GPT-3.5 Turbo 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.
GPT-3.5 Turbo:
Reasoning: First, we find the sum of 48/56 and 95/23: 48/56 + 95/23 = (48*23 + 95*56) / (56*23) = (1104 + 5320) / 1288 = 6424 / 1288 = 5. Next, we subtract 34/26 from the result: 5 - 34/26 = 5 - (34*56) / (26*56) = 5 - 1904 / 1456 = 5 - 47/36 = (5*36 - 47) / 36 = 163 / 36. ### Answer: 163/36.
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?
GPT-3.5 Turbo:
First, we add the fractions 88/9 and 28/65: 88/9 + 28/65 = (88*65 + 9*28) / (9*65) = (5720 + 252) / 585 = 5972 / 585 Next, we subtract the fraction 18/37 from the result: 5972/585 - 18/37 = (5972*37 - 18*585) / (585*37) = (221564 - 10530) / 21645 = 211034 / 21645 Therefore, the result expressed as a simple fraction is 211034/21645. ### Answer: 211034/21645.
Expected answer: 210434/21645
Correct? No
Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?
GPT-3.5 Turbo:
To simplify (63 / 41) + (44 / 50), we need to find a common denominator for the fractions. The least common multiple of 41 and 50 is 2050. Converting the fractions to have a common denominator: (63 / 41) * (50 / 50) = 3150 / 2050 (44 / 50) * (41 / 41) = 1804 / 2050 Adding the fractions: (3150 + 1804) / 2050 = 4954 / 2050 Simplifying the fraction: 4954 and 2050 share a common factor of 2. 4954 / 2050 = 2477 / 1025 ### Answer: 2477/1025.
Expected answer: 2477/1025
Correct? Yes
Problem: After finding the result of (63 / 41) + (44 / 50), what is the answer if you add up the result twice? Answer as a simplified fraction.
GPT-3.5 Turbo:
The result of (63 / 41) + (44 / 50) is 2477/1025. Adding the result twice: 2477/1025 + 2477/1025 = (2477 + 2477) / 1025 = 4954 / 1025 Simplifying the fraction: 4954 and 1025 share a common factor of 1. 4954 / 1025 = 4954 / 1025 ### Answer: 4954/1025.
Expected answer: 4954/1025
Correct? Yes
Problem: Instead of the previous scenario, now consider a change to the operation. What will be the result if we use (63 / 37) instead of (63 / 41) to find the sum of (63 / 37) + (44 / 50)?. Remember to simplify your answer to its lowest form.
GPT-3.5 Turbo:
To simplify (63 / 37) + (44 / 50), we need to find a common denominator for the fractions. The least common multiple of 37 and 50 is 1850. Converting the fractions to have a common denominator: (63 / 37) * (50 / 50) = 3150 / 1850 (44 / 50) * (37 / 37) = 1628 / 1850 Adding the fractions: (3150 + 1628) / 1850 = 4778 / 1850 Simplifying the fraction: 4778 and 1850 share a common factor of 2. 4778 / 1850 = 2389 / 925 ### Answer: 2389/925.
Expected answer: 2389/925
Correct? Yes
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.
GPT-3.5 Turbo:
To find the total amount of cake, we need to add the fractions together. First, we need to find a common denominator for 41 and 77, which is 41 * 77 = 3157. John had 71/41 of a cake left, which is equivalent to (71*77)/(41*77) = 547/3157 of a cake. Emily added 41/77 of another cake, which is equivalent to (41*41)/(77*41) = 1681/3157 of a cake. Adding these fractions together, we get: 547/3157 + 1681/3157 = 2228/3157. Therefore, there are 2228/3157 of a cake in total. ### Answer: 2228/3157.
Expected answer: 7148/3157
Correct? No
Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.
GPT-3.5 Turbo:
To add fractions, we need to have a common denominator. The least common multiple of 65 and 35 is 455. 10/65 + 56/35 = (10*7)/(65*7) + (56*13)/(35*13) = 70/455 + 728/455 = (70 + 728)/455 = 798/455. ### Answer: 798/455.
Expected answer: 114/65
Correct? Yes
Problem: Following the result of the previous calculation (10/65 + 56/35), subtract your answer from 34. What's the resultant value? Answer as a simple fraction.
GPT-3.5 Turbo:
Subtracting 798/455 from 34 is the same as finding 34 - 798/455. To subtract fractions, we need to have a common denominator. The least common multiple of 455 and 1 is 455. 34 - 798/455 = (34*455)/455 - 798/455 = 15470/455 - 798/455 = (15470 - 798)/455 = 14672/455. ### Answer: 14672/455.
Expected answer: 2096/65
Correct? Yes
Problem: Given your previous calculation with the 10/65 + 56/35, imagine instead that you started with 25 instead of 10 in the first fraction. What would be the outcome of 25/65 + 56/35? Answer as a simplified fraction.
GPT-3.5 Turbo:
To add fractions, we need to have a common denominator. The least common multiple of 65 and 35 is 455. 25/65 + 56/35 = (25*7)/(65*7) + (56*13)/(35*13) = 175/455 + 728/455 = (175 + 728)/455 = 903/455. ### Answer: 903/455.
Expected answer: 129/65
Correct? Yes
Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.
GPT-3.5 Turbo:
To add the fractions 75/81 and 97/47, we need to find a common denominator. The least common multiple of 81 and 47 is 81*47 = 3807. Converting the fractions to have a common denominator: 75/81 = (75*47)/(81*47) = 3525/3807 97/47 = (97*81)/(47*81) = 7833/3807 Adding the fractions: 3525/3807 + 7833/3807 = (3525 + 7833)/3807 = 11358/3807 ### Answer: 11358/3807.
Expected answer: 3794/1269
Correct? No
Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.
GPT-3.5 Turbo:
To subtract the fractions, we need to find a common denominator. The common denominator for 1 and 53 is 53. 88/1 - 38/53 = 88/1 - 38/53 = 88*53/1*53 - 38/53 = 4644/53 - 38/53 = (4644 - 38)/53 = 4606/53. ### Answer: 4606/53.
Expected answer: 4626/53
Correct? No
Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?
GPT-3.5 Turbo:
First, we simplify the fractions: 80/94 = 40/47 78/59 = 78/59 Now, we add the fractions: (40/47) + (78/59) = (40*59 + 78*47) / (47*59) = (2360 + 3666) / 2773 = 6026 / 2773 ### Answer: 6026/2773.
Expected answer: 6026/2773
Correct? Yes
Problem: After evaluating ((80 / 94) + (78 / 59)), add the result to (6 / 31). What is the total when simplified?
GPT-3.5 Turbo:
We already found that ((80 / 94) + (78 / 59)) = 6026/2773. Now, we add (6026/2773) to (6/31): (6026/2773) + (6/31) = (6026*31 + 6*2773) / (2773*31) = (186806 + 16638) / 86063 = 203444 / 86063 ### Answer: 203444/86063.
Expected answer: 203444/85963
Correct? No
Problem: Recalculate the previous problem but this time instead of adding (78 / 59), add (78 / 20) to (80 / 94). What is the new total when simplified?
GPT-3.5 Turbo:
First, we simplify the fractions: 80/94 = 40/47 78/20 = 39/10 Now, we add the fractions: (40/47) + (39/10) = (40*10 + 39*47) / (47*10) = (400 + 1833) / 470 = 2233 / 470 ### Answer: 2233/470.
Expected answer: 2233/470
Correct? Yes
Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of 89/56 and 48/50, we need to first find a common denominator. The least common multiple of 56 and 50 is 280. Converting 89/56 to have a denominator of 280, we get (89/56) * (5/5) = 445/280. Converting 48/50 to have a denominator of 280, we get (48/50) * (56/56) = 2688/280. Now, adding the two fractions together, we get 445/280 + 2688/280 = 3133/280. ### Answer: 3133/280.
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.
GPT-3.5 Turbo:
First, let's find the sum of 96/11 and 12/5: 96/11 + 12/5 = (96*5 + 12*11) / (11*5) = (480 + 132) / 55 = 612/55. Now, let's subtract 38/87 from the sum: 612/55 - 38/87 = (612*87 - 38*55) / (55*87) = (53144 - 2090) / 4785 = 51054/4785 = 1134/106. ### Answer: 1134/106.
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.
GPT-3.5 Turbo:
Given that 82 divided by 9 is 82/9 and 82 divided by 63 is 82/63, the resulting value after subtracting them is (82/9) - (82/63) = (82*7 - 82*1) / (9*7) = (574 - 82) / 63 = 492 / 63 = 164 / 21. Therefore, the resulting value is 164/21. ### Answer: 164/21.
Expected answer: 164/21
Correct? Yes
Problem: In our previous question, we originally had a value of 82 divided by 9 and subtracted 82 divided by 63 from it. Now let's change it up. What would have been the result if, originally, the number we subtracted wasn't 82 divided by 63 but instead 37 divided by 63? What's the new result? Please provide your answer as a simplified fraction.
GPT-3.5 Turbo:
Given that we are subtracting 37 divided by 63 from 82 divided by 9, the new result would be (82/9) - (37/63) = (82*7 - 37*1) / (9*7) = (574 - 37) / 63 = 537 / 63 = 179 / 21. Therefore, the new result is 179/21. ### Answer: 179/21.
Expected answer: 179/21
Correct? Yes
Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.
GPT-3.5 Turbo:
First, let's simplify the fractions: 23/3 = 7 2/3 80/91 cannot be simplified further. 26/24 = 13/12 Now, let's calculate the expression: 7 2/3 - (80/91 + 13/12) = 7 2/3 - (960/1092 + 143/1092) = 7 2/3 - 1103/1092 = 23/3 - 1103/1092 = (23*364 - 1103*3) / (3*1092) = (8372 - 3309) / 3276 = 5063 / 3276 ### Answer: 5063/3276.
Expected answer: 6229/1092
Correct? No
Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?
GPT-3.5 Turbo:
To add the fractions 37/18 and 24/60, we need to find a common denominator. The least common multiple of 18 and 60 is 180. Converting 37/18 to have a denominator of 180: 37/18 = (37*10)/(18*10) = 370/180 Converting 24/60 to have a denominator of 180: 24/60 = (24*3)/(60*3) = 72/180 Now, we can add the fractions: 370/180 + 72/180 = (370 + 72)/180 = 442/180 Simplifying the fraction 442/180: 442/180 = 221/90 ### Answer: 221/90.
Expected answer: 221/90
Correct? Yes
Problem: If the initial sum of 37/18 and 24/60 is added to the fraction 92/28, what would the new total be? Answer as a simplified fraction.
GPT-3.5 Turbo:
We already found that the sum of 37/18 and 24/60 is 221/90. Adding 221/90 to 92/28: To add these fractions, we need to find a common denominator. The least common multiple of 90 and 28 is 2520. Converting 221/90 to have a denominator of 2520: 221/90 = (221*28)/(90*28) = 6168/2520 Converting 92/28 to have a denominator of 2520: 92/28 = (92*90)/(28*90) = 8280/2520 Now, we can add the fractions: 6168/2520 + 8280/2520 = (6168 + 8280)/2520 = 14448/2520 Simplifying the fraction 14448/2520: 14448/2520 = 603/105 ### Answer: 603/105.
Expected answer: 3617/630
Correct? No
Problem: If instead of the original sum of 37/18 and 24/60, we now have the sum of 37/18 and 24/72, what would the new total be? Please express your answer as a simplified fraction.
GPT-3.5 Turbo:
To add the fractions 37/18 and 24/72, we need to find a common denominator. The least common multiple of 18 and 72 is 72. Converting 37/18 to have a denominator of 72: 37/18 = (37*4)/(18*4) = 148/72 Now, we can add the fractions: 148/72 + 24/72 = (148 + 24)/72 = 172/72 Simplifying the fraction 172/72: 172/72 = 43/18 ### Answer: 43/18.
