Claude-3 Haiku 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.
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Add the first two fractions 48/56 + 95/23 To add fractions, we need to find a common denominator. The least common denominator (LCD) of 56 and 23 is 1288. 48/56 = 864/1288 95/23 = 1240/1288 864/1288 + 1240/1288 = 2104/1288 Step 2: Subtract the third fraction 2104/1288 - 34/26 To subtract fractions, we need to convert the second fraction to have the same denominator as the first. 34/26 = 442/1288 2104/1288 - 442/1288 = 1662/1288 Step 3: Simplify the final result 1662/1288 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 8. 1662/1288 = 207.75/161 ### Answer: 207.75/161
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Add the fractions 88/9 and 28/65. To add fractions, we need to find the least common denominator (LCD). The LCD of 9 and 65 is 585. So we convert the fractions to have the same denominator of 585: 88/9 = 6520/585 28/65 = 260/585 Now we can add the fractions: 6520/585 + 260/585 = 6780/585 Step 2: Subtract the fraction 18/37 from the result. Again, we need to convert the fractions to have the same denominator. The LCD of 585 and 37 is 21645. 6780/585 = 21780/21645 18/37 = 486/21645 Now we can subtract the fractions: 21780/21645 - 486/21645 = 21294/21645 Step 3: Express the result as a simple fraction. To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 21294 and 21645 is 21. Dividing both the numerator and denominator by 21, we get: 21294/21645 = 1014/1030 ### Answer: 1014/1030
Expected answer: 210434/21645
Correct? No
Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (63 / 41) + (44 / 50) 2) First, let's calculate the individual fractions: (63 / 41) = 1.53658536585366 (44 / 50) = 0.88 3) Now, we add the two fractions: 1.53658536585366 + 0.88 = 2.41658536585366 4) To simplify this to the lowest terms, we need to find the greatest common factor (GCF) of the numerator and denominator. The numerator is 2.41658536585366 and the denominator is 1. The GCF of 2.41658536585366 and 1 is 1. 5) Dividing both the numerator and denominator by the GCF of 1, we get: 2.41658536585366 / 1 = 2.41658536585366 ### Answer: 2.41658536585366
Expected answer: 2477/1025
Correct? No
Problem: John had 71/41 of a cake left and Emily added 41/77 of another cake to it. How much cake is there in total? Give your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) John had 71/41 of a cake left. 2) Emily added 41/77 of another cake to it. 3) To find the total amount of cake, we need to add the two fractions together. 4) To add fractions, we need to find a common denominator. The least common denominator of 41 and 77 is 3157. 5) 71/41 = 5477/3157 and 41/77 = 1547/3157. 6) 5477/3157 + 1547/3157 = 7024/3157. 7) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 7. 8) 7024/3157 = 1003/451. ### Answer: 1003/451
Expected answer: 7148/3157
Correct? No
Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 10/65 + 56/35 2) First, we need to find a common denominator for the fractions. The least common multiple of 65 and 35 is 455. 3) So we can rewrite the fractions with the common denominator of 455: 10/65 = 70/455 56/35 = 364/455 4) Now we can add the fractions: 70/455 + 364/455 = 434/455 ### Answer: 434/455
Expected answer: 114/65
Correct? No
Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.
