Claude-3 Haiku on 7.NS.A.1-fraction
Common Core Standard 7.NS.A.1-fraction
This standard covers the following:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Problem: Math problem: Determine the value of the sum when adding (74 / 63) and (91 / 78).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to calculate the value of (74 / 63): 74 / 63 = 1.1746 2) Next, we need to calculate the value of (91 / 78): 91 / 78 = 1.1667 3) Now, we add the two values together: 1.1746 + 1.1667 = 2.3413 ### Answer: 2.3413
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common denominator is 25. 3) To convert 94/5 to have a denominator of 25, we multiply the numerator and denominator by 5: 94/5 = 470/25 4) Now we can add the two fractions: 470/25 + 1/25 = 471/25 ### Answer: 471/25
Expected answer: 471/25
Correct? Yes
Problem: If the sum from the previous problem is then added to 73/89, what is the final result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) From the previous problem, the sum was 471/25. 2) Now we need to add 73/89 to 471/25. 3) To do this, we need to find a common denominator. The least common denominator is 2225 (the product of 25 and 89). 4) Converting the fractions to have a denominator of 2225: 471/25 = 4239/2225 73/89 = 1825/2225 5) Now we can add the fractions: 4239/2225 + 1825/2225 = 6064/2225 ### Answer: 6064/2225
Expected answer: 43744/2225
Correct? No
Problem: If instead of adding 94/5 you had added 94/89 to 1/25 in the previous problem, what would have been the result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common denominator is 2225 (the product of 89 and 25). 3) To convert 94/89 to have a denominator of 2225, we multiply the numerator and denominator by 25: 94/89 = 2350/2225 4) To convert 1/25 to have a denominator of 2225, we multiply the numerator and denominator by 89: 1/25 = 89/2225 5) Now we can add the two fractions: 2350/2225 + 89/2225 = 2439/2225 ### Answer: 2439/2225
Expected answer: 2439/2225
Correct? Yes
Problem: What is the result of subtracting 48/20 from 49/8? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to convert the fractions to have a common denominator. The common denominator will be the least common multiple of 20 and 8, which is 40. 49/8 = 49 * 5/40 = 245/40 48/20 = 48 * 2/40 = 96/40 2) Now we can subtract the fractions: 245/40 - 96/40 = 149/40 3) The final answer is the simplified fraction 149/40. ### Answer: 149/40
Expected answer: 149/40
Correct? Yes
Problem: Suppose we had made a mistake in the original problem and it was actually 48/14 we were to subtract from 49/8. What would the result have been in that case? Please answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to convert the fractions to have a common denominator. The common denominator will be the least common multiple of 14 and 8, which is 56. 49/8 = 49 * 7/56 = 343/56 48/14 = 48 * 4/56 = 192/56 2) Now we can subtract the fractions: 343/56 - 192/56 = 151/56 3) The final answer is the simplified fraction 151/56. ### Answer: 151/56
Expected answer: 151/56
Correct? Yes
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1) First, we need to evaluate the expression (45 / 5): 45 / 5 = 9 2) Next, we need to evaluate the expression (6 / 47): 6 / 47 = 0.127659574468085 3) Now, we can subtract the two values: 9 - 0.127659574468085 = 8.872340425531915 ### Answer: 8.872340425531915
Expected answer: 417/47
Correct? Yes
Problem: After finding the value of ((45 / 5) - (6 / 47)), what would be the result if you add this value to itself?
Claude-3 Haiku:
Okay, let's work this out step-by-step: 1) First, we calculated the value of ((45 / 5) - (6 / 47)) to be: 8.872340425531915 2) Now, we need to add this value to itself: 8.872340425531915 + 8.872340425531915 = 17.744680851063830 ### Answer: 17.744680851063830
Expected answer: 834/47
Correct? No
Problem: After reconsideration, suppose there were actually 63 oranges instead of 45. Now calculate the value of the expression ((63 / 5) - (6 / 47)).
Claude-3 Haiku:
Okay, let's recalculate the expression with the new information: 1) First, we need to evaluate the expression (63 / 5): 63 / 5 = 12.6 2) Next, we need to evaluate the expression (6 / 47): 6 / 47 = 0.127659574468085 3) Now, we can subtract the two values: 12.6 - 0.127659574468085 = 12.472340425531915 ### Answer: 12.472340425531915
Expected answer: 2931/235
Correct? No
Problem: What is the sum of 22/49 and 72/35? Provide your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 22/49 and 72/35. 2) To add fractions, we need to find the least common denominator (LCD). 3) The LCD of 49 and 35 is 245. 4) We need to convert the fractions to have the same denominator of 245. 5) 22/49 = 110/245 6) 72/35 = 495/245 7) Now we can add the fractions: 110/245 + 495/245 = 605/245. 8) To simplify the fraction, we can divide the numerator and denominator by their greatest common factor, which is 5. 9) 605/245 = 121/49. ### Answer: 121/49
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (39 / 9) - 39 divided by 9 is 4.33 2) (44 / 69) - 44 divided by 69 is 0.64 3) (39 / 9) - (44 / 69) - 4.33 - 0.64 = 3.69 ### Answer: 3.69
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 49/79 and 18/21. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 79 and 21 is 1659. 3) Convert the fractions to have the LCD of 1659: 49/79 = 1047/1659 18/21 = 1386/1659 4) Now we can add the fractions: 1047/1659 + 1386/1659 = 2433/1659 5) Simplifying the fraction, we get: 2433/1659 = 1.47 ### Answer: 1.47
Expected answer: 817/553
Correct? No
Problem: What is the sum of 95/46 and 65/31?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 95/46 and 65/31. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 46 and 31 is 1426. 3) Convert the fractions to have the LCD of 1426: 95/46 = 1425/1426 65/31 = 1365/1426 4) Now we can add the fractions: 1425/1426 + 1365/1426 = 2790/1426 5) Simplifying the final answer: 2790/1426 = 1.95 ### Answer: 1.95
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 25/63 and 74/6 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 63 and 6 is 378. 3) We need to convert the fractions to have the same denominator of 378: 25/63 = (25 * 6)/378 = 150/378 74/6 = (74 * 63)/378 = 4662/378 4) Now we can add the fractions: 150/378 + 4662/378 = 4812/378 5) Simplifying the final answer: 4812/378 = 12.73 ### Answer: 12.73
Expected answer: 802/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions: 79/91 and 100/47 2) To find the sum, we need to find a common denominator for the two fractions. 3) The least common denominator (LCD) of 91 and 47 is 4277. 4) So we need to convert the fractions to have a denominator of 4277: 79/91 = (79 * 47)/91 * 47 = 3713/4277 100/47 = (100 * 91)/47 * 91 = 9100/4277 5) Now we can add the fractions: 3713/4277 + 9100/4277 = 12813/4277 ### Answer: 12813/4277
Expected answer: 12813/4277
Correct? Yes
Problem: After finding the sum of 79/91 and 100/47, what is the result if you add this sum to itself?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 79/91 and 100/47 to be 12813/4277. 2) Now we need to add this sum to itself. 3) 12813/4277 + 12813/4277 = 25626/4277 4) Simplifying the fraction, we get: 25626/4277 = 6 ### Answer: 6
Expected answer: 25626/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((55 / 47) + (72 / 21)) 2) First, let's calculate the individual parts: (55 / 47) = 1.1702127659574468 (72 / 21) = 3.4285714285714284 3) Now, we add the two parts together: 1.1702127659574468 + 3.4285714285714284 = 4.5987841945288752 4) Rounding the final answer to 4 decimal places: ### Answer: 4.5988
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions: 86/62 and 99/41 2) To find the sum, we need to find a common denominator for the two fractions. 3) The least common denominator (LCD) of 62 and 41 is 2,542. 4) We need to convert the fractions to have the LCD of 2,542: 86/62 = (86 * 41) / (62 * 41) = 3,526 / 2,542 99/41 = (99 * 62) / (41 * 62) = 6,138 / 2,542 5) Now we can add the fractions: 3,526 / 2,542 + 6,138 / 2,542 = 9,664 / 2,542 6) Simplifying the final fraction, we get: 9,664 / 2,542 = 3.8 ### Answer: 3.8
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 87/88 and 24/13. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 88 and 13 is 1144. 3) We need to convert the fractions to have the LCD of 1144: 87/88 = 1012/1144 24/13 = 208/1144 4) Now we can add the fractions: 1012/1144 + 208/1144 = 1220/1144 5) Simplifying the fraction, we get: 1220/1144 = 61/57 ### Answer: 61/57
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate (68 / 33) 68 / 33 = 2.0606060606060606 Step 2: Calculate (70 / 25) 70 / 25 = 2.8 Step 3: Add the two results together 2.0606060606060606 + 2.8 = 4.8606060606060606 Step 4: Simplify the answer 4.8606060606060606 can be simplified to approximately 4.86. ### Answer: 4.86
Expected answer: 802/165
Correct? No
Problem: What is the summation of 35/97 and 11/9? Express the result in simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the summation of 35/97 and 11/9. 2) To add fractions, we need to find the least common denominator (LCD). 3) The LCD of 97 and 9 is 873. 4) We need to convert the fractions to have the same denominator of 873. 5) 35/97 = 315/873 6) 11/9 = 97/873 7) Now we can add the fractions: 315/873 + 97/873 = 412/873 8) To express the result in simplest form, we need to find the greatest common factor (GCF) of the numerator and denominator. 9) The GCF of 412 and 873 is 29. 10) Dividing both the numerator and denominator by 29, we get: 412/873 = 14/29. ### Answer: 14/29
Expected answer: 1382/873
Correct? No
Problem: What is the result of subtracting 79/70 from 11/5?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to convert the fractions to have a common denominator. The least common denominator is 70. 2) 11/5 = 154/70 3) 79/70 4) 154/70 - 79/70 = (154 - 79)/70 = 75/70 ### Answer: 75/70
Expected answer: 15/14
Correct? Yes
Problem: What is the result when you add 62/46 to your previous answer from subtracting 79/70 from 11/5?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Previous answer: 75/70 2) We need to convert 62/46 to have a common denominator of 70. 3) 62/46 = 90/70 4) 75/70 + 90/70 = 165/70 ### Answer: 165/70
Expected answer: 779/322
Correct? No
Problem: Previously, we solved for the difference when you subtracted 79/70 from 11/5. Now, consider what happens if you originally started with 61/5 instead of 11/5. What would be the result when you subtract 79/70 from this new value?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to convert the fractions to have a common denominator. The least common denominator is 70. 2) 61/5 = 854/70 3) 79/70 4) 854/70 - 79/70 = (854 - 79)/70 = 775/70 ### Answer: 775/70
Expected answer: 155/14
Correct? Yes
Problem: What is the sum of 68/16 and 52/78?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 68/16 = 4.25 2) 52/78 = 0.6666... 3) The sum of 4.25 and 0.6666... is 4.25 + 0.6666... = 4.9166... ### Answer: 4.9166...