Expected answer: 43/18
Correct? Yes
Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to have a common denominator. The least common multiple of 41 and 62 is 41*62 = 2542. Converting 33/41 to have a denominator of 2542, we get (33*62)/(41*62) = 2046/2542. Converting 95/62 to have a denominator of 2542, we get (95*41)/(62*41) = 3895/2542. Adding the fractions, we get 2046/2542 + 3895/2542 = 5941/2542. ### Answer: 5941/2542.
Expected answer: 5941/2542
Correct? Yes
Problem: After finding the sum of 33/41 and 95/62, add that sum to 95/62 once again. What is the final simplified fraction?
GPT-3.5 Turbo:
Reasoning: We already found that the sum of 33/41 and 95/62 is 5941/2542. Adding 5941/2542 to 95/62, we need to have a common denominator. The least common multiple of 2542 and 62 is 2542*62 = 157604. Converting 5941/2542 to have a denominator of 157604, we get (5941*62)/(2542*62) = 368542/157604. Converting 95/62 to have a denominator of 157604, we get (95*2542)/(62*2542) = 241390/157604. Adding the fractions, we get 368542/157604 + 241390/157604 = 609932/157604. Simplifying the fraction, we get 609932/157604 = 386/99. ### Answer: 386/99.
Expected answer: 4918/1271
Correct? No
Problem: After reconsidering the previous problem, suppose instead of 95/62, we now have 83/62. What would the sum of 33/41 and 83/62 be? Write your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to have a common denominator. The least common multiple of 41 and 62 is 41*62 = 2542. Converting 33/41 to have a denominator of 2542, we get (33*62)/(41*62) = 2046/2542. Converting 83/62 to have a denominator of 2542, we get (83*41)/(62*41) = 3403/2542. Adding the fractions, we get 2046/2542 + 3403/2542 = 5449/2542. ### Answer: 5449/2542.
Expected answer: 5449/2542
Correct? Yes
Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.
GPT-3.5 Turbo:
First, we simplify ((30 / 11) + (72 / 38)): (30 / 11) + (72 / 38) = (30 * 38 + 72 * 11) / (11 * 38) = (1140 + 792) / 418 = 1932 / 418. Next, we add (1932 / 418) to (81 / 34): (1932 / 418) + (81 / 34) = (1932 * 34 + 81 * 418) / (418 * 34) = (65688 + 33858) / 14172 = 99546 / 14172 = 16591 / 2362. ### Answer: 16591/2362.
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.
GPT-3.5 Turbo:
First, we simplify the fractions: 64 / 34 = 32 / 17 3 / 24 = 1 / 8 41 / 96 = 41 / 96 Now, we add the fractions: (32 / 17) + (1 / 8) = (256 / 136 + 17 / 136) = 273 / 136 Adding this result to 41 / 96: (273 / 136) + (41 / 96) = (273 * 3 / 136 * 3) + (41 * 17 / 96 * 17) = 819 / 408 + 697 / 1632 = (819 * 4 / 408 * 4) + (697 * 3 / 1632 * 3) = 3276 / 1632 + 2091 / 4896 = (3276 * 3 / 1632 * 3) + (2091 * 4 / 4896 * 4) = 9828 / 4896 + 8364 / 4896 = 18192 / 4896 = 126 / 34 = 63 / 17 ### Answer: 63/17.
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?
GPT-3.5 Turbo:
To add fractions, we need to find a common denominator. The common denominator for 73 and 77 is 73*77 = 5621. So, we rewrite 83/73 and 53/77 with the common denominator: 83/73 = (83*77)/(73*77) = 6401/5621 53/77 = (53*73)/(77*73) = 3869/5621 Now, we add the fractions: 6401/5621 + 3869/5621 = (6401 + 3869)/5621 = 10270/5621 Next, we add 80/76 to the result: 10270/5621 + 80/76 = (10270*76 + 80*5621)/(5621*76) = 781720/427196 The final answer in simplified fraction form is 781720/427196. ### Answer: 781720/427196.
Expected answer: 307360/106799
Correct? No
Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.
GPT-3.5 Turbo:
To add fractions, we need to find a common denominator. The least common multiple of 20 and 66 is 60. Converting 27/20 to have a denominator of 60: 27/20 = (27*3)/(20*3) = 81/60 Converting 14/66 to have a denominator of 60: 14/66 = (14*10)/(66*10) = 140/660 = 7/33 Now, we can add the fractions: 81/60 + 7/33 = (81*33)/(60*33) + 7*20/(33*20) = 2673/1980 + 140/1980 = 2813/1980 Simplifying the fraction: 2813/1980 = 187/132 ### Answer: 187/132.
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.
GPT-3.5 Turbo:
First, we simplify the fractions: 32 / 14 = 16 / 7 22 / 47 = 22 / 47 Now, we subtract the fractions: (16 / 7) - (22 / 47) = (16 * 47 - 22 * 7) / (7 * 47) = (752 - 154) / 329 = 598 / 329 ### Answer: 598/329.
Expected answer: 598/329
Correct? Yes
Problem: If you take the result of ((32 / 14) - (22 / 47)) you calculated earlier, what would be the value you get when you add this result to itself? Write your answer as a simplified fraction.
GPT-3.5 Turbo:
We found that ((32 / 14) - (22 / 47)) = 598/329. Adding this result to itself: 598/329 + 598/329 = (598 + 598) / 329 = 1196 / 329 ### Answer: 1196/329.
Expected answer: 1196/329
Correct? Yes
Problem: Suppose instead of having 32/14 part of the original mixture, you actually had 71/14 part, and the same fraction (22/47) was subtracted from it. In that case, what would be the new result of the calculation: ((71 / 14) - (22 / 47))? Write your answer as a simplified fraction.
GPT-3.5 Turbo:
First, we simplify the fractions: 71 / 14 = 71 / 14 22 / 47 = 22 / 47 Now, we subtract the fractions: (71 / 14) - (22 / 47) = (71 * 47 - 22 * 14) / (14 * 47) = (3337 - 308) / 658 = 3029 / 658 ### Answer: 3029/658.
Expected answer: 3029/658
Correct? Yes
Problem: What is the sum of 74/61 and 41/53 expressed in fractions?
GPT-3.5 Turbo:
To find the sum of 74/61 and 41/53, we need to find a common denominator for the fractions. The least common multiple of 61 and 53 is 61*53 = 3233. Converting 74/61 to have a denominator of 3233: (74/61) * (53/53) = 3922/3233 Converting 41/53 to have a denominator of 3233: (41/53) * (61/61) = 2501/3233 Adding the two fractions: 3922/3233 + 2501/3233 = 6423/3233 ### Answer: 6423/3233.
Expected answer: 6423/3233
Correct? Yes
Problem: Assuming you already calculated the sum of 74/61 and 41/53, what would be the total if you added 83/4 to the result? Answer as a simplified fraction.
GPT-3.5 Turbo:
Adding 83/4 to the sum of 74/61 and 41/53: 6423/3233 + 83/4 = (6423*4 + 83*3233) / (3233*4) = (25692 + 267439) / 12932 = 293131 / 12932 ### Answer: 293131/12932.
Expected answer: 294031/12932
Correct? No
Problem: Previously you calculated the sum of 74/61 and 41/53. Now, let's consider if the second fraction was actually 41/88 instead of 41/53. What would be the new total of 74/61 and 41/88? Answer as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of 74/61 and 41/88, we need to find a common denominator for the fractions. The least common multiple of 61 and 88 is 61*88 = 5368. Converting 74/61 to have a denominator of 5368: (74/61) * (88/88) = 6512/5368 Converting 41/88 to have a denominator of 5368: (41/88) * (61/61) = 2501/5368 Adding the two fractions: 6512/5368 + 2501/5368 = 9013/5368 Simplifying the fraction: 9013/5368 = 59/35 ### Answer: 59/35.
Expected answer: 9013/5368
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?
GPT-3.5 Turbo:
First, let's simplify the expression 94 / 2 - 74 / 57: 94 / 2 = 47 74 / 57 ≈ 1.2982 47 - 1.2982 ≈ 45.7018 Next, let's add this result to 56 / 97: 45.7018 + 56 / 97 ≈ 45.7018 + 0.5773 ≈ 46.2791 Therefore, the final fraction is approximately 46.2791. ### Answer: 46.2791.
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.
GPT-3.5 Turbo:
To find the sum of 14/89, 24/34, and 44/87, we first need to find a common denominator for the fractions. The least common multiple of 89, 34, and 87 is 89*34*87 = 264366. Converting the fractions to have a common denominator of 264366: 14/89 = (14*2974)/(89*2974) = 41516/264366, 24/34 = (24*7781)/(34*7781) = 186744/264366, 44/87 = (44*3042)/(87*3042) = 133848/264366. Adding the fractions together: 41516/264366 + 186744/264366 + 133848/264366 = (41516 + 186744 + 133848)/264366 = 361108/264366. Therefore, the sum of 14/89, 24/34, and 44/87 is 361108/264366, which simplifies to 180554/132183. ### Answer: 180554/132183.
Expected answer: 180194/131631
Correct? No
Problem: What would you get if you add 73/30 to 8/60?
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to have a common denominator. In this case, the common denominator is 30. So, we rewrite 8/60 as 1/15. Now, we have 73/30 + 1/15 = (73*2)/(30*2) + 1/15 = 146/60 + 4/60 = 150/60 = 5/2. ### Answer: 5/2.
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.
GPT-3.5 Turbo:
Let's first add the first two fractions: 82/49 + 45/60 = (82*60 + 45*49) / (49*60) = (4920 + 2205) / 2940 = 7125 / 2940 Now, let's add this result to the third fraction: 7125/2940 + 99/59 = (7125*59 + 2940*99) / (2940*59) = (420375 + 290460) / 173460 = 710835 / 173460 Therefore, the resulting sum is 710835/173460. ### Answer: 710835/173460.
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.
GPT-3.5 Turbo:
Step 1: \( \frac{91}{16} - \frac{76}{30} \)
To subtract these fractions, we need to find a common denominator. The least common multiple of 16 and 30 is 240.
\( \frac{91 \times 15}{16 \times 15} - \frac{76 \times 8}{30 \times 8} \)
\( = \frac{1365}{240} - \frac{608}{240} \)
\( = \frac{1365 - 608}{240} \)
\( = \frac{757}{240} \)
Step 2: \( \frac{757}{240} + \frac{18}{44} \)
To add these fractions, we need to find a common denominator. The least common multiple of 240 and 44 is 5280.
\( \frac{757 \times 22}{240 \times 22} + \frac{18 \times 120}{44 \times 120} \)
\( = \frac{16654}{5280} + \frac{2160}{5280} \)
\( = \frac{16654 + 2160}{5280} \)
\( = \frac{18814}{5280} \)
Rounded to the nearest hundredth, \( \frac{18814}{5280} \approx 3.56 \).
### Answer: 3.56
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.
GPT-3.5 Turbo:
First, let's find the result of ((8 / 91) + (49 / 5)): (8 / 91) + (49 / 5) = (8 * 5 + 49 * 91) / (91 * 5) = (40 + 4459) / 455 = 4499 / 455. Now, let's subtract (32 / 76) from the result: 4499 / 455 - 32 / 76 = (4499 * 76 - 32 * 455) / (455 * 76) = (341524 - 14560) / 34580 = 326964 / 34580 = 163482 / 17290 = 81741 / 8645. ### Answer: 81741 / 8645.
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.
GPT-3.5 Turbo:
Calculating ((75 / 45) + (5 / 49)): (75 / 45) + (5 / 49) = (5/3) + (5/49) = (245/147) + (15/147) = 260/147 Adding this value with 3 / 58: 260/147 + 3/58 = (260*58 + 3*147) / (147*58) = 15080 + 441 / 8526 = 15521 / 8526 ### Answer: 15521/8526.
