LLemma 7B on 5.NF.A.1
Common Core Standard 5.NF.A.1
This standard covers the following:
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Problem: John has been learning to add and subtract fractions at school. He was given a problem during his homework that puzzled him. He had to take the sum of 48/56 and 95/23 and then subtract 34/26 from the result. What was the value that John found for this operation? Answer in simplest form.
LLemma 7B:
Reasoning: John's problem is a combination of two operations: addition and subtraction. John's first step is to add the fractions. He can use a common denominator to add the fractions. The common denominator is <<23*56=1272>>1272. John can use the common denominator to write equivalent fractions with the common denominator. 48/56 = <<48*23/56*23=1008/1272>>1008/1272 95/23 = <<95*56/23*56=5080/1272>>5080/1272 John can add the numerators and keep the common denominator. 1008/1272 + 5080/1272 = <<1008+5080/1272=6088/1272>>6088/1272 John can write the sum as a single fraction. 48/56 + 95/23 = 6088/1272 John's next step is to subtract 34/26 from the sum. He can use a common denominator to subtract the fractions. The common denominator is <<26*1272=32344>>32344. John can use the common denominator to write equivalent fractions with the common denominator. 34/26 = <<34*1272/26*1272=42168/32344>>42168/32344 John can subtract the numerators and keep the common denominator. 6088/1272 - 42168/32344 = <<6088-42168/1272=36080/1272>>36080/1272 John can write the difference as a single fraction. 48/56 + 95/23 - 34/26 = 36080/1272 John can simplify the fraction. 36080/1272 = <<36080/1272=280>>280 ### Answer: 280
Expected answer: 7702/2093
Correct? No
Problem: First, add the fractions 88/9 and 28/65. Then subtract the fraction 18/37 from the result. What is the result expressed as a simple fraction?
LLemma 7B:
Reasoning: 88/9 + 28/65 = <<88/9+28/65=1003/65>>1003/65 1003/65 - 18/37 = <<1003/65-18/37=1003/65*37/37-18/37=1003*37-18*65/37*65=1003*37-18*65/65*65=1003*37-18*65/65^2=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18*65/4225=1003*37-18
Expected answer: 210434/21645
Correct? No
Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?
LLemma 7B:
Reasoning: 63/41 = <<63/41=1.5>>1.5 44/50 = <<44/50=0.88>>0.88 1.5 + 0.88 = <<1.5+0.88=2.38>>2.38 ### Answer: 2.38
Expected answer: 2477/1025
Correct? No
Problem: John had 71/41 of a cake left and Emily added 41/77 of another cake to it. How much cake is there in total? Give your answer as a simplified fraction.
LLemma 7B:
Reasoning: John had 71/41 of a cake left. Emily added 41/77 of another cake to it. John had 71/41 of a cake left and Emily added 41/77 of another cake to it. ### Answer: 71/41+41/77=<<71/41+41/77=118/77>>118/77
Expected answer: 7148/3157
Correct? No
Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.
LLemma 7B:
Reasoning: 10/65 = <<10/65=1/6>>1/6 56/35 = <<56/35=17/7>>17/7 1/6 + 17/7 = <<1/6+17/7=17/21>>17/21 ### Answer: 17/21
Expected answer: 114/65
Correct? No
Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.
LLemma 7B:
Reasoning: 75/81 is a repeating decimal. 97/47 is a repeating decimal. ### Answer: 75/81 + 97/47 = <<75/81 + 97/47 = 1586/3891>>1586/3891
Expected answer: 3794/1269
Correct? No
Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.
LLemma 7B:
Reasoning: 88/1 - 38/53 = <<88/1 - 38/53 = 4402/53>>4402/53 ### Answer: 4402/53
Expected answer: 4626/53
Correct? No
Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?
LLemma 7B:
Reasoning: 80/94 = <<80/94=0.83870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870967741935483870
Expected answer: 6026/2773
Correct? No
Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 89/56 + 48/50 = <<89/56+48/50>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>> 89/56 + 48/50 = <<(89*50)/(56*50)+(48*56)/(50*56)>>
Expected answer: 3569/1400
Correct? No
Problem: What is the result when you subtract 38/87 from the sum of 96/11 and 12/5? Please leave your answer as a fraction.
LLemma 7B:
Reasoning: 96/11 + 12/5 = <<(96*5+12*11)/(11*5)=(480+132)/55=612/55>>612/55 38/87 - 612/55 = <<(38*55-612*87)/(87*55)=(2030-5152)/(4965)=-3122/4965>>-3122/4965 ### Answer: -3122/4965
Expected answer: 51154/4785
Correct? No
Problem: If you have a number that's 82 divided by 9 and from this you subtract 82 divided by 63, what's the resulting value? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 82/9 - 82/63 = <<82/9 - 82/63>> ### Answer: 1/3
Expected answer: 164/21
Correct? No
Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.
LLemma 7B:
Reasoning: 23/3 minus the sum of 80/91 and 26/24 = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (80/91 + 26/24) = 23/3 - (
Expected answer: 6229/1092
Correct? No
Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?
LLemma 7B:
Reasoning: 37/18 = <<37/18=11/6>>11/6 and 24/60 = <<24/60=1/5>>1/5 11/6 + 1/5 = <<11/6+1/5=11/30+6/30=17/30>>17/30 ### Answer: 17/30
Expected answer: 221/90
Correct? No
Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 33/41 + 95/62 = <<33/41 + 95/62 = 1223/2542>>1223/2542 ### Answer: 1223/2542
Expected answer: 5941/2542
Correct? No
Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.
