in 481 times at bat, then she got hits [ANS] \\% of the times she was at bat. Answer should be correct to 1 decimal place. Jack's batting average is 0.301. He was at bat 143 times. That means he got [ANS] hits.", "answer_v1": [ "0.34", "0.288981", "28.9", "43" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Baseball batting averages are somewhat similar to percentages except that they are usually rounded to three decimal places and include the decimal point. That is, if a player got 3 hits in 10 at bats then she had a hit $\\frac {3}{10}=.300$ of the times she was at bat. Her batting average is listed as.300 in the newspapers. a) If Fred got 12 hits in 50 times at bat, his batting average is [ANS]. b) If Mary got 159 hits in 451 times at bat, her batting average is [ANS]. If Mary got 159 hits in 451 times at bat, then she got hits [ANS] \\% of the times she was at bat. Answer should be correct to 1 decimal place. Jack's batting average is 0.26. He was at bat 150 times. That means he got [ANS] hits.", "answer_v2": [ "0.24", "0.35255", "35.3", "39" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Baseball batting averages are somewhat similar to percentages except that they are usually rounded to three decimal places and include the decimal point. That is, if a player got 3 hits in 10 at bats then she had a hit $\\frac {3}{10}=.300$ of the times she was at bat. Her batting average is listed as.300 in the newspapers. a) If Fred got 14 hits in 50 times at bat, his batting average is [ANS]. b) If Mary got 139 hits in 461 times at bat, her batting average is [ANS]. If Mary got 139 hits in 461 times at bat, then she got hits [ANS] \\% of the times she was at bat. Answer should be correct to 1 decimal place. Jack's batting average is 0.289. He was at bat 142 times. That means he got [ANS] hits.", "answer_v3": [ "0.28", "0.301518", "30.2", "41" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0313", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "1", "keywords": [], "problem_v1": ".\n$\\begin{array}{ccc}\\hline Flavor of Soft Drink & & Number of People \\\\ \\hline & & \\\\ \\hline Cola & & 57 \\\\ \\hline Orange & & 29 \\\\ \\hline LemonLime & & 34 \\\\ \\hline RootBeer & & 41 \\\\ \\hline Cherry & & 22 \\\\ \\hline Grape & & 21 \\\\ \\hline \\end{array}$\nA group of people are asked their soft drink preferences. The results are listed in a table (at right). The percent of those who prefer orange soda is [ANS]\n(Answer should be correct to one decimal place)", "answer_v1": [ "14.2" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": ".\n$\\begin{array}{ccc}\\hline Flavor of Soft Drink & & Number of People \\\\ \\hline & & \\\\ \\hline Cola & & 47 \\\\ \\hline Orange & & 33 \\\\ \\hline LemonLime & & 40 \\\\ \\hline RootBeer & & 38 \\\\ \\hline Cherry & & 20 \\\\ \\hline Grape & & 29 \\\\ \\hline \\end{array}$\nA group of people are asked their soft drink preferences. The results are listed in a table (at right). The percent of those who prefer orange soda is [ANS]\n(Answer should be correct to one decimal place)", "answer_v2": [ "15.9" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": ".\n$\\begin{array}{ccc}\\hline Flavor of Soft Drink & & Number of People \\\\ \\hline & & \\\\ \\hline Cola & & 50 \\\\ \\hline Orange & & 29 \\\\ \\hline LemonLime & & 41 \\\\ \\hline RootBeer & & 38 \\\\ \\hline Cherry & & 21 \\\\ \\hline Grape & & 20 \\\\ \\hline \\end{array}$\nA group of people are asked their soft drink preferences. The results are listed in a table (at right). The percent of those who prefer orange soda is [ANS]\n(Answer should be correct to one decimal place)", "answer_v3": [ "14.6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0314", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "4", "keywords": [], "problem_v1": "The percentage change from 3.3 inches to 9 inches (to 1 decimal place) is [ANS]", "answer_v1": [ "172.7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The percentage change from 2.5 inches to 11 inches (to 1 decimal place) is [ANS]", "answer_v2": [ "340" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The percentage change from 2.8 inches to 10 inches (to 1 decimal place) is [ANS]", "answer_v3": [ "257.1" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0315", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "3", "keywords": [], "problem_v1": "A standard six-sided die was rolled 50 times, and the outcomes are in the table shown.\n$\\begin{array}{ccc}\\hline Outcome & & # of Occurrences \\\\ \\hline & & \\\\ \\hline 1 & & 11 \\\\ \\hline & & \\\\ \\hline 2 & & 6 \\\\ \\hline & & \\\\ \\hline 3 & & 10 \\\\ \\hline & & \\\\ \\hline 4 & & 7 \\\\ \\hline & & \\\\ \\hline 5 & & 10 \\\\ \\hline & & \\\\ \\hline 6 & & 6 \\\\ \\hline \\end{array}$ [ANS] \\% of the rolls resulted in a prime number.", "answer_v1": [ "52" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A standard six-sided die was rolled 50 times, and the outcomes are in the table shown.\n$\\begin{array}{ccc}\\hline Outcome & & # of Occurrences \\\\ \\hline & & \\\\ \\hline 1 & & 5 \\\\ \\hline & & \\\\ \\hline 2 & & 12 \\\\ \\hline & & \\\\ \\hline 3 & & 13 \\\\ \\hline & & \\\\ \\hline 4 & & 4 \\\\ \\hline & & \\\\ \\hline 5 & & 6 \\\\ \\hline & & \\\\ \\hline 6 & & 10 \\\\ \\hline \\end{array}$ [ANS] \\% of the rolls resulted in a prime number.", "answer_v2": [ "62" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A standard six-sided die was rolled 50 times, and the outcomes are in the table shown.\n$\\begin{array}{ccc}\\hline Outcome & & # of Occurrences \\\\ \\hline & & \\\\ \\hline 1 & & 7 \\\\ \\hline & & \\\\ \\hline 2 & & 10 \\\\ \\hline & & \\\\ \\hline 3 & & 10 \\\\ \\hline & & \\\\ \\hline 4 & & 7 \\\\ \\hline & & \\\\ \\hline 5 & & 7 \\\\ \\hline & & \\\\ \\hline 6 & & 9 \\\\ \\hline \\end{array}$ [ANS] \\% of the rolls resulted in a prime number.", "answer_v3": [ "54" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0316", "subject": "Arithmetic", "topic": "Percents", "subtopic": "Applications", "level": "5", "keywords": [], "problem_v1": "A mixture of 60 liters of paint is 25\\% red tint, 30\\% yellow tint and 45\\% water. 8 liters of yellow tint are added to the original mixture. The percent of yellow tint in the new mixture is [ANS]. Answer must be correct to 1 decimal place.", "answer_v1": [ "38.2" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A mixture of 30 liters of paint is 25\\% red tint, 30\\% yellow tint and 45\\% water. 10 liters of yellow tint are added to the original mixture. The percent of yellow tint in the new mixture is [ANS]. Answer must be correct to 1 decimal place.", "answer_v2": [ "47.5" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A mixture of 40 liters of paint is 25\\% red tint, 30\\% yellow tint and 45\\% water. 8 liters of yellow tint are added to the original mixture. The percent of yellow tint in the new mixture is [ANS]. Answer must be correct to 1 decimal place.", "answer_v3": [ "41.7" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0317", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical", "square root", "fraction", "multiply" ], "problem_v1": "Simplify the expression ${\\sqrt{\\frac{3}{8}} \\cdot \\sqrt{\\frac{5}{8}}}$. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\sqrt{\\frac{3}{8}} \\cdot \\sqrt{\\frac{5}{8}}=}$ [ANS]", "answer_v1": [ "[sqrt(15)]/8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the expression ${\\sqrt{\\frac{7}{2}} \\cdot \\sqrt{\\frac{1}{2}}}$. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\sqrt{\\frac{7}{2}} \\cdot \\sqrt{\\frac{1}{2}}=}$ [ANS]", "answer_v2": [ "[sqrt(7)]/2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the expression ${\\sqrt{\\frac{5}{4}} \\cdot \\sqrt{\\frac{3}{4}}}$. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\sqrt{\\frac{5}{4}} \\cdot \\sqrt{\\frac{3}{4}}=}$ [ANS]", "answer_v3": [ "[sqrt(15)]/4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0318", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical" ], "problem_v1": "Simplify the expression. Use sqrt for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${{\\sqrt{150}}+{\\sqrt{54}}+{\\sqrt{27}}+{\\sqrt{48}}=}$ [ANS]", "answer_v1": [ "8*sqrt(6)+7*sqrt(3)" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the expression. Use sqrt for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${{\\sqrt{8}}+{\\sqrt{18}}+{\\sqrt{180}}+{\\sqrt{45}}=}$ [ANS]", "answer_v2": [ "5*sqrt(2)+9*sqrt(5)" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the expression. Use sqrt for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${{\\sqrt{48}}+{\\sqrt{27}}+{\\sqrt{18}}+{\\sqrt{72}}=}$ [ANS]", "answer_v3": [ "7*sqrt(3)+9*sqrt(2)" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0319", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical", "FOIL", "difference of squares", "square root" ], "problem_v1": "Multiply by using the FOIL method. Simplify and combine like radicals if necessary. Use sqrt for the square root symbol (Example: ${\\sqrt{2}=}$ sqrt(2).) ${({\\sqrt{11}}+{\\sqrt{7}})({\\sqrt{11}}-{\\sqrt{7}})=}$ [ANS]", "answer_v1": [ "4" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Multiply by using the FOIL method. Simplify and combine like radicals if necessary. Use sqrt for the square root symbol (Example: ${\\sqrt{2}=}$ sqrt(2).) ${({\\sqrt{5}}+{\\sqrt{13}})({\\sqrt{5}}-{\\sqrt{13}})=}$ [ANS]", "answer_v2": [ "-8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Multiply by using the FOIL method. Simplify and combine like radicals if necessary. Use sqrt for the square root symbol (Example: ${\\sqrt{2}=}$ sqrt(2).) ${({\\sqrt{6}}+{\\sqrt{11}})({\\sqrt{6}}-{\\sqrt{11}})=}$ [ANS]", "answer_v3": [ "-5" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0320", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical", "square root", "rationalize", "denominator" ], "problem_v1": "Rationalize the denominator. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\frac{15}{\\sqrt{30}}=}$ [ANS]", "answer_v1": [ "[sqrt(30)]/2" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Rationalize the denominator. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\frac{4}{\\sqrt{6}}=}$ [ANS]", "answer_v2": [ "2*sqrt(6)/3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Rationalize the denominator. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${\\frac{7}{\\sqrt{14}}=}$ [ANS]", "answer_v3": [ "[sqrt(14)]/2" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0321", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical", "FOIL" ], "problem_v1": "Expand and simplify the expression. Use sqrt() for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${\\left(7-8 {\\sqrt{7}}\\right)^2=}$ [ANS]", "answer_v1": [ "497-112*sqrt(7)" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Expand and simplify the expression. Use sqrt() for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${\\left(10-5 {\\sqrt{5}}\\right)^2=}$ [ANS]", "answer_v2": [ "225-100*sqrt(5)" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Expand and simplify the expression. Use sqrt() for the square root symbol (Example: $\\sqrt{2}=$ sqrt(2).)\n${\\left(7-4 {\\sqrt{5}}\\right)^2=}$ [ANS]", "answer_v3": [ "129-56*sqrt(5)" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0322", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "simplify", "radical", "square root" ], "problem_v1": "Simplify the radical ${\\sqrt{275}}$. If it cannot be simplified, simply type its value as the answer. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${{\\sqrt{275}}=}$ [ANS]", "answer_v1": [ "5*sqrt(11)" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Simplify the radical ${\\sqrt{98}}$. If it cannot be simplified, simply type its value as the answer. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${{\\sqrt{98}}=}$ [ANS]", "answer_v2": [ "7*sqrt(2)" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Simplify the radical ${\\sqrt{125}}$. If it cannot be simplified, simply type its value as the answer. Use sqrt() for the square root symbol. For example: $\\sqrt{2}=$ sqrt(2).\n${{\\sqrt{125}}=}$ [ANS]", "answer_v3": [ "5*sqrt(5)" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0323", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "powers" ], "problem_v1": "Rationalize the denominator of expression \\frac{1}{\\sqrt{6}} i.e., write it in the form of \\frac{\\sqrt{a}}{b}. Your answer for $a$ is: [ANS]\nYour answer for $b$ is: [ANS]", "answer_v1": [ "6", "6" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Rationalize the denominator of expression \\frac{1}{\\sqrt{2}} i.e., write it in the form of \\frac{\\sqrt{a}}{b}. Your answer for $a$ is: [ANS]\nYour answer for $b$ is: [ANS]", "answer_v2": [ "2", "2" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Rationalize the denominator of expression \\frac{1}{\\sqrt{3}} i.e., write it in the form of \\frac{\\sqrt{a}}{b}. Your answer for $a$ is: [ANS]\nYour answer for $b$ is: [ANS]", "answer_v3": [ "3", "3" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0324", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "exponent" ], "problem_v1": "Evaluate the expression \\frac{\\sqrt{343}}{\\sqrt{7}} Your answer is [ANS]", "answer_v1": [ "7" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression \\frac{\\sqrt{36}}{\\sqrt{9}} Your answer is [ANS]", "answer_v2": [ "2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression \\frac{\\sqrt{112}}{\\sqrt{7}} Your answer is [ANS]", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0325", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "powers" ], "problem_v1": "If you rationalize the denominator of \\frac{1}{7\\sqrt{5}-4\\sqrt{3}} then you will get \\frac{r\\sqrt{5}+s\\sqrt{3}}{n} where $r$, $s$, and $n$ are all positive integers (with no common factors). $r=$ [ANS]\n$s=$ [ANS]\n$n=$ [ANS]\n[NOTE: Your answers cannot be algebraic expressions.]", "answer_v1": [ "7", "4", "197" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "If you rationalize the denominator of \\frac{1}{11\\sqrt{5}-2\\sqrt{3}} then you will get \\frac{r\\sqrt{5}+s\\sqrt{3}}{n} where $r$, $s$, and $n$ are all positive integers (with no common factors). $r=$ [ANS]\n$s=$ [ANS]\n$n=$ [ANS]\n[NOTE: Your answers cannot be algebraic expressions.]", "answer_v2": [ "11", "2", "593" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "If you rationalize the denominator of \\frac{1}{7\\sqrt{5}-2\\sqrt{3}} then you will get \\frac{r\\sqrt{5}+s\\sqrt{3}}{n} where $r$, $s$, and $n$ are all positive integers (with no common factors). $r=$ [ANS]\n$s=$ [ANS]\n$n=$ [ANS]\n[NOTE: Your answers cannot be algebraic expressions.]", "answer_v3": [ "7", "2", "233" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0326", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "powers" ], "problem_v1": "Evaluate the expression $\\sqrt{\\frac{12\\cdot 27}{4}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v1": [ "9" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Evaluate the expression $\\sqrt{\\frac{10\\cdot 2}{5}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v2": [ "2" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Evaluate the expression $\\sqrt{\\frac{8\\cdot 8}{4}}$. [ANS]\n[NOTE: Your answer cannot be an algebraic expression.]", "answer_v3": [ "4" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0327", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "exponent" ], "problem_v1": "The expression \\frac{\\sqrt{81}}{\\sqrt{36}} equals [ANS]/[ANS].", "answer_v1": [ "9", "6" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "The expression \\frac{\\sqrt{9}}{\\sqrt{64}} equals [ANS]/[ANS].", "answer_v2": [ "3", "8" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "The expression \\frac{\\sqrt{25}}{\\sqrt{36}} equals [ANS]/[ANS].", "answer_v3": [ "5", "6" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0328", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "exponent" ], "problem_v1": "The expression \\sqrt{180}-\\sqrt{45} equals [ANS] $\\times\\sqrt{5}$.", "answer_v1": [ "3" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "The expression \\sqrt{125}-\\sqrt{80} equals [ANS] $\\times\\sqrt{5}$.", "answer_v2": [ "1" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "The expression \\sqrt{125}-\\sqrt{45} equals [ANS] $\\times\\sqrt{5}$.", "answer_v3": [ "2" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0329", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "radical expression", "rationalize the denominator" ], "problem_v1": "Rationalize the denominator.\n$\\begin{array}{cccc}\\hline & \\frac{1-\\sqrt{3}}{3 \\sqrt{7}-\\sqrt{21}}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$\nType an exact answer using radical notation if necessary. ", "answer_v1": [ "-4.58258", "21" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Rationalize the denominator.\n$\\begin{array}{cccc}\\hline & \\frac{1-\\sqrt{10}}{10 \\sqrt{7}-\\sqrt{70}}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$\nType an exact answer using radical notation if necessary. ", "answer_v2": [ "-8.3666", "70" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Rationalize the denominator.\n$\\begin{array}{cccc}\\hline & \\frac{1-\\sqrt{2}}{2 \\sqrt{7}-\\sqrt{14}}=& & [ANS] [ANS] \\\\ \\hline \\end{array}$\nType an exact answer using radical notation if necessary. ", "answer_v3": [ "-3.74166", "14" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0330", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [], "problem_v1": "Simplify.