Expected answer: 15521/8526
Correct? Yes
Problem: Now, suppose you take the earlier result from calculating ((75 / 45) + (5 / 49)), added it to the value you got from adding that result to 3 / 58, what would be the new outcome? Once again, please provide the answer as a simplified fraction.
GPT-3.5 Turbo:
Adding the earlier result ((75 / 45) + (5 / 49)) to the value from adding that result to 3 / 58: 260/147 + 15521/8526 = (260*8526 + 15521*147) / (147*8526) = 2227560 + 2281987 / 1256422 = 4509547 / 1256422 ### Answer: 4509547/1256422.
Expected answer: 30601/8526
Correct? No
Problem: Recalling the previous problem, suppose we had ((75 / 45) + (5 / 49)). But instead of adding 3 / 58 to that result, what if we were to add 3 / 17 instead? Calculate the new outcome, and provide the answer as a simplified fraction.
GPT-3.5 Turbo:
Calculating ((75 / 45) + (5 / 49)): (75 / 45) + (5 / 49) = (5/3) + (5/49) = (245/147) + (15/147) = 260/147 Adding this value with 3 / 17: 260/147 + 3/17 = (260*17 + 3*147) / (147*17) = 4420 + 441 / 2499 = 4861 / 2499 ### Answer: 4861/2499.
Expected answer: 4861/2499
Correct? Yes
Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.
GPT-3.5 Turbo:
First, we find a common denominator for the fractions: ((43/15) - (33/95)) = ((43*19)/(15*19) - (33*3)/(95*3)) = (817/285 - 99/285) = 718/285 = 358/143 = 2.5. ### Answer: 2.5
Expected answer: 718/285
Correct? No
Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.
GPT-3.5 Turbo:
First, we find the sum of the two fractions: (78/45) + (89/36) = (624/360) + (890/360) = (624 + 890) / 360 = 1514 / 360. Next, we add this sum to itself: (1514/360) + (1514/360) = (3028/360) = 1514/180. ### Answer: 1514/180.
Expected answer: 757/90
Correct? Yes
Problem: After finding the sum of ((78 / 45) + (89 / 36)) added to itself, what is the resultant value when that sum is added to the original ((78 / 45) + (89 / 36))? Answer as a simple fraction.
GPT-3.5 Turbo:
First, we add the sum of the two fractions to itself: 1514/180 + 1514/180 = 3028/180 = 1514/90. Next, we add this sum to the original sum: 1514/90 + 1514/360 = (1514*4 + 1514) / 360 = 6060/360 + 1514/360 = 7574/360. ### Answer: 7574/360.
Expected answer: 757/60
Correct? No
Problem: Previously, you calculated the sum of ((78 / 45) + (89 / 36)) added to itself. But what if the first fraction was instead (78 / 93)? In that case, what would be the new result of ((78 / 93) + (89 / 36)) added to itself? Please give your answer as a simple fraction.
GPT-3.5 Turbo:
First, we find the sum of the new fractions: (78/93) + (89/36) = (288/279) + (890/360) = (288*360 + 890*279) / (279*360) = (103680 + 248310) / 100440 = 351990 / 100440 = 11733 / 3348. Next, we add this sum to itself: (11733/3348) + (11733/3348) = (23466/3348) = 7833/1116. ### Answer: 7833/1116.
Expected answer: 3695/558
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?
GPT-3.5 Turbo:
Let's first divide 93 by 34 to get a fraction value: 93/34. Now, let's subtract 77/74 from this fraction: (93/34) - (77/74). To subtract these fractions, we need to find a common denominator, which is the least common multiple of 34 and 74, which is 34*74 = 2516. Now, we rewrite the fractions with the common denominator: (93/34)*(74/74) - (77/74)*(34/34) = (93*74)/(34*74) - (77*34)/(74*34) = (6862/2516) - (2618/2516) = (6862 - 2618)/2516 = 4244/2516 = 1061/629 Therefore, the result as a simplified fraction is 1061/629. ### Answer: 1061/629.
Expected answer: 1066/629
Correct? No
Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To find the sum of fractions, we need to have a common denominator. The least common multiple of 35 and 85 is 595. Converting 86/35 to have a denominator of 595: 86/35 * 17/17 = 1462/595 Converting 68/85 to have a denominator of 595: 68/85 * 7/7 = 476/595 Adding the two fractions: 1462/595 + 476/595 = 1938/595 ### Answer: 1938/595.
Expected answer: 114/35
Correct? Yes
Problem: After finding the sum of 86/35 and 68/85, add the result to 86/35 again. Express your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: We already found that the sum of 86/35 and 68/85 is 1938/595. Now, we need to add 86/35 to this result. Converting 86/35 to have a denominator of 595: 86/35 * 17/17 = 1462/595 Adding 1938/595 and 1462/595: 1938/595 + 1462/595 = 3400/595 Converting the sum to a simplified fraction: 3400/595 = 680/119 ### Answer: 680/119.
Expected answer: 40/7
Correct? Yes
Problem: Reconsider the previous problem where you found the sum of 86/35 and 68/85. What if there were a mistake and the original fraction was actually 86/75, not 86/35? Find the sum of the revised fraction, 86/75, with 68/85. Express your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To find the sum of fractions, we need to have a common denominator. The least common multiple of 75 and 85 is 1275. Converting 86/75 to have a denominator of 1275: 86/75 * 17/17 = 1462/1275 Converting 68/85 to have a denominator of 1275: 68/85 * 15/15 = 1020/1275 Adding the two fractions: 1462/1275 + 1020/1275 = 2482/1275 ### Answer: 2482/1275.
Expected answer: 146/75
Correct? Yes
Problem: What is the sum of 99/53 and 67/94 in simplest form?
GPT-3.5 Turbo:
To find the sum of fractions, we need to have a common denominator. The least common multiple of 53 and 94 is 53*94 = 4982. Converting the fractions: 99/53 = (99*94)/(53*94) = 9306/4982 67/94 = (67*53)/(94*53) = 3551/4982 Adding the fractions: 9306/4982 + 3551/4982 = (9306 + 3551)/4982 = 12857/4982 The sum of 99/53 and 67/94 in simplest form is 12857/4982. ### Answer: 12857/4982.
Expected answer: 12857/4982
Correct? Yes
Problem: What if you were to add the fraction 50/56 to the sum you previously found (of 99/53 and 67/94)? What is the resulting value in its simplest form?
GPT-3.5 Turbo:
We already found the sum of 99/53 and 67/94 to be 12857/4982. To add 50/56 to this sum, we need to find a common denominator. The least common multiple of 56 and 4982 is 56*4982 = 279392. Converting the fractions: 50/56 = (50*4982)/(56*4982) = 249100/279392 Adding the fractions: 12857/4982 + 249100/279392 = (12857*279392 + 249100*4982)/(4982*279392) = (3593183444 + 1241918200)/1393921664 = 4835101644/1393921664 The resulting value in its simplest form is 4835101644/1393921664. ### Answer: 4835101644/1393921664.
Expected answer: 242273/69748
Correct? No
Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?
GPT-3.5 Turbo:
To subtract fractions, we need a common denominator. The least common multiple of 27 and 33 is 297. 74/27 = (74*11)/(27*11) = 814/297 56/33 = (56*9)/(33*9) = 504/297 Now, we can subtract the fractions: 814/297 - 504/297 = (814 - 504)/297 = 310/297 ### Answer: 310/297
Expected answer: 310/297
Correct? Yes
Problem: If you then add 92/70 to the result of 74/27 minus 56/33, what fraction do you now have? Please answer as a simplified fraction.
GPT-3.5 Turbo:
We already found that 74/27 - 56/33 = 310/297. Now, let's add 92/70 to this result: 92/70 = (92*3)/(70*3) = 276/210 Adding this to 310/297: 310/297 + 276/210 = (310*210 + 276*297)/(297*210) = (65100 + 81972)/62370 = 147072/62370 Now, we simplify this fraction: 147072/62370 = 7368/3118 = 3684/1559 ### Answer: 3684/1559
Expected answer: 24512/10395
Correct? No
Problem: What if we had 77/27 instead of 74/27 in the beginning? What would the fraction be if you subtracted 56/33 from this? Please answer as a simplified fraction.
GPT-3.5 Turbo:
If we have 77/27 instead of 74/27, we get: 77/27 = (77*9)/(27*9) = 693/297 Now, we can subtract 56/33 from this: 693/297 - 504/297 = (693 - 504)/297 = 189/297 To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 27: 189/297 = (189/27)/(297/27) = 7/11 ### Answer: 7/11
Expected answer: 343/297
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.
GPT-3.5 Turbo:
First, we need to find the sum of 96/40 and 11/99: 96/40 + 11/99 = (96*99 + 11*40) / (40*99) = (9504 + 440) / 3960 = 9944 / 3960 = 1243 / 495. Now, we need to subtract 91/65 from 1243/495: 1243/495 - 91/65 = (1243*65 - 91*495) / (495*65) = (80895 - 45045) / 32175 = 35850 / 32175 = 716 / 6435. ### Answer: 716/6435.
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?
GPT-3.5 Turbo:
Let's first calculate h: 1) 10 divided by 5 is 2, and 35 divided by 27 is approximately 1.296. So, h = 2 + 1.296 = 3.296. Now, let's calculate p: 2) Adding 47 divided by 99 to h: p = 3.296 + 47/99 ≈ 3.296 + 0.4747 ≈ 3.7707. ### Answer: p ≈ 3.7707.
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?
GPT-3.5 Turbo:
First, we need to find a common denominator for the fractions 90/81 and 2/66. The least common multiple of 81 and 66 is 594. Converting 90/81 to have a denominator of 594: 90/81 * 594/594 = 5940/729 Converting 2/66 to have a denominator of 594: 2/66 * 9/9 = 18/594 Adding the fractions: 5940/729 + 18/594 = (5940 + 729*18) / 729*594 = (5940 + 13122) / 430086 = 19062 / 430086 Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6: 19062 / 430086 = 3177 / 71681 ### Answer: 3177/71681.
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?
GPT-3.5 Turbo:
To find the total length of both pieces of ribbon, we need to add the length of one piece to the length of the other piece. 56/41 + 56/41 = 112/41 So, both pieces of ribbon together would be 112/41 yards long. ### Answer: 112/41 yards.
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?
GPT-3.5 Turbo:
To find the total length of all the pieces of ribbon, we need to add the length of each piece together. 56/41 + 56/41 + 56/41 + 56/41 = 224/41 So, all the pieces of ribbon together would be 224/41 yards long. ### Answer: 224/41 yards.
Expected answer: 224/41
Correct? Yes
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?
GPT-3.5 Turbo:
If Oliver initially had a piece of ribbon that was 63/41 yards long, and he receives another piece of the same length, the total length of both pieces of ribbon would be: 63/41 + 63/41 = 126/41 So, both pieces of ribbon together would be 126/41 yards long. ### Answer: 126/41 yards.
Expected answer: 126/41
Correct? Yes
Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to find a common denominator. The common denominator for 75 and 92 is 75 * 92 = 6900. Converting the fractions: 92/75 = (92 * 92)/(75 * 92) = 8464/6900 66/92 = (66 * 75)/(92 * 75) = 4950/6900 Adding the fractions: 8464/6900 + 4950/6900 = (8464 + 4950)/6900 = 13414/6900 Simplifying the fraction: 13414/6900 = 6707/3450 ### Answer: 6707/3450.
Expected answer: 6707/3450
Correct? Yes
Problem: Following the previous problem, what is the result of 97/17 minus the sum of 92/75 + 66/92? Give your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: First, we need to find the sum of 92/75 and 66/92 from the previous problem: 92/75 + 66/92 = 6707/3450 Now, we can subtract the sum from 97/17: 97/17 - 6707/3450 = (97*3450 - 6707*17) / (17*3450) = (333150 - 113819) / 58650 = 219331 / 58650 ### Answer: 219331/58650.