LLemma 7B:
Reasoning: ((30 / 11) + (72 / 38)) = <<(30 / 11) + (72 / 38)>> (81 / 34) = <<81 / 34>> ((30 / 11) + (72 / 38)) + (81 / 34) = <<(30 / 11) + (72 / 38)>> + <<81 / 34>> ### Answer: <<(30 / 11) + (72 / 38)>> + <<81 / 34>>
Expected answer: 49773/7106
Correct? No
Problem: What is the result of adding (64 / 34) + (3 / 24) and then adding the result to (41 / 96)? Answer as a simplified fraction.
LLemma 7B:
Reasoning: (64 / 34) + (3 / 24) = <<(64+3)/(34+24)=(67/58)>>67/58 (67/58) + (41 / 96) = <<(67+41)/(58+96)=(108/154)=(108/154)>>108/154 ### Answer: 108/154
Expected answer: 3973/1632
Correct? No
Problem: Daniel has to solve a math problem for his homework that includes fractions. Initially, he has been asked to add 83/73 and 53/77. The result of this step he saved as 'w'. Then, he needs to add 80/76 to the result 'w'. How would he calculate the final answer in simplified fraction form?
LLemma 7B:
Reasoning: Daniel can add 83/73 and 53/77 by adding the numerators and keeping the denominator the same. 83/73 + 53/77 = (83+53)/73 = 136/73 Daniel can add 80/76 to 136/73 by adding the numerators and keeping the denominator the same. 136/73 + 80/76 = (136+80)/73 = 216/73 ### Answer: 216/73
Expected answer: 307360/106799
Correct? No
Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.
LLemma 7B:
Reasoning: 27/20 = <<27/20=1.35>>1.35 and 14/66 = <<14/66=0.21>>0.21 27/20 + 14/66 = <<27/20+14/66=1.56>>1.56 ### Answer: 1.56
Expected answer: 1031/660
Correct? No
Problem: What is the result of the expression ((32 / 14) - (22 / 47))? Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 32/14 = <<32/14=2>>2, 22/47 = <<22/47=1/2>>1/2. ((32 / 14) - (22 / 47)) = <<(32/14)-(22/47)=(2)-(1/2)=1>>1 ### Answer: 1
Expected answer: 598/329
Correct? No
Problem: What is the sum of 74/61 and 41/53 expressed in fractions?
LLemma 7B:
Reasoning: 74/61 + 41/53 = <<74/61 + 41/53>> ### Answer: 115/314
Expected answer: 6423/3233
Correct? No
Problem: First, find out the result of 94 / 2 - 74 / 57. Then add the result to 56 / 97. What fraction do you get?
LLemma 7B:
Reasoning: 94 / 2 - 74 / 57 = <<94/2-74/57=1.05>>1.05 56 / 97 + 1.05 = <<56/97+1.05=1.05>>1.05 ### Answer: 1.05
Expected answer: 255877/5529
Correct? No
Problem: What is the sum of 14/89 and the sum of 24/34 and 44/87? Give your answer as a simplified fraction.
LLemma 7B:
Reasoning: 14/89 + 24/34 = <<14/89+24/34=14/89+7/89=21/89>>21/89 44/87 + 24/34 = <<44/87+24/34=44/87+12/87=56/87>>56/87 21/89 + 56/87 = <<21/89+56/87=21/89+28/89=49/89=49/89*89/89=49/89*89/89=49/89>>49/89 ### Answer: 49/89
Expected answer: 180194/131631
Correct? No
Problem: What would you get if you add 73/30 to 8/60?
LLemma 7B:
Reasoning: 73/30 = <<73/30=2.46>>2.46 and 8/60 = <<8/60=0.133333333333333>>0.133333333333333. 2.46 + 0.133333333333333 = <<2.46+0.133333333333333=2.59333333333333>>2.59333333333333 ### Answer: 2.59333333333333
Expected answer: 77/30
Correct? No
Problem: Suppose you have the following three fractions: 82/49, 45/60, and 99/59. If you add the first fraction (82/49) with the second one (45/60), call this result 'd'. Then, add 'd' to the third fraction (99/59). What would be the resulting sum? Please provide your answer as a simplified fraction.
LLemma 7B:
Reasoning: 82/49 + 45/60 = <<(82*60)/(49*60) + (45*49)/(60*49) = (82*60 + 45*49)/(49*60) = (49*141)/(49*60) = 141/60>>141/60 141/60 + 99/59 = <<(141*59)/(60*59) + (99*60)/(59*60) = (141*59 + 99*60)/(60*59) = (59*230)/(59*60) = 230/60>>230/60 ### Answer: 230/60
Expected answer: 47429/11564
Correct? No
Problem: Solve the following two steps: first, subtract 76/30 from 91/16 and second, add the answer to 18/44. Round the final answer to the nearest hundredth.
LLemma 7B:
Reasoning: 91/16 - 76/30 = <<91/16-76/30=1.05>>1.05 1.05 + 18/44 = <<1.05+18/44=1.11>>1.11 ### Answer: 1.11
Expected answer: 9407/2640
Correct? No
Problem: Calculate the result of ((8 / 91) + (49 / 5)) and subtract (32 / 76) from the result. Provide your answer as a simplified fraction.
LLemma 7B:
Reasoning: ((8 / 91) + (49 / 5)) = <<(8 / 91) + (49 / 5)>> ((8 / 91) + (49 / 5)) = <<(8 / 91) + (49 / 5)>> (32 / 76) = <<32 / 76>> ((8 / 91) + (49 / 5)) - (32 / 76) = <<(8 / 91) + (49 / 5)>> - <<32 / 76>> ((8 / 91) + (49 / 5)) - (32 / 76) = <<(8 / 91) + (49 / 5)>> - <<32 / 76>> ### Answer: <<(8 / 91) + (49 / 5)>> - <<32 / 76>>
Expected answer: 81841/8645
Correct? No
Problem: Calculate the value of ((75 / 45) + (5 / 49)) first. Then add this value with 3 / 58. Provide the answer as a simple fraction.
