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.
Gemma 2B:
### Answer: 103/56
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?
Gemma 2B:
Reasoning: 88/9 - 28/65 = 88/9 - 4/65 = (88/9)(1/65) - (4/65)(1/9) = 1440/585 - 40/585 = 1400/585. The final answer is 1400/585.
Expected answer: 210434/21645
Correct? No
Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?
Gemma 2B:
Reasoning: (63 / 41) + (44 / 50) = (189 / 205) + (88 / 205) = 277 / 205. The result of (63 / 41) + (44 / 50) when simplified to the lowest terms is 277 / 205.
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.
Gemma 2B:
Reasoning: After Emily added 41/77 of another cake to the 71/41 cake, the total was 71/41 + 41/77 = <<71/41+41/77=142/59>>142/59 cake is left. ### Answer: 142/59
Expected answer: 7148/3157
Correct? No
Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.
Gemma 2B:
Reasoning: 10/65 + 56/35 = (10/65) + (56/35) = 60/65 = 4/5. ### Answer: 4/5
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.
Gemma 2B:
Reasoning: 75/81 + 97/47 = (75*47)/(81*47) + (97*81)/(47*81) = 3125/3405. ### Answer: 3125/3405
Expected answer: 3794/1269
Correct? No
Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.
Gemma 2B:
Reasoning: 88/1 - 38/53 = (88)(53)/(1)(53) - (38)(1)(1) = 4888/53 - 38/53 = 4510/53. ### Answer: 4510/53
Expected answer: 4626/53
Correct? No
Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?
Gemma 2B:
Reasoning: (80/94) + (78/59) = (80/94) + (14/59) = (408+140)/940 = 548/940 = 0.58. ### Answer: 0.58
Expected answer: 6026/2773
Correct? No
Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 89/56 + 48/50 = (89 x 50)/(56 x 50) + (48 x 56)/(56 x 50) = 4450/2880 = 11/8. ### Answer: 11/8
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.
Gemma 2B:
Reasoning: (96/11 + 12/5) - 38/87 = (192/55) - (38/87) = (154/55) - (4/55) = 150/55 = 2.7. ### Answer: 2.7
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.
Gemma 2B:
Reasoning: 82/9 - 82/63 = 82(1/9 - 1/63) = 82(5/63) = 5/3. ### Answer: 5/3
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.
Gemma 2B:
Reasoning: 23/3 - (80/91 + 26/24) = 23/3 - (40/36) = 23/3 - 10/12 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23/3 - 5/6 = 23
Expected answer: 6229/1092
Correct? No
Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?
Gemma 2B:
Reasoning: 37/18 = <<(37/18)::1::(18/37)>>1 and 24/60 = <<(24/60)::1::(60/24)>>1. Therefore, 37/18 + 24/60 = 1 + 1 = 2. ### Answer: 2
Expected answer: 221/90
Correct? No
Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 33/41 = 33/41, and 95/62 = 95/62. The sum is 33/41 + 95/62 = (33)(62)/(41)(62) + (95)(41)/(62)(41) = 195/247.
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.
Gemma 2B:
Reasoning: (30/11) + (72/38) = (30/11) + (18/38) = (30+18)/11 = 48/11. (81/34) + (48/11) = (81+48)/34 = 129/34. The final answer is 129/34.
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.
Gemma 2B:
Reasoning: (64 / 34) + (3 / 24) = 1.8 + 0.125 = 1.925. (41 / 96) + 1.925 = 0.4375 + 1.925 = 2.3625. Therefore, (64 / 34) + (3 / 24) + (41 / 96) = 1.925 + 1.925 + 2.3625 = 6.25.
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?
Gemma 2B:
### Answer: 135/91
Expected answer: 307360/106799
Correct? No
Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.
Gemma 2B:
Reasoning: 27/20 = <<27/20=0.135>>0.135 and 14/66 = <<14/66=0.222>>0.222. Adding these fractions, we get 0.135 + 0.222 = 0.357.
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.
Gemma 2B:
Reasoning: (32/14) - (22/47) = 32/14 - 22/47 = (32 * 47)/(14 * 47) - (22 * 14)/(47 * 14) = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576 = 140/576 - 294/576
Expected answer: 598/329
Correct? No
Problem: What is the sum of 74/61 and 41/53 expressed in fractions?