Expected answer: 220631/58650
Correct? No
Problem: Following the previous problem, consider instead if there were 83/75 of something instead of 92/75. What would be the new total when you add 66/92 to it? Please provide your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: The new fraction is 83/75. Converting the fractions: 83/75 = (83 * 92)/(75 * 92) = 7616/6900 Adding the fractions: 7616/6900 + 4950/6900 = (7616 + 4950)/6900 = 12566/6900 Simplifying the fraction: 12566/6900 = 6283/3450 ### Answer: 6283/3450.
Expected answer: 6293/3450
Correct? No
Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.
GPT-3.5 Turbo:
Reasoning: To find the sum of fractions, we need to have a common denominator. The common denominator for 65 and 22 is 65*22 = 1430. 32/65 = (32*22)/(65*22) = 704/1430 73/22 = (73*65)/(22*65) = 4745/1430 Adding the two fractions together: 704/1430 + 4745/1430 = (704 + 4745)/1430 = 5449/1430 ### Answer: 5449/1430.
Expected answer: 5449/1430
Correct? Yes
Problem: Following up on the previous question, what is the sum of your answer from that problem and 24/71? Leave your answer as an unsimplified fraction.
GPT-3.5 Turbo:
Reasoning: We already have the fraction 5449/1430 from the previous question. Adding 24/71 to 5449/1430: 24/71 = (24*20)/(71*20) = 480/1420 Adding the two fractions together: 5449/1430 + 480/1420 = (5449*71 + 480*20)/(1430*71) = (386479 + 9600)/101230 = 396079/101230 ### Answer: 396079/101230.
Expected answer: 421199/101530
Correct? No
Problem: In the earlier problem, we considered the sum of 32/65 and 73/22. But what if the fraction was 53/65 instead of 32/65? What would the new sum be? Please leave your answer as an unsimplified fraction.
GPT-3.5 Turbo:
Reasoning: Using the same common denominator of 1430: 53/65 = (53*22)/(65*22) = 1166/1430 Adding this new fraction to 73/22: 1166/1430 + 4745/1430 = (1166 + 4745)/1430 = 5911/1430 ### Answer: 5911/1430.
Expected answer: 5911/1430
Correct? Yes
Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.
GPT-3.5 Turbo:
To find the difference between 51/34 and 12/86, we need to first find a common denominator. The least common multiple of 34 and 86 is 86. Converting 51/34 to have a denominator of 86, we get 51/34 * 2/2 = 102/68. Now, we can find the difference: 102/86 - 12/86 = 90/86 = 45/43. ### Answer: 45/43.
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?
GPT-3.5 Turbo:
First, convert the whole number 51 to a fraction with a denominator of 1: 51 = 51/1. Next, add the fractions: 51/1 + 93/8 = (51*8 + 93*1) / (1*8) = 408 + 93 / 8 = 501 / 8. Finally, add the fraction 501/8 to 58/44: 501/8 + 58/44 = (501*44 + 58*8) / (8*44) = 22044 + 464 / 352 = 22508 / 352. The final result as a simplified fraction is 22508/352. ### Answer: 22508/352.
Expected answer: 5627/88
Correct? Yes
Problem: After completing the initial calculation, you realize there was an extra component to your math problem. You must now also add the fraction 38/53 to your previous result. What is the new total, expressed as a simplified fraction?
GPT-3.5 Turbo:
First, add the fraction 22508/352 to 38/53: 22508/352 + 38/53 = (22508*53 + 38*352) / (352*53) = (1190024 + 13376) / 18656 = 1203396 / 18656. The new total, expressed as a simplified fraction, is 1203396/18656. ### Answer: 1203396/18656.
Expected answer: 301575/4664
Correct? No
Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.
GPT-3.5 Turbo:
Reasoning: To subtract the fractions, we need to have a common denominator. The least common multiple of 5 and 25 is 25. So, we rewrite the fractions with a common denominator: 82/5 - 98/25 = (82*5)/(5*5) - 98/25 = 410/25 - 98/25 = (410 - 98)/25 = 312/25. ### Answer: 312/25.
Expected answer: 312/25
Correct? Yes
Problem: Given the result you obtained previously from calculating 82/5 - 98/25, what would you get if you added this result to itself?
GPT-3.5 Turbo:
Reasoning: If we add 312/25 to itself, we get: 312/25 + 312/25 = (312 + 312)/25 = 624/25. ### Answer: 624/25.
Expected answer: 624/25
Correct? Yes
Problem: If you originally had 82/5 oranges and instead of taking away 98/25 of them, you took away 98/90 oranges, how many oranges would you have left? Write the answer in the simplest form.
GPT-3.5 Turbo:
Reasoning: To subtract 98/90 from 82/5, we need to have a common denominator. The least common multiple of 5 and 90 is 90. So, we rewrite the fractions with a common denominator: 82/5 - 98/90 = (82*18)/(5*18) - 98/90 = 1476/90 - 98/90 = (1476 - 98)/90 = 1378/90. ### Answer: 1378/90.
Expected answer: 689/45
Correct? Yes
Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.
GPT-3.5 Turbo:
(64 / 50) + (70 / 22) = (64*22 + 70*50) / (50*22) = (1408 + 3500) / 1100 = 4908 / 1100 = 1227 / 275 ### Answer: 1227 / 275.
Expected answer: 1227/275
Correct? Yes
Problem: In the previous question, we considered a situation where we added the fractions (64 / 50) and (70 / 22). Now imagine we made a slight error in our calculations, and the initial fraction was actually (64 / 49), not (64 / 50). How would that affect our total sum? Calculate (64 / 49) + (70 / 22) and provide your answer as an unsimplified fraction.
GPT-3.5 Turbo:
(64 / 49) + (70 / 22) = (64*22 + 70*49) / (49*22) = (1408 + 3430) / 1078 = 4838 / 1078 = 2419 / 539 ### Answer: 2419 / 539.
Expected answer: 2419/539
Correct? Yes
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?
GPT-3.5 Turbo:
Let's first calculate the value of s: s = 24/6 + 40/53 s = 4 + 0.7547 s = 4.7547 Now, let's find the value of b: b = s + s b = 4.7547 + 4.7547 b = 9.5094 ### Answer: 9.5094
Expected answer: 504/53
Correct? No
Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.
GPT-3.5 Turbo:
Calculating ((80 / 90) + (52 / 11)): (80 / 90) simplifies to (8 / 9). (52 / 11) simplifies to 4 and 8/11 as a mixed number. Adding (8 / 9) and 4 and 8/11: 8/9 + 4 and 8/11 = 4 and (8/9 + 8/11) = 4 and ((88 + 72) / 99) = 4 and (160 / 99) = 4 and 56/99. ### Answer: 4 56/99.
Expected answer: 556/99
Correct? No
Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to have a common denominator. The least common multiple of 18 and 74 is 18*74 = 1332. Converting 12/18 to have a denominator of 1332: 12/18 = (12*74)/(18*74) = 888/1332 Converting 91/74 to have a denominator of 1332: 91/74 = (91*18)/(74*18) = 1638/1332 Adding the fractions: 888/1332 + 1638/1332 = (888 + 1638)/1332 = 2526/1332 = 423/222 ### Answer: 423/222.
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.
GPT-3.5 Turbo:
To find the sum of the fractions 7/2 and 51/25, we need to first find a common denominator. The least common multiple of 2 and 25 is 50. Converting 7/2 to have a denominator of 50, we get 7/2 * 25/25 = 175/50. Converting 51/25 to have a denominator of 50, we get 51/25 * 2/2 = 102/50. Now, adding the fractions 175/50 and 102/50, we get (175 + 102)/50 = 277/50. ### Answer: 277/50.
Expected answer: 277/50
Correct? Yes
Problem: Following up on the previous question, add the fraction 86/39 to the sum of 7/2 and 51/25. Express your answer as a simple fraction.
GPT-3.5 Turbo:
First, we need to find a common denominator for the fractions 277/50 and 86/39. The least common multiple of 50 and 39 is 1950. Converting 277/50 to have a denominator of 1950, we get 277/50 * 39/39 = 10743/1950. Converting 86/39 to have a denominator of 1950, we get 86/39 * 50/50 = 4300/1950. Now, adding the fractions 10743/1950 and 4300/1950, we get (10743 + 4300)/1950 = 15043/1950. ### Answer: 15043/1950.
Expected answer: 15103/1950
Correct? No
Problem: In the previous problem, you were asked to find the sum of 7/2 and 51/25. Now suppose that instead of 7/2, the fraction was 7/22. How would this change the result? Calculate 7/22 + 51/25 as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of the fractions 7/22 and 51/25, we need to find a common denominator. The least common multiple of 22 and 25 is 550. Converting 7/22 to have a denominator of 550, we get 7/22 * 25/25 = 175/550. Converting 51/25 to have a denominator of 550, we get 51/25 * 22/22 = 1122/550. Now, adding the fractions 175/550 and 1122/550, we get (175 + 1122)/550 = 1297/550. ### Answer: 1297/550.
Expected answer: 1297/550
Correct? Yes
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.
GPT-3.5 Turbo:
First, simplify the expression ((68 / 69) + (93 / 7)): (68 / 69) + (93 / 7) = (68 * 7 + 93 * 69) / (69 * 7) = (476 + 6417) / 483 = 6893 / 483 Now, add (3 / 46) to the above result: 6893 / 483 + 3 / 46 = (6893 * 46 + 3 * 483) / (483 * 46) = (317878 + 1449) / 22158 = 319327 / 22158 ### Answer: 319327/22158.
Expected answer: 13849/966
Correct? No
Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.
GPT-3.5 Turbo:
To add the fractions 31/98 and 60/4, we need to find a common denominator. The least common multiple of 98 and 4 is 98. Converting 60/4 to an equivalent fraction with denominator 98: 60/4 = (60*24)/(4*24) = 1440/96 Now, we can add the fractions: 31/98 + 1440/96 = (31*96 + 1440*98)/(98*96) = (2976 + 141120)/9408 = 144096/9408 = 1512/98 = 756/49 ### Answer: 756/49.
Expected answer: 1501/98
Correct? No
Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.
GPT-3.5 Turbo:
First, simplify the fractions: 3/2 = 1 1/2 = 3/2 24/36 = 2/3 Now, add the fractions: 3/2 + 24/36 = 3/2 + 2/3 To add these fractions, we need a common denominator, which is 6. 3/2 = 9/6 2/3 = 4/6 Now, add the fractions: 9/6 + 4/6 = 13/6 Therefore, ((3 / 2) + (24 / 36)) = 13/6. ### Answer: 13/6.
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.
GPT-3.5 Turbo:
First, we add ((3 / 2) + (24 / 36)): (3/2) + (24/36) = 13/6 Now, we add 13/6 to 7/2: 13/6 + 7/2 To add these fractions, we need a common denominator, which is 6: 13/6 + 7/2 = 13/6 + 21/6 Now, add the fractions: 13/6 + 21/6 = 34/6 Therefore, ((3 / 2) + (24 / 36)) + 7/2 = 34/6. ### Answer: 34/6.
Expected answer: 17/3
Correct? Yes
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.
GPT-3.5 Turbo:
First, simplify the fractions: 3/2 = 1 1/2 = 3/2 32/36 = 8/9 Now, add the fractions: 3/2 + 32/36 = 3/2 + 8/9 To add these fractions, we need a common denominator, which is 18. 3/2 = 27/18 8/9 = 16/18 Now, add the fractions: 27/18 + 16/18 = 43/18 Therefore, ((3 / 2) + (32 / 36)) = 43/18. ### Answer: 43/18.
Expected answer: 43/18
Correct? Yes
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?