\n(a) $-\\sqrt[5]{243}=$ [ANS]\n(b) $\\sqrt[4]{-81}=$ [ANS]\nWrite your answer using radical notation if necessary or write not real if the answer is not a real number. ", "answer_v1": [ "-3", "not real" ], "answer_type_v1": [ "NV", "TF" ], "options_v1": [ [], [] ], "problem_v2": "Simplify.\n(a) $\\sqrt{-25}=$ [ANS]\n(b) $-\\sqrt[5]{32}=$ [ANS]\nWrite your answer using radical notation if necessary or write not real if the answer is not a real number. ", "answer_v2": [ "not real", "-2" ], "answer_type_v2": [ "TF", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Simplify.\n(a) $\\sqrt[3]{-27}=$ [ANS]\n(b) $-\\sqrt[4]{81}=$ [ANS]\nWrite your answer using radical notation if necessary or write not real if the answer is not a real number. ", "answer_v3": [ "-3", "-3" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0331", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "radicals", "exponents" ], "problem_v1": "Change the radical 5 \\sqrt{27} into simplest radical form $A \\sqrt{C}$, where $A$ and $C$ are all integers. Answer: $A=$ [ANS] and $C=$ [ANS]", "answer_v1": [ "5*3", "3" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Change the radical-5 \\sqrt{27} into simplest radical form $A \\sqrt{C}$, where $A$ and $C$ are all integers. Answer: $A=$ [ANS] and $C=$ [ANS]", "answer_v2": [ "-5*3", "3" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Change the radical 3 \\sqrt{27} into simplest radical form $A \\sqrt{C}$, where $A$ and $C$ are all integers. Answer: $A=$ [ANS] and $C=$ [ANS]", "answer_v3": [ "3*3", "3" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0332", "subject": "Arithmetic", "topic": "Irrational numbers", "subtopic": "Simplify radical numbers", "level": "2", "keywords": [ "algebra", "radicals" ], "problem_v1": "Determine whether the following equalities are true or false. Enter \"T\" for true and \"F\" for false.\n$\\begin{array}{ccc}\\hline [ANS] & 1. & \\frac{2}{\\sqrt[3]{3}}=\\frac{2\\sqrt{9}}{3} \\\\ \\hline [ANS] & 2. & \\frac{\\sqrt{11}}{24}=\\frac{24}{\\sqrt{11}} \\\\ \\hline [ANS] & 3. & \\sqrt[5]{-32}=-2 \\\\ \\hline [ANS] & 4. & \\frac{\\sqrt{2}}{2}=\\sqrt{\\frac{10}{20}\\;} \\\\ \\hline \\end{array}$", "answer_v1": [ "F", "F", "T", "T" ], "answer_type_v1": [ "TF", "TF", "TF", "TF" ], "options_v1": [ [], [], [], [] ], "problem_v2": "Determine whether the following equalities are true or false. Enter \"T\" for true and \"F\" for false.\n$\\begin{array}{ccc}\\hline [ANS] & 1. & \\frac{\\sqrt{11}}{24}=\\frac{24}{\\sqrt{11}} \\\\ \\hline [ANS] & 2. & \\frac{\\sqrt{2}}{2}=\\sqrt{\\frac{10}{20}\\;} \\\\ \\hline [ANS] & 3. & \\frac{2}{\\sqrt[3]{3}}=\\frac{2\\sqrt{9}}{3} \\\\ \\hline [ANS] & 4. & \\sqrt[3]{16}=2 \\\\ \\hline \\end{array}$", "answer_v2": [ "F", "T", "F", "F" ], "answer_type_v2": [ "TF", "TF", "TF", "TF" ], "options_v2": [ [], [], [], [] ], "problem_v3": "Determine whether the following equalities are true or false. Enter \"T\" for true and \"F\" for false.\n$\\begin{array}{ccc}\\hline [ANS] & 1. & \\frac{1}{\\sqrt{2}}=\\frac{\\sqrt{2}}{2} \\\\ \\hline [ANS] & 2. & \\sqrt[3]{16}=2 \\\\ \\hline [ANS] & 3. & \\frac{2}{\\sqrt[3]{3}}=\\frac{2\\sqrt{9}}{3} \\\\ \\hline [ANS] & 4. & \\sqrt[5]{-32}=-2 \\\\ \\hline \\end{array}$", "answer_v3": [ "T", "F", "F", "T" ], "answer_type_v3": [ "TF", "TF", "TF", "TF" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0334", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Converting", "level": "2", "keywords": [ "Integer", "Binary", "Decimal" ], "problem_v1": "Convert the following integers from binary notation to decimal notation:\n(a) $1100001010$ [ANS]\n(b) $1001110000$ [ANS]", "answer_v1": [ "778", "624" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Convert the following integers from binary notation to decimal notation:\n(a) $10101110$ [ANS]\n(b) $1110101011$ [ANS]", "answer_v2": [ "174", "939" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Convert the following integers from binary notation to decimal notation:\n(a) $101111110$ [ANS]\n(b) $1010000101$ [ANS]", "answer_v3": [ "382", "645" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0335", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Converting", "level": "2", "keywords": [ "Integer", "Binary", "One's Complement" ], "problem_v1": "One's complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less than $2^{n-1}$, a total of $n$ bits is used. The leftmost bit is used to represent the sign: this bit is 0 for positive integers and 1 for negative integers.\nFor positive integers, the remaining bits are identical to the binary representation of the integer. Thus using 4 bits, the One's complement representation of 5 is 0101. For negative integers, the remaining bits are found by first finding the binary representation of the absolute value of the integer and then taking the complement of each of these bits in the binary representation. (Thus 1's and 0's get switched) Thus for example using 4 bits, the One's complement representation of-5 is 1010, where the initial 1 is to indicate the sign, and the subsequent 010 is the complement of 101 the binary representation of 5. Find the One's Complement representations, using bit strings of length six, of the following integers. (Your answers must be bit strings of length 6):\n(a) $28$ [ANS]\n(b) $25$ [ANS]\n(c) $-27$ [ANS]\n(d) $-20$ [ANS]", "answer_v1": [ "011100", "011001", "100100", "101011" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "One's complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less than $2^{n-1}$, a total of $n$ bits is used. The leftmost bit is used to represent the sign: this bit is 0 for positive integers and 1 for negative integers.\nFor positive integers, the remaining bits are identical to the binary representation of the integer. Thus using 4 bits, the One's complement representation of 5 is 0101. For negative integers, the remaining bits are found by first finding the binary representation of the absolute value of the integer and then taking the complement of each of these bits in the binary representation. (Thus 1's and 0's get switched) Thus for example using 4 bits, the One's complement representation of-5 is 1010, where the initial 1 is to indicate the sign, and the subsequent 010 is the complement of 101 the binary representation of 5. Find the One's Complement representations, using bit strings of length six, of the following integers. (Your answers must be bit strings of length 6):\n(a) $17$ [ANS]\n(b) $30$ [ANS]\n(c) $-18$ [ANS]\n(d) $-21$ [ANS]", "answer_v2": [ "010001", "011110", "101101", "101010" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "One's complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less than $2^{n-1}$, a total of $n$ bits is used. The leftmost bit is used to represent the sign: this bit is 0 for positive integers and 1 for negative integers.\nFor positive integers, the remaining bits are identical to the binary representation of the integer. Thus using 4 bits, the One's complement representation of 5 is 0101. For negative integers, the remaining bits are found by first finding the binary representation of the absolute value of the integer and then taking the complement of each of these bits in the binary representation. (Thus 1's and 0's get switched) Thus for example using 4 bits, the One's complement representation of-5 is 1010, where the initial 1 is to indicate the sign, and the subsequent 010 is the complement of 101 the binary representation of 5. Find the One's Complement representations, using bit strings of length six, of the following integers. (Your answers must be bit strings of length 6):\n(a) $21$ [ANS]\n(b) $25$ [ANS]\n(c) $-20$ [ANS]\n(d) $-24$ [ANS]", "answer_v3": [ "010101", "011001", "101011", "100111" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0336", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Converting", "level": "2", "keywords": [ "Integers", "Factorials", "Cantor Expansion" ], "problem_v1": "A Cantor expansion is a sum of the form a_n n!+a_{n-1} (n-1)!+\\dots a_2 2!+a_1 1! where $0 \\leq a_i \\leq i$ are integers for $i=1,2,\\dots n$. For example, the Cantor expansion of 17 is $17=2(3!)+2(2!)+1(1!).$ Note that $17=1(3!)+5(2!)+1(1!)$ is correct but is not a valid Cantor expansion of 17 since we insist the coefficient of n! is no more than n. Thus the coefficient of 2! should be a 0,1 or 2 for example. Complete the following Cantor expansions of:\n(a) $17$=[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (b) $181$=[ANS] $(5!)$+[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (c) $79$=[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$", "answer_v1": [ "2", "2", "1", "1", "2", "2", "0", "1", "3", "1", "0", "1" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v2": "A Cantor expansion is a sum of the form a_n n!+a_{n-1} (n-1)!+\\dots a_2 2!