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 81 and 47 is 3,807. 3) To convert 75/81 to an equivalent fraction with denominator 3,807, we multiply the numerator and denominator by 47: 75/81 = (75 * 47) / (81 * 47) = 3,525 / 3,807 4) To convert 97/47 to an equivalent fraction with denominator 3,807, we multiply the numerator and denominator by 81: 97/47 = (97 * 81) / (47 * 81) = 7,857 / 3,807 5) Now we can add the fractions: 3,525/3,807 + 7,857/3,807 = 11,382/3,807 ### Answer: 11,382/3,807
Expected answer: 3794/1269
Correct? Yes
Problem: After calculating the result of adding 75/81 and 97/47, what do you get when you add that result to 52/71? Provide your answer as an unsimplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the result of adding 75/81 and 97/47 to be 11,382/3,807. 2) Now we need to add 52/71 to that result. 3) To add the fractions, we need to find a common denominator. The least common multiple of 3,807 and 71 is 270,297. 4) Convert 11,382/3,807 to an equivalent fraction with denominator 270,297: 11,382/3,807 = (11,382 * 71) / (3,807 * 71) = 807,282/270,297 5) Convert 52/71 to an equivalent fraction with denominator 270,297: 52/71 = (52 * 3,807) / (71 * 3,807) = 197,964/270,297 6) Now we can add the fractions: 807,282/270,297 + 197,964/270,297 = 1,005,246/270,297 ### Answer: 1,005,246/270,297
Expected answer: 335362/90099
Correct? No
Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 88/1 = 88 2) 38/53 = 38/53 3) 88 - 38/53 = 88 - (38/53) 4) To subtract the fractions, we need to find a common denominator. The least common denominator is 53. 5) 88 - (38/53) = (88*53 - 38)/53 = (4664 - 38)/53 = 4626/53 6) The fraction is now simplified. ### Answer: 4626/53
Expected answer: 4626/53
Correct? Yes
Problem: After calculating the result of 88/1 - 38/53, add it to 25/79. What is the final value, and answer as a simplified fraction?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 88/1 - 38/53 = 4626/53 (from the previous problem) 2) 4626/53 + 25/79 3) To add the fractions, we need to find a common denominator. The least common denominator is 4167 (the least common multiple of 53 and 79). 4) 4626/53 = 4167/53 * 53/53 = 4167/53 5) 25/79 = 4167/79 * 79/79 = 4167/79 6) 4167/53 + 4167/79 = (4167*79 + 4167*53)/4167 = 329,293/4167 7) The fraction is now simplified. ### Answer: 329,293/4167
Expected answer: 366779/4187
Correct? No
Problem: Previous problem: What is 88/1 - 38/53? Now consider if the second fraction (38/53) was changed to 38/93 instead. So, what is 88/1 - 38/93? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 88/1 = 88 2) 38/93 = 38/93 3) 88 - 38/93 = 88 - (38/93) 4) To subtract the fractions, we need to find a common denominator. The least common denominator is 93. 5) 88 - (38/93) = (88*93 - 38)/93 = (8184 - 38)/93 = 8146/93 6) The fraction is now simplified. ### Answer: 8146/93
Expected answer: 8146/93
Correct? Yes
Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Evaluate the first part of the expression: (80 / 94) 80 / 94 = 0.8510638297872341 2) Evaluate the second part of the expression: (78 / 59) 78 / 59 = 1.3220338983050848 3) Add the two parts together: 0.8510638297872341 + 1.3220338983050848 = 2.1730977280923189 4) Simplify the final answer: 2.1730977280923189 ### Answer: 2.173
Expected answer: 6026/2773
Correct? No
Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 89/56 and 48/50. 2) To add fractions, we need to find the least common denominator (LCD). The LCD of 56 and 50 is 280. 3) Now we need to convert the fractions to have the same denominator of 280: 89/56 = 89 * (280/56) = 445/280 48/50 = 48 * (280/50) = 268/280 4) Now we can add the fractions: 445/280 + 268/280 = 713/280 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 713 and 280 is 7. 713/280 = 101/40 ### Answer: 101/40
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 96/11 and 12/5. 96/11 + 12/5 = (96 * 5 + 11 * 12) / (11 * 5) = (480 + 132) / 55 = 612 / 55 2. Now, we need to subtract 38/87 from the sum. 612/55 - 38/87 = (612 * 87 - 38 * 55) / (55 * 87) = (53,244 - 2,090) / 4,785 = 51,154 / 4,785 Therefore, the final answer is 51,154/4,785. ### Answer: 51,154/4,785
Expected answer: 51154/4785
Correct? Yes
Problem: After you find the result subtracting 38/87 from the sum of 96/11 and 12/5, add that result back to the initial sum of 96/11 and 12/5. What is the final result? Please leave your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 96/11 and 12/5. 96/11 + 12/5 = (96 * 5 + 11 * 12) / (11 * 5) = (480 + 132) / 55 = 612 / 55 2. Next, we need to subtract 38/87 from the sum. 612/55 - 38/87 = (612 * 87 - 38 * 55) / (55 * 87) = (53,244 - 2,090) / 4,785 = 51,154 / 4,785 3. Finally, we need to add the result back to the initial sum. 612/55 + 51,154/4,785 = (612 * 4,785 + 51,154 * 55) / (55 * 4,785) = (2,928,420 + 2,813,470) / 262,175 = 5,741,890 / 262,175 Therefore, the final result is 5,741,890/262,175. ### Answer: 5,741,890/262,175