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 21/75 and 44/47. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 75 and 47 is 3,525. 3) Now we need to convert the fractions to have the same denominator of 3,525: 21/75 = 945/3,525 44/47 = 3,120/3,525 4) Now we can add the fractions: 945/3,525 + 3,120/3,525 = 4,065/3,525 5) Simplifying the final answer: 4,065/3,525 = 1.15 ### Answer: 1.15
Expected answer: 1429/1175
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (77/5) - 77 divided by 5 is 15.4 2) (4/11) - 4 divided by 11 is 0.3636 3) (15.4 + 0.3636) - 15.4 + 0.3636 = 15.7636 ### Answer: 15.7636
Expected answer: 867/55
Correct? No
Problem: What's the sum of 60/48 and 37/47?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 60/48 - To add fractions, we need to find a common denominator. - The least common denominator (LCD) of 48 and 47 is 2256. - So we need to convert both fractions to have a denominator of 2256. - 60/48 = (60 * 47) / (48 * 47) = 2820 / 2256 2) 37/47 - 37/47 = (37 * 48) / (47 * 48) = 1776 / 2256 3) Adding the fractions: - 2820/2256 + 1776/2256 = 4596/2256 ### Answer: 4596/2256
Expected answer: 383/188
Correct? Yes
Problem: After finding the sum of 60/48 and 37/47, what would you get if you then added 35/35 to your result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Finding the sum of 60/48 and 37/47: - 60/48 = 2820/2256 - 37/47 = 1776/2256 - 2820/2256 + 1776/2256 = 4596/2256 2) Adding 35/35 to the result: - 35/35 = 1 - 4596/2256 + 1 = 4597/2256 ### Answer: 4597/2256
Expected answer: 571/188
Correct? No
Problem: After reconsidering her grocery list, Jane decided to buy 60/45 kilograms of apples instead of 60/48. If she still buys 37/47 kilograms of oranges, what would be the total weight of the apples and oranges she buys?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Apples: - Jane decided to buy 60/45 kilograms of apples instead of 60/48 kilograms. - To add fractions, we need to find a common denominator. - The least common denominator (LCD) of 45 and 47 is 2115. - So we need to convert both fractions to have a denominator of 2115. - 60/45 = (60 * 47) / (45 * 47) = 2820 / 2115 2) Oranges: - Jane still buys 37/47 kilograms of oranges. - 37/47 = (37 * 45) / (47 * 45) = 1665 / 2115 3) Total weight: - Total weight = Weight of apples + Weight of oranges - Total weight = 2820/2115 + 1665/2115 = 4485/2115 ### Answer: 4485/2115
Expected answer: 299/141
Correct? Yes
Problem: Solve ((14 / 72) + (25 / 6)).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((14 / 72) + (25 / 6)) 2) First, we need to convert the fractions to have a common denominator. 3) The common denominator will be the least common multiple of 72 and 6, which is 72. 4) 14/72 = 14 * (1/72) = 7/36 5) 25/6 = 25 * (12/72) = 300/72 6) Now we can add the fractions: 7) 7/36 + 300/72 = (7*2 + 300)/72 = 314/72 8) Simplifying the fraction, we get: 9) 314/72 = 4 + 26/72 = 4 + 13/36 ### Answer: 4 + 13/36
Expected answer: 157/36
Correct? Yes
Problem: In addition to the calculation you did in the last question, let's add another operation. Solve ((14 / 24) + ((14 / 72) + (25 / 6))).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((14 / 24) + ((14 / 72) + (25 / 6))) 2) First, we need to convert the fractions to have a common denominator. 3) The common denominator will be the least common multiple of 24, 72, and 6, which is 72. 4) 14/24 = 14 * (3/72) = 42/72 5) 14/72 = 14 * (1/72) = 7/36 6) 25/6 = 25 * (12/72) = 300/72 7) Now we can add the fractions: 8) 42/72 + (7/36 + 300/72) = 42/72 + (7*2 + 300)/72 = 42/72 + 314/72 = 356/72 9) Simplifying the fraction, we get: 10) 356/72 = 4 + 92/72 = 4 + 23/18 ### Answer: 4 + 23/18
Expected answer: 89/18
Correct? No
Problem: In the previous problem, we calculated the sum ((14 / 72) + (25 / 6)). But what if we made a mistake and it wasn't 25/6 of something added, but it was actually 90/6? Given this new information, what would be the new value of ((14 / 72) + (90 / 6))?
Claude-3 Haiku:
Okay, let's solve this step-by-step with the new information: 1) ((14 / 72) + (90 / 6)) 2) First, we need to convert the fractions to have a common denominator. 3) The common denominator will be the least common multiple of 72 and 6, which is 72. 4) 14/72 = 14 * (1/72) = 7/36 5) 90/6 = 90 * (12/72) = 1080/72 6) Now we can add the fractions: 7) 7/36 + 1080/72 = (7*2 + 1080)/72 = 1094/72 8) Simplifying the fraction, we get: 9) 1094/72 = 15 + 14/72 = 15 + 7/36 ### Answer: 15 + 7/36
Expected answer: 547/36
Correct? Yes
Problem: What is the sum of 84/97 and 25/2?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 84/97 and 25/2 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 97 and 2 is 194. 3) We need to convert the fractions to have the same denominator of 194: 84/97 = 84*2/194 = 168/194 25/2 = 25*97/194 = 2425/194 4) Now we can add the fractions: 168/194 + 2425/194 = 2593/194 ### Answer: 2593/194
Expected answer: 2593/194
Correct? Yes
Problem: After finding the sum of 84/97 and 25/2, subtract 100/71 from your result. What is the new result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 84/97 and 25/2 to be 2593/194. 2) Now we need to subtract 100/71 from 2593/194. 3) To subtract fractions, we need to find a common denominator. The least common denominator (LCD) of 194 and 71 is 13778. 4) We need to convert the fractions to have the same denominator of 13778: 2593/194 = 2593*71/13778 = 184107/13778 100/71 = 100*194/13778 = 2740/13778 5) Now we can subtract the fractions: 184107/13778 - 2740/13778 = 181367/13778 ### Answer: 181367/13778
Expected answer: 164703/13774
Correct? No
Problem: After previously finding the sum of 84/97 and 25/2, now consider a new scenario. What if, instead of having 84 parts out of 97, we had 84 parts out of 96? What then would be the sum of these fractions: 84/96 and 25/2?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 84/96 and 25/2 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 96 and 2 is 96. 3) We don't need to convert the second fraction since it already has a denominator of 2, which is a factor of 96. 4) Now we can add the fractions: 84/96 + 25/2 = 84/96 + 50/96 = 134/96 ### Answer: 134/96
Expected answer: 107/8
Correct? No
Problem: What is the difference between the fractions 66/20 and 4/78?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the difference between the two fractions: 66/20 and 4/78. 2) To find the difference, we need to find a common denominator for the two fractions. The least common denominator (LCD) of 20 and 78 is 1560. 3) Now we need to convert the fractions to have the same denominator of 1560. 66/20 = (66 * 78) / (20 * 78) = 5148/1560 4/78 = (4 * 20) / (78 * 20) = 80/1560 4) Now we can find the difference between the two fractions: 5148/1560 - 80/1560 = (5148 - 80)/1560 = 5068/1560 ### Answer: 5068/1560
Expected answer: 1267/390
Correct? Yes
Problem: After finding the difference between the fractions 66/20 and 4/78, what would the result be if you add 6/15 to your answer?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the difference between the fractions 66/20 and 4/78 to be 5068/1560. 2) Now we need to add 6/15 to this answer. 3) To add the fractions, we need to find a common denominator. The least common denominator (LCD) of 1560 and 15 is 7800. 4) Converting the fractions to have the same denominator of 7800: 5068/1560 = (5068 * 5)/7800 = 25340/7800 6/15 = (6 * 520)/7800 = 3120/7800 5) Now we can add the fractions: 25340/7800 + 3120/7800 = 28460/7800 ### Answer: 28460/7800
Expected answer: 1423/390
Correct? Yes
Problem: Suppose that instead of having 66/20 in the original problem, we have 66/21. What would be the difference between the fractions 66/21 and 4/78?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the difference between the two fractions: 66/21 and 4/78. 2) To find the difference, we need to find a common denominator for the two fractions. The least common denominator (LCD) of 21 and 78 is 1638. 3) Now we need to convert the fractions to have the same denominator of 1638. 66/21 = (66 * 78) / (21 * 78) = 5148/1638 4/78 = (4 * 21) / (78 * 21) = 84/1638 4) Now we can find the difference between the two fractions: 5148/1638 - 84/1638 = (5148 - 84)/1638 = 5064/1638 ### Answer: 5064/1638
Expected answer: 844/273
Correct? Yes
Problem: Calculate the expression: 83 divided by 37 minus 12 divided by 14.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. 83 divided by 37 - 83 / 37 = 2.2432432432432432 2. 12 divided by 14 - 12 / 14 = 0.8571428571428571 3. Subtract the second result from the first result - 2.2432432432432432 - 0.8571428571428571 = 1.3861003861003861 ### Answer: 1.3861003861003861
Expected answer: 359/259
Correct? Yes
Problem: After finding the value of 83 divided by 37 minus 12 divided by 14, add to your result the quantity 32 divided by 65. What sum do you get?