Gemma 2B:
Reasoning: 74/61 + 41/53 = (74*53)/(61*53) + (41*61)/(61*53) = 3802/3203. ### Answer: 3802/3203
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?
Gemma 2B:
Reasoning: 94 / 2 - 74 / 57 = <<(94/2)-(74/57)>> = <<(47)(2)/(1)(57) >> = 196/57. Then add 56 / 97 to the result: 196/57 + 56 / 97 = 252/57.
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.
Gemma 2B:
Reasoning: 14/89 + (24/34 + 44/87) = 14/89 + 24/34 + 44/87 = 14/89 + 36/89 = 50/89.
Expected answer: 180194/131631
Correct? No
Problem: What would you get if you add 73/30 to 8/60?
Gemma 2B:
Reasoning: 73/30 + 8/60 = (73/30) + (8/60) = (73+8)/60 = 81/60. ### Answer: 1.35
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.
Gemma 2B:
### Answer: 127/78
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.
Gemma 2B:
Reasoning: 91/16 - 76/30 = <<(91/16)-(76/30) = 0.375>>0.375. 18/44 + 0.375 = <<(18/44)+(0.375) = 0.4375>>0.4375. The final answer is 0.4375.
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.
Gemma 2B:
Reasoning: ((8 / 91) + (49 / 5)) = (80/455) + (96/455) = 176/455. (32 / 76) = (32/76). Therefore, the final answer is 176/455 - 32/76 = 144/455.
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.
Gemma 2B:
Reasoning: (75/45) + (5/49) = 1.5 + 0.1 = 1.6. 1.6 + 3/58 = 9/58 + 3/58 = 12/58. Therefore, the answer is 12/58.
Expected answer: 15521/8526
Correct? No
Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.
Gemma 2B:
Reasoning: (43 / 15) - (33 / 95) = (695/150) - (33/95) = (695-33)/150 = 662/150. The answer in its lowest terms is 4.4.
Expected answer: 718/285
Correct? No
Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.
Gemma 2B:
Reasoning: (78 / 45) + (89 / 36) = (19/60) + (26/72) = (45/72). Therefore, the sum is 45/72.
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?
Gemma 2B:
Answer: 13/14
Expected answer: 1066/629
Correct? No
Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: 86/35 = <<86/35>>1 and 68/85 = <<68/85>>1. The sum is 1+1 = <<1+1=2>>2. ### Answer: 2
Expected answer: 114/35
Correct? No
Problem: What is the sum of 99/53 and 67/94 in simplest form?
Gemma 2B:
Reasoning: 99/53 = <<99/53=1.97>>1.97 and 67/94 = <<67/94=0.7>>0.7. The sum is 1.97+0.7 = <<1.97+0.7=2.67>>2.67. ### Answer: 2.67
Expected answer: 12857/4982
Correct? No
Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?
Gemma 2B:
Reasoning: 74/27 - 56/33 = (74/27) รท (56/33) = (74/27) * (33/56) = 11/8. ### Answer: 11/8
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.
Gemma 2B:
Reasoning: 96/40 = <<96/40>>1, 11/99 = <<11/99>>0.1. Therefore, 96/40 + 11/99 = 1 + 0.1 = 1.1. ### Answer: 1.1
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?
Gemma 2B:
### Answer: 10.5 Reasoning: 10/5 + 35/27 = 2 + 1.33 = 3.33. Then, 47/99 + 3.33 = 4.73.
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?
Gemma 2B:
Reasoning: 90/81 + 2/66 = 90/81 + 1/33 = 30/33 = 10/11. The result is 10/11.
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?
Gemma 2B:
Reasoning: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, then the two pieces of ribbon would be together for 56/41 + 1 = <<56/41+1=1.22>>1.22 yards long. ### Answer: 1.22
Expected answer: 112/41
Correct? No
Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.
Gemma 2B:
Reasoning: 92/75 + 66/92 = (92*92)/(75*92) + (66*75)/(92*75) = 848/6600 = 4/30. ### Answer: 4/30
Expected answer: 6707/3450
Correct? No
Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.