LLemma 7B:
Reasoning: 75/45 = <<75/45=1.5>>1.5, 5/49 = <<5/49=0.1>>0.1, 3/58 = <<3/58=0.05>>0.05. ((75 / 45) + (5 / 49)) = <<(75/45)+(5/49)>>1.55 ((75 / 45) + (5 / 49)) + (3 / 58) = <<(75/45)+(5/49)+(3/58)>>1.555 ### Answer: 1.555
Expected answer: 15521/8526
Correct? No
Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.
LLemma 7B:
Reasoning: 43/15 = <<43/15=2.8666666666666665>> 33/95 = <<33/95=0.34935064935064935>> ((43 / 15) - (33 / 95)) = <<43/15-33/95=0.001111111111111111>> ### Answer: 0.001111111111111111
Expected answer: 718/285
Correct? No
Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.
LLemma 7B:
Reasoning: 78/45 + 89/36 = <<78/45+89/36=1.5>>1.5 1.5 + 1.5 = <<1.5+1.5=3>>3
Expected answer: 757/90
Correct? No
Problem: Let's consider that 93 is divided by 34 to get a fraction value, from which is subtracted another fraction 77/74. What would be the result as a simplified fraction?
LLemma 7B:
Reasoning: 93/34 = <<93/34=2.7185185185185185>> 77/74 = <<77/74=1.0116279069767441>> 93/34 - 77/74 = <<93/34 - 77/74>> ### Answer: 2.697297297297297
Expected answer: 1066/629
Correct? No
Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 86/35 + 68/85 = <<86/35 + 68/85>> ### Answer: 154/17
Expected answer: 114/35
Correct? No
Problem: What is the sum of 99/53 and 67/94 in simplest form?
LLemma 7B:
Reasoning: 99/53 = <<99/53=1.84210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526
Expected answer: 12857/4982
Correct? No
Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?
LLemma 7B:
Reasoning: 74/27 minus 56/33 = <<74/27-56/33>> 74/27 minus 56/33 = <<(74*33-56*27)/(27*33)>> 74/27 minus 56/33 = <<(2462-1536)/(851)>> 74/27 minus 56/33 = <<826/851>> ### Answer: 826/851
Expected answer: 310/297
Correct? No
Problem: Find the result when you subtract 91/65 from the sum of 96/40 and 11/99. Leave your answer as a simplified fraction.
LLemma 7B:
Reasoning: 96/40 + 11/99 = <<(96*99+11*40)/(40*99)>> <<(96*99+11*40)/(40*99)>> = <<(9552+440)/(40*99)>> <<(9552+440)/(40*99)>> = <<9992/3960>> 91/65 - 9992/3960 = <<(91*3960-9992*65)/(65*3960)>> <<(91*3960-9992*65)/(65*3960)>> = <<(3603800-6689760)/(65*3960)>> <<(3603800-6689760)/(65*3960)>> = <<-3085960/246000>> -3085960/246000 = <<-3085960/246000>> ### Answer: -3085960/246000
Expected answer: 10/9
Correct? No
Problem: Calculate the sum of the following expressions: 1) Divide 10 by 5 and add that result to 35 divided by 27. This will give you a value h. 2) Then, add 47 divided by 99 to h. This will give you a value p. What is the value of p?
LLemma 7B:
Reasoning: 1) 10/5+35/27 = <<10/5+35/27=10/5+35/27>> <<10/5+35/27=10/5+35/27>> = <<10/5+35/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+13/27>> = <<2+13/27=2+13/27>> <<2+13/27=2+1
Expected answer: 1120/297
Correct? No
Problem: Consider the fraction 90/81. Add it to 2/66 and simplify your answer to the simplest form. What is the result?
LLemma 7B:
Reasoning: 90/81 = <<90/81=10/9>>10/9 2/66 = <<2/66=1/33>>1/33 10/9 + 1/33 = <<10/9+1/33=10/9*33/33+1/33=330/297+1/33=331/297>>331/297 ### Answer: 331/297
Expected answer: 113/99
Correct? No
Problem: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, how long would both pieces of ribbon be together?
LLemma 7B:
Reasoning: 56/41 + 56/41 = <<56/41+56/41=112/41>>112/41 ### Answer: 112/41
Expected answer: 112/41
Correct? Yes
Problem: If Oliver receives two more pieces of ribbon, with each being 56/41 yards long, how long would all the pieces of ribbon be when added together?
LLemma 7B:
Reasoning: 56/41 + 56/41 + 56/41 = <<56/41+56/41+56/41=168/41>>168/41 ### Answer: 168/41
Expected answer: 224/41
Correct? No
Problem: If Oliver initially had a piece of ribbon that was 63/41 yards long instead of 56/41 yards, and he still receives a second piece of the same length, how long would both pieces of ribbon be when put together?
LLemma 7B:
Reasoning: 63/41 + 63/41 = <<63/41+63/41=126/41>>126/41 ### Answer: 126/41
Expected answer: 126/41
Correct? Yes
Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.
LLemma 7B:
Reasoning: 92/75 = <<92/75=1.28>>1.28 and 66/92 = <<66/92=0.72>>0.72. 1.28 + 0.72 = <<1.28+0.72=1.9999999999999998>>1.9999999999999998 ### Answer: 1.9999999999999998
Expected answer: 6707/3450
Correct? No
Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.