Claude-3 Haiku:
Okay, let's continue the calculation: 1. 83 divided by 37 minus 12 divided by 14 - 2.2432432432432432 - 0.8571428571428571 = 1.3861003861003861 2. Add 32 divided by 65 to the result - 32 / 65 = 0.4923076923076923 - 1.3861003861003861 + 0.4923076923076923 = 1.8784080784080784 ### Answer: 1.8784080784080784
Expected answer: 31623/16835
Correct? No
Problem: Suppose instead of dividing 83 by 37 as in the previous problem, you divided 83 by 38 and then subtracted 12 divided by 14. What would be the result in that case?
Claude-3 Haiku:
Okay, let's work through this step-by-step: 1. 83 divided by 38 - 83 / 38 = 2.1842105263157895 2. 12 divided by 14 - 12 / 14 = 0.8571428571428571 3. Subtract the second result from the first result - 2.1842105263157895 - 0.8571428571428571 = 1.3270676691729324 ### Answer: 1.3270676691729324
Expected answer: 353/266
Correct? No
Problem: What is the sum of 95/57 and 28/80?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 95/57 and 28/80. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 57 and 80 is 3,360. 3) We need to convert the fractions to have the same denominator of 3,360. 95/57 = (95 * 59)/3,360 = 5,605/3,360 28/80 = (28 * 42)/3,360 = 1,176/3,360 4) Now we can add the fractions: 5,605/3,360 + 1,176/3,360 = 6,781/3,360 5) Simplifying the final answer: 6,781/3,360 = 2.0179 ### Answer: 2.0179
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 14/57 and 92/42. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 57 and 42 is 1,194. 3) We need to convert the fractions to have the same denominator of 1,194: 14/57 = 14 * 21 / 57 * 21 = 294/1,197 92/42 = 92 * 28.43 / 42 * 28.43 = 2,612.56/1,194 4) Now we can add the fractions: 294/1,197 + 2,612.56/1,194 = 2,906.56/1,194 5) Simplifying the final answer: 2,906.56/1,194 = 2.43 ### Answer: 2.43
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((77 / 55) + (6 / 5)) 2) First, let's calculate (77 / 55): 77 / 55 = 1.4 3) Next, let's calculate (6 / 5): 6 / 5 = 1.2 4) Now, let's add the two results together: 1.4 + 1.2 = 2.6 ### Answer: 2.6
Expected answer: 13/5
Correct? Yes
Problem: If we add the previously calculated result to 39/64, what fraction do we get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We previously calculated the result as 2.6. 2) Now we need to add 39/64 to 2.6. 3) To add a decimal and a fraction, we need to convert the decimal to a fraction. 4) 2.6 = 2 + 6/10 = 26/10 5) Now we can add 26/10 and 39/64: 26/10 + 39/64 = (26*64 + 39*10) / (10*64) = (1664 + 390) / 640 = 2054 / 640 = 3 + 414/640 = 3 + 13/20 ### Answer: 3 13/20
Expected answer: 1027/320
Correct? No
Problem: Let's change the previous problem a bit. Instead of adding 6/5, what if we added 6/79 to 77/55? What fraction would we get then?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((77 / 55) + (6 / 79)) 2) First, let's calculate (77 / 55): 77 / 55 = 1.4 3) Next, let's calculate (6 / 79): 6 / 79 = 0.076 4) Now, let's add the two results together: 1.4 + 0.076 = 1.476 5) To express the final result as a fraction, we need to find the common denominator. The common denominator is 55 * 79 = 4,345. 6) So the final answer is: 1.476 = 64.408 / 43.45 ### Answer: 64.408/4,345
Expected answer: 583/395
Correct? No
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (56 / 8) - 56 divided by 8 is 7 2) (90 / 86) - 90 divided by 86 is approximately 1.0465 3) Adding the two results: - 7 + 1.0465 = 8.0465 Therefore, the value of (56 / 8) + (90 / 86) is 8.0465. ### Answer: 8.0465
Expected answer: 346/43
Correct? No
Problem: What is the sum of 23/20 and 82/97?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 23/20 and 82/97. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 20 and 97 is 1940. 3) Convert the fractions to have the LCD of 1940: 23/20 = 1150/1940 82/97 = 1688/1940 4) Now we can add the fractions: 1150/1940 + 1688/1940 = 2838/1940 5) Simplifying the final answer: 2838/1940 = 1.4639 ### Answer: 1.4639
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 54/88 and 28/10. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 88 and 10 is 880. 3) Now we need to convert the fractions to have the same denominator of 880: 54/88 = (54 * 10)/880 = 540/880 28/10 = (28 * 88)/880 = 2,464/880 4) Now we can add the fractions: 540/880 + 2,464/880 = 3,004/880 5) To simplify the final answer, we can divide both the numerator and denominator by their greatest common factor, which is 4. 3,004/880 = 751/220 ### Answer: 751/220
Expected answer: 751/220
Correct? Yes
Problem: After finding the sum of 54/88 and 28/10, add this to 21/13 and find the resulting value.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 54/88 and 28/10 to be 751/220 in the previous problem. 2) Now we need to add 21/13 to 751/220. 3) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 220 and 13 is 2,860. 4) Now we need to convert the fractions to have the same denominator of 2,860: 751/220 = (751 * 13)/2,860 = 9,763/2,860 21/13 = (21 * 220)/2,860 = 4,620/2,860 5) Now we can add the fractions: 9,763/2,860 + 4,620/2,860 = 14,383/2,860 6) To simplify the final answer, we can divide both the numerator and denominator by their greatest common factor, which is 20. 14,383/2,860 = 719.15/143 ### Answer: 719.15/143
Expected answer: 14383/2860
Correct? Yes
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 7 / 69 - 7 divided by 69 is 0.101449275362 2) 71 / 47 - 71 divided by 47 is 1.51063829787 3) Add the two results: - 0.101449275362 + 1.51063829787 = 1.612087573232 ### Answer: 1.612087573232
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for 15/32 and 65/15. 2) The least common multiple of 32 and 15 is 480. 3) So we need to convert both fractions to have a denominator of 480. 4) 15/32 = 225/480 5) 65/15 = 2,600/480 6) Now we can add the fractions: 225/480 + 2,600/480 = 2,825/480 7) Simplifying the fraction, we get: 2,825/480 = 5,650/960 = 37 2/3 ### Answer: 37 2/3
Expected answer: 461/96
Correct? No
Problem: What is the sum of 4/31 and 76/11?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 4/31 and 76/11. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 31 and 11 is 341. 3) We need to convert the fractions to have the LCD of 341: 4/31 = 4*11/31*11 = 44/341 76/11 = 76*31/11*31 = 2356/341 4) Now we can add the fractions: 44/341 + 2356/341 = 2400/341 5) Simplifying the final answer, we get: 2400/341 ### Answer: 2400/341
Expected answer: 2400/341
Correct? Yes
Problem: After finding the sum of 4/31 and 76/11, from that result subtract the fraction 63/35. What is the final result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 4/31 and 76/11 to be 2400/341. 2) Now we need to subtract the fraction 63/35 from 2400/341. 3) To subtract fractions, we need to find a common denominator. The least common denominator (LCD) of 341 and 35 is 11935. 4) We need to convert the fractions to have the LCD of 11935: 2400/341 = 2400*35/341*35 = 84000/11935 63/35 = 63*341/35*341 = 21483/11935 5) Now we can subtract the fractions: 84000/11935 - 21483/11935 = 62517/11935 ### Answer: 62517/11935
Expected answer: 8931/1705
Correct? Yes
Problem: In the previous problem, instead of adding 4/31 to 76/11, what would the result be if we started with 42/31 and added it to 76/11 instead?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 42/31 and 76/11. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 31 and 11 is 341. 3) We need to convert the fractions to have the LCD of 341: 42/31 = 42*11/31*11 = 462/341 76/11 = 76*31/11*31 = 2356/341 4) Now we can add the fractions: 462/341 + 2356/341 = 2818/341 5) Simplifying the final answer, we get: 2818/341 ### Answer: 2818/341
Expected answer: 2818/341
Correct? Yes
Problem: What is the sum when you add 82/15 to 100/12?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common multiple of 15 and 12 is 60. 3) So we need to convert the fractions to have a denominator of 60. 4) 82/15 = (82 * 4)/60 = 328/60 5) 100/12 = (100 * 5)/60 = 500/60 6) Now we can add the fractions: 328/60 + 500/60 = 828/60 ### Answer: 828/60
Expected answer: 69/5
Correct? Yes
Problem: Now, in addition to the previous question, what is the sum when you add the fraction 46/83 to the result of adding 82/15 and 100/12?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) From the previous question, we found that the sum of 82/15 and 100/12 is 828/60. 2) Now we need to add 46/83 to 828/60. 3) We need to find a common denominator for the two fractions. 4) The least common multiple of 60 and 83 is 4980. 5) So we need to convert the fractions to have a denominator of 4980. 6) 828/60 = (828 * 83)/4980 = 68,724/4980 7) 46/83 = (46 * 60)/4980 = 2,760/4980 8) Now we can add the fractions: 68,724/4980 + 2,760/4980 = 71,484/4980 ### Answer: 71,484/4980
Expected answer: 5957/415
Correct? Yes
Problem: Now suppose we made an adjustment. Instead of adding 82/15 to 100/12, we are going to add 61/15 to 100/12. What would be the new sum?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common multiple of 15 and 12 is 60. 3) So we need to convert the fractions to have a denominator of 60. 4) 61/15 = (61 * 4)/60 = 244/60 5) 100/12 = (100 * 5)/60 = 500/60 6) Now we can add the fractions: 244/60 + 500/60 = 744/60 ### Answer: 744/60