Gemma 2B:
Reasoning: 32/65 + 73/22 = (32*22)/(65*22) + (73*65)/(22*65) = 64/130 + 455/130 = 519/130. ### Answer: 519/130
Expected answer: 5449/1430
Correct? No
Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.
Gemma 2B:
Reasoning: 51/34 = 1.5 and 12/86 = 0.13. The difference between 51/34 and 12/86 is 1.5 - 0.13 = 1.37. ### Answer: 1.37
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?
Gemma 2B:
### Answer: 141/92
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.
Gemma 2B:
Reasoning: Subtract the fractions by finding a common denominator. The least common multiple of 5 and 25 is 100. Convert the fractions to equivalent fractions with the same denominator: 82/5 = 164/100 and 98/25 = 392/100. Subtract the fractions: 164/100 - 392/100 = 164/100 - 392/100 = -228/100. ### Answer: -228
Expected answer: 312/25
Correct? No
Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.
Gemma 2B:
Reasoning: (64 / 50) + (70 / 22) = (128/100) + (35/110) = (163/110). ### Answer: 163/110
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?
Gemma 2B:
Reasoning: 24/6 + 40/53 = s. s = 24/6 + 40/53 = 40/53. Therefore, b = 40/53.
Expected answer: 504/53
Correct? No
Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.
Gemma 2B:
Reasoning: (80/90) + (52/11) = 8/9 + 4/5 = (40+36)/45 = 76/45 = 14/5. Therefore, the mixed number is 14 1/5.
Expected answer: 556/99
Correct? No
Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: 12/18 = 4/9, and 91/74 = 7/7. Adding these fractions, we get 4/9 + 7/7 = 56/68 = 7/8. ### Answer: 7/8
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.
Gemma 2B:
Reasoning: 7/2 = <<7/2>> and 51/25 = <<51/25>>. The sum of these fractions is 7/2 + 51/25 = (7)(5) + (51)(2) / (25)(5) = 35 + 10.2 = 45.2. ### Answer: 45.2
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.
Gemma 2B:
Reasoning: The expression is a monomial because it has only one term. The terms are added together, resulting in a monomial expression. (68 / 69) + (93 / 7) = (48/34) + (138/49) = 16/49 + 138/49 = 156/49 = 3.5. ### Answer: 3.5
Expected answer: 13849/966
Correct? No
Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 31/98 + 60/4 = (31*4)/(98*4) + (60*98)/(4*98) = 126/392 + 544/392 = 670/392 = 11/8. ### Answer: 11/8
Expected answer: 1501/98
Correct? No
Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.
Gemma 2B:
Reasoning: The answer is the average of the fractions 3/2 and 24/36. (3/2) + (24/36) = (6 + 8) / 36 = 14 / 36 = 7 / 18. Therefore, the answer is 7 / 18.
Expected answer: 13/6
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?
Gemma 2B:
### Answer: 1/2
Expected answer: 108002/14391
Correct? No
Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.
Gemma 2B:
Reasoning: Let x be the value of 29/23. Then, 2x = 29/23 * 2 = 29/11. Therefore, x = 29/11 / 2 = 29/22. ### Answer: 29/22
Expected answer: 58/23
Correct? No
Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 29/20 = <<29/20>>0.145, and 17/72 = <<17/72>>0.024. The sum is 0.145 + 0.024 = 0.169, which is a simplified fraction of 63/40.
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.
Gemma 2B:
Reasoning: (36 / 27) + (80 / 10) - (73 / 79) = 1.33 + 8 - 0.92 = 1.39. ### Answer: 1.39
Expected answer: 1993/237
Correct? No
Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.
Gemma 2B:
Reasoning: (86 / 71) + (91 / 75) = 1.25 + 1.18 = 2.43. ### Answer: 2.43
Expected answer: 12911/5325
Correct? No
Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)
Gemma 2B:
Reasoning: First, we add the fractions with denominators of 75, 43, and 62: (21/75) + (74/43) + (10/62) = (153 + 342 + 170) / 315 = 565 / 315 = 1.83.