+a_1 1! where $0 \\leq a_i \\leq i$ are integers for $i=1,2,\\dots n$. For example, the Cantor expansion of 17 is $17=2(3!)+2(2!)+1(1!).$ Note that $17=1(3!)+5(2!)+1(1!)$ is correct but is not a valid Cantor expansion of 17 since we insist the coefficient of n! is no more than n. Thus the coefficient of 2! should be a 0,1 or 2 for example. Complete the following Cantor expansions of:\n(a) $2$=[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (b) $251$=[ANS] $(5!)$+[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (c) $84$=[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$", "answer_v2": [ "0", "1", "0", "2", "0", "1", "2", "1", "3", "2", "0", "0" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [], [], [], [], [], [] ], "problem_v3": "A Cantor expansion is a sum of the form a_n n!+a_{n-1} (n-1)!+\\dots a_2 2!+a_1 1! where $0 \\leq a_i \\leq i$ are integers for $i=1,2,\\dots n$. For example, the Cantor expansion of 17 is $17=2(3!)+2(2!)+1(1!).$ Note that $17=1(3!)+5(2!)+1(1!)$ is correct but is not a valid Cantor expansion of 17 since we insist the coefficient of n! is no more than n. Thus the coefficient of 2! should be a 0,1 or 2 for example. Complete the following Cantor expansions of:\n(a) $20$=[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (b) $163$=[ANS] $(5!)$+[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$ (c) $44$=[ANS] $(4!)$+[ANS] $(3!)$+[ANS] $(2!)$+[ANS] $(1!)$", "answer_v3": [ "3", "1", "0", "1", "1", "3", "0", "1", "1", "3", "1", "0" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0337", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Converting", "level": "2", "keywords": [ "discrete mathematics", "integers", "binary numbers" ], "problem_v1": "The decimal number 28 written in binary is [ANS]\nThe decimal number 25 written in binary is [ANS]\nThe decimal number 103 written in binary is [ANS]\nThe decimal number 110 written in binary is [ANS]\nThe decimal number 333 written in binary is [ANS]\nThe decimal number 340 written in binary is [ANS]", "answer_v1": [ "11100", "11001", "1100111", "1101110", "101001101", "101010100" ], "answer_type_v1": [ "OE", "OE", "OE", "OE", "OE", "OE" ], "options_v1": [ [], [], [], [], [], [] ], "problem_v2": "The decimal number 17 written in binary is [ANS]\nThe decimal number 30 written in binary is [ANS]\nThe decimal number 73 written in binary is [ANS]\nThe decimal number 85 written in binary is [ANS]\nThe decimal number 498 written in binary is [ANS]\nThe decimal number 337 written in binary is [ANS]", "answer_v2": [ "10001", "11110", "1001001", "1010101", "111110010", "101010001" ], "answer_type_v2": [ "OE", "OE", "OE", "OE", "OE", "OE" ], "options_v2": [ [], [], [], [], [], [] ], "problem_v3": "The decimal number 21 written in binary is [ANS]\nThe decimal number 25 written in binary is [ANS]\nThe decimal number 81 written in binary is [ANS]\nThe decimal number 99 written in binary is [ANS]\nThe decimal number 308 written in binary is [ANS]\nThe decimal number 344 written in binary is [ANS]", "answer_v3": [ "10101", "11001", "1010001", "1100011", "100110100", "101011000" ], "answer_type_v3": [ "OE", "OE", "OE", "OE", "OE", "OE" ], "options_v3": [ [], [], [], [], [], [] ] }, { "id": "Arithmetic_0338", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Converting", "level": "2", "keywords": [ "color vectors", "HTML", "hexadecimal" ], "problem_v1": "HTML, the markup language of the web, specifies colors using the RGB model. It uses a two-digit hexadecimal (that is, base 16) representation for each component of the vector, and concatenates the three numbers together to form one large, six-digit number. For instance, the HTML color code #80FF3B has red component 80, green component FF, and blue component 3B. In hexadecimal, the digits 0 through 9 have their usual meanings, but the letters A through F also function as digits, and have the meanings 10 through 15, respectively. Because hexadecimal means base 16, a two-digit number such as 3B thus has the meaning $16 \\cdot 3+11=59$. The 16 is used because the 3 is in the 16s place, and the 11 is the meaning of the digit B. (If you found this introduction to hexadecimal notation too brief, consult the web for more details.) What is the maximum number representable with two hexadecimal digits? Answer: [ANS]\nIf your answer to the previous part represents 100\\% (full intensity), then what percentage does the number CD represent? Answer: [ANS] \\% What hexadecimal number represents 40\\%? Answer: [ANS]\nWhat RGB color vector does the HTML color vector AEC36E represent? Answer: $\\langle$ [ANS], [ANS], [ANS] $\\rangle$ What HTML color vector represents half-intensity white light (a medium gray)? (You may need to round off to the nearest whole number.) Answer: [ANS]", "answer_v1": [ "255", "80.3922", "66", "0.682353", "0.764706", "0.431373", "808080" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [] ], "problem_v2": "HTML, the markup language of the web, specifies colors using the RGB model. It uses a two-digit hexadecimal (that is, base 16) representation for each component of the vector, and concatenates the three numbers together to form one large, six-digit number. For instance, the HTML color code #80FF3B has red component 80, green component FF, and blue component 3B. In hexadecimal, the digits 0 through 9 have their usual meanings, but the letters A through F also function as digits, and have the meanings 10 through 15, respectively. Because hexadecimal means base 16, a two-digit number such as 3B thus has the meaning $16 \\cdot 3+11=59$. The 16 is used because the 3 is in the 16s place, and the 11 is the meaning of the digit B. (If you found this introduction to hexadecimal notation too brief, consult the web for more details.) What is the maximum number representable with two hexadecimal digits? Answer: [ANS]\nIf your answer to the previous part represents 100\\% (full intensity), then what percentage does the number 2F represent? Answer: [ANS] \\% What hexadecimal number represents 40\\%? Answer: [ANS]\nWhat RGB color vector does the HTML color vector 5075F0 represent? Answer: $\\langle$ [ANS], [ANS], [ANS] $\\rangle$ What HTML color vector represents one-quarter-intensity white light (a dark gray)? (You may need to round off to the nearest whole number.) Answer: [ANS]", "answer_v2": [ "255", "18.4314", "66", "0.313725", "0.458824", "0.941176", "404040" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [] ], "problem_v3": "HTML, the markup language of the web, specifies colors using the RGB model. It uses a two-digit hexadecimal (that is, base 16) representation for each component of the vector, and concatenates the three numbers together to form one large, six-digit number. For instance, the HTML color code #80FF3B has red component 80, green component FF, and blue component 3B. In hexadecimal, the digits 0 through 9 have their usual meanings, but the letters A through F also function as digits, and have the meanings 10 through 15, respectively. Because hexadecimal means base 16, a two-digit number such as 3B thus has the meaning $16 \\cdot 3+11=59$. The 16 is used because the 3 is in the 16s place, and the 11 is the meaning of the digit B. (If you found this introduction to hexadecimal notation too brief, consult the web for more details.) What is the maximum number representable with two hexadecimal digits? Answer: [ANS]\nIf your answer to the previous part represents 100\\% (full intensity), then what percentage does the number 5D represent? Answer: [ANS] \\% What hexadecimal number represents 40\\%? Answer: [ANS]\nWhat RGB color vector does the HTML color vector 6AA05B represent? Answer: $\\langle$ [ANS], [ANS], [ANS] $\\rangle$ What HTML color vector represents three-quarters-intensity white light (a light gray)? (You may need to round off to the nearest whole number.) Answer: [ANS]", "answer_v3": [ "255", "36.4706", "66", "0.415686", "0.627451", "0.356863", "BFBFBF" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "EX" ], "options_v3": [ [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0339", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Addition/subtraction", "level": "3", "keywords": [ "discrete mathematics", "integers", "binary numbers" ], "problem_v1": "Add the following binary numbers $\\begin{array}{cc}\\hline & 11100 \\\\ \\hline+& 11001 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 1100111 \\\\ \\hline+& 1101110 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 101001101 \\\\ \\hline+& 101010100 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$", "answer_v1": [ "110101", "11010101", "1010100001" ], "answer_type_v1": [ "OE", "OE", "OE" ], "options_v1": [ [], [], [] ], "problem_v2": "Add the following binary numbers $\\begin{array}{cc}\\hline & 10001 \\\\ \\hline+& 11110 