Expected answer: 62/5
Correct? Yes
Problem: Calculate the result of the expression ((92 / 29) + (41 / 33)). Write your answer as a simplified fraction or a whole number.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Evaluate the first part of the expression: (92 / 29) 92 / 29 = 3.172413793103448 2) Evaluate the second part of the expression: (41 / 33) 41 / 33 = 1.2424242424242424 3) Add the two parts together: (3.172413793103448) + (1.2424242424242424) = 4.414838035527691 4) Simplify the result: 4.414838035527691 = 4 21/29 ### Answer: 4 21/29
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 57/29 and 14/98. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 29 and 98 is 2,842. 3) We need to convert the fractions to have the LCD of 2,842: 57/29 = (2,842/29) * 57 = 1,980 14/98 = (2,842/98) * 14 = 406 4) Now we can add the fractions: 1,980 + 406 = 2,386 5) The final answer is 2,386/2,842. ### Answer: 2,386/2,842
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 70/25 - To simplify this fraction, we need to find the common denominator. - The common denominator is 25 * 28 = 700. - 70/25 = (70 * 28) / (25 * 28) = 1960/700 = 28/10 2) 83/28 - To simplify this fraction, we need to find the common denominator. - The common denominator is 25 * 28 = 700. - 83/28 = (83 * 25) / (28 * 25) = 2075/700 = 29.64/10 3) Adding the two fractions: - 28/10 + 29.64/10 = 57.64/10 ### Answer: 57.64
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common multiple of 73 and 23 is 1,679. 3) So we need to convert the fractions to have a denominator of 1,679. 4) 50/73 = (50 * 23) / (73 * 23) = 1,150 / 1,679 5) 20/23 = (20 * 73) / (23 * 73) = 1,460 / 1,679 6) Now we can add the fractions: 1,150/1,679 + 1,460/1,679 = 2,610/1,679 7) Simplifying, we get: 2,610/1,679 = 1 + 931/1,679 ### Answer: 1 + 931/1,679
Expected answer: 2610/1679
Correct? Yes
Problem: If you add 83/35 to the result of adding the fractions 50/73 and 20/23, what is the total value?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the result of adding the fractions 50/73 and 20/23 in the previous problem: 1 + 931/1,679 2) Now we need to add 83/35 to that result. 3) First, we need to convert all the fractions to have a common denominator. The least common multiple of 1,679, 35 is 58,765. 4) 1 + 931/1,679 = 58,765/58,765 + 31,089/58,765 = 89,854/58,765 5) 83/35 = 2,365/58,765 6) Now we can add the two fractions: 89,854/58,765 + 2,365/58,765 = 92,219/58,765 7) Simplifying, we get: 92,219/58,765 = 1 + 33,454/58,765 ### Answer: 1 + 33,454/58,765
Expected answer: 230707/58765
Correct? No
Problem: In the previous scenario, instead of having 50/73 of an hour left to complete your project, you have 50/57 of an hour left. Now, if you still have the additional 20/23 of an hour, how much total time do you have now?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have 50/57 of an hour left to complete the project. 2) We also have an additional 20/23 of an hour. 3) To add these fractions, we need to find a common denominator. 4) The least common multiple of 57 and 23 is 1,311. 5) So we need to convert the fractions to have a denominator of 1,311. 6) 50/57 = (50 * 23) / (57 * 23) = 1,150 / 1,311 7) 20/23 = (20 * 57) / (23 * 57) = 1,140 / 1,311 8) Now we can add the fractions: 1,150/1,311 + 1,140/1,311 = 2,290/1,311 9) Simplifying, we get: 2,290/1,311 = 1 + 979/1,311 ### Answer: 1 + 979/1,311
Expected answer: 2290/1311
Correct? Yes
Problem: What is the value of ((49 / 57) + (89 / 99))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((49 / 57) + (89 / 99)) 2) First, let's calculate the individual fractions: (49 / 57) = 0.8596 (89 / 99) = 0.8989 3) Now, we add the two fractions: 0.8596 + 0.8989 = 1.7585 ### Answer: 1.7585
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 94 / 35 - To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor (GCF). - The GCF of 94 and 35 is 7. - 94 / 7 = 13 - 35 / 7 = 5 - So 94 / 35 = 13 / 5 2) 23 / 49 - To simplify this fraction, we can divide both the numerator and denominator by their GCF. - The GCF of 23 and 49 is 1. - So 23 / 49 = 23 / 49 3) 13 / 5 - 23 / 49 - To subtract these fractions, we need to find a common denominator. - The least common multiple (LCM) of 5 and 49 is 245. - 13 / 5 = 49 / 245 - 23 / 49 = 23 / 245 - 49 / 245 - 23 / 245 = 26 / 245 ### Answer: 26/245
Expected answer: 543/245
Correct? No
Problem: Calculate the sum of 58/30 and 49/37 and leave your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 58/30 = 1.93333... 2) 49/37 = 1.32432... 3) To find the sum, we add the two fractions: 58/30 + 49/37 = (58 * 37 + 49 * 30) / (30 * 37) = (2146 + 1470) / 1110 = 3616 / 1110 = 326/100 ### Answer: 326/100
Expected answer: 1808/555
Correct? No
Problem: Calculate the sum of 45/53 and 71/50.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 45/53 and 71/50. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 53 and 50 is 2650. 3) Now we need to convert the fractions to have the same denominator of 2650: 45/53 = (45 * 50) / (53 * 50) = 2250/2650 71/50 = (71 * 53) / (50 * 53) = 3763/2650 4) Now we can add the fractions: 2250/2650 + 3763/2650 = 6013/2650 5) Simplifying the final answer: 6013/2650 = 2.27 ### Answer: 2.27
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 36/72 and 49/1 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 72 and 1 is 72. 3) We need to convert the second fraction to have a denominator of 72: 49/1 = 49/72 * 72/72 = 49/72 4) Now we can add the fractions: 36/72 + 49/72 = 85/72 5) Simplifying the final answer: 85/72 = 1 13/72 ### Answer: 1 13/72
Expected answer: 99/2
Correct? No
Problem: What is the sum of 61/20 and 29/15?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the common denominator for 61/20 and 29/15. 2) The least common multiple of 20 and 15 is 60. 3) So we need to convert both fractions to have a denominator of 60. 4) 61/20 = (61 * 3)/60 = 183/60 5) 29/15 = (29 * 4)/60 = 116/60 6) Now we can add the fractions: 183/60 + 116/60 = 299/60 ### Answer: 299/60
Expected answer: 299/60
Correct? Yes
Problem: After finding the sum of 61/20 and 29/15, add that result to 58/31. What is the final answer?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 61/20 and 29/15 to be 299/60. 2) Now we need to add 58/31 to 299/60. 3) To do this, we need to find the common denominator for 299/60 and 58/31. 4) The least common multiple of 60 and 31 is 1860. 5) So we need to convert both fractions to have a denominator of 1860. 6) 299/60 = (299 * 31)/1860 = 9269/1860 7) 58/31 = (58 * 60)/1860 = 3480/1860 8) Now we can add the fractions: 9269/1860 + 3480/1860 = 12749/1860 ### Answer: 12749/1860
Expected answer: 12749/1860
Correct? Yes
Problem: Previously you found the sum of 61/20 and 29/15. Now let's change the 15 in the denominator of the second fraction to 67, so that we are adding 61/20 and 29/67. What will the new sum be?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the common denominator for 61/20 and 29/67. 2) The least common multiple of 20 and 67 is 1340. 3) So we need to convert both fractions to have a denominator of 1340. 4) 61/20 = (61 * 67)/1340 = 4087/1340 5) 29/67 = (29 * 20)/1340 = 580/1340 6) Now we can add the fractions: 4087/1340 + 580/1340 = 4667/1340 ### Answer: 4667/1340
Expected answer: 4667/1340
Correct? Yes
Problem: Solve the expression ((33 / 90) + (77 / 79)). Give your answer as an unsimplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((33 / 90) + (77 / 79)) 2) First, we need to find the common denominator for the two fractions. The least common multiple of 90 and 79 is 7110. 3) So we need to convert the fractions to have a denominator of 7110: (33 / 90) = (2310 / 7110) (77 / 79) = (7700 / 7110) 4) Now we can add the fractions: (2310 / 7110) + (7700 / 7110) = (10010 / 7110) ### Answer: (10010 / 7110)
Expected answer: 3179/2370
Correct? No
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 30/79 and 29/6. 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 79 and 6 is 474. 4) We need to convert the fractions to have the LCD of 474: 30/79 = (30 * 6)/79 * 6 = 180/474 29/6 = (29 * 79)/6 * 79 = 2291/474 5) Now we can add the fractions: 180/474 + 2291/474 = 2471/474 ### Answer: 2471/474
Expected answer: 2471/474
Correct? Yes
Problem: After finding the sum of 30/79 and 29/6, subtract 44/75 from it. What is the result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 30/79 and 29/6 to be 2471/474 in the previous problem. 2) Now we need to subtract 44/75 from 2471/474. 3) To do this, we need to find a common denominator. The least common denominator (LCD) of 474 and 75 is 3555. 4) We need to convert the fractions to have the LCD of 3555: 2471/474 = (2471 * 75)/474 * 75 = 185325/3555 44/75 = (44 * 474)/75 * 474 = 20856/3555 5) Now we can subtract the fractions: 185325/3555 - 20856/3555 = 164469/3555 ### Answer: 164469/3555
Expected answer: 54823/11850
Correct? No
Problem: After recalculating, you realized you had 30/97 instead of 30/79. Now, add that to 29/6. What is the new result?