LLemma 7B:
Reasoning: 32/65 + 73/22 = <<32/65+73/22=1009/1430>>1009/1430 ### Answer: 1009/1430
Expected answer: 5449/1430
Correct? No
Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.
LLemma 7B:
Reasoning: 51/34 = <<51/34=1.5>>1.5 and 12/86 = <<12/86=0.14>>0.14. The difference between 51/34 and 12/86 is <<1.5-0.14=1.36>>1.36. ### Answer: 1.36
Expected answer: 117/86
Correct? No
Problem: First take the whole number 51 and add it to the fraction 93/8. Take that sum and add it to the fraction 58/44. What is the final result as a simplified fraction?
LLemma 7B:
Reasoning: 51+93/8 = <<51+93/8=51+11.125=62.125>>62.125 62.125+58/44 = <<62.125+58/44=62.125+1.22727272727273>>63.3527272727273 ### Answer: 63 21/44
Expected answer: 5627/88
Correct? No
Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.
LLemma 7B:
Reasoning: 82/5 - 98/25 = 164/25 - 98/25 = <<164/25-98/25=66/25=2 11/25>>2 11/25 ### Answer: 2 11/25
Expected answer: 312/25
Correct? No
Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.
LLemma 7B:
Reasoning: 64/50 = <<64/50=1.28>>1.28 and 70/22 = <<70/22=3.18>>3.18 (64 / 50) + (70 / 22) = <<64/50+70/22=1.28+3.18=4.46>>4.46 ### Answer: 4.46
Expected answer: 1227/275
Correct? No
Problem: John calculated s by adding 24 divided by 6 to 40 divided by 53. He then added s to itself to get b. Can you find the value of b?
LLemma 7B:
Reasoning: John calculated s by adding 24 divided by 6 to 40 divided by 53. <<24/6=4>>24/6=4 <<40/53=0.75>>40/53=0.75 <<4+0.75=4.75>>4+0.75=4.75 <<s=4.75>>s=4.75 John calculated s by adding 24 divided by 6 to 40 divided by 53. <<s+s=4.75+4.75=9.5>>s+s=4.75+4.75=9.5 ### Answer: 9.5
Expected answer: 504/53
Correct? No
Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.
LLemma 7B:
Reasoning: 80/90 = <<80/90=8/9>>8/9 52/11 = <<52/11=4/11>>4/11 (80/90) + (52/11) = <<8/9+4/11=32/99>>32/99 32/99 = <<32/99=1 23/99>>1 23/99 ### Answer: 1 23/99
Expected answer: 556/99
Correct? No
Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 12/18 + 91/74 = <<12/18 + 91/74>> = <<(12*74)/(18*74) + (91*18)/(74*18)>> = <<(848)/(1306) + (1658)/(1306)>> = <<(848 + 1658)/(1306)>> = <<(2506)/(1306)>> = <<2506/1306>> = <<2506/1306>> ### Answer: 2506/1306
Expected answer: 421/222
Correct? No
Problem: Find the sum of the fractions 7/2 and 51/25. Write your answer as a simple fraction.
LLemma 7B:
Reasoning: 7/2 + 51/25 = <<7/2 + 51/25 = 357/50>>357/50 ### Answer: 357/50
Expected answer: 277/50
Correct? No
Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.
LLemma 7B:
Reasoning: (68 / 69) + (93 / 7) = <<68/69+93/7>>11/7 3 / 46 = <<3/46>>1/14 11/7 + 1/14 = <<11/7+1/14>>15/14 ### Answer: 15/14
Expected answer: 13849/966
Correct? No
Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 31/98 + 60/4 = <<31/98 + 60/4>> = <<(31*4)/(98*4) + (60*98)/(4*98)>> = <<124/392 + 5880/392>> = <<124+5880/392>> = <<5904/392>> = <<154 1/2>> ### Answer: 154 1/2
Expected answer: 1501/98
Correct? No
Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.
LLemma 7B:
Reasoning: 3/2 = <<3/2=1.5>>1.5 and 24/36 = <<24/36=0.6666666666666666>>0.6666666666666666. ((3 / 2) + (24 / 36)) = <<(3/2)+(24/36)>>1.5+0.6666666666666666 = <<1.5+0.6666666666666666>>2.1666666666666665 ### Answer: 2.1666666666666665
Expected answer: 13/6
Correct? Yes
Problem: After completing the calculation for ((3 / 2) + (24 / 36)), add the result to 7/2 and give your answer as a simplified fraction.
LLemma 7B:
Reasoning: 7/2 = <<7/2=3.5>>3.5 and 2.1666666666666665 = <<2.1666666666666665=2.1666666666666665>>2.1666666666666665. (((3 / 2) + (24 / 36)) + (7 / 2)) = <<((3/2)+(24/36))+(7/2)>>(1.5+0.6666666666666666)+3.5 = <<1.5+0.6666666666666666+3.5>>5.1666666666666665 ### Answer: 5.1666666666666665
Expected answer: 17/3
Correct? No
Problem: Suppose instead of having 3/2, we had (32/36) as part of the calculation along with what you previously calculated. Can you determine the new total if you calculate ((3 / 2) + (32 / 36))? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 3/2 = <<3/2=1.5>>1.5 and 32/36 = <<32/36=0.8888888888888888>>0.8888888888888888. ((3 / 2) + (32 / 36)) = <<(3/2)+(32/36)>>1.5+0.8888888888888888 = <<1.5+0.8888888888888888>>2.3888888888888887 ### Answer: 2.3888888888888887
Expected answer: 43/18
Correct? No
Problem: Firstly, calculate the sum of 92/54 and 90/13, then from the result take away 46/41. What's the result as a simplified fraction?