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 1001001 \\\\ \\hline+& 1010101 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 111110010 \\\\ \\hline+& 101010001 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$", "answer_v2": [ "101111", "10011110", "1101000011" ], "answer_type_v2": [ "OE", "OE", "OE" ], "options_v2": [ [], [], [] ], "problem_v3": "Add the following binary numbers $\\begin{array}{cc}\\hline & 10101 \\\\ \\hline+& 11001 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 1010001 \\\\ \\hline+& 1100011 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$\n$\\begin{array}{cc}\\hline & 100110100 \\\\ \\hline+& 101011000 \\\\ \\hline & [ANS] \\\\ \\hline \\end{array}$", "answer_v3": [ "101110", "10110100", "1010001100" ], "answer_type_v3": [ "OE", "OE", "OE" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0340", "subject": "Arithmetic", "topic": "Other bases", "subtopic": "Multiplication", "level": "2", "keywords": [], "problem_v1": "Using the multiplication table, compute $651 _{8} \\times 32 _{8}$\n$\\begin{array}{cccccccc}\\hline \\times & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 2 & 2 & 4 & 6 & 10 & 12 & 14 & 16 \\\\ \\hline 3 & 3 & 6 & 11 & 14 & 17 & 22 & 25 \\\\ \\hline 4 & 4 & 10 & 14 & 20 & 24 & 30 & 34 \\\\ \\hline 5 & 5 & 12 & 17 & 24 & 31 & 36 & 43 \\\\ \\hline 6 & 6 & 14 & 22 & 30 & 36 & 44 & 52 \\\\ \\hline 7 & 7 & 16 & 25 & 34 & 43 & 52 & 61 \\\\ \\hline \\end{array}$ 61 $651 _{8} \\times 32 _{8}=$ [ANS] (Write your answer in base 8, of course.)", "answer_v1": [ "25452" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Using the multiplication table, compute $173 _{8} \\times 52 _{8}$\n$\\begin{array}{cccccccc}\\hline \\times & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 2 & 2 & 4 & 6 & 10 & 12 & 14 & 16 \\\\ \\hline 3 & 3 & 6 & 11 & 14 & 17 & 22 & 25 \\\\ \\hline 4 & 4 & 10 & 14 & 20 & 24 & 30 & 34 \\\\ \\hline 5 & 5 & 12 & 17 & 24 & 31 & 36 & 43 \\\\ \\hline 6 & 6 & 14 & 22 & 30 & 36 & 44 & 52 \\\\ \\hline 7 & 7 & 16 & 25 & 34 & 43 & 52 & 61 \\\\ \\hline \\end{array}$ 61 $173 _{8} \\times 52 _{8}=$ [ANS] (Write your answer in base 8, of course.)", "answer_v2": [ "12056" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Using the multiplication table, compute $354 _{8} \\times 62 _{8}$\n$\\begin{array}{cccccccc}\\hline \\times & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline 2 & 2 & 4 & 6 & 10 & 12 & 14 & 16 \\\\ \\hline 3 & 3 & 6 & 11 & 14 & 17 & 22 & 25 \\\\ \\hline 4 & 4 & 10 & 14 & 20 & 24 & 30 & 34 \\\\ \\hline 5 & 5 & 12 & 17 & 24 & 31 & 36 & 43 \\\\ \\hline 6 & 6 & 14 & 22 & 30 & 36 & 44 & 52 \\\\ \\hline 7 & 7 & 16 & 25 & 34 & 43 & 52 & 61 \\\\ \\hline \\end{array}$ 61 $354 _{8} \\times 62 _{8}=$ [ANS] (Write your answer in base 8, of course.)", "answer_v3": [ "27030" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0341", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "2", "keywords": [ "units", "conversion" ], "problem_v1": "An unscented beeswax candle melts at 145 $^\\circ$ F. What is the temperature in degrees Celsius? [ANS]\ndegrees Kelvin? [ANS]\ndegrees Rankine? [ANS]", "answer_v1": [ "62.7777777777778", "335.927777777778", "604.67" ], "answer_type_v1": [ "NV", "NV", "NV" ], "options_v1": [ [], [], [] ], "problem_v2": "A styrofoam plate melts at 165 $^\\circ$ F. What is the temperature in degrees Celsius? [ANS]\ndegrees Kelvin? [ANS]\ndegrees Rankine? [ANS]", "answer_v2": [ "73.8888888888889", "347.038888888889", "624.67" ], "answer_type_v2": [ "NV", "NV", "NV" ], "options_v2": [ [], [], [] ], "problem_v3": "A plastic food storage container melts at 180 $^\\circ$ F. What is the temperature in degrees Celsius? [ANS]\ndegrees Kelvin? [ANS]\ndegrees Rankine? [ANS]", "answer_v3": [ "82.2222222222222", "355.372222222222", "639.67" ], "answer_type_v3": [ "NV", "NV", "NV" ], "options_v3": [ [], [], [] ] }, { "id": "Arithmetic_0342", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "American" ], "problem_v1": "It\u2019s given that $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversions.\n${0.4 \\text{yards}=}$ [ANS] ${\\text{feet}}$\n${0.18 \\text{feet}=}$ [ANS] ${\\text{yards}}$", "answer_v1": [ "1.2", "0.06" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "It\u2019s given that $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversions.\n${0.14 \\text{yards}=}$ [ANS] ${\\text{feet}}$\n${0.27 \\text{feet}=}$ [ANS] ${\\text{yards}}$", "answer_v2": [ "0.42", "0.09" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "It\u2019s given that $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversions.\n${0.23 \\text{yards}=}$ [ANS] ${\\text{feet}}$\n${0.18 \\text{feet}=}$ [ANS] ${\\text{yards}}$", "answer_v3": [ "0.69", "0.06" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0343", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "metric" ], "problem_v1": "It\u2019s given that $1 \\text{gram}=1000 \\text{milligrams}$. Do the following unit conversions.\n${0.007 \\text{grams}=}$ [ANS] ${\\text{milligrams}}$\n${62 \\text{milligrams}=}$ [ANS] ${\\text{grams}}$", "answer_v1": [ "7", "0.062" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "It\u2019s given that $1 \\text{gram}=1000 \\text{milligrams}$. Do the following unit conversions.\n${0.001 \\text{grams}=}$ [ANS] ${\\text{milligrams}}$\n${93 \\text{milligrams}=}$ [ANS] ${\\text{grams}}$", "answer_v2": [ "1", "0.093" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "It\u2019s given that $1 \\text{gram}=1000 \\text{milligrams}$. Do the following unit conversions.\n${0.003 \\text{grams}=}$ [ANS] ${\\text{milligrams}}$\n${64 \\text{milligrams}=}$ [ANS] ${\\text{grams}}$", "answer_v3": [ "3", "0.064" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0344", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "time" ], "problem_v1": "Do the following unit conversion.\n${8 \\text{weeks}=}$ [ANS] ${\\text{seconds}}$", "answer_v1": [ "4.8384E+06" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Do the following unit conversion.\n${2 \\text{weeks}=}$ [ANS] ${\\text{seconds}}$", "answer_v2": [ "1.2096E+06" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Do the following unit conversion.\n${4 \\text{weeks}=}$ [ANS] ${\\text{seconds}}$", "answer_v3": [ "2.4192E+06" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0345", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "metric" ], "problem_v1": "It\u2019s given that $1 \\text{decimeter}=100 \\text{millimeters}$. Do the following unit conversions.\n${7 \\text{decimeters}=}$ [ANS] ${\\text{millimeters}}$\n${62000 \\text{millimeters}=}$ [ANS] ${\\text{decimeters}}$", "answer_v1": [ "700", "620" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "It\u2019s given that $1 \\text{decimeter}=100 \\text{millimeters}$. Do the following unit conversions.\n${1 \\text{decimeters}=}$ [ANS] ${\\text{millimeters}}$\n${93000 \\text{millimeters}=}$ [ANS] ${\\text{decimeters}}$", "answer_v2": [ "100", "930" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "It\u2019s given that $1 \\text{decimeter}=100 \\text{millimeters}$. Do the following unit conversions.\n${3 \\text{decimeters}=}$ [ANS] ${\\text{millimeters}}$\n${64000 \\text{millimeters}=}$ [ANS] ${\\text{decimeters}}$", "answer_v3": [ "300", "640" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0346", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "metric" ], "problem_v1": "It\u2019s given that $1 \\text{kilometer}=1000 \\text{meters}$ and $1 \\text{meter}=100 \\text{centimeters}$. Do the following unit conversion.\n${777000 \\text{centimeters}=}$ [ANS] ${\\text{kilometers}}$", "answer_v1": [ "7.77" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{kilometer}=1000 \\text{meters}$ and $1 \\text{meter}=100 \\text{centimeters}$. Do the following unit conversion.\n${175000 \\text{centimeters}=}$ [ANS] ${\\text{kilometers}}$", "answer_v2": [ "1.75" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{kilometer}=1000 \\text{meters}$ and $1 \\text{meter}=100 \\text{centimeters}$. Do the following unit conversion.\n${382000 \\text{centimeters}=}$ [ANS] ${\\text{kilometers}}$", "answer_v3": [ "3.82" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0347", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "American" ], "problem_v1": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversion.\n${0.077 \\text{miles}=}$ [ANS] ${\\text{inches}}$", "answer_v1": [ "4878.72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversion.\n${0.018 \\text{miles}=}$ [ANS] ${\\text{inches}}$", "answer_v2": [ "1140.48" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversion.\n${0.038 \\text{miles}=}$ [ANS] ${\\text{inches}}$", "answer_v3": [ "2407.68" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0348", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "American", "application" ], "problem_v1": "It\u2019s given that $1 \\text{pound (lb)}=16 \\text{ounces (oz)}$. A baker owns a small business. He produces bread in bags. Each bag needs $3.04$ oz of dough. The baker purchased $11.4$ lb of dough. How many bags of bread can be produced? Solution: The baker can produce [ANS] bags of bread with $11.4$ lb of dough.", "answer_v1": [ "60" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{pound (lb)}=16 \\text{ounces (oz)}$. A baker owns a small business. He produces bread in bags. Each bag needs $3.2$ oz of dough. The baker purchased $12.4$ lb of dough. How many bags of bread can be produced? Solution: The baker can produce [ANS] bags of bread with $12.4$ lb of dough.", "answer_v2": [ "62" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{pound (lb)}=16 \\text{ounces (oz)}$. A baker owns a small business. He produces bread in bags. Each bag needs $4.8$ oz of dough. The baker purchased $16.2$ lb of dough. How many bags of bread can be produced? Solution: The baker can produce [ANS] bags of bread with $16.2$ lb of dough.", "answer_v3": [ "54" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0349", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "time", "application" ], "problem_v1": "A machine can produce a nail every $7.5$ seconds. If the machine keeps running for $4$ days without stop, how many nails can be produced? Solution: The machine can produce [ANS] nails in $4$ days.", "answer_v1": [ " 46080" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A machine can produce a nail every $2.5$ seconds. If the machine keeps running for $5$ days without stop, how many nails can be produced? Solution: The machine can produce [ANS] nails in $5$ days.", "answer_v2": [ " 172800" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A machine can produce a nail every $4.5$ seconds. If the machine keeps running for $4$ days without stop, how many nails can be produced? Solution: The machine can produce [ANS] nails in $4$ days.", "answer_v3": [ " 76800" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0350", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "metric" ], "problem_v1": "It\u2019s given that $1 \\text{liter}=1000 \\text{milliliters}$. Do the following unit conversions.\n${8 \\text{liters}=}$ [ANS] ${\\text{milliliters}}$\n${62000 \\text{milliliters}=}$ [ANS] ${\\text{liters}}$", "answer_v1": [ " 8000", " 62" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "It\u2019s given that $1 \\text{liter}=1000 \\text{milliliters}$. Do the following unit conversions.\n${2 \\text{liters}=}$ [ANS] ${\\text{milliliters}}$\n${93000 \\text{milliliters}=}$ [ANS] ${\\text{liters}}$", "answer_v2": [ " 2000", " 93" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "It\u2019s given that $1 \\text{liter}=1000 \\text{milliliters}$. Do the following unit conversions.\n${4 \\text{liters}=}$ [ANS] ${\\text{milliliters}}$\n${64000 \\text{milliliters}=}$ [ANS] ${\\text{liters}}$", "answer_v3": [ " 4000", " 64" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0351", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "American", "fraction" ], "problem_v1": "It\u2019s given that $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversions. Use fractions in your answer when needed.\n${{{\\textstyle\\frac{1}{6}}} \\text{feet}=}$ [ANS] ${\\text{inches}}$\n${{6} \\text{inches}=}$ [ANS] ${\\text{feet}}$", "answer_v1": [ "2", "1/2" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "It\u2019s given that $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversions. Use fractions in your answer when needed.\n${{{\\textstyle\\frac{1}{2}}} \\text{feet}=}$ [ANS] ${\\text{inches}}$\n${{8} \\text{inches}=}$ [ANS] ${\\text{feet}}$", "answer_v2": [ "6", "2/3" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "It\u2019s given that $1 \\text{foot}=12 \\text{inches}$. Do the following unit conversions. Use fractions in your answer when needed.\n${{{\\textstyle\\frac{2}{3}}} \\text{feet}=}$ [ANS] ${\\text{inches}}$\n${{3} \\text{inches}=}$ [ANS] ${\\text{feet}}$", "answer_v3": [ "8", "1/4" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0352", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "time", "application", "decimal" ], "problem_v1": "Each second, an atom clock runs $0.0008$ second slower than usual. This clock and a normal clock start running side by side. After $6$ days, how much slower would the slower clock run compared to the normal clock? Solution: After $6$ days, the slower clock would be [ANS] seconds slower than the normal clock. (Don\u2019t round your answer.)", "answer_v1": [ "414.72" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Each second, an atom clock runs $0.0002$ second slower than usual. This clock and a normal clock start running side by side. After $9$ days, how much slower would the slower clock run compared to the normal clock? Solution: After $9$ days, the slower clock would be [ANS] seconds slower than the normal clock. (Don\u2019t round your answer.)", "answer_v2": [ "155.52" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Each second, an atom clock runs $0.0004$ second slower than usual. This clock and a normal clock start running side by side. After $6$ days, how much slower would the slower clock run compared to the normal clock? Solution: After $6$ days, the slower clock would be [ANS] seconds slower than the normal clock. (Don\u2019t round your answer.)", "answer_v3": [ "207.36" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0353", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "American" ], "problem_v1": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversion.\n${19008 \\text{yards}=}$ [ANS] ${\\text{miles}}$", "answer_v1": [ "10.8" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversion.\n${10032 \\text{yards}=}$ [ANS] ${\\text{miles}}$", "answer_v2": [ "5.7" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{mile}=5280 \\text{feet}$ and $1 \\text{yard}=3 \\text{feet}$. Do the following unit conversion.\n${8448 \\text{yards}=}$ [ANS] ${\\text{miles}}$", "answer_v3": [ "4.8" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0355", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "metric" ], "problem_v1": "It\u2019s given that $1 \\text{metric ton}=1000 \\text{kilograms}$ and $1 \\text{kilogram}=1000 \\text{grams}$. (Note that a metric ton is different from a US ton.) Do the following unit conversion.\n${777 \\text{grams}=}$ [ANS] ${\\text{metric tons}}$", "answer_v1": [ "0.000777" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{metric ton}=1000 \\text{kilograms}$ and $1 \\text{kilogram}=1000 \\text{grams}$. (Note that a metric ton is different from a US ton.) Do the following unit conversion.\n${175 \\text{grams}=}$ [ANS] ${\\text{metric tons}}$", "answer_v2": [ "0.000175" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{metric ton}=1000 \\text{kilograms}$ and $1 \\text{kilogram}=1000 \\text{grams}$. (Note that a metric ton is different from a US ton.) Do the following unit conversion.\n${382 \\text{grams}=}$ [ANS] ${\\text{metric tons}}$", "answer_v3": [ "0.000382" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0357", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "American" ], "problem_v1": "It\u2019s given that $1 \\text{ton}=2000 \\text{lb}$ and $1 \\text{lb}=16 \\text{oz}$.Do the following unit conversion.\n${243200 \\text{oz}=}$ [ANS] ${\\text{tons}}$", "answer_v1": [ "7.6" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "It\u2019s given that $1 \\text{ton}=2000 \\text{lb}$ and $1 \\text{lb}=16 \\text{oz}$.Do the following unit conversion.\n${60800 \\text{oz}=}$ [ANS] ${\\text{tons}}$", "answer_v2": [ "1.9" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "It\u2019s given that $1 \\text{ton}=2000 \\text{lb}$ and $1 \\text{lb}=16 \\text{oz}$.Do the following unit conversion.