Claude-3 Haiku:
Okay, let's solve this with the correct fractions: 1) We have the fractions 30/97 and 29/6. 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 97 and 6 is 582. 4) We need to convert the fractions to have the LCD of 582: 30/97 = (30 * 6)/97 * 6 = 180/582 29/6 = (29 * 97)/6 * 97 = 2813/582 5) Now we can add the fractions: 180/582 + 2813/582 = 2993/582 ### Answer: 2993/582
Expected answer: 2993/582
Correct? Yes
Problem: What is the answer when you subtract 11/66 from 59/2?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to convert the fractions to have a common denominator. The least common denominator is 66. 2) 59/2 = 59/2 * 33/33 = 1947/66 3) 11/66 = 11/66 4) Now we can subtract the fractions: 1947/66 - 11/66 = 1936/66 ### Answer: 1936/66
Expected answer: 88/3
Correct? Yes
Problem: What is the sum of 63/51 and the result of subtracting 11/66 from 59/2?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Subtracting 11/66 from 59/2: 59/2 = 1947/66 11/66 1947/66 - 11/66 = 1936/66 2) Now we need to add 63/51 to the result: 63/51 1936/66 To add these, we need to convert them to have a common denominator. The least common denominator is 3366. 63/51 = 63/51 * 66/66 = 4158/3366 1936/66 = 1936/66 * 51/51 = 98,736/3366 4158/3366 + 98,736/3366 = 102,894/3366 ### Answer: 102,894/3366
Expected answer: 1559/51
Correct? Yes
Problem: What would the result be if we subtracted 11/31 instead of 11/66 from 59/2 in the previous problem?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to convert the fractions to have a common denominator. The least common denominator is 62. 2) 59/2 = 59/2 * 31/31 = 1829/62 3) 11/31 = 11/31 * 2/2 = 22/62 4) Now we can subtract the fractions: 1829/62 - 22/62 = 1807/62 ### Answer: 1807/62
Expected answer: 1807/62
Correct? Yes
Problem: Consider these two fractions: 58/23 and 25/26. What is the sum when those two fractions are added together?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 58/23 and 25/26 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 23 and 26 is 598. 3) Now we need to convert the fractions to have the LCD of 598: 58/23 = (58 * 26)/23 * 26 = 1508/598 25/26 = (25 * 23)/26 * 23 = 575/598 4) Now we can add the fractions: 1508/598 + 575/598 = 2083/598 5) Simplifying the final answer: 2083/598 = 3.48 ### Answer: 3.48
Expected answer: 2083/598
Correct? No
Problem: Calculate the sum of the fractions 70/13 and 17/52.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 70/13 and 17/52. 2) To add fractions, we need to find a common denominator. 3) The least common denominator (LCD) of 13 and 52 is 52. 4) To convert 70/13 to have a denominator of 52, we multiply the numerator and denominator by 4: 70/13 = (70 * 4) / (13 * 4) = 280/52 5) Now we can add the fractions: 280/52 + 17/52 = (280 + 17)/52 = 297/52 6) Simplifying the fraction, we get: 297/52 = 5 and 47/52 ### Answer: 5 and 47/52
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 78/44 and 17/91. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 44 and 91 is 3,964. 3) We need to convert the fractions to have the same denominator of 3,964. 4) 78/44 = (78 * 90)/3,964 = 7,020/3,964 5) 17/91 = (17 * 43)/3,964 = 731/3,964 6) Now we can add the fractions: 7,020/3,964 + 731/3,964 = 7,751/3,964 7) Simplifying the fraction, we get 7,751/3,964. ### Answer: 7,751/3,964
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions: 43/4 and 71/4 2) To find the sum, we need to have a common denominator. In this case, the common denominator is 4. 3) 43/4 + 71/4 = (43 + 71)/4 4) 43 + 71 = 114 5) 114/4 = 28.5 ### Answer: 28.5
Expected answer: 57/2
Correct? Yes
Problem: What is the sum of 43/4 and 71/4 plus 92/79?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have three fractions: 43/4, 71/4, and 92/79 2) To find the sum, we need to have a common denominator. The least common denominator (LCD) is 316 (4 * 79). 3) Convert the fractions to have the LCD of 316: 43/4 = 79/4 * 316/316 = 9,979/316 71/4 = 79/4 * 316/316 = 16,471/316 92/79 = 92/79 * 316/316 = 3,668/316 4) Now we can add the fractions: 9,979/316 + 16,471/316 + 3,668/316 = 30,118/316 5) Simplifying, we get: 30,118/316 = 95.25 ### Answer: 95.25
Expected answer: 4687/158
Correct? No
Problem: What if instead of adding 71/4, we added 71/89 to 43/4? What would be the new total?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions: 43/4 and 71/89 2) To find the sum, we need to have a common denominator. In this case, the common denominator is 356 (4 * 89). 3) 43/4 = 107/356 4) 71/89 = 80/356 5) 107/356 + 80/356 = 187/356 6) Simplifying the fraction, we get 187/356. ### Answer: 187/356
Expected answer: 4111/356
Correct? No
Problem: What is the result of adding the fractions 17/74 and 53/27?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common multiple of 74 and 27 is 1998. 3) So we need to convert the fractions to have a denominator of 1998. 4) 17/74 = 17 * (1998/74) = 459/1998 5) 53/27 = 53 * (1998/27) = 3906/1998 6) Now we can add the fractions: 459/1998 + 3906/1998 = 4365/1998 7) Simplifying the fraction, we get: 4365/1998 = 29/13. ### Answer: 29/13
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (76/76) - This is equal to 1, since any number divided by itself is 1. 2) (96/16) - This is equal to 6, since 96 divided by 16 is 6. 3) Combining the two parts: - (76/76) + (96/16) = 1 + 6 = 7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After finding the value of (76/76) + (96/16), what is the result when you add the solution to itself?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the value of (76/76) + (96/16) to be 7. 2) To find the result when we add the solution to itself, we simply need to double the previous answer. 3) 7 + 7 = 14 ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: You originally calculated (76/76) + (96/16). Now reconsider your thought, what would be the new total if the second fraction was 96/33 instead of 96/16?
Claude-3 Haiku:
Okay, let's recalculate with the new information: 1) (76/76) - This is still equal to 1, since any number divided by itself is 1. 2) (96/33) - This is equal to 2.9090909, since 96 divided by 33 is approximately 2.9090909. 3) Combining the two parts: - (76/76) + (96/33) = 1 + 2.9090909 = 3.9090909 ### Answer: 3.9090909
Expected answer: 43/11
Correct? No
Problem: What is the result of ((94 / 14) - (50 / 90))? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((94 / 14) - (50 / 90)) 2) First, let's calculate the numerators and denominators separately: Numerator: 94 / 14 = 6.714285714 Numerator: 50 / 90 = 0.555555556 3) Now we can subtract the two numerators: 6.714285714 - 0.555555556 = 6.158730158 4) To express this as a simplified fraction, we need to find the common denominator. The common denominator is 14 * 90 = 1260. 5) 6.158730158 = 6 * 1260/1260 + 0.158730158 * 1260/1260 = 6 * 1260/1260 + 20/1260 6) Simplifying the fraction: 6 * 1260/1260 + 20/1260 = 7560/1260 + 20/1260 = 7580/1260 ### Answer: 7580/1260
Expected answer: 388/63
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Convert the fractions to have a common denominator: 30/7 - 29/79 = (30*79 - 29*7) / (7*79) 2) Perform the subtraction: (30*79 - 29*7) / (7*79) = (2370 - 203) / 553 = 2167 / 553 3) Simplify the fraction: 2167 / 553 = 3 and 61/553 ### Answer: 3 and 61/553
Expected answer: 2404/553
Correct? No
Problem: What is the sum of 60/79 and 53/38?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 60/79 and 53/38. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 79 and 38 is 2,382 (79 * 38). 3) Now we need to convert the fractions to have the LCD of 2,382. 4) 60/79 = (60 * 2,382) / (79 * 2,382) = 142,920 / 188,178 5) 53/38 = (53 * 2,382) / (38 * 2,382) = 126,146 / 90,516 6) Now we can add the fractions: 142,920 / 188,178 + 126,146 / 90,516 = 269,066 / 278,694 7) Simplifying the final fraction, we get: 269,066 / 278,694 = 269,066 / 278,694 ### Answer: 269,066 / 278,694
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. The least common multiple of 48 and 84 is 336. 2) Now we can rewrite the fractions with the common denominator of 336: 39/48 = 273/336 19/84 = 76/336 3) Now we can add the fractions: 273/336 + 76/336 = 349/336 4) Simplifying the final answer: 349/336 = 1 13/336 ### Answer: 1 13/336
Expected answer: 349/336
Correct? Yes
Problem: After calculating the value of 39/48 + 19/84, what would be the result if you added the obtained result to itself?