LLemma 7B:
Reasoning: 92/54 + 90/13 = <<92/54+90/13=116/69>>116/69. 116/69 - 46/41 = <<116/69-46/41=10/131>>10/131. ### Answer: 10/131
Expected answer: 108002/14391
Correct? No
Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.
LLemma 7B:
Reasoning: 29/23 = <<29/23=1.21739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347
Expected answer: 58/23
Correct? No
Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 29/20 + 17/72 = <<29/20 + 17/72>> 29/20 + 17/72 = <<29/20 + 17/72>> ### Answer: 119/120
Expected answer: 607/360
Correct? No
Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.
LLemma 7B:
Reasoning: 36/27 = <<36/27=1.3333333333333333>>1.3333333333333333, 80/10 = <<80/10=8>>8, 73/79 = <<73/79=0.929588319644263>>0.929588319644263 ((36 / 27) + (80 / 10)) - (73 / 79) = <<(36/27)+(80/10)-(73/79)>>(1.3333333333333333+8)-0.929588319644263 = <<1.3333333333333333+8-0.929588319644263>>9.333333333333333-0.929588319644263 = <<9.333333333333333-0.929588319644263>>8.403755015998927 ### Answer: 8.403755015998927
Expected answer: 1993/237
Correct? No
Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.
LLemma 7B:
Reasoning: 86/71 = <<86/71=1.20>>1.20 91/75 = <<91/75=1.24>>1.24 1.20 + 1.24 = <<1.20+1.24=2.44>>2.44 ### Answer: 2.44
Expected answer: 12911/5325
Correct? No
Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)
LLemma 7B:
Reasoning: 21/75 = <<21/75=2/5>>2/5, 74/43 = <<74/43=2/3>>2/3, 10/62 = <<10/62=5/31>>5/31 ((21/75) + (74/43)) + (10/62) = <<(2/5)+(2/3)+(5/31)>> = <<(2/5)*(3/3)+(2/3)*(5/5)+(5/31)*(31/31)>> = <<(6/15)+(10/15)+(5/31)>> = <<(6/15)+(10/15)+(5/31)>> = <<(6+10+5)/(15)>> = <<(11+5)/(15)>> = <<(16/15)>> = <<(16/15)*(2/2)>> = <<(32/30)>> = <<(32/30)*(3/3)>> = <<(96/90)>> = <<(96/90)*(10/10)>> = <<(960/900)>> = <<(960/900)*(1/1)>> = <<(960/900)*(10/10)>> = <<(960/900)*(100/100)>> = <<(96000/90000)>> = <<(96000/90000)*(1/1)>> = <<(96000/90000)*(10/10)>> = <<(96000/90000)*(100/100)>> = <<(9600000/9000000)>> = <<(9600000/9000000)*(1/1)>> = <<(9600000/9000000)*(10/10)>> = <<(9600000/9000000)*(100/100)>> = <<(960000000/900000000)>> ### Answer: 960000000/900000000
Expected answer: 72056/33325
Correct? No
Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.
LLemma 7B:
Reasoning: 75/66 = <<75/66=1.1111111111111112>>1.1111111111111112 81/61 = <<81/61=1.3181818181818182>>1.3181818181818182 (75 / 66) + (81 / 61) = <<1.1111111111111112 + 1.3181818181818182>>2.43 ### Answer: 2.43
Expected answer: 3307/1342
Correct? No
Problem: Consider two identical fractions, t, each equal to sum of 53/18 and 21/99. Find the total sum, l, of these fractions and present your answer as a simple fraction.
LLemma 7B:
Reasoning: 53/18 + 21/99 = <<53/18 + 21/99 = 53/18 + 21/99 * 2/2 = 106/36 + 42/36 = 148/36 = 44/9>>44/9 l = 2t = <<2t = 2 * 44/9 = 88/9>>88/9 ### Answer: 88/9
Expected answer: 625/99
Correct? No
Problem: First, calculate the result of 58/49 + 31/34. Then, add that result to the fraction 74/38. What is the final result as a simple fraction?
LLemma 7B:
Reasoning: 58/49 + 31/34 = <<58/49+31/34=1.05>>1.05 74/38 + 1.05 = <<74/38+1.05=2.05>>2.05 ### Answer: 2.05
Expected answer: 127971/31654
Correct? No
Problem: Calculate the sum of 100 divided by 76 and 29 divided by 14. Please provide your answer as a simplified fraction or decimal.
LLemma 7B:
Reasoning: 100/76 + 29/14 = <<100/76 + 29/14>> ### Answer: 1.19047619047619
Expected answer: 901/266
Correct? No
Problem: Given that Evan has read 51/18 of his novel, and Olivia has read (8/42) after reading the same amount of novel as Evan, how much of the novel has Olivia read in total? Answer as a simplified fraction.
LLemma 7B:
Reasoning: Evan has read 51/18 of his novel. Olivia has read (8/42) of the same amount as Evan. Olivia has read (51/18) + (8/42) = <<(51/18) + (8/42) = (51*42)/(18*42) + (8*18)/(18*42) = (51*42 + 8*18)/(18*42) = (2042)/(756) = (2042/2)/(756/2) = (1021)/(378) = (378*2 + 193)/(378) = (378*2)/(378) + (193)/(378) = 2 + (193)/(378) = 2 + (193/378)>> (193/378) of the novel. Olivia has read (193/378) of the novel. ### Answer: (193/378)
Expected answer: 127/42
Correct? No
Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.