GPT-3.5 Turbo:
First, let's calculate the sum of 92/54 and 90/13: 92/54 + 90/13 = (92*13 + 90*54) / (54*13) = (1196 + 4860) / 702 = 6056 / 702 Next, let's subtract 46/41 from the result: 6056/702 - 46/41 = (6056*41 - 46*702) / (702*41) = (248296 - 32492) / 28782 = 215804 / 28782 The result as a simplified fraction is 215804/28782. ### Answer: 215804/28782.
Expected answer: 108002/14391
Correct? No
Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.
GPT-3.5 Turbo:
Reasoning: Twice the value of 29/23 is 2 * (29/23) = 58/23, which cannot be simplified further. ### Answer: 58/23.
Expected answer: 58/23
Correct? Yes
Problem: After calculating the value of 2*(29/23), subtract this result from 32/5. What is the resulting fraction in simplest form?
GPT-3.5 Turbo:
First, we calculate 2*(29/23) = 58/23. Next, we subtract 58/23 from 32/5: 32/5 - 58/23 = (32*23 - 58*5) / (5*23) = (736 - 290) / 115 = 446 / 115. The resulting fraction in simplest form is 446/115. ### Answer: 446/115.
Expected answer: 446/115
Correct? Yes
Problem: If the initial number was 36/23 instead of 29/23 in our previous problem, what would now be the value of two times this new fraction? Simplify your answer to the simplest form.
GPT-3.5 Turbo:
Reasoning: The new fraction is 36/23. Twice this new fraction is 2 * (36/23) = 72/23, which cannot be simplified further. ### Answer: 72/23.
Expected answer: 72/23
Correct? Yes
Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.
GPT-3.5 Turbo:
To add fractions, we need to find a common denominator. The least common multiple of 20 and 72 is 360. Converting 29/20 to have a denominator of 360: 29/20 * 18/18 = 522/360 Converting 17/72 to have a denominator of 360: 17/72 * 5/5 = 85/360 Adding the fractions: 522/360 + 85/360 = 607/360 ### Answer: 607/360.
Expected answer: 607/360
Correct? Yes
Problem: After finding the sum of 29/20 and 17/72 in the previous question, now subtract 9/68 from that sum to obtain a new value. What is the simplified fraction of this new answer?
GPT-3.5 Turbo:
We already found the sum of 29/20 and 17/72 to be 607/360 in the previous question. Subtracting 9/68 from 607/360: 607/360 - 9/68 To subtract fractions, we need a common denominator. The least common multiple of 360 and 68 is 12240. Converting 607/360 to have a denominator of 12240: 607/360 * 34/34 = 20638/12240 Converting 9/68 to have a denominator of 12240: 9/68 * 180/180 = 1620/12240 Subtracting the fractions: 20638/12240 - 1620/12240 = 19018/12240 Simplifying the fraction: 19018/12240 = 4754/3060 = 2377/1530 ### Answer: 2377/1530.
Expected answer: 9509/6120
Correct? No
Problem: In the previous problem, you found the sum of 29/20 and 17/72. Now, imagine that instead of having 29/20 of a quantity, you only had 29/5. What would be the sum of 29/5 and 17/72? Keep your answer as a simplified fraction.
GPT-3.5 Turbo:
To add fractions, we need to find a common denominator. The least common multiple of 5 and 72 is 360. Converting 29/5 to have a denominator of 360: 29/5 * 72/72 = 2088/360 Converting 17/72 to have a denominator of 360: 17/72 * 5/5 = 85/360 Adding the fractions: 2088/360 + 85/360 = 2173/360 ### Answer: 2173/360.
Expected answer: 2173/360
Correct? Yes
Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.
GPT-3.5 Turbo:
Calculating each part of the expression: (36 / 27) = 1.333... (80 / 10) = 8 (73 / 79) = 0.924... Putting it all together: (1.333... + 8) - 0.924... = 8.409... ### Answer: 8.409
Expected answer: 1993/237
Correct? No
Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.
GPT-3.5 Turbo:
To find the sum of the two fractions, we first need to find a common denominator. The least common multiple of 71 and 75 is 71 * 75 = 5325. Converting the fractions: (86 / 71) * (75 / 75) = 6450 / 5325 (91 / 75) * (71 / 71) = 6461 / 5325 Adding the fractions: (6450 + 6461) / 5325 = 12911 / 5325 Converting to a decimal: 12911 / 5325 ≈ 2.42 ### Answer: 2.42
Expected answer: 12911/5325
Correct? No
Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)
GPT-3.5 Turbo:
First, we need to find a common denominator for the fractions in the expression. The least common multiple of 75, 43, and 62 is 75 * 43 * 62 = 19350. Converting each fraction to have the common denominator of 19350: (21/75) * (258/258) = 5508/19350 (74/43) * (450/450) = 3180/19350 (10/62) * (315/315) = 3150/19350 Adding the fractions together: (5508/19350) + (3180/19350) + (3150/19350) = 11838/19350 Simplifying the fraction: 11838 and 19350 share a common factor of 6, so dividing both by 6: 11838/6 = 1973 19350/6 = 3225 Therefore, the final simplified fraction is 1973/3225. ### Answer: 1973/3225.
Expected answer: 72056/33325
Correct? No
Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.
GPT-3.5 Turbo:
First, we find a common denominator for the fractions: ((75 / 66) + (81 / 61)) = (75*61 / 66*61) + (81*66 / 61*66) = (4575 / 4026) + (5346 / 4026) = (4575 + 5346) / 4026 = 9921 / 4026. The fraction 9921/4026 can be reduced to its lowest terms by dividing both the numerator and denominator by their greatest common divisor, which is 3: 9921 / 4026 = 3307 / 1342. ### Answer: 3307/1342.
Expected answer: 3307/1342
Correct? Yes
Problem: After you have computed ((75 / 66) + (81 / 61)), what is the result if you additionally add (47 / 19) to that sum? Give your response as a simplified fraction.
GPT-3.5 Turbo:
We already found that ((75 / 66) + (81 / 61)) = 3307/1342. Now, we add (47 / 19) to this sum: 3307/1342 + 47/19 = (3307*19 + 47*1342) / (1342*19) = (62833 + 63374) / 25498 = 126207 / 25498. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 13: 126207 / 25498 = 9701 / 1961. ### Answer: 9701/1961.
Expected answer: 125907/25498
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.
GPT-3.5 Turbo:
Given fractions: t = 53/18 + 21/99 To find the common denominator, we need to find the least common multiple (LCM) of 18 and 99: 18 = 2 * 3^2 99 = 3^2 * 11 LCM(18, 99) = 2 * 3^2 * 11 = 594 Rewrite the fractions with the common denominator: t = (53*33)/(18*33) + (21*6)/(99*6) t = 1854/594 + 126/594 t = 1980/594 Since we have two identical fractions, the total sum l is: l = 2 * t l = 2 * 1980/594 l = 3960/594 l = 220/33 ### Answer: 220/33.
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?
GPT-3.5 Turbo:
First, find a common denominator for the fractions 58/49 and 31/34. The least common multiple of 49 and 34 is 49*34 = 1666. Converting the fractions to have a denominator of 1666: 58/49 = (58*34)/(49*34) = 1972/1666 31/34 = (31*49)/(34*49) = 1519/1666 Adding the fractions: 1972/1666 + 1519/1666 = (1972 + 1519)/1666 = 3491/1666 Now, add 74/38 to the result: 3491/1666 + 74/38 = (3491*38 + 74*1666)/(1666*38) = (132458 + 123524)/63308 = 255982/63308 ### Answer: 255982/63308.
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.
GPT-3.5 Turbo:
To find the sum of 100 divided by 76 and 29 divided by 14, we first calculate each division separately: 100 divided by 76 is approximately 1.3158 (rounded to four decimal places). 29 divided by 14 is approximately 2.0714 (rounded to four decimal places). Adding these two results together, we get 1.3158 + 2.0714 ≈ 3.3872. ### Answer: 3.3872
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.
GPT-3.5 Turbo:
To find out how much of the novel Olivia has read, we first need to find the fraction of the novel Evan has read. Evan has read 51/18 of the novel, which simplifies to 17/6. Olivia has read the same amount of the novel as Evan, which is 17/6. Olivia has read an additional 8/42 of the novel, which simplifies to 4/21. To find out how much of the novel Olivia has read in total, we add the fractions: 17/6 + 4/21 = (17*7)/(6*7) + 4/21 = 119/42 + 4/21 = (119*2)/(42*2) + 4/21 = 238/84 + 4/21 = 238/84 + 16/84 = 254/84 = 127/42. Therefore, Olivia has read 127/42 of the novel in total. ### Answer: 127/42.
Expected answer: 127/42
Correct? Yes
Problem: Building off of the previous question and given that Evan then continues to read and finishes the same amount of his novel as Olivia had read in total, how much of the novel has Evan read now? Answer as a simplified fraction.
GPT-3.5 Turbo:
Since Olivia has read 127/42 of the novel, Evan continues to read and finishes the same amount as Olivia had read. Therefore, Evan reads an additional 127/42 of the novel. To find out how much of the novel Evan has read in total, we add the fractions: 17/6 + 127/42 = (17*7)/(6*7) + 127/42 = 119/42 + 127/42 = (119+127)/42 = 246/42 = 123/21. Therefore, Evan has read 123/21 of the novel in total. ### Answer: 123/21.
Expected answer: 41/7
Correct? Yes
Problem: In the previous scenario, let's now instead assume that Olivia initially read 3/42 of her novel, instead of 8/42, before reading the same amount as Evan. Now how much of the novel has Olivia read altogether? Answer as a simplified fraction.
GPT-3.5 Turbo:
Given that Olivia initially read 3/42 of the novel, which simplifies to 1/14. Olivia then read the same amount of the novel as Evan, which is 17/6. To find out how much of the novel Olivia has read in total, we add the fractions: 1/14 + 17/6 = (1*6)/(14*6) + 17/6 = 6/84 + 17/6 = 6/84 + 238/84 = 244/84 = 61/21. Therefore, Olivia has read 61/21 of the novel in total. ### Answer: 61/21.
Expected answer: 61/21
Correct? Yes
Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.
GPT-3.5 Turbo:
To find the sum of 48 divided by 13 and 31 divided by 22, we first calculate each division: 48 divided by 13 is approximately 3.6923 (rounded to four decimal places). 31 divided by 22 is approximately 1.4091 (rounded to four decimal places). Adding these two results together, we get: 3.6923 + 1.4091 = 5.1014. ### Answer: 5.1014
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.
GPT-3.5 Turbo:
First, we find the value of 24/86 + 76/77: 24/86 + 76/77 = (24*77 + 76*86) / (86*77) = (1848 + 6536) / 6638 = 8384 / 6638 = 1.262 Next, we subtract this answer from 27/6: 27/6 - 1.262 = 4.5 - 1.262 = 3.238 ### Answer: 3.238
Expected answer: 21415/6622
Correct? No
Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of 73/39 and 49/14, we need to first find a common denominator. The least common multiple of 39 and 14 is 546. Converting 73/39 to have a denominator of 546: (73/39) * (14/14) = 1022/546 Converting 49/14 to have a denominator of 546: (49/14) * (39/39) = 1911/546 Now, adding the fractions: 1022/546 + 1911/546 = 2933/546 Therefore, the sum of 73/39 and 49/14 is 2933/546. ### Answer: 2933/546.
Expected answer: 419/78
Correct? Yes
Problem: After finding the sum of 73/39 and 49/14 (the last problem), now add the result to 21/80. What is the new total? Express your answer as a simplified fraction.
GPT-3.5 Turbo:
The sum of 73/39 and 49/14 is 2933/546 from the previous calculation. To add 2933/546 and 21/80, we need to find a common denominator. The least common multiple of 546 and 80 is 43680. Converting 2933/546 to have a denominator of 43680: (2933/546) * (80/80) = 234640/43680 Converting 21/80 to have a denominator of 43680: (21/80) * (546/546) = 10986/43680 Now, adding the fractions: 234640/43680 + 10986/43680 = 245626/43680 Therefore, the new total after adding 21/80 to the sum of 73/39 and 49/14 is 245626/43680, which can be simplified to 122813/21840. ### Answer: 122813/21840.