Claude-3 Haiku:
Okay, let's work this out step-by-step: 1) We calculated the value of 39/48 + 19/84 to be 1 13/336. 2) To add this result to itself, we simply double the numerator and keep the same denominator: 1 13/336 + 1 13/336 = 2 26/336 3) Simplifying the final answer: 2 26/336 = 2 13/168 ### Answer: 2 13/168
Expected answer: 349/168
Correct? Yes
Problem: If instead of adding 39/48 and 19/84, you were to add 39/48 and 19/13, what would be the result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. The least common multiple of 48 and 13 is 624. 2) Now we can rewrite the fractions with the common denominator of 624: 39/48 = 507/624 19/13 = 117/624 3) Now we can add the fractions: 507/624 + 117/624 = 624/624 4) Simplifying the final answer: 624/624 = 1 ### Answer: 1
Expected answer: 473/208
Correct? No
Problem: What is the sum of 16/86 and 60/3?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 16/86 and 60/3 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 86 and 3 is 258. 3) We need to convert the fractions to have the same denominator of 258: 16/86 = (16 * 3)/258 = 48/258 60/3 = (60 * 86)/258 = 5160/258 4) Now we can add the fractions: 48/258 + 5160/258 = 5208/258 5) Simplifying the final answer, we get: 5208/258 = 20. ### Answer: 20.
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((95 / 69) + (67 / 9)) 2) First, we need to evaluate the two fractions: 95 / 69 = 1.3768115942028986 67 / 9 = 7.444444444444445 3) Now we can add the two fractions: 1.3768115942028986 + 7.444444444444445 = 8.821256038647344 ### Answer: 8.821256038647344
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 95 / 16 - 95 divided by 16 is 5.9375 2) 43 / 60 - 43 divided by 60 is 0.7166 3) 5.9375 - 0.7166 - 5.9375 - 0.7166 = 5.2209 ### Answer: 5.2209
Expected answer: 1253/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to convert the fractions to have a common denominator. 38/8 = 19/4 4/16 = 1/4 2) Now we can add the fractions: 19/4 + 1/4 = 20/4 3) Simplifying the final answer: 20/4 = 5 ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: Recalling the fraction calculation from the previous problem (38/8 and 4/16), what is the new total if you were to add 32/64 to this sum?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) From the previous problem, we had: 19/4 + 1/4 = 20/4 2) Now we need to add 32/64 to this sum. 3) First, we need to convert 32/64 to have the same denominator as 20/4, which is 4. 32/64 = 5/4 4) Now we can add the fractions: 20/4 + 5/4 = 25/4 5) Simplifying the final answer: 25/4 = 6.25 ### Answer: 6.25
Expected answer: 11/2
Correct? No
Problem: In the previous problem, we considered the sum of the fractions 38/8 and 4/16 and then added 32/64. Now, instead of 38/8, let's consider 12/8. What would be the new sum if you added 12/8 and 4/16 together?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to convert the fractions to have a common denominator. 12/8 = 3/2 4/16 = 1/4 2) Now we can add the fractions: 3/2 + 1/4 = (3*4 + 1*2)/8 = 14/8 3) Simplifying the final answer: 14/8 = 7/4 ### Answer: 7/4
Expected answer: 7/4
Correct? Yes
Problem: Calculate the result of 67 / 15 - 27 / 12.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Calculate 67 / 15: 67 / 15 = 4.4666... 2. Calculate 27 / 12: 27 / 12 = 2.25 3. Subtract the two results: 4.4666... - 2.25 = 2.2166... ### Answer: 2.2166...
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 38/59 and 80/94. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 59 and 94 is 5,566. 3) Now we need to convert the fractions to have the same denominator of 5,566: 38/59 = (38 * 94) / (59 * 94) = 3,572 / 5,566 80/94 = (80 * 59) / (94 * 59) = 4,720 / 5,566 4) Now we can add the fractions: 3,572 / 5,566 + 4,720 / 5,566 = 8,292 / 5,566 5) Simplifying the final answer: 8,292 / 5,566 = 1.49 ### Answer: 1.49
Expected answer: 4146/2773
Correct? No
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 10/14 = 0.7142857142857143 2) 70/20 = 3.5 3) 0.7142857142857143 + 3.5 = 4.2142857142857145 ### Answer: 4.2142857142857145
Expected answer: 59/14
Correct? Yes
Problem: After calculating the sum of 10/14 and 70/20, add this result to 100/20. What is the new total?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 10/14 = 0.7142857142857143 2) 70/20 = 3.5 3) 0.7142857142857143 + 3.5 = 4.2142857142857145 4) 100/20 = 5 5) 4.2142857142857145 + 5 = 9.2142857142857145 ### Answer: 9.2142857142857145
Expected answer: 129/14
Correct? No
Problem: After reviewing your previous calculation, you realize that the first fraction was not 10/14 but actually 10/18. Now find the sum of the corrected fraction, 10/18 and the same second fraction, 70/20. What is the revised total?
Claude-3 Haiku:
Okay, let's recalculate this with the corrected first fraction: 1) 10/18 = 0.5555555555555556 2) 70/20 = 3.5 3) 0.5555555555555556 + 3.5 = 4.055555555555556 ### Answer: 4.055555555555556
Expected answer: 73/18
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to convert the fractions to have a common denominator. The least common denominator is 220. 2) 33/5 = 132/220 3) 19/44 = 19/220 4) Now we can subtract the fractions: 132/220 - 19/220 = 113/220 ### Answer: 113/220
Expected answer: 1357/220
Correct? No
Problem: Find the result for (97 / 13) + (62 / 22). Answer as a decimal to the nearest hundredth.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (97 / 13) - 97 divided by 13 is 7.46 2) (62 / 22) - 62 divided by 22 is 2.82 3) Adding the two results: - 7.46 + 2.82 = 10.28 Rounding to the nearest hundredth, the final answer is: ### Answer: 10.28
Expected answer: 1470/143
Correct? No
Problem: What is the sum of 78 divided by 35 and 30 divided by 60?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. 78 divided by 35: 78 / 35 = 2.2285714286 2. 30 divided by 60: 30 / 60 = 0.5 3. Sum of the two results: 2.2285714286 + 0.5 = 2.7285714286 ### Answer: 2.7285714286
Expected answer: 191/70
Correct? No
Problem: What is the sum of 49/75 and 88/58?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 49/75 and 88/58. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 75 and 58 is 2,900. 3) Convert the fractions to have the LCD of 2,900: 49/75 = 1,960/2,900 88/58 = 2,400/2,900 4) Now we can add the fractions: 1,960/2,900 + 2,400/2,900 = 4,360/2,900 5) Simplifying the final answer: 4,360/2,900 = 2.18 ### Answer: 2.18
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 50 / 2 = 25 2) 50 / 32 = 1.5625 3) 25 - 1.5625 = 23.4375 ### Answer: 23.4375
Expected answer: 375/16
Correct? Yes
Problem: Following up on our previous question, what is the result when you add (72 / 81) to the difference between (50 / 2) and (50 / 32)?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) From the previous question, we found that (50 / 2) - (50 / 32) = 23.4375 2) Now we need to add (72 / 81) to that difference 3) 72 / 81 = 0.8888888888888888 4) 23.4375 + 0.8888888888888888 = 24.3264888888888888 ### Answer: 24.3264888888888888
Expected answer: 3503/144
Correct? No
Problem: Following the previous problem, consider this change, what would the result be if instead of dividing by 32, you divide 50 by 91? What would be the new result for ((50 / 2) - (50 / 91))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 50 / 2 = 25 2) 50 / 91 = 0.5495 3) 25 - 0.5495 = 24.4505 ### Answer: 24.4505
Expected answer: 2225/91
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((77 / 30) + (18 / 51)) 2) First, let's calculate the individual parts: (77 / 30) = 2.5666666667 (18 / 51) = 0.3529411765 3) Now, we add the two parts together: 2.5666666667 + 0.3529411765 = 2.9196078432 ### Answer: 2.9196078432
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (36 / 37) = 0.972972972972973 2) (8 / 4) = 2 3) 0.972972972972973 + 2 = 2.972972972972973 ### Answer: 2.972972972972973
Expected answer: 110/37
Correct? Yes
Problem: First, calculate (36 / 37) + (8 / 4). Then, add the result to itself. What is the final result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (36 / 37) = 0.972972972972973 2) (8 / 4) = 2 3) 0.972972972972973 + 2 = 2.972972972972973 4) 2.972972972972973 + 2.972972972972973 = 5.945945945945946 ### Answer: 5.945945945945946
Expected answer: 220/37
Correct? No
Problem: Initially, you calculated (36 / 37) + (8 / 4) and added the result to itself. Now, suppose the initial calculation was actually (36 / 37) + (8 / 56) instead. What is the new result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (36 / 37) = 0.972972972972973 2) (8 / 56) = 0.142857142857143 3) 0.972972972972973 + 0.142857142857143 = 1.115830115830116 ### Answer: 1.115830115830116
Expected answer: 289/259
Correct? No
Problem: Calculate the result of (57 / 22) - (72 / 48) expressing your answer as a fraction in the simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (57 / 22) - (72 / 48) 2) First, let's calculate the individual fractions: (57 / 22) = 2.59 (72 / 48) = 1.5 3) Now, we can subtract the two fractions: 2.59 - 1.5 = 1.09 4) To express the answer as a simplified fraction, we need to find the common denominator. The common denominator is 22 * 48 = 1056. 5) Converting 1.09 to a fraction: 1.09 = 109/100 6) Multiplying the numerator and denominator by 10.56 to get the common denominator of 1056: 109/100 * 10.56 = 1152.04/1056 7) Simplifying the fraction: 1152.04/1056 = 18/16 = 9/8 ### Answer: 9/8
Expected answer: 12/11
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. 48 divided by 16: 48 / 16 = 3 2. 12 divided by 29: 12 / 29 = 0.4137931034482759 3. Sum of the two results: 3 + 0.4137931034482759 = 3.4137931034482759 ### Answer: 3.4137931034482759
Expected answer: 99/29
Correct? Yes
Problem: If the sum of 48 divided by 16 and 12 divided by 29 is represented as a variable, what would be the value if we add this variable to itself?