LLemma 7B:
Reasoning: 48/13 = <<48/13=3.62>>3.62 and 31/22 = <<31/22=1.36>>1.36 3.62+1.36 = <<3.62+1.36=4.98>>4.98 ### Answer: 4.98
Expected answer: 1459/286
Correct? No
Problem: First, find the value of 24/86 + 76/77. Subtract your answer from 27/6. Write out your process and show your work.
LLemma 7B:
Reasoning: 24/86 + 76/77 = <<24/86 + 76/77 = 1/2 + 1/1 = 3/2>>3/2 27/6 - 3/2 = <<27/6 - 3/2 = 9/2 - 3/2 = 6/2 = 3>>3 ### Answer: 3
Expected answer: 21415/6622
Correct? No
Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 73/39 + 49/14 = <<73/39 + 49/14>> = <<(73*14 + 49*39)/(39*14)>> = <<(1078 + 1841)/506>> = <<2919/506>> = <<583/101>> ### Answer: 583/101
Expected answer: 419/78
Correct? No
Problem: What is the sum of 75/65 and 7/39? Simplify your answer.
LLemma 7B:
Reasoning: 75/65 = <<75/65=1.12>>1.12 and 7/39 = <<7/39=0.17>>0.17. 1.12+0.17 = <<1.12+0.17=1.29>>1.29 ### Answer: 1.29
Expected answer: 4/3
Correct? No
Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?
LLemma 7B:
Reasoning: 79/1 - 30/92 = <<79-30/1*92=49/92>>49/92 61/63 - 49/92 = <<61/63-49/92=1/1860>>1/1860 ### Answer: 1/1860
Expected answer: 225191/2898
Correct? No
Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.
LLemma 7B:
Reasoning: 58/26 = <<58/26=2>>2 2+2 = <<2+2=4>>4 ### Answer: 4
Expected answer: 58/13
Correct? No
Problem: If Alex has 69/63 gallons of orange juice and he bought additional 77/5 gallons, giving him a total of 'k' gallons. Later, he received another 47/71 gallons of orange juice from Sally. How many gallons did Alex have in total?
LLemma 7B:
Reasoning: Alex has 69/63+77/5 = <<(69*5+77*63)/(63*5)=100>>100 gallons. ### Answer: 100
Expected answer: 127907/7455
Correct? No
Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 100/61 = <<100/61=1.6153846153846154>> 39/6 = <<39/6=6.5>>6.5 67/49 = <<67/49=1.3684210526315789>> ((100 / 61) + ((39 / 6) + (67 / 49))) = <<100/61+((39/6)+(67/49))>>1.6153846153846154+6.5+1.3684210526315789 = <<1.6153846153846154+6.5+1.3684210526315789>>8.883706143591734 ### Answer: 8.883706143591734
Expected answer: 56831/5978
Correct? No
Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.
LLemma 7B:
Reasoning: 85/1 = <<85/1=85>>85 and 83/69 = <<83/69=1>>1. 85+1 = <<85+1=86>>86 and 1+69 = <<1+69=70>>70. 86+70 = <<86+70=156>>156. ### Answer: 156
Expected answer: 5948/69
Correct? No
Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?
LLemma 7B:
Reasoning: 92/13 + 43/86 = <<92/13 + 43/86 = 1001/108>>1001/108 ### Answer: 1001/108
Expected answer: 197/26
Correct? No
Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?
LLemma 7B:
Reasoning: 67/32 + 10/98 = <<67/32 + 10/98 = 203/32>>203/32 ### Answer: 203/32
Expected answer: 3443/1568
Correct? No
Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.
LLemma 7B:
Reasoning: 59/52 + 70/32 = <<59/52+70/32=59/52+105/64=164/320=82/160=41/80>>41/80 ### Answer: 41/80
Expected answer: 691/208
Correct? No
Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?
LLemma 7B:
Reasoning: 48 divided by 5 subtracted from 11 divided by 65 is <<48/5-11/65=1.05>>1.05. 28 divided by 2 is <<28/2=14>>14. 1.05+14=<<1.05+14=15.05>>15.05. ### Answer: 15.05
Expected answer: 1523/65
Correct? No
Problem: What is the result when you add 20/52 to 75/82? Simplify your answer to the smallest possible fraction.
LLemma 7B:
Reasoning: 20/52 = <<20/52=4/13>>4/13 and 75/82 = <<75/82=15/14>>15/14. 4/13 + 15/14 = <<4/13+15/14=117/182>>117/182. 117/182 = <<117/182=117/91>>117/91. 117/91 = <<117/91=117/91>>117/91. ### Answer: 117/91
Expected answer: 1385/1066
Correct? No
Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 92/84 - 31/5 = <<92/84-31/5>> = <<(92-31)/84=61/84>> ### Answer: 61/84
Expected answer: 536/105
Correct? No
Problem: Calculate the following: Double the sum of 81/90 and 94/49.
LLemma 7B:
Reasoning: 81/90 + 94/49 = <<81/90+94/49=175/450=175/90=175/90=19/9>>19/9 Double the sum of 81/90 and 94/49 = <<2*(81/90+94/49)=2*19/9=38/9>>38/9 ### Answer: 38/9
Expected answer: 1381/245
Correct? No
Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.
LLemma 7B:
Reasoning: 69/21 = <<69/21=3>>3 and 10/92 = <<10/92=1/9>>1/9. The difference between 69/21 and 10/92 is <<3-1/9=22/9>>22/9. ### Answer: 22/9
Expected answer: 1023/322
Correct? No
Problem: First, find the result of (26 / 87) + (92 / 88). Then add the result to (26 / 57). What's the answer?