\n${115200 \\text{oz}=}$ [ANS] ${\\text{tons}}$", "answer_v3": [ "3.6" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0358", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "metric", "application", "decimal" ], "problem_v1": "A snail crawls $8$ millimeters per second. How many centimeters can it crawl in $40$ seconds? Solution: The snail can crawl [ANS] centimeters in $40$ seconds.", "answer_v1": [ "32" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A snail crawls $2$ millimeters per second. How many centimeters can it crawl in $50$ seconds? Solution: The snail can crawl [ANS] centimeters in $50$ seconds.", "answer_v2": [ "10" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A snail crawls $4$ millimeters per second. How many centimeters can it crawl in $40$ seconds? Solution: The snail can crawl [ANS] centimeters in $40$ seconds.", "answer_v3": [ "16" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0362", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "metric", "application", "decimal" ], "problem_v1": "A factory ordered $15.26$ tons of plastics to make smart phones. Each phone will use $43.6$ grams of plastics. How many smart phones can be made from this order? Solution: This order can be used to produce [ANS] smart phones.", "answer_v1": [ " 350000" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A factory ordered $3.42$ tons of plastics to make smart phones. Each phone will use $22.8$ grams of plastics. How many smart phones can be made from this order? Solution: This order can be used to produce [ANS] smart phones.", "answer_v2": [ " 150000" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A factory ordered $5.92$ tons of plastics to make smart phones. Each phone will use $29.6$ grams of plastics. How many smart phones can be made from this order? Solution: This order can be used to produce [ANS] smart phones.", "answer_v3": [ " 200000" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0363", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "metric", "application", "decimal" ], "problem_v1": "A mountain moves toward the west by $7.6$ millimeters per year. In the past $6$ million years, how many kilometers did the mountain move toward the west? Solution: The mountain moved to the west by [ANS] kilometers in $6$ million years.", "answer_v1": [ " 45" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A mountain moves toward the west by $1.9$ millimeters per year. In the past $2$ million years, how many kilometers did the mountain move toward the west? Solution: The mountain moved to the west by [ANS] kilometers in $2$ million years.", "answer_v2": [ " 3" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A mountain moves toward the west by $3.6$ millimeters per year. In the past $3$ million years, how many kilometers did the mountain move toward the west? Solution: The mountain moved to the west by [ANS] kilometers in $3$ million years.", "answer_v3": [ " 10" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0364", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "time" ], "problem_v1": "Do the following unit conversion. Use decimals in your answer if needed.\n${252 \\text{seconds}=}$ [ANS] ${\\text{hours}}$", "answer_v1": [ "0.07" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Do the following unit conversion. Use decimals in your answer if needed.\n${36 \\text{seconds}=}$ [ANS] ${\\text{hours}}$", "answer_v2": [ "0.01" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Do the following unit conversion. Use decimals in your answer if needed.\n${108 \\text{seconds}=}$ [ANS] ${\\text{hours}}$", "answer_v3": [ "0.03" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0365", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "rate", "proportion", "unit", "conversion", "time" ], "problem_v1": "Do the following unit conversions.\n${21 \\text{hours}=}$ [ANS] ${\\text{minutes}}$\n${7800 \\text{seconds}=}$ [ANS] ${\\text{minutes}}$", "answer_v1": [ "1260", "130" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Do the following unit conversions.\n${12 \\text{hours}=}$ [ANS] ${\\text{minutes}}$\n${8820 \\text{seconds}=}$ [ANS] ${\\text{minutes}}$", "answer_v2": [ "720", "147" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Do the following unit conversions.\n${15 \\text{hours}=}$ [ANS] ${\\text{minutes}}$\n${7860 \\text{seconds}=}$ [ANS] ${\\text{minutes}}$", "answer_v3": [ "900", "131" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0366", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "metric", "application", "decimal" ], "problem_v1": "Hill A is $5.56$ kilometers in height, while Hill B is $730$ meters in height. What is the difference in their height? Answer this question in both meters and kilometers.\nQuestion 1: The difference in these two hills\u2019 height is [ANS] meters.\nQuestion 2: The difference in these two hills\u2019 height is [ANS] kilometers. Use decimal in your answer.", "answer_v1": [ "4830", "4.83" ], "answer_type_v1": [ "NV", "NV" ], "options_v1": [ [], [] ], "problem_v2": "Hill A is $3.92$ kilometers in height, while Hill B is $490$ meters in height. What is the difference in their height? Answer this question in both meters and kilometers.\nQuestion 1: The difference in these two hills\u2019 height is [ANS] meters.\nQuestion 2: The difference in these two hills\u2019 height is [ANS] kilometers. Use decimal in your answer.", "answer_v2": [ "3430", "3.43" ], "answer_type_v2": [ "NV", "NV" ], "options_v2": [ [], [] ], "problem_v3": "Hill A is $3.63$ kilometers in height, while Hill B is $520$ meters in height. What is the difference in their height? Answer this question in both meters and kilometers.\nQuestion 1: The difference in these two hills\u2019 height is [ANS] meters.\nQuestion 2: The difference in these two hills\u2019 height is [ANS] kilometers. Use decimal in your answer.", "answer_v3": [ "3110", "3.11" ], "answer_type_v3": [ "NV", "NV" ], "options_v3": [ [], [] ] }, { "id": "Arithmetic_0367", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "unit", "conversion", "metric", "application", "decimal" ], "problem_v1": "A chemistry teacher will order saline for a lab lesson for the upcoming school year. Each experiment will use $17$ milliliters of saline, and approximately $6200$ experiments will be conducted in this school year. How many liters of saline should the teacher order? Solution: The teacher should order [ANS] liters of saline for the school year.", "answer_v1": [ "105.4" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A chemistry teacher will order saline for a lab lesson for the upcoming school year. Each experiment will use $6$ milliliters of saline, and approximately $9300$ experiments will be conducted in this school year. How many liters of saline should the teacher order? Solution: The teacher should order [ANS] liters of saline for the school year.", "answer_v2": [ "55.8" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A chemistry teacher will order saline for a lab lesson for the upcoming school year. Each experiment will use $10$ milliliters of saline, and approximately $6400$ experiments will be conducted in this school year. How many liters of saline should the teacher order? Solution: The teacher should order [ANS] liters of saline for the school year.", "answer_v3": [ "64" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0368", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "1", "keywords": [ "unit", "conversion", "American", "application" ], "problem_v1": "A $6$-yard string will be cut into nine-inch strings. How many nine-inch strings can be made? Solution: [ANS] nine-inch strings can be made.", "answer_v1": [ "24" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "A $9$-yard string will be cut into two-inch strings. How many two-inch strings can be made? Solution: [ANS] two-inch strings can be made.", "answer_v2": [ "162" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "A $6$-yard string will be cut into four-inch strings. How many four-inch strings can be made? Solution: [ANS] four-inch strings can be made.", "answer_v3": [ "54" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0369", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "3", "keywords": [ "scale", "area" ], "problem_v1": "A map shows the size of Grand Rapids to be a rectangle $2.5 cm$ by $2.2 cm$. The scale of the map is 1cm=$4$ miles. What is the actual size of Grand Rapids? [ANS] $mi$ by [ANS] $mi$ What is the map area of Grand Rapids? [ANS] $cm ^2$ What is the actual area of Grand Rapids? [ANS] $mi ^2$", "answer_v1": [ "10", "8.8", "5.5", "88" ], "answer_type_v1": [ "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [] ], "problem_v2": "A map shows the size of Grand Rapids to be a rectangle $1.1 cm$ by $2.9 cm$. The scale of the map is 1cm=$2$ miles. What is the actual size of Grand Rapids? [ANS] $mi$ by [ANS] $mi$ What is the map area of Grand Rapids? [ANS] $cm ^2$ What is the actual area of Grand Rapids? [ANS] $mi ^2$", "answer_v2": [ "2.2", "5.8", "3.19", "12.76" ], "answer_type_v2": [ "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [] ], "problem_v3": "A map shows the size of Grand Rapids to be a rectangle $1.6 cm$ by $2.2 cm$. The scale of the map is 1cm=$3$ miles. What is the actual size of Grand Rapids? [ANS] $mi$ by [ANS] $mi$ What is the map area of Grand Rapids? [ANS] $cm ^2$ What is the actual area of Grand Rapids? [ANS] $mi ^2$", "answer_v3": [ "4.8", "6.6", "3.52", "31.68" ], "answer_type_v3": [ "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [] ] }, { "id": "Arithmetic_0370", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "4", "keywords": [], "problem_v1": "Jeff bought 8 quarts of juice for a party. One glass holds 8 fluid