Expected answer: 17579/3120
Correct? No
Problem: After finding the sum of 73/6 and 49/14 (instead of 73/39 as in the previous question), what would be the new total? Please express it as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of 73/6 and 49/14, we need to first find a common denominator. The least common multiple of 6 and 14 is 42. Converting 73/6 to have a denominator of 42: (73/6) * (7/7) = 511/42 Converting 49/14 to have a denominator of 42: (49/14) * (3/3) = 147/42 Now, adding the fractions: 511/42 + 147/42 = 658/42 Therefore, the sum of 73/6 and 49/14 is 658/42, which simplifies to 329/21. ### Answer: 329/21.
Expected answer: 47/3
Correct? Yes
Problem: What is the sum of 75/65 and 7/39? Simplify your answer.
GPT-3.5 Turbo:
To find the sum of 75/65 and 7/39, we need to find a common denominator first. The least common multiple of 65 and 39 is 195. Converting 75/65 to have a denominator of 195, we get (75/65) * (3/3) = 225/195. Converting 7/39 to have a denominator of 195, we get (7/39) * (5/5) = 35/195. Now, adding the fractions, we get 225/195 + 35/195 = 260/195. Simplifying the fraction 260/195, we get 4/3. ### Answer: 4/3.
Expected answer: 4/3
Correct? Yes
Problem: You previously calculated the sum of 75/65 and 7/39. Now, add the fraction 65/97 to your result. What is your new total?
GPT-3.5 Turbo:
To add 65/97 to the previous result of 4/3, we need to find a common denominator. The least common multiple of 3 and 97 is 291. Converting 4/3 to have a denominator of 291, we get (4/3) * (97/97) = 388/291. Converting 65/97 to have a denominator of 291, we get (65/97) * (3/3) = 195/291. Now, adding the fractions, we get 388/291 + 195/291 = 583/291. Simplifying the fraction 583/291, we get 2. ### Answer: 2.
Expected answer: 583/291
Correct? No
Problem: In a previous calculation, you found the sum of 75/65 and 7/39. Now, suppose we had originally used 75/65 and 7/47 instead. What would be the sum of these two fractions?
GPT-3.5 Turbo:
To find the sum of 75/65 and 7/47, we need to find a common denominator first. The least common multiple of 65 and 47 is 3055. Converting 75/65 to have a denominator of 3055, we get (75/65) * (47/47) = 3525/3055. Converting 7/47 to have a denominator of 3055, we get (7/47) * (65/65) = 455/3055. Now, adding the fractions, we get 3525/3055 + 455/3055 = 3980/3055. Simplifying the fraction 3980/3055, we get 796/611. ### Answer: 796/611.
Expected answer: 796/611
Correct? Yes
Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?
GPT-3.5 Turbo:
First, calculate 79/1 - 30/92: 79/1 - 30/92 = 79 - 30/92 = 79 - 15/46 = (79*46 - 15)/46 = (3634 - 15)/46 = 3619/46 Next, subtract 61/63 from the result: 3619/46 - 61/63 = (3619*63 - 46*61)/(46*63) = (227997 - 2806)/(2898) = 225191/2898 Therefore, the value obtained is 225191/2898. ### Answer: 225191/2898.
Expected answer: 225191/2898
Correct? Yes
Problem: After you've calculated 79/1 - 30/92, and then subtracted 61/63 from the result, further subtract 59/7 from that resultant value. What fraction do you end up with?
GPT-3.5 Turbo:
First, we have the result from the previous calculation: 3619/46 - 61/63 = 225191/2898. Now, subtract 59/7 from this result: 225191/2898 - 59/7 = (225191*7 - 59*2898)/(2898*7) = (1576337 - 171282)/(20286) = 1405055/20286 Therefore, the final fraction obtained is 1405055/20286. ### Answer: 1405055/20286.
Expected answer: 200765/2898
Correct? No
Problem: After recalculating the previous problem, let's change the first fraction: instead of subtracting 30/92 from 79/1, we're going to subtract 3/92 instead. After that, we still need to subtract 61/63 from the result. What is the value after these operations?
GPT-3.5 Turbo:
First, calculate 79/1 - 3/92: 79/1 - 3/92 = 79 - 3/92 = 79 - 1/31 = (79*31 - 1)/31 = (2449 - 1)/31 = 2448/31 Next, subtract 61/63 from the result: 2448/31 - 61/63 = (2448*63 - 31*61)/(31*63) = (154224 - 1891)/(1953) = 152333/1953 Therefore, the value obtained is 152333/1953. ### Answer: 152333/1953.
Expected answer: 452083/5796
Correct? No
Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.
GPT-3.5 Turbo:
Reasoning: (58 / 26) + (58 / 26) = 2 * (58 / 26) = 2 * (29 / 13) = 58 / 13 = <<58/13=4.46>>4.46. ### Answer: 4.46
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?
GPT-3.5 Turbo:
To find the total amount of orange juice Alex had, we first need to add the amount he had initially with the additional amount he bought: 69/63 + 77/5 = (69*5 + 63*77)/(63*5) = (345 + 4851)/315 = 5196/315 = 116/7 gallons. Then, we add the amount he received from Sally: 116/7 + 47/71 = (116*71 + 7*47)/(7*71) = (8236 + 329)/4977 = 8565/4977 = 285/166 gallons. ### Answer: 285/166 gallons.
Expected answer: 127907/7455
Correct? No
Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.
GPT-3.5 Turbo:
First, we simplify the fractions within the parentheses: - 100 / 61 is already simplified. - 39 / 6 simplifies to 13 / 2. - 67 / 49 simplifies to 67 / 49. Next, we add the fractions: ((100 / 61) + ((39 / 6) + (67 / 49))) = (100 / 61) + (13 / 2) + (67 / 49) = (100 / 61) + (13 * 61 / 2 * 61) + (67 * 2 / 49 * 2) = (100 / 61) + (793 / 122) + (134 / 98) = (100 * 122 + 793 * 61 + 134 * 61) / (61 * 122) = (12200 + 48373 + 8174) / 7442 = 68747 / 7442 Therefore, ((100 / 61) + ((39 / 6) + (67 / 49))) simplifies to 68747 / 7442. ### Answer: 68747/7442.
Expected answer: 56831/5978
Correct? No
Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.
GPT-3.5 Turbo:
Reasoning: To find the sum of 85/1 and 83/69, we need to find a common denominator. The least common multiple of 1 and 69 is 69. So, we rewrite 85/1 as 85/1 * 69/69 = 85*69/1*69 = 5865/69. Now we can add the fractions: 5865/69 + 83/69 = (5865 + 83)/69 = 5948/69. This fraction cannot be simplified further. ### Answer: 5948/69.
Expected answer: 5948/69
Correct? Yes
Problem: After calculating the sum of 85/1 and 83/69, what is the result if you then add 21/86 to that sum?
GPT-3.5 Turbo:
Reasoning: We already found that the sum of 85/1 and 83/69 is 5948/69. Now, we need to add 21/86 to this sum. To do this, we need to find a common denominator, which is 69*86 = 5924. So, we rewrite 21/86 as 21*69/86*69 = 1449/5924. Now we can add the fractions: 5948/69 + 1449/5924 = (5948*5924 + 1449*69)/(69*5924) = 35207332/409956. This fraction cannot be simplified further. ### Answer: 35207332/409956.
Expected answer: 512977/5934
Correct? No
Problem: In the previous problem, instead of adding 83/69, what would be the result if you added 83/52 to 85/1 instead?
GPT-3.5 Turbo:
Reasoning: To find the sum of 85/1 and 83/52, we need to find a common denominator. The least common multiple of 1 and 52 is 52. So, we rewrite 85/1 as 85/1 * 52/52 = 85*52/1*52 = 4420/52. Now we can add the fractions: 4420/52 + 83/52 = (4420 + 83)/52 = 4503/52. This fraction cannot be simplified further. ### Answer: 4503/52.
Expected answer: 4503/52
Correct? Yes
Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?
GPT-3.5 Turbo:
To find the sum of 92/13 and 43/86, we need to first find a common denominator. The least common multiple of 13 and 86 is 13*86 = 1118. Converting 92/13 to have a denominator of 1118, we get (92/13) * (86/86) = 794/1118. Converting 43/86 to have a denominator of 1118, we get (43/86) * (13/13) = 559/1118. Now, adding the two fractions together, we get (794/1118) + (559/1118) = 1353/1118. Therefore, the sum of 92/13 and 43/86 as a simplified fraction is 1353/1118. ### Answer: 1353/1118.
Expected answer: 197/26
Correct? No
Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to find a common denominator. The least common multiple of 32 and 98 is 32*98 = 3136. Converting 67/32 to have a denominator of 3136, we get (67*98)/(32*98) = 6566/3136. Converting 10/98 to have a denominator of 3136, we get (10*32)/(98*32) = 320/3136. Adding the two fractions, we get (6566 + 320)/3136 = 6886/3136. ### Answer: 6886/3136.
Expected answer: 3443/1568
Correct? Yes
Problem: Now, to the sum of 67/32 and 10/98, add 14/59. What is the final result as a simplified fraction?
GPT-3.5 Turbo:
Reasoning: We already found that the sum of 67/32 and 10/98 is 6886/3136. To add 14/59 to this sum, we need to find a common denominator. The least common multiple of 3136 and 59 is 3136*59 = 184624. Converting 6886/3136 to have a denominator of 184624, we get (6886*59)/(3136*59) = 405634/184624. Converting 14/59 to have a denominator of 184624, we get (14*3136)/(59*3136) = 43904/184624. Adding the two fractions, we get (405634 + 43904)/184624 = 449538/184624. ### Answer: 449538/184624.
Expected answer: 225089/92512
Correct? No
Problem: Let's reconsider the previous problem. Instead of a fraction of 67/32, consider a fraction of 43/32. Keeping the second fraction of 10/98 the same, what would be the new sum expressed as a simplified fraction?
GPT-3.5 Turbo:
Reasoning: Using the same common denominator of 3136, we have: 43/32 = (43*98)/(32*98) = 4214/3136 10/98 = 320/3136 Adding the two fractions, we get (4214 + 320)/3136 = 4534/3136. ### Answer: 4534/3136.
Expected answer: 2267/1568
Correct? Yes
Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.
GPT-3.5 Turbo:
To find the sum of 59/52 and 70/32, we need to first find a common denominator. The least common multiple of 52 and 32 is 416. Converting 59/52 to have a denominator of 416: 59/52 * 8/8 = 472/416 Converting 70/32 to have a denominator of 416: 70/32 * 13/13 = 910/416 Now, adding the fractions: 472/416 + 910/416 = (472 + 910) / 416 = 1382/416 Simplifying the fraction: 1382/416 = 691/208 ### Answer: 691/208.
Expected answer: 691/208
Correct? Yes
Problem: After finding the sum of 59/52 and 70/32, add this to 42/41. What is the final sum as a simplified fraction?
GPT-3.5 Turbo:
To add 691/208 and 42/41, we need to find a common denominator. The least common multiple of 208 and 41 is 8528. Converting 691/208 to have a denominator of 8528: 691/208 * 41/41 = 28331/8528 Converting 42/41 to have a denominator of 8528: 42/41 * 208/208 = 8736/8528 Now, adding the fractions: 28331/8528 + 8736/8528 = (28331 + 8736) / 8528 = 37067/8528 Simplifying the fraction: 37067/8528 = 4633/1066 ### Answer: 4633/1066.
Expected answer: 37067/8528
Correct? No
Problem: After recalculating the original problem with 74/52 instead of 59/52 and still adding this to 70/32, what is the new sum as a simplified fraction?