LLemma 7B:
Reasoning: (26 / 87) + (92 / 88) = <<26/87+92/88>>1.25 (26 / 57) = <<26/57>>0.44 1.25 + 0.44 = <<1.25+0.44>>1.69 ### Answer: 1.69
Expected answer: 21825/12122
Correct? No
Problem: What is the result if you add 78/66, 28/6, and 90/34 together? Please provide your answer as a simplified fraction.
LLemma 7B:
Reasoning: 78/66 + 28/6 + 90/34 = <<78/66+28/6+90/34>> ### Answer: 100/11
Expected answer: 4766/561
Correct? No
Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.
LLemma 7B:
Reasoning: 12/7 = <<12/7=1.71428571428571428571428571428571>> 9/23 = <<9/23=0.39130434782608695652173913043478>> 1.71428571428571428571428571428571 - 0.39130434782608695652173913043478 = <<1.71428571428571428571428571428571 - 0.39130434782608695652173913043478=1.3229513664405357692309577982129>> ### Answer: 1.3229513664405357692309577982129
Expected answer: 213/161
Correct? No
Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.
LLemma 7B:
Reasoning: 95/18 + 51/61 = <<95/18 + 51/61>> ### Answer: 119/109
Expected answer: 6713/1098
Correct? No
Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.
LLemma 7B:
Reasoning: 93/46 - 51/84 = (93 x 84)/(46 x 84) - (51 x 46)/(84 x 46) = <<(93 x 84 - 51 x 46)/(46 x 84)>>. (93 x 84 - 51 x 46)/(46 x 84) = (93 x 84)/(46 x 84) - (51 x 46)/(84 x 46) = 93/46 - 51/84 = <<93/46 - 51/84>>. ### Answer: 93/46 - 51/84
Expected answer: 911/644
Correct? Yes
Problem: Following the previous question, now calculate the result of the subtraction (93 / 46) - (51 / 84) and then add the fraction 35 / 27 to the result. What is the final answer when simplified?
LLemma 7B:
Reasoning: 93/46 - 51/84 + 35/27 = (93 x 84)/(46 x 84) - (51 x 46)/(84 x 46) + (35 x 46)/(27 x 46) = <<(93 x 84 - 51 x 46 + 35 x 46)/(46 x 84)>>. (93 x 84 - 51 x 46 + 35 x 46)/(46 x 84) = (93 x 84)/(46 x 84) - (51 x 46)/(84 x 46) + (35 x 46)/(27 x 46) = 93/46 - 51/84 + 35/27 = <<93/46 - 51/84 + 35/27>>. ### Answer: 93/46 - 51/84 + 35/27
Expected answer: 47137/17388
Correct? No
Problem: Following the previous question, let's imagine that instead of subtracting (51/84), you were actually subtracting (78/84) from (93/46). What would be the result in that case? Simplify your answer to the simplest form.
LLemma 7B:
Reasoning: 93/46 - 78/84 = (93 x 84)/(46 x 84) - (78 x 46)/(84 x 46) = <<(93 x 84 - 78 x 46)/(46 x 84)>>. (93 x 84 - 78 x 46)/(46 x 84) = (93 x 84)/(46 x 84) - (78 x 46)/(84 x 46) = 93/46 - 78/84 = <<93/46 - 78/84>>. ### Answer: 93/46 - 78/84
Expected answer: 176/161
Correct? No
Problem: Calculate the sum of the fractions 12/70 and 84/9. Please provide your answer in simplified form.
LLemma 7B:
Reasoning: 12/70 + 84/9 = <<12/70 + 84/9 = 12/70 + 16/15 = 4/35 + 4/3 = 8/35 = 8/35 * 7/7 = 56/245>>56/245 ### Answer: 56/245
Expected answer: 998/105
Correct? No
Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?
LLemma 7B:
Reasoning: 32/3 - 40/92 = <<32/3 - 40/92 = 1.05>>1.05 1.05 x 2 = <<1.05*2=2.1>>2.1 ### Answer: 2.1
Expected answer: 1412/69
Correct? No
Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.
LLemma 7B:
Reasoning: 79/24 + 79/24 = <<79/24+79/24=79/12>>79/12. ### Answer: 79/12
Expected answer: 79/12
Correct? Yes
Problem: In continuation to the previous problem, now find out what is the sum of two times the previously found sum. In other words, calculate (79/24 + 79/24) + (79/24 + 79/24). Please answer as a simplified fraction.
LLemma 7B:
Reasoning: (79/24 + 79/24) + (79/24 + 79/24) = <<(79/24+79/24)+(79/24+79/24)=79/12+79/12>>79/6. ### Answer: 79/6
Expected answer: 79/6
Correct? Yes
Problem: In the previous problem, you added together two fractions of 79/24. Now, consider if those were fractions of 79/20 instead. What would be the total if you added together two fractions of 79/20? Please express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 79/20 + 79/20 = <<79/20+79/20=79/10>>79/10. ### Answer: 79/10
Expected answer: 79/10
Correct? Yes
Problem: What is the sum of 91/76 and 12/22? Please simplify your fraction.
LLemma 7B:
Reasoning: 91/76 + 12/22 = <<91/76 + 12/22>> = <<(91*22)/(76*22) + (12*76)/(22*76)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 + 12*76)/(76*22)>> = <<(91*22 +
Expected answer: 1457/836
Correct? No
Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?