Claude-3 Haiku:
Okay, let's break this down: 1. We found the sum of 48 divided by 16 and 12 divided by 29 to be 3.4137931034482759. 2. Let's represent this sum as a variable, let's call it 'x'. x = 3.4137931034482759 3. Now, we need to find the value if we add this variable to itself. x + x = 3.4137931034482759 + 3.4137931034482759 x + x = 6.8275862068965518 ### Answer: 6.8275862068965518
Expected answer: 198/29
Correct? No
Problem: Earlier, we found the sum of 48 divided by 16 and 12 divided by 29. Now, consider if the second fraction was 12 divided by 32 instead of 12 divided by 29. What would be the new sum?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. 48 divided by 16: 48 / 16 = 3 2. 12 divided by 32: 12 / 32 = 0.375 3. Sum of the two results: 3 + 0.375 = 3.375 ### Answer: 3.375
Expected answer: 27/8
Correct? No
Problem: What is the sum of 37/20 and 16/75? Write your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 37/20 and 16/75 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 20 and 75 is 300. 3) We need to convert the fractions to have a denominator of 300: 37/20 = 111/300 16/75 = 64/300 4) Now we can add the fractions: 111/300 + 64/300 = 175/300 5) To simplify the fraction, we can divide the numerator and denominator by their greatest common factor, which is 25. 175/300 = 7/12 ### Answer: 7/12
Expected answer: 619/300
Correct? No
Problem: Calculate the summation: 83/40 + 6/8.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the summation: 83/40 + 6/8 2) To add fractions, we need to find the least common denominator (LCD). The LCD of 40 and 8 is 40. 3) We need to convert the fractions to have the same denominator of 40. 6/8 = 6/8 * (5/5) = 30/40 4) Now we can add the fractions: 83/40 + 30/40 = 113/40 ### Answer: 113/40
Expected answer: 113/40
Correct? Yes
Problem: After finding the result of 83/40 + 6/8, subtract 24/64 from it. What do you get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the result of 83/40 + 6/8 to be 113/40 in the previous problem. 2) Now we need to subtract 24/64 from 113/40. 3) To subtract fractions, we need to find the least common denominator (LCD). The LCD of 40 and 64 is 640. 4) We need to convert the fractions to have the same denominator of 640. 113/40 = 113/40 * (16/16) = 1808/640 24/64 = 24/64 * (10/10) = 240/640 5) Now we can subtract the fractions: 1808/640 - 240/640 = 1568/640 ### Answer: 1568/640
Expected answer: 49/20
Correct? Yes
Problem: After adjusting our original calculation, we now have 83/18 instead of 83/40. So now, what is the result of 83/18 + 6/8?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the summation: 83/18 + 6/8 2) To add fractions, we need to find the least common denominator (LCD). The LCD of 18 and 8 is 72. 3) We need to convert the fractions to have the same denominator of 72. 83/18 = 83/18 * (4/4) = 332/72 6/8 = 6/8 * (9/9) = 54/72 4) Now we can add the fractions: 332/72 + 54/72 = 386/72 ### Answer: 386/72
Expected answer: 193/36
Correct? Yes
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. The least common multiple of 69 and 61 is 4209. 2) Now we can convert the fractions to have the same denominator of 4209: 37/69 = (37 * 61)/4209 = 2257/4209 67/61 = (67 * 69)/4209 = 4623/4209 3) Now we can add the fractions: 2257/4209 + 4623/4209 = 6880/4209 4) Simplifying the result: 6880/4209 = 1.6333... ### Answer: 1.6333...
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 89/84 and 75/34. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 84 and 34 is 252. 3) Convert the fractions to have the LCD of 252: 89/84 = 89 * (252/84) = 267/252 75/34 = 75 * (252/34) = 555/252 4) Now we can add the fractions: 267/252 + 555/252 = 822/252 5) Simplifying the final answer, we get: 822/252 = 41/12. ### Answer: 41/12
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for the two fractions. 2) The least common multiple of 78 and 83 is 6474. 3) So we need to convert the fractions to have a denominator of 6474. 4) 51/78 = (51 * 83)/6474 = 4233/6474 5) 44/83 = (44 * 78)/6474 = 3432/6474 6) Now we can add the fractions: 4233/6474 + 3432/6474 = 7665/6474 7) Simplifying the result, we get: 7665/6474 = 1.18. ### Answer: 1.18
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 99/85 and 77/55. 2) To add fractions, we need to find a common denominator. 3) The least common multiple of 85 and 55 is 425. 4) So we need to convert both fractions to have a denominator of 425. 5) 99/85 = (99 * 5)/425 = 495/425 6) 77/55 = (77 * 8)/425 = 616/425 7) Now we can add the fractions: 495/425 + 616/425 = 1111/425 ### Answer: 1111/425
Expected answer: 218/85
Correct? No
Problem: What is the value of 97 / 56 - 31 / 52? Represent your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step:
1) 97 / 56
- To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1.
- So 97 / 56 = 97/56
2) 31 / 52
- To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1.
- So 31 / 52 = 31/52
3) Now we subtract the two fractions:
- 97/56 - 31/52
- To subtract fractions, we need to find a common denominator.
- The least common multiple of 56 and 52 is 728.
- So we convert both fractions to have a denominator of 728:
- 97/56 = 728/728
- 31/52 = 448/728
- 728/728 - 448/728 = 280/728
4) To simplify the final fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4.
- 280/728 = 70/182
### Answer: 70/182
Expected answer: 827/728
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate the first fraction (78 / 74) 78 / 74 = 1.054054054 Step 2: Calculate the second fraction (72 / 51) 72 / 51 = 1.411764706 Step 3: Add the two fractions together 1.054054054 + 1.411764706 = 2.465818760 ### Answer: 2.465818760
Expected answer: 1551/629
Correct? No
Problem: What is the result of the operation (33 / 23) - (12 / 75)? Express your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (33 / 23) - (12 / 75) 2) First, we need to find the value of (33 / 23) - 33 / 23 = 1.43478 3) Next, we need to find the value of (12 / 75) - 12 / 75 = 0.16 4) Now we can subtract the two values: - 1.43478 - 0.16 = 1.27478 5) To express the answer as a fraction, we need to find the simplest form. - The numerator is 1.27478 and the denominator is 1. - Simplifying, the final answer is: ### Answer: 127478/100
Expected answer: 733/575
Correct? No
Problem: What is the result of the operation 85/42 - 98/99? Simplify your answer to the nearest hundredth.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 85/42 - This can be simplified to 2.02 2) 98/99 - This can be simplified to 0.99 3) Now we subtract the two values: - 2.02 - 0.99 = 1.03 4) Rounding to the nearest hundredth: - 1.03 rounded to the nearest hundredth is 1.03 ### Answer: 1.03
Expected answer: 1433/1386
Correct? No
Problem: What is the sum of 19/30 and 75/77? Express your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 19/30 and 75/77. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 30 and 77 is 2310. 3) Convert the fractions to have the LCD of 2310: 19/30 = 633/2310 75/77 = 2325/2310 4) Now we can add the fractions: 633/2310 + 2325/2310 = 2958/2310 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 2958 and 2310 is 2. 2958/2310 = 1479/1155 ### Answer: 1479/1155
Expected answer: 3713/2310
Correct? No
Problem: What is the sum of 57/66 and 39/64? Please express your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 57/66 and 39/64. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 66 and 64 is 3,960. 3) Convert the fractions to have the LCD of 3,960: 57/66 = 3,240/3,960 39/64 = 2,430/3,960 4) Now we can add the fractions: 3,240/3,960 + 2,430/3,960 = 5,670/3,960 5) Simplifying the fraction, we get: 5,670/3,960 = 189/132 ### Answer: 189/132
Expected answer: 1037/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 80/13 and 2/48. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 13 and 48 is 624. 3) We need to convert the fractions to have the same denominator of 624. 4) 80/13 = (80 * 48)/13 * 48 = 3840/624 5) 2/48 = (2 * 13)/48 * 13 = 26/624 6) Now we can add the fractions: 3840/624 + 26/624 = 3866/624. ### Answer: 3866/624
Expected answer: 1933/312
Correct? Yes
Problem: What is the sum if you add the result of 80/13 + 2/48 to itself?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 80/13 and 2/48 in the previous problem: 3840/624 + 26/624 = 3866/624 2) Now we need to add this result to itself: 3866/624 + 3866/624 = 7732/624 ### Answer: 7732/624
Expected answer: 1933/156
Correct? Yes
Problem: What would be the result if you were to add 80/5 and 2/48 instead of 80/13 and 2/48?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 80/5 and 2/48. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 5 and 48 is 240. 3) We need to convert the fractions to have the same denominator of 240. 4) 80/5 = (80 * 48)/5 * 48 = 3840/240 5) 2/48 = (2 * 5)/48 * 5 = 10/240 6) Now we can add the fractions: 3840/240 + 10/240 = 3850/240. ### Answer: 3850/240
Expected answer: 385/24
Correct? Yes
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Calculate the first part of the expression: (55 / 30) - 55 / 30 = 1.833333 2. Calculate the second part of the expression: (1 / 72) - 1 / 72 = 0.013889 3. Subtract the second part from the first part: - 1.833333 - 0.013889 = 1.819444 ### Answer: 1.819444
Expected answer: 131/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 69/21 and 71/86 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 21 and 86 is 1806. 3) We need to convert the fractions to have the same denominator of 1806: 69/21 = (69 * 86)/1806 = 5934/1806 71/86 = (71 * 21)/1806 = 1491/1806 4) Now we can add the fractions: 5934/1806 + 1491/1806 = 7425/1806 ### Answer: 7425/1806
Expected answer: 2475/602
Correct? Yes
Problem: After finding the sum of the fractions 69/21 and 71/86, add the result to 86/62. What is the result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of the fractions 69/21 and 71/86 to be 7425/1806. 2) Now we need to add 86/62 to 7425/1806. 3) To add the fractions, we need to find a common denominator. The least common denominator (LCD) of 1806 and 62 is 112,172. 4) We need to convert the fractions to have the same denominator of 112,172: 7425/1806 = (7425 * 62)/112,172 = 460,350/112,172 86/62 = (86 * 1806)/112,172 = 155,316/112,172 5) Now we can add the fractions: 460,350/112,172 + 155,316/112,172 = 615,666/112,172 ### Answer: 615,666/112,172
Expected answer: 102611/18662
Correct? No
Problem: Suppose instead that the fractions in the previous problem were 69/60 and 71/86. What is the sum of these fractions?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 69/60 and 71/86 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 60 and 86 is 1290. 3) We need to convert the fractions to have the same denominator of 1290: 69/60 = (69 * 21)/1290 = 1449/1290 71/86 = (71 * 15)/1290 = 1065/1290 4) Now we can add the fractions: 1449/1290 + 1065/1290 = 2514/1290 ### Answer: 2514/1290
Expected answer: 1699/860
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the common denominator for the two fractions. 2) The least common multiple of 60 and 45 is 180. 3) Now we can convert the fractions to have a common denominator of 180: 24/60 = 72/180 42/45 = 84/180 4) Now we can add the numerators: 72/180 + 84/180 = 156/180 5) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 12. 6) 156/180 = 13/15. ### Answer: 13/15
Expected answer: 4/3
Correct? No
Problem: What is the sum of 64/76 and 35/33?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 64/76 and 35/33. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 76 and 33 is 2,508 (76 * 33). 3) Now we need to convert the fractions to have the LCD of 2,508: 64/76 = (64 * 33)/76 * 33 = 2,112/2,508 35/33 = (35 * 76)/33 * 76 = 2,660/2,508 4) Now we can add the fractions: 2,112/2,508 + 2,660/2,508 = 4,772/2,508 5) Simplifying the final fraction, we get: 4,772/2,508 = 1.9 ### Answer: 1.9
Expected answer: 1193/627
Correct? No
Problem: What is the sum of 47/16 and 96/10? Please, express your answer as a mixed fraction if necessary.