ounces of juice. The total number of glasses that Jeff can fill is [ANS]. [1 quart=32 fluid ounces]", "answer_v1": [ "32" ], "answer_type_v1": [ "NV" ], "options_v1": [ [] ], "problem_v2": "Jeff bought 5 quarts of juice for a party. One glass holds 8 fluid ounces of juice. The total number of glasses that Jeff can fill is [ANS]. [1 quart=32 fluid ounces]", "answer_v2": [ "20" ], "answer_type_v2": [ "NV" ], "options_v2": [ [] ], "problem_v3": "Jeff bought 6 quarts of juice for a party. One glass holds 8 fluid ounces of juice. The total number of glasses that Jeff can fill is [ANS]. [1 quart=32 fluid ounces]", "answer_v3": [ "24" ], "answer_type_v3": [ "NV" ], "options_v3": [ [] ] }, { "id": "Arithmetic_0371", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "4", "keywords": [], "problem_v1": "A movie is 115 minutes long. 60 minutes=1 hour Which statement about the movie is true? [ANS] A. The movie is more than 2 hours long. B. The movie is exactly two hours long. C. The movie is less than two hours long.", "answer_v1": [ "C" ], "answer_type_v1": [ "MCS" ], "options_v1": [ [ "A", "B", "C" ] ], "problem_v2": "A movie is 115 minutes long. 60 minutes=1 hour Which statement about the movie is true? [ANS] A. The movie is less than two hours long. B. The movie is exactly two hours long. C. The movie is more than 2 hours long.", "answer_v2": [ "A" ], "answer_type_v2": [ "MCS" ], "options_v2": [ [ "A", "B", "C" ] ], "problem_v3": "A movie is 115 minutes long. 60 minutes=1 hour Which statement about the movie is true? [ANS] A. The movie is more than 2 hours long. B. The movie is less than two hours long. C. The movie is exactly two hours long.", "answer_v3": [ "B" ], "answer_type_v3": [ "MCS" ], "options_v3": [ [ "A", "B", "C" ] ] }, { "id": "Arithmetic_0372", "subject": "Arithmetic", "topic": "Units", "subtopic": "Conversions", "level": "2", "keywords": [ "prealgebra", "common core", "metric", "conversion" ], "problem_v1": "Complete each statement:\n75 mL=[ANS] L 239 mm=[ANS] m 32 kg=[ANS] g 1671 cm=[ANS] mm 38 km=[ANS] m 2.48 g=[ANS] kg 52 L=[ANS] mL", "answer_v1": [ "75/1000", "239/1000", "32*1000", "1671*10", "38*1000", "2.48/1000", "52*1000" ], "answer_type_v1": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v1": [ [], [], [], [], [], [], [] ], "problem_v2": "Complete each statement:\n33 mL=[ANS] L 195 mm=[ANS] m 30 kg=[ANS] g 2911 cm=[ANS] mm 22 km=[ANS] m 2.46 g=[ANS] kg 18 L=[ANS] mL", "answer_v2": [ "33/1000", "195/1000", "30*1000", "2911*10", "22*1000", "2.46/1000", "18*1000" ], "answer_type_v2": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v2": [ [], [], [], [], [], [], [] ], "problem_v3": "Complete each statement:\n47 mL=[ANS] L 219 mm=[ANS] m 32 kg=[ANS] g 1489 cm=[ANS] mm 26 km=[ANS] m 2.49 g=[ANS] kg 73 L=[ANS] mL", "answer_v3": [ "47/1000", "219/1000", "32*1000", "1489*10", "26*1000", "2.49/1000", "73*1000" ], "answer_type_v3": [ "NV", "NV", "NV", "NV", "NV", "NV", "NV" ], "options_v3": [ [], [], [], [], [], [], [] ] }, { "id": "Arithmetic_0374", "subject": "Arithmetic", "topic": "Units", "subtopic": "Interpretation", "level": "4", "keywords": [ "prealgebra", "common core", "metric system" ], "problem_v1": "For each of the following, select the most appropriate unit of measurement:\nThe amount of water when you flush a toilet uses [ANS] The volume for a thermometer uses [ANS] The volume of a jug of milk uses [ANS] The amount of water passing over Niagara Falls in a day uses [ANS] The amount of liquid in a Coke can uses [ANS]", "answer_v1": [ "liters", "milliliiters", "liters", "kiloliters", "milliliiters" ], "answer_type_v1": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v1": [ [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ] ], "problem_v2": "For each of the following, select the most appropriate unit of measurement:\nThe amount of water consumed by New York City each day uses [ANS] The volume for food coloring to make green eggs and ham uses [ANS] The amount of liquid in a juice box uses [ANS] The amount of water when you flush a toilet uses [ANS] The volume of a large Coke bottle uses [ANS]", "answer_v2": [ "kiloliters", "milliliiters", "milliliiters", "liters", "liters" ], "answer_type_v2": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v2": [ [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ] ], "problem_v3": "For each of the following, select the most appropriate unit of measurement:\nThe volume for food coloring to make green eggs and ham uses [ANS] The amount of water in Lake Michigan uses [ANS] The amount of water used in a shower uses [ANS] The volume of a container of gasoline uses [ANS] The amount of liquid in a juice box uses [ANS]", "answer_v3": [ "milliliiters", "kiloliters", "liters", "liters", "milliliiters" ], "answer_type_v3": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v3": [ [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ], [ "kiloliters", "liters", "deciliters", "centiliters", "milliliiters", "gigaliters" ] ] }, { "id": "Arithmetic_0375", "subject": "Arithmetic", "topic": "Units", "subtopic": "Interpretation", "level": "4", "keywords": [ "prealgebra", "common core", "metric system" ], "problem_v1": "For each of the following, select the most appropriate unit of measurement:\nThe mass of a booger uses [ANS] The mass of a pair of earrings uses [ANS] The weight of an passenger airplane uses [ANS] The mass in the sun uses [ANS] The weight for a hot dog uses [ANS]", "answer_v1": [ "milligrams", "grams", "kilograms", "kilograms", "grams" ], "answer_type_v1": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v1": [ [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ] ], "problem_v2": "For each of the following, select the most appropriate unit of measurement:\nThe mass in the moon uses [ANS] The mass of a watchband uses [ANS] The weight for a banana uses [ANS] The mass of a booger uses [ANS] The weight of a Postal service delivery truck uses [ANS]", "answer_v2": [ "kilograms", "grams", "grams", "milligrams", "kilograms" ], "answer_type_v2": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v2": [ [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ] ], "problem_v3": "For each of the following, select the most appropriate unit of measurement:\nThe mass of a watchband uses [ANS] The mass in Jupiter uses [ANS] The mass of a human hair uses [ANS] The weight of a sports car uses [ANS] The weight for a banana uses [ANS]", "answer_v3": [ "grams", "kilograms", "milligrams", "kilograms", "grams" ], "answer_type_v3": [ "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v3": [ [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ], [ "kilograms", "grams", "decigrams", "centigrams", "milligrams", "gigagrams" ] ] }, { "id": "Arithmetic_0376", "subject": "Arithmetic", "topic": "Units", "subtopic": "Interpretation", "level": "4", "keywords": [ "prealgebra", "common core", "metric system" ], "problem_v1": "For each of the following, select the most appropriate unit of measurement:\nThe thickness of an eyeglass lens uses [ANS] The height of an old oak tree uses [ANS] The distance you drive on a summer vacation uses [ANS] How far LeBron James shoots a free throw uses [ANS] How far it is to the sun uses [ANS] The length of fruit rollups uses [ANS]", "answer_v1": [ "millimeters", "meters", "kilometers", "meters", "kilometers", "centimeters" ], "answer_type_v1": [ "MCS", "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v1": [ [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ] ], "problem_v2": "For each of the following, select the most appropriate unit of measurement:\nHow far it is to Jupiter uses [ANS] How far LeBron James shoots a free throw uses [ANS] The height of the Empire State Building uses [ANS] The length of a Oscar Mayer hot dog uses [ANS] The thickness of an toenail uses [ANS] The distance you drive on a summer vacation uses [ANS]", "answer_v2": [ "kilometers", "meters", "meters", "centimeters", "millimeters", "kilometers" ], "answer_type_v2": [ "MCS", "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v2": [ [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ] ], "problem_v3": "For each of the following, select the most appropriate unit of measurement:\nThe thickness of an toenail uses [ANS] How far it is to the sun uses [ANS] How far LeBron James shoots a free throw uses [ANS] The length of a Dole banana uses [ANS] The distance of a 3 hour airplane flight uses [ANS] The height of the Empire State Building uses [ANS]", "answer_v3": [ "millimeters", "kilometers", "meters", "centimeters", "kilometers", "meters" ], "answer_type_v3": [ "MCS", "MCS", "MCS", "MCS", "MCS", "MCS" ], "options_v3": [ [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ], [ "kilometers", "meters", "decimeters", "centimeters", "millimeters", "gigameters" ] ] } ]