LLemma 7B:
Reasoning: 88/93+6/47 = <<88/93+6/47=1.0000000000000002>>1.0000000000000002 1.0000000000000002+92/4 = <<1.0000000000000002+92/4=25.5>>25.5 ### Answer: 25.5
Expected answer: 105227/4371
Correct? No
Problem: Calculate the sum of 95/83 and the result of 52/21 + 75/67. Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 95/83 + 52/21 + 75/67 = <<95/83 + 52/21 + 75/67>> ### Answer: 111/16
Expected answer: 553562/116781
Correct? No
Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 73/27 = <<73/27=2>>2 2 - (23/48) = <<2-(23/48)=104/48>>104/48 ### Answer: 104/48
Expected answer: 961/432
Correct? No
Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.
LLemma 7B:
Reasoning: 78/2 = <<78/2=39>>39 and 70/23 = <<70/23=3.0434782608695652>>3.0434782608695652 (78/2) - (70/23) = <<39-3.0434782608695652=35.956521739130435>>35.956521739130435 ### Answer: 35.956521739130435
Expected answer: 827/23
Correct? Yes
Problem: Continue from the previous problem where we calculated (78 / 2) - (70 / 23). Using the result from that equation, add it to 92/67. State your answer as a simplified fraction. What do you get?
LLemma 7B:
Reasoning: 92/67 = <<92/67=1.35135135135135>>1.35135135135135 (78/2) - (70/23) + 92/67 = <<35.956521739130435+1.35135135135135=37.30787299048378>>37.30787299048378 ### Answer: 37.30787299048378
Expected answer: 57525/1541
Correct? No
Problem: In the previous problem, we calculated the value of the expression by subtracting (70 / 23) from (78 / 2). This time, suppose we replaced the total number of parts originally (78 in the previous problem) with a new value, 36. Make that substitution and then calculate the expression (36 / 2) - (70 / 23). What is your answer now?
LLemma 7B:
Reasoning: 36/2 = <<36/2=18>>18 and 70/23 = <<70/23=3.0434782608695652>>3.0434782608695652 (36/2) - (70/23) = <<18-3.0434782608695652=14.956521739130435>>14.956521739130435 ### Answer: 14.956521739130435
Expected answer: 344/23
Correct? No
Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.
LLemma 7B:
Reasoning: 34/1 = <<34/1=34>>34 and 53/4 = <<53/4=13>>13. 34+13 = <<34+13=47>>47 ### Answer: 47
Expected answer: 189/4
Correct? No
Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 3/36 = <<3/36=1/12>>1/12 and 97/96 = <<97/96=1/1>><<1/1+1/12=1/12+1/1=13/12=11/6>>11/6 The sum of 3/36 and 97/96 is <<11/6>>11/6. ### Answer: 11/6
Expected answer: 35/32
Correct? No
Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.
LLemma 7B:
Reasoning: 92/95 = <<92/95=0.96225>>0.96225 4/74 = <<4/74=0.05263>>0.05263 0.96225 + 0.05263 = <<0.96225+0.05263=0.99288>>0.99288 ### Answer: 0.99288
Expected answer: 3594/3515
Correct? No
Problem: If the value of a variable 'v' is 69/47, what is the value of 'd' if 'd' equals 88/72 + 'v'? Please write your answer as a fraction.
LLemma 7B:
Reasoning: 88/72 = <<88/72=11/9>>11/9 <<d=11/9+69/47=11*47/9*47+69*9/47*9=53/9>>53/9 ### Answer: 53/9
Expected answer: 1138/423
Correct? No
Problem: Let's say there is a wholesaler who has 41/26 barrels of olive oil in their warehouse. They sell a portion of the oil which is equivalent to 41/72 barrels. How much olive oil do they have now? Express your answer as a simple fraction.
LLemma 7B:
Reasoning: 41/72 - 41/26 = <<41/72-41/26=1/26>>1/26 barrels of oil. Therefore, the wholesaler has <<41/26+1/26=42/26>>42/26 barrels of oil now. ### Answer: 42/26
Expected answer: 943/936
Correct? No
Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.
LLemma 7B:
Reasoning: 85/75 = <<85/75=1.1>>1.1 and 88/56 = <<88/56=1.5>>1.5 1.1+1.5 = <<1.1+1.5=2.6>>2.6 ### Answer: 2.6
Expected answer: 284/105
Correct? No
Problem: What is the result of adding 12 over 33 to 49 over 2? Write your answer as a mixed fraction.
LLemma 7B:
Reasoning: 12/33 + 49/2 = <<12/33 + 49/2 = 12/33 + 245/66 = 12/33 + 41/33 = 53/33 = 17/11 = 16 2/11>>16 2/11 ### Answer: 16 2/11
Expected answer: 547/22
Correct? No
Problem: What is the result of adding two fractions, where each fraction is 78/65?
LLemma 7B:
Reasoning: 78/65 + 78/65 = <<78/65+78/65=156/65>>156/65 ### Answer: 156/65
Expected answer: 12/5
Correct? Yes
Problem: After obtaining the result from the previous problem, where you added two fractions both equal to 78/65, what would you get if you add the result to 71/32?
LLemma 7B:
Reasoning: 156/65 + 71/32 = <<156/65+71/32=156/65+156/32>>156/65+156/32 ### Answer: 156/65+156/32
Expected answer: 739/160
Correct? No
Problem: Suppose that instead of having two fractions both equal to 78/65 like in the previous problem, they were both equal to 78/78. What would be the result of adding these two fractions together?
LLemma 7B:
Reasoning: 78/78 + 78/78 = <<78/78+78/78=156/78>>156/78 ### Answer: 156/78
Expected answer: 2
Correct? Yes
Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.
LLemma 7B:
Reasoning: 16/7 + 11/90 = <<16/7 + 11/90 = 144/90 + 11/90 = (144+11)/90 = 155/90 = 31/18>>31/18 ### Answer: 31/18
Expected answer: 1517/630
Correct? No