Expected answer: 72056/33325
Correct? No
Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.
Gemma 2B:
Reasoning: The least common multiple of 66 and 61 is 396. So, we can rewrite the fractions as: (75/66) = 75/66 and (81/61) = 81/61 Then, we can add them: 75/66 + 81/61 = (525 + 515) / 396 = 1040/396 = 10/9. The final answer is 10/9.
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.
Gemma 2B:
Reasoning: We can rewrite the fractions as: t = (53/18) + (21/99) = (99*53 + 18*21) / (18*99) = 53/18. Therefore, l = 53/18. ### Answer: 53/18
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?
Gemma 2B:
Reasoning: 58/49 + 31/34 = <<58/49+31/34=109/147>>109/147. Finally, add 109/147 to 74/38 = <<109/147+74/38=183/147>>183/147.
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.
Gemma 2B:
Reasoning: 100/76 = <<100/76=1.25>>1.25 and 29/14 = <<29/14=2.07>>2.07. The sum of 100/76 and 29/14 is 1.25 + 2.07 = <<1.25+2.07=3.32>>3.32.
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.
Gemma 2B:
Reasoning: Evan has read 51/18 of his novel, which is equivalent to 51/(18 * 4) = 51/72. Olivia has read (8/42) of the novel after reading the same amount of novel as Evan, which is equivalent to 8/(42 * 4) = 8/168. Therefore, Olivia has read 8/168 of the novel in total. ### Answer: 8/168
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.
Gemma 2B:
Reasoning: 48/13 = <<48/13=4>>4 and 31/22 = <<31/22=1.41>>1.41. The sum is 4+1.41 = 5.41.
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.
Gemma 2B:
Reasoning: 24/86 + 76/77 = 24/86 + 76/77 = 24/86 + 76/77 = 27/6.
Expected answer: 21415/6622
Correct? No
Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.
Gemma 2B:
Reasoning: 73/39 + 49/14 = (73*14)/(39*14) + (49*39)/(14*39) = 962/516 = 0.194. ### Answer: 0.194
Expected answer: 419/78
Correct? No
Problem: What is the sum of 75/65 and 7/39? Simplify your answer.
Gemma 2B:
Reasoning: 75/65 = <<75/65=1.25>>1.25 and 7/39 = <<7/39=0.18>>0.18. The sum is 1.25+0.18 = <<1.25+0.18=1.43>>1.43.
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?
Gemma 2B:
### Answer: 0.11
Expected answer: 225191/2898
Correct? No
Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.
Gemma 2B:
Reasoning: 58 / 26 = <<58/26=2>>2, and 58 / 26 = <<58/26=2>>2. Therefore, (58 / 26) + (58 / 26) = 2 + 2 = 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?
Gemma 2B:
Reasoning: Alex bought 69/63 + 77/5 = <<69/63+77/5>> gallons. After receiving 47/71 gallons from Sally, Alex had 69/63 + 77/5 - 47/71 = <<(69/63 + 77/5 - 47/71)>> gallons. ### Answer: 72
Expected answer: 127907/7455
Correct? No
Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.
Gemma 2B:
Reasoning: (100/61) + ((39/6) + (67/49)) = 1.64 + 6.57 + 1.43 = 9.64. ### Answer: 9.64
Expected answer: 56831/5978
Correct? No
Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.
Gemma 2B:
Reasoning: 85/1 = 85 and 83/69 = 0.125. The sum is 85 + 0.125 = 85.125. ### Answer: 85.125
Expected answer: 5948/69
Correct? No
Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?
Gemma 2B:
Reasoning: 92/13 = <<92/13>> and 43/86 = <<43/86>>. The sum is 92/13 + 43/86 = <<92/13 + 43/86>> = <<(92ร86+43ร13)/(13ร86)>> = <<(784+543)/(1326>> = <<1327/1326>> = 1.
Expected answer: 197/26
Correct? No
Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?
Gemma 2B:
Reasoning: 67/32 = <<67/32>> and 10/98 = <<10/98>>. The sum is 67/32 + 10/98 = <<67/32 + 10/98>> = <<(67ร98+10ร32)/32ร98>> = <<(6562+320)/32ร98>> = <<6882/32ร98>> = <<21.5>>.