GPT-3.5 Turbo:
To find the sum of 74/52 and 70/32, we need to first find a common denominator. The least common multiple of 52 and 32 is 416. Converting 74/52 to have a denominator of 416: 74/52 * 8/8 = 592/416 Converting 70/32 to have a denominator of 416: 70/32 * 13/13 = 910/416 Now, adding the fractions: 592/416 + 910/416 = (592 + 910) / 416 = 1502/416 Simplifying the fraction: 1502/416 = 751/208 ### Answer: 751/208.
Expected answer: 751/208
Correct? Yes
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?
GPT-3.5 Turbo:
Let's first calculate 48 divided by 5 which is 48/5 = 9.6. Then, we calculate 11 divided by 65 which is 11/65 ≈ 0.1692. Next, we subtract 9.6 from 0.1692 which gives us approximately -9.4308. Finally, we add this result to 28 divided by 2 which is 28/2 = 14. Therefore, the final answer is 14 - 9.4308 ≈ 4.5692. ### Answer: 4.5692
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.
GPT-3.5 Turbo:
To add 20/52 and 75/82, we need to find a common denominator, which is 52*82 = 4264. 20/52 = 820/4264 75/82 = 3300/4264 820/4264 + 3300/4264 = 4120/4264 = 206/213 ### Answer: 206/213.
Expected answer: 1385/1066
Correct? No
Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.
GPT-3.5 Turbo:
We first find a common denominator for 84 and 5, which is 420. Then, we rewrite the fractions with the common denominator: 31/5 = 31 * 84 / 5 * 84 = 2604/420, 92/84 = 92 * 5 / 84 * 5 = 460/420. Subtracting the fractions gives us: 2604/420 - 460/420 = (2604 - 460) / 420 = 2144/420 = 536/105. ### Answer: 536/105.
Expected answer: 536/105
Correct? Yes
Problem: In the previous problem, we subtracted 67/84 from 31/5. The result was a certain simplified fraction, but what if instead of 92/84, we had only subtracted 67/84 from 31/5? What would the result be as a simplified fraction with this modification?
GPT-3.5 Turbo:
We first find a common denominator for 84 and 5, which is 420. Then, we rewrite the fractions with the common denominator: 31/5 = 31 * 84 / 5 * 84 = 2604/420, 67/84 = 67 * 5 / 84 * 5 = 335/420. Subtracting the fractions gives us: 2604/420 - 335/420 = (2604 - 335) / 420 = 2269/420. To simplify this fraction, we find the greatest common divisor (GCD) of 2269 and 420, which is 1. Therefore, the fraction is already in its simplest form. ### Answer: 2269/420.
Expected answer: 2269/420
Correct? Yes
Problem: Calculate the following: Double the sum of 81/90 and 94/49.
GPT-3.5 Turbo:
Reasoning: The sum of 81/90 and 94/49 is (81/90) + (94/49) = (81*49 + 94*90) / (90*49) = (3969 + 8460) / 4410 = 12429 / 4410. Doubling this sum gives 2 * (12429 / 4410) = 24858 / 4410 = 562/99. ### Answer: 562/99.
Expected answer: 1381/245
Correct? No
Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.
GPT-3.5 Turbo:
To find the difference between two fractions, we need to have a common denominator. The common denominator for 21 and 92 is 21 * 92 = 1932. Converting 69/21 and 10/92 to have a common denominator: 69/21 = (69 * 92) / (21 * 92) = 6348/1932 10/92 = (10 * 21) / (92 * 21) = 210/1932 Now, we can find the difference: 6348/1932 - 210/1932 = 6138/1932 = 319/96 ### Answer: 319/96.
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?
GPT-3.5 Turbo:
First, calculate (26 / 87) + (92 / 88): (26 / 87) + (92 / 88) = 0.2989 + 1.0455 = 1.3444 Now, add the result to (26 / 57): 1.3444 + (26 / 57) = 1.3444 + 0.4561 = 1.8005 ### Answer: 1.8005
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.
GPT-3.5 Turbo:
To add the fractions, we need to find a common denominator. The least common multiple of 66, 6, and 34 is 66*6*34 = 13,608. 78/66 = (78*206)/ (66*206) = 5088/8168 28/6 = (28*2268)/ (6*2268) = 6384/13608 90/34 = (90*399)/ (34*399) = 3591/13608 Adding the fractions together: 5088/8168 + 6384/13608 + 3591/13608 = (5088 + 6384 + 3591) / 13608 = 15063 / 13608 ### Answer: 15063/13608.
Expected answer: 4766/561
Correct? No
Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.
GPT-3.5 Turbo:
To subtract fractions, we need a common denominator. The least common multiple of 7 and 23 is 7 * 23 = 161. (12/7) - (9/23) = (12*23/161) - (9*7/161) = (276/161) - (63/161) = (276 - 63) / 161 = 213/161. ### Answer: 213/161.
Expected answer: 213/161
Correct? Yes
Problem: After finding the result of (12 / 7) - (9 / 23), use your answer as t. Then, calculate (40 / 11) - t. What do you find? Please express your answer as a simplified fraction.
GPT-3.5 Turbo:
Given t = 213/161, we can substitute this into the expression (40/11) - t: (40/11) - (213/161) = (40*161/11*161) - (213*11/161*11) = (6440/1771) - (2343/1771) = (6440 - 2343) / 1771 = 4097/1771. ### Answer: 4097/1771.
Expected answer: 4097/1771
Correct? Yes
Problem: In the previous problem, you calculated (12 / 7) - (9 / 23) which accounted for certain quantities of two different fruits. Now suppose you actually had 12/7th of a crate of oranges but only 9/48th of a crate of apples. In that case, what would be the resulting difference in fractions between the two fruit quantities? Simplify your answer to the lowest terms.
GPT-3.5 Turbo:
To find the difference between the fractions representing the quantities of oranges and apples, we need to find a common denominator. The least common multiple of 7 and 48 is 336. (12/7) - (9/48) = (12*48/336) - (9*7/336) = (576/336) - (63/336) = (576 - 63) / 336 = 513/336. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3. 513/336 = (513 ÷ 3) / (336 ÷ 3) = 171/112. ### Answer: 171/112.
Expected answer: 171/112
Correct? Yes
Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to find a common denominator. The least common multiple of 18 and 61 is 18 * 61 = 1098. Converting 95/18 to have a denominator of 1098: (95/18) * (61/61) = 5775/1098 Converting 51/61 to have a denominator of 1098: (51/61) * (18/18) = 928/1098 Now, adding the fractions: 5775/1098 + 928/1098 = 6703/1098 ### Answer: 6703/1098.
Expected answer: 6713/1098
Correct? No
Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.
GPT-3.5 Turbo:
To subtract fractions, we need to have a common denominator. The least common multiple of 46 and 84 is 2 * 23 * 3 * 7 = 966. Converting the fractions to have a common denominator: (93/46) = (93/46) * (21/21) = 1953/966 (51/84) = (51/84) * (11/11) = 561/966 Subtracting the fractions: (1953/966) - (561/966) = (1953 - 561) / 966 = 1392 / 966 The simplified fraction is 232/161. ### Answer: 232/161.
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.
GPT-3.5 Turbo:
To add fractions, we need to have a common denominator. In this case, the least common multiple of 70 and 9 is 630. Converting 12/70 to an equivalent fraction with a denominator of 630: 12/70 = (12*9)/(70*9) = 108/630 Converting 84/9 to an equivalent fraction with a denominator of 630: 84/9 = (84*70)/(9*70) = 588/630 Now, adding the fractions: 108/630 + 588/630 = (108 + 588) / 630 = 696 / 630 Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 6: 696/630 = (696 ÷ 6) / (630 ÷ 6) = 116/105 ### Answer: 116/105.
Expected answer: 998/105
Correct? No
Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?
GPT-3.5 Turbo:
First, let's find the result of subtracting 40/92 from 32/3: 32/3 - 40/92 = (32*92 - 40*3) / (3*92) = (2944 - 120) / 276 = 2824 / 276 = 353/69 Now, let's double the result: 2 * 353/69 = 706/69 ### Answer: 706/69
Expected answer: 1412/69
Correct? No
Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: The sum of 79/24 and 79/24 is 79/24 + 79/24 = (79+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.
GPT-3.5 Turbo:
Reasoning: The sum of (79/24 + 79/24) + (79/24 + 79/24) is (79/12) + (79/12) = 2*(79/12) = 158/12 = 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.
GPT-3.5 Turbo:
Reasoning: The sum of 79/20 and 79/20 is 79/20 + 79/20 = (79+79)/20 = 158/20 = 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.
GPT-3.5 Turbo:
To find the sum of 91/76 and 12/22, we need to find a common denominator first. The least common multiple of 76 and 22 is 836. Converting 91/76 to have a denominator of 836, we get (91*11)/(76*11) = 1001/836. Converting 12/22 to have a denominator of 836, we get (12*38)/(22*38) = 456/836. Now, adding the fractions: 1001/836 + 456/836 = 1457/836. ### Answer: 1457/836.
Expected answer: 1457/836
Correct? Yes
Problem: The previous problem asked to calculate the sum of 91/76 and 12/22. Now, what would be the sum if you added 94/59 to the result of the previous problem? Please give your answer as a simplified fraction.
GPT-3.5 Turbo:
The previous sum we found was 1457/836. To find the sum of 1457/836 and 94/59, we need to find a common denominator. The least common multiple of 836 and 59 is 49204. Converting 1457/836 to have a denominator of 49204, we get (1457*59)/(836*59) = 85963/49204. Converting 94/59 to have a denominator of 49204, we get (94*836)/(59*836) = 78584/49204. Now, adding the fractions: 85963/49204 + 78584/49204 = 164547/49204. Simplifying the fraction, we get: 164547/49204 = 3.34 (rounded to two decimal places). ### Answer: 164547/49204.
Expected answer: 164547/49324
Correct? No
Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?
GPT-3.5 Turbo:
First, we need to find a common denominator for 88/93 and 6/47. The least common multiple of 93 and 47 is 93*47 = 4361. Converting 88/93 to have a denominator of 4361, we get 88/93 * 47/47 = 4104/4361. Converting 6/47 to have a denominator of 4361, we get 6/47 * 93/93 = 558/4361. Adding 4104/4361 and 558/4361, we get (4104 + 558)/4361 = 4662/4361. Now, we add 4662/4361 to 92/4. Converting 92/4 to have a denominator of 4361, we get 92/4 * 1090/1090 = 100280/4361. Adding 4662/4361 and 100280/4361, we get (4662 + 100280)/4361 = 105942/4361. ### Answer: 105942/4361.
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.
GPT-3.5 Turbo:
Calculating the sum of 95/83 and 52/21 + 75/67: 95/83 + 52/21 + 75/67 To add fractions, we need a common denominator. The least common multiple of 83, 21, and 67 is 83*21*67 = 114471. Converting each fraction to have a denominator of 114471: (95/83)*(114471/114471) + (52/21)*(5461/5461) + (75/67)*(1713/1713) = 10845/114471 + 28852/114471 + 128475/114471 = (10845 + 28852 + 128475)/114471 = 167172/114471 = 167172/114471 ### Answer: 167172/114471.
Expected answer: 553562/116781
Correct? No
Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.
GPT-3.5 Turbo:
To simplify the expression ((73 / 27) - (23 / 48)), we need to find a common denominator for the fractions. First, we find the least common multiple (LCM) of 27 and 48, which is 432. Rewriting the fractions with the common denominator: ((73 * 16) / (27 * 16)) - ((23 * 9) / (48 * 9)) = (1168 / 432) - (207 / 432) Now, subtracting the fractions: (1168 - 207) / 432 = 961 / 432 Therefore, ((73 / 27) - (23 / 48)) simplifies to 961/432. ### Answer: 961/432.