Claude-3 Haiku:
Okay, let's solve this step-by-step:
1) 47/16
- To convert this to a mixed fraction, we divide 47 by 16:
- 47 / 16 = 2 with a remainder of 15
- So 47/16 = 2 15/16
2) 96/10
- To convert this to a mixed fraction, we divide 96 by 10:
- 96 / 10 = 9 with a remainder of 6
- So 96/10 = 9 6/10
3) Now we add the two mixed fractions:
- 2 15/16 + 9 6/10
- First, we need to convert 9 6/10 to an improper fraction:
- 9 6/10 = (9 * 10 + 6) / 10 = 96/10
- Now we can add the fractions:
- 2 15/16 + 96/10
- To add these, we need to find the least common denominator, which is 160.
- 2 15/16 = (2 * 10 + 15) / 16 = 35/16
- 96/10 = (96 * 16) / 160 = 1536/160
- 35/16 + 1536/160 = (35 * 10 + 1536) / 160 = 1886/160
4) Simplifying the mixed fraction:
- 1886/160 = 11 86/160 = 11 43/80
### Answer: 11 43/80
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (58 / 2) - 58 divided by 2 is 29 2) (31 / 32) - 31 divided by 32 is 0.96875 3) (58 / 2) + (31 / 32) - 29 + 0.96875 = 29.96875 Therefore, the result of the operation (58 / 2) + (31 / 32) is: ### Answer: 29.96875
Expected answer: 959/32
Correct? Yes
Problem: After you have calculated the result of the operation (58 / 2) + (31 / 32), subtract 90 / 58 from your answer. What is the final result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (58 / 2) + (31 / 32) - 29 + 0.96875 = 29.96875 2) Subtracting 90 / 58 from the result - 90 / 58 = 1.55172413793103 - 29.96875 - 1.55172413793103 = 28.41702586206897 Therefore, the final result is: ### Answer: 28.41702586206897
Expected answer: 26371/928
Correct? No
Problem: In the problem of adding (58 / 2) + (31 / 32), what would the result be if we originally had (58 / 2) + (10 / 32) instead? Now, compute the value.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (58 / 2) - 58 divided by 2 is 29 2) (10 / 32) - 10 divided by 32 is 0.3125 3) (58 / 2) + (10 / 32) - 29 + 0.3125 = 29.3125 Therefore, the result of the operation (58 / 2) + (10 / 32) is: ### Answer: 29.3125
Expected answer: 469/16
Correct? No
Problem: What is the sum of 26/90 and 50/26 when calculated as a fraction?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 26/90 and 50/26. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 90 and 26 is 2,340. 3) Convert the fractions to have the LCD of 2,340: 26/90 = 650/2,340 50/26 = 4,830/2,340 4) Now we can add the fractions: 650/2,340 + 4,830/2,340 = 5,480/2,340 5) Simplifying the fraction, we get: 5,480/2,340 = 274/117 ### Answer: 274/117
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 80/98 and 92/82. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 98 and 82 is 7,854. 3) Now we need to convert the fractions to have the same denominator of 7,854: 80/98 = (80 * 80)/7,854 92/82 = (92 * 96)/7,854 4) Now we can add the fractions: (80 * 80)/7,854 + (92 * 96)/7,854 = 6,400/7,854 + 8,832/7,854 = 15,232/7,854 5) Simplifying the final fraction, we get: 15,232/7,854 = 1.94 ### Answer: 1.94
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 89/44 and 69/5. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 44 and 5 is 220. 3) We need to convert the fractions to have the same denominator of 220: 89/44 = 89 * 5/44 * 5 = 445/220 69/5 = 69 * 44/5 * 44 = 3036/220 4) Now we can add the fractions: 445/220 + 3036/220 = 3481/220 ### Answer: 3481/220
Expected answer: 3481/220
Correct? Yes
Problem: What would be the result if you added together the sum of 89/44 and 69/5 to itself?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 89/44 and 69/5 to be 3481/220 in the previous problem. 2) Now we need to add this sum to itself: 3481/220 + 3481/220 = 6962/220 3) To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2. 6962/220 = 3481/110 ### Answer: 3481/110
Expected answer: 3481/110
Correct? Yes
Problem: What would be the result if we instead added 89/44 and 69/38, rather than 89/44 and 69/5 as was done in the original problem?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 89/44 and 69/38. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 44 and 38 is 1,672. 3) We need to convert the fractions to have the same denominator of 1,672: 89/44 = 89 * 38/44 * 38 = 3,382/1,672 69/38 = 69 * 44/38 * 44 = 2,904/1,672 4) Now we can add the fractions: 3,382/1,672 + 2,904/1,672 = 6,286/1,672 ### Answer: 6,286/1,672
Expected answer: 3209/836
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 79/32 - 79 divided by 32 is 2.46875 2) 52/55 - 52 divided by 55 is 0.945454545 3) 2.46875 - 0.945454545 - 2.46875 - 0.945454545 = 1.523295455 ### Answer: 1.523295455
Expected answer: 2681/1760
Correct? No
Problem: If Wooden Treasures, a furniture workshop, cuts a log into pieces. Each piece is 45/2 feet long. If they sell a piece of wood that is 18/90 feet shorter than the usual length, how long is the piece they sold?
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1) Each piece of wood cut from the log is 45/2 feet long. 2) The usual length of the piece of wood is 45/2 feet. 3) The piece they sold is 18/90 feet shorter than the usual length. 4) To find the length of the piece they sold, we need to subtract 18/90 feet from the usual length of 45/2 feet. 5) 45/2 feet - 18/90 feet = (45 - 18)/2 * 90 = 27/180 feet. 6) Simplifying, 27/180 feet = 9/60 feet. ### Answer: 9/60 feet.
Expected answer: 223/10
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 99/92 and 15/74. 2) To add fractions, we need to find the least common denominator (LCD). 3) The LCD of 92 and 74 is 5,368 (the least common multiple of 92 and 74). 4) Now we need to convert the fractions to have the same denominator of 5,368. 5) 99/92 = (99 * 58)/5,368 = 5,742/5,368 6) 15/74 = (15 * 72)/5,368 = 1,080/5,368 7) Now we can add the fractions: 5,742/5,368 + 1,080/5,368 = 6,822/5,368 8) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. 9) The GCF of 6,822 and 5,368 is 4. 10) Dividing both the numerator and denominator by 4, we get: 1,705/1,342. ### Answer: 1,705/1,342
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 54/1 = 54 2) 62/30 = 2.0666... (rounded to 4 decimal places) 3) 54 + 2.0666... = 56.0666... To express the answer in simplest terms, we can simplify the decimal: 56.0666... = 56.07 (rounded to 2 decimal places) ### Answer: 56.07
Expected answer: 841/15
Correct? No
Problem: What value do you get by adding 85/29 and 47/7?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to add the fractions 85/29 and 47/7. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 29 and 7 is 203. 3) We need to convert the fractions to have the LCD of 203: 85/29 = 585/203 47/7 = 1351/203 4) Now we can add the fractions: 585/203 + 1351/203 = 1936/203 5) Simplifying the final fraction, we get: 1936/203 = 9.5 ### Answer: 9.5
Expected answer: 1958/203
Correct? No