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.
Gemma 2B:
Reasoning: 59/52 + 70/32 = (59 x 32)/(52 x 32) + (70 x 52)/(32 x 52) = 176/160 + 360/160 = 536/160 = 13/4. ### Answer: 13/4
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?
Gemma 2B:
### Answer: 12
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.
Gemma 2B:
Reasoning: 20/52 = <<20/52=1/2>>1/2, 75/82 = <<75/82=5/8>>5/8. Adding 1/2 and 5/8 gives 13/8. The smallest possible fraction of 13/8 is 1/8. ### Answer: 1/8
Expected answer: 1385/1066
Correct? No
Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 31/5 - 92/84 = (31*84)/(5*84) - (92*5)/(84*5). = 2561/4200 - 46,8/4200 = 2095/4200. ### Answer: 2095/4200
Expected answer: 536/105
Correct? No
Problem: Calculate the following: Double the sum of 81/90 and 94/49.
Gemma 2B:
Reasoning: Double the sum of 81/90 and 94/49 is: (81/90 + 94/49) * 2 = (81/90 + 94/49) * 2/1 = (162/360 + 85/360) = 247/360. ### Answer: 247/360
Expected answer: 1381/245
Correct? No
Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.
Gemma 2B:
Reasoning: 69/21 - 10/92 = <<(69/21)-(10/92)>> = <<(69/21)-(10/92)>> = <<(69-10)/21-92>> = <<59/21-92>> = <<(59-92)/21>> = <<-33/21>>. ### Answer: -33/21
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?
Gemma 2B:
Reasoning: (26 / 87) + (92 / 88) = 0.29 + 0.10 = 0.39. Then, add 0.39 to 26 / 57 = 0.52. ### Answer: 0.52
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.
Gemma 2B:
Reasoning: 78/66 = 1.33, 28/6 = 4.8, and 90/34 = 2.73. Adding these fractions gives 1.33 + 4.8 + 2.73 = 9.83. The result is 9.83 as a simplified fraction.
Expected answer: 4766/561
Correct? No
Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.
Gemma 2B:
Reasoning: The least common multiple of 7 and 23 is 69. So, (12/7) - (9/23) = (12 * 23/7 * 23) - (9 * 7/23 * 7). Simplifying the numerator, we get: (12/7) - (9/23) = (276/165) - (81/165) = (276 - 81)/165 = 195/165. ### Answer: 1.22
Expected answer: 213/161
Correct? No
Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.
Gemma 2B:
Reasoning: 95/18 = 5/2, and 51/61 = 3/17. The sum is 5/2 + 3/17 = (5)(17) + (3)(2) = 85 + 6 = 91. ### Answer: 91
Expected answer: 6713/1098
Correct? No
Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.
Gemma 2B:
Reasoning: Subtract the numerators and keep the denominator the same. (93 / 46) - (51 / 84) = 93/46 - 51/84 = (93/46) - (7/46) = 86/46 = 19/21.
Expected answer: 911/644
Correct? No
Problem: Calculate the sum of the fractions 12/70 and 84/9. Please provide your answer in simplified form.
Gemma 2B:
Reasoning: We can add the numerators and keep the denominator the same. 12/70 + 84/9 = (12ร9)/(70ร9) + (84ร7)/(9ร70) = 108/630 + 596/630 = 604/630 = 4/3. ### Answer: 4/3
Expected answer: 998/105
Correct? No
Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?
Gemma 2B:
Reasoning: 32/3 = 16, 40/92 = 0.4166, and 0.4166 x 2 = 0.8332. Therefore, 32/3 - 40/92 = 16 - 0.8332 = 15.16.
Expected answer: 1412/69
Correct? No
Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.
Gemma 2B:
Reasoning: 79/24 + 79/24 = 158/24 = 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.
Gemma 2B:
### Answer: 158/24
Expected answer: 79/6
Correct? No
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.
Gemma 2B:
### Answer: 79/20
Expected answer: 79/10
Correct? No
Problem: What is the sum of 91/76 and 12/22? Please simplify your fraction.