Expected answer: 961/432
Correct? Yes
Problem: What is the value of the original expression ((73 / 27) - (23 / 48)) minus the fraction 61/59? Answer as a simplified fraction.
GPT-3.5 Turbo:
We already found that the original expression ((73 / 27) - (23 / 48)) simplifies to 961/432. Subtracting the fraction 61/59 from 961/432: (961/432) - (61/59) To subtract these fractions, we need to find a common denominator, which is 432 * 59 = 25488. Rewriting the fractions with the common denominator: (961 * 59) / (432 * 59) - (61 * 432) / (59 * 432) = (56699 / 25488) - (26352 / 25488) Now, subtracting the fractions: (56699 - 26352) / 25488 = 30347 / 25488 Therefore, ((73 / 27) - (23 / 48)) - 61/59 simplifies to 30347/25488. ### Answer: 30347/25488.
Expected answer: 30347/25488
Correct? Yes
Problem: In the previous question, we calculated the value of the expression ((73 / 27) - (23 / 48)). Now, suppose we made a mistake and the original fraction was actually 65/27, not 73/27. What would the value of the new expression be? Answer as a simplified fraction.
GPT-3.5 Turbo:
Given the corrected expression ((65 / 27) - (23 / 48)), we need to find a common denominator for the fractions. First, we find the least common multiple (LCM) of 27 and 48, which is 432. Rewriting the fractions with the common denominator: ((65 * 16) / (27 * 16)) - ((23 * 9) / (48 * 9)) = (1040 / 432) - (207 / 432) Now, subtracting the fractions: (1040 - 207) / 432 = 833 / 432 Therefore, the corrected expression ((65 / 27) - (23 / 48)) simplifies to 833/432. ### Answer: 833/432.
Expected answer: 833/432
Correct? Yes
Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.
GPT-3.5 Turbo:
First, we simplify the expression: (78 / 2) - (70 / 23) = 39 - (70 / 23). Next, we convert 39 to a fraction with a denominator of 23: 39 = (39 * 23) / 23 = 897 / 23. Now, we substitute this back into the expression: 897/23 - 70/23 = (897 - 70) / 23 = 827 / 23. Therefore, the simplified expression is 827/23 as a fraction. ### Answer: 827/23.
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?
GPT-3.5 Turbo:
Continuing from the previous problem, we have: (78 / 2) - (70 / 23) = 827/23. Now, we add 827/23 to 92/67: 827/23 + 92/67. To add these fractions, we need to find a common denominator, which is 23 * 67 = 1541. Rewriting the fractions with the common denominator: (827 * 67) / 1541 + (92 * 23) / 1541 = 55409/1541 + 2116/1541 = (55409 + 2116) / 1541 = 57525 / 1541. Therefore, the result of adding 827/23 to 92/67 is 57525/1541 as a simplified fraction. ### Answer: 57525/1541.
Expected answer: 57525/1541
Correct? Yes
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?
GPT-3.5 Turbo:
Substitute 36 for the total number of parts in the expression: (36 / 2) - (70 / 23) = 18 - (70 / 23). Now, we convert 18 to a fraction with a denominator of 23: 18 = (18 * 23) / 23 = 414 / 23. Substitute this back into the expression: 414/23 - 70/23 = (414 - 70) / 23 = 344 / 23. Therefore, the simplified expression is 344/23 as a fraction. ### Answer: 344/23.
Expected answer: 344/23
Correct? Yes
Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.
GPT-3.5 Turbo:
Reasoning: To add 34/1 and 53/4, we need to find a common denominator, which is 4. Converting 34/1 to have a denominator of 4, we get 34/1 = 136/4. Now, we can add 136/4 + 53/4 = 189/4. Converting 189/4 to a mixed number, we get 47 1/4. ### 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.
GPT-3.5 Turbo:
Reasoning: We already found that 34/1 + 53/4 = 47 1/4. Now, we need to add 24/67 to 47 1/4. To add 24/67 to 47 1/4, we first convert 47 1/4 to an improper fraction: 47 1/4 = 189/4. Adding 24/67 to 189/4, we get (24*4 + 67*189)/(67*4) = (96 + 12663)/268 = 12759/268. Converting 12759/268 to a mixed number, we get 47 95/268. ### Answer: 47 95/268.
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.
GPT-3.5 Turbo:
Reasoning: To add 34/97 and 53/4, we need to find a common denominator, which is 97*4 = 388. Converting 34/97 to have a denominator of 388, we get 34/97 = 136/388. Converting 53/4 to have a denominator of 388, we get 53/4 = 477/388. Now, we can add 136/388 + 477/388 = 613/388. Converting 613/388 to a mixed number, we get 1 225/388. ### Answer: 1 225/388.
Expected answer: 5277/388
Correct? No
Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need a common denominator. The least common multiple of 36 and 96 is 144. So, we rewrite the fractions with a denominator of 144: 3/36 = 12/144 97/96 = 145/144 Now, we add the fractions: 12/144 + 145/144 = 157/144 ### Answer: 157/144.
Expected answer: 35/32
Correct? No
Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.
GPT-3.5 Turbo:
First, we find a common denominator for the fractions: ((92 / 95) + (4 / 74)) = ((92 * 74) / (95 * 74)) + ((4 * 95) / (74 * 95)) = (6808 / 7030) + (380 / 7030) = (6808 + 380) / 7030 = 7188 / 7030. ### Answer: 7188/7030.
Expected answer: 3594/3515
Correct? Yes
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.
GPT-3.5 Turbo:
Given that \( v = \frac{69}{47} \), we can substitute this value into the expression for \( d \) to find its value:
\[ d = \frac{88}{72} + v = \frac{88}{72} + \frac{69}{47} = \frac{88 \times 47 + 72 \times 69}{72 \times 47} = \frac{4136 + 4968}{3384} = \frac{9104}{3384} = \frac{2276}{846} \]
Therefore, the value of \( d \) is \( \frac{2276}{846} \).
### Answer: \( \frac{2276}{846} \)
Expected answer: 1138/423
Correct? Yes
Problem: Following from the last question, if we now have a new variable 'r' which is defined as 92/22 + 'd', what is the value of 'r'? Please write your answer as a fraction.
GPT-3.5 Turbo:
Given that \( d = \frac{2276}{846} \), we can substitute this value into the expression for \( r \) to find its value:
\[ r = \frac{92}{22} + d = \frac{92}{22} + \frac{2276}{846} = \frac{92 \times 846 + 22 \times 2276}{22 \times 846} = \frac{77832 + 50172}{18612} = \frac{128004}{18612} = \frac{64002}{9306} = \frac{32001}{4653} \]
Therefore, the value of \( r \) is \( \frac{32001}{4653} \).
### Answer: \( \frac{32001}{4653} \)
Expected answer: 31976/4653
Correct? No
Problem: In the problem from before, let's consider that variable 'v' no longer represents 69/47, but is now represented by 69/8. Given that change, what is the new value for 'd' if 'd' continues to be defined as the sum of 88/72 and 'v'? Write your answer as a fraction.
GPT-3.5 Turbo:
Given that \( v = \frac{69}{8} \), we can substitute this new value into the expression for \( d \) to find its value:
\[ d = \frac{88}{72} + v = \frac{88}{72} + \frac{69}{8} = \frac{88 \times 8 + 72 \times 69}{72 \times 8} = \frac{704 + 4968}{576} = \frac{5672}{576} = \frac{1981}{202} \]
Therefore, the new value of \( d \) is \( \frac{1981}{202} \).
### Answer: \( \frac{1981}{202} \)
Expected answer: 709/72
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.
GPT-3.5 Turbo:
To find out how much olive oil the wholesaler has left, we need to subtract the portion they sold from the total amount they had initially. Total amount of olive oil = 41/26 barrels Amount sold = 41/72 barrels Amount left = Total amount - Amount sold Amount left = 41/26 - 41/72 To subtract these fractions, we need a common denominator, which is 72 in this case. Amount left = (41/26)*(72/72) - (41/72) Amount left = 2952/1872 - 533/1872 Amount left = (2952 - 533)/1872 Amount left = 2419/1872 ### Answer: 2419/1872.
Expected answer: 943/936
Correct? No
Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.
GPT-3.5 Turbo:
To find the sum of 85/75 and 88/56, we first need to find a common denominator. The least common multiple of 75 and 56 is 420. 85/75 = (85*4)/(75*4) = 340/300 88/56 = (88*7)/(56*7) = 616/392 Now, we add the fractions: 340/300 + 616/392 = (340*392 + 616*300) / (300*392) = (133280 + 184800) / 117600 = 318080 / 117600 Converting this fraction to a decimal gives us: 318080 / 117600 ≈ 2.704 ### Answer: 2.704
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.
GPT-3.5 Turbo:
To add 12/33 and 49/2, we need to find a common denominator, which is 33*2 = 66. 12/33 = 8/22 = 4/11 49/2 = 24.5 Now, adding 4/11 and 24.5, we get: 4/11 + 24.5 = 4/11 + 24.5 = 4/11 + 267.5/11 = 271.5/11 = 24 3/11 ### Answer: 24 3/11.
Expected answer: 547/22
Correct? No
Problem: What is the result of adding two fractions, where each fraction is 78/65?
GPT-3.5 Turbo:
Reasoning: To add two fractions, we need to have a common denominator. In this case, the common denominator is 65. So, we have: 78/65 + 78/65 = (78 + 78) / 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?
GPT-3.5 Turbo:
Reasoning: We already found that 78/65 + 78/65 = 156/65. Now, to add 156/65 and 71/32, we need to find a common denominator, which is 65*32 = 2080. Converting 156/65 and 71/32 to have a common denominator of 2080, we get: 156/65 * 32/32 = 4992/2080, 71/32 * 65/65 = 4555/2080. Adding these two fractions together, we get: 4992/2080 + 4555/2080 = 9547/2080. ### Answer: 9547/2080.
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?
GPT-3.5 Turbo:
Reasoning: If both fractions are equal to 78/78, then the sum of the fractions would be: 78/78 + 78/78 = (78 + 78) / 78 = 156 / 78 = 2. ### Answer: 2.
Expected answer: 2
Correct? Yes
Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.
GPT-3.5 Turbo:
Reasoning: To add fractions, we need to find a common denominator. The least common multiple of 7 and 90 is 630. We rewrite 16/7 as 16*90/7*90 = 1440/630 and 11/90 as 11*7/90*7 = 77/630. Adding these fractions gives us (1440 + 77)/630 = 1517/630, which is the simplified fraction. ### Answer: 1517/630.
Expected answer: 1517/630
Correct? Yes
Problem: After finding the sum of 16/7 and 11/90, add your answer to 38/69. What is this new sum, expressed as a simplified fraction?
GPT-3.5 Turbo:
Reasoning: We already found the sum of 16/7 and 11/90 to be 1517/630. To add this sum to 38/69, we need to find a common denominator. The least common multiple of 630 and 69 is 630*69 = 43470. We rewrite 1517/630 as 1517*69/630*69 = 104673/43470 and 38/69 as 38*630/69*630 = 23820/43470. Adding these fractions gives us (104673 + 23820)/43470 = 128493/43470, which is the simplified fraction. ### Answer: 128493/43470.
Expected answer: 42871/14490
Correct? No
Problem: In the previous problem, you calculated the sum of 16/7 and 11/90. Now, let's consider if there were actually 99 parts out of 90 (as strange as that might sound) instead of 11 parts out of 90. What would be the sum of 16/7 and 99/90, expressed as a simplified fraction?
GPT-3.5 Turbo:
Reasoning: If we have 99 parts out of 90 instead of 11 parts out of 90, we rewrite 99/90 as 99*7/90*7 = 693/630. Adding this to 16/7 gives us (1440 + 693)/630 = 2133/630, which is the simplified fraction. ### Answer: 2133/630.
Expected answer: 237/70
Correct? Yes