Gemma 2B:
Reasoning: 91/76 + 12/22 = (91/76) + (12/76) = 103/76. The sum of 91/76 and 12/22 is 103/76.
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?
Gemma 2B:
### Answer: 100/47
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.
Gemma 2B:
Reasoning: 95/83 = 0.113, 52/21 = 2.42, 75/67 = 1.15. The sum is 0.113 + 2.42 + 1.15 = 5.68. ### Answer: 5.68
Expected answer: 553562/116781
Correct? No
Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 73/27 - 23/48 = (2196/81 - 915/81) = (1281/81). Therefore, (73/27 - 23/48) = 1281/81.
Expected answer: 961/432
Correct? No
Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.
Gemma 2B:
Reasoning: (78 / 2) - (70 / 23) = (39 / 10) - (35/ 103) = (39/10) - (35/103) = (39 - 35) / (10) = 4/103. ### Answer: 4/103
Expected answer: 827/23
Correct? No
Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.
Gemma 2B:
Reasoning: 34/1 + 53/4 = (34 x 4) / (1 x 4) + (53 x 1) / (4 x 1) = 136/4 + 53/4 = 189/4. ### Answer: 47 1/4
Expected answer: 189/4
Correct? Yes
Problem: Following the result of the previous problem, what is the sum of 24/67 and the result you got from adding 34/1 to 53/4? Express your answer as a mixed number.
Gemma 2B:
Reasoning: 24/67 + (189/4) = (24 x 4) / (67 x 4) + (189 x 7) / (4 x 7) = 96/291 + 147/28 = 243/291. ### Answer: 243/291
Expected answer: 12759/268
Correct? No
Problem: Let's reconsider the problem where you were adding fractions. Previously, it was asked to add 34/1 to 53/4. Now consider whether it may have been 34/97 instead of 34/1. What will be the result if you add 34/97 to 53/4? Write your answer as a mixed number.
Gemma 2B:
Reasoning: 34/97 + 53/4 = (34 x 4) / (97 x 4) + (53 x 97) / (4 x 97) = 136/394 + 471/394 = 607/394. ### Answer: 16 3/4
Expected answer: 5277/388
Correct? No
Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 3/36 = 1/12 and 97/96 = 13/16. The sum is 1/12 + 13/16 = 41/48. ### Answer: 41/48
Expected answer: 35/32
Correct? No
Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.
Gemma 2B:
Reasoning: The numerator of the first fraction is 92/95, and the numerator of the second fraction is 4/74. Adding these fractions gives 92/95 + 4/74 = (720+60)/950 = 780/950 = 7/5. ### Answer: 7/5
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.
Gemma 2B:
Reasoning: $$d = \frac{88}{72} + 69/47$$ $$d = \frac{88}{72} + \frac{47}{72}$$ $$d = \frac{135}{72}$$ ### Answer: 1.906
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.
Gemma 2B:
Reasoning: 41/72 = 7/12. After selling the oil, they have 41/72 - 7/12 = 7/12 barrels of olive oil.
Expected answer: 943/936
Correct? No
Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.
Gemma 2B:
Reasoning: 85/75 = <<85/75=1.2>>1.2 and 88/56 = <<88/56=1.6>>1.6. The sum is 1.2+1.6 = <<1.2+1.6=2.8>>2.8.
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.
Gemma 2B:
Reasoning: 12/33 + 49/2 = (12*2)/(33*2) + (49*3)/(2*33) = 24/66 + 147/66 = 171/66. ### Answer: 171/66
Expected answer: 547/22
Correct? No
Problem: What is the result of adding two fractions, where each fraction is 78/65?
Gemma 2B:
Answer: 123/65 Reasoning: 78/65 + 78/65 = 156/65 = 123/65.
Expected answer: 12/5
Correct? No
Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.
Gemma 2B:
Reasoning: 16/7 = <<16/7>> and 11/90 = <<11/90>>. The sum is 16/7 + 11/90 = <<16/7 + 11/90>> = <<(16)(90)/(7)(90)+(11)(7)/(90)>> = <<1920/630>> = <<32/15>>. ### Answer: 32/15
Expected answer: 1517/630
Correct? No