Expected answer: 104398/4785
Correct? No
Problem: After considering the fruit you have, suppose you actually started off with a fraction of the fruits, having 96/58 oranges, and still having 12/5 apples. If you subtracted 38/87 of your total fruits for charity, what fraction of fruits would you have left? Please leave your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. First, we need to find the total number of fruits you started with. Oranges: 96/58 Apples: 12/5 Total fruits = 96/58 + 12/5 = (96 * 5 + 58 * 12) / (58 * 5) = (480 + 696) / 290 = 1,176 / 290 2. Now, we need to subtract 38/87 of the total fruits for charity. Total fruits - 38/87 = (1,176 * 87 - 38 * 290) / (290 * 87) = (102,312 - 11,020) / 25,230 = 91,292 / 25,230 Therefore, the fraction of fruits you have left is 91,292/25,230. ### Answer: 91,292/25,230
Expected answer: 1574/435
Correct? Yes
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.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1) 82 divided by 9 is 9.11 (rounded to two decimal places). 2) 82 divided by 63 is 1.30 (rounded to two decimal places). 3) Now we subtract 1.30 from 9.11: 9.11 - 1.30 = 7.81 To express this as a simplified fraction, we need to find the common denominator. The least common denominator of 9 and 63 is 567. 9.11 = 511/63 1.30 = 82/63 Subtracting the fractions: 511/63 - 82/63 = 429/63 ### Answer: 429/63
Expected answer: 164/21
Correct? No
Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. Calculate 23/3: 23/3 = 7.6666... (repeating decimal) 2. Calculate 80/91: 80/91 = 0.8791... 3. Calculate 26/24: 26/24 = 1.0833... 4. Add 80/91 and 26/24: 0.8791... + 1.0833... = 1.9624... 5. Subtract the sum from 23/3: 23/3 - 1.9624... = 7.6666... - 1.9624... = 5.7042... 6. Express the final answer as a simple fraction: 5.7042... = 171/30 ### Answer: 171/30
Expected answer: 6229/1092
Correct? No
Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find the common denominator for the two fractions: - The least common multiple of 18 and 60 is 180. 2) Now we can convert the fractions to have the same denominator: - 37/18 = 37 * 10/180 = 370/180 - 24/60 = 24 * 3/180 = 72/180 3) Now we can add the fractions: - 370/180 + 72/180 = 442/180 4) Finally, we need to simplify the fraction to the lowest terms: - The greatest common factor of 442 and 180 is 2. - 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find the sum of 37/18 and 24/60: - 37/18 = 370/180 - 24/60 = 72/180 - 370/180 + 72/180 = 442/180 2) Now we need to add 92/28 to the sum: - 92/28 = 322/98 3) Adding the fractions: - 442/180 + 322/98 = 79,596/17,640 4) Simplifying the fraction to the lowest terms: - The greatest common factor of 79,596 and 17,640 is 12. - 79,596/17,640 = 6,633/1,470 ### Answer: 6,633/1,470
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find the common denominator for the two fractions: - The least common multiple of 18 and 72 is 72. 2) Now we can convert the fractions to have the same denominator: - 37/18 = 37 * 4/72 = 148/72 - 24/72 = 24/72 3) Now we can add the fractions: - 148/72 + 24/72 = 172/72 4) Finally, we need to simplify the fraction to the lowest terms: - The greatest common factor of 172 and 72 is 4. - 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 33/41 and 95/62. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 41 and 62 is 2,822 (the least common multiple of 41 and 62). 3) Now we need to convert the fractions to have the same denominator of 2,822: 33/41 = (33 * 69)/2,822 = 2,277/2,822 95/62 = (95 * 46)/2,822 = 4,370/2,822 4) Now we can add the fractions: 2,277/2,822 + 4,370/2,822 = 6,647/2,822 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 6,647 and 2,822 is 1. 6) Therefore, the simplified fraction is: 6,647/2,822 ### Answer: 6,647/2,822
Expected answer: 5941/2542
Correct? No
Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Evaluate the first expression ((30 / 11) + (72 / 38)) (30 / 11) = 2.727272727 (72 / 38) = 1.894736842 (2.727272727) + (1.894736842) = 4.622009569 Step 2: Add the result to (81 / 34) (81 / 34) = 2.382352941 4.622009569 + 2.382352941 = 7.004362510 Step 3: Simplify the final result as a fraction The numerator is 7.004362510 * 10,000 = 70,043.62510 The denominator is 1 * 10,000 = 10,000 The simplified fraction is 70,043/10,000. ### Answer: 70,043/10,000
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate (64 / 34) + (3 / 24) (64 / 34) = 1.88235294117647 (3 / 24) = 0.125 1.88235294117647 + 0.125 = 2.00735294117647 Step 2: Add the result from Step 1 to (41 / 96) (41 / 96) = 0.427083333333333 2.00735294117647 + 0.427083333333333 = 2.43443627450980 Step 3: Simplify the final result as a fraction The numerator is 2.43443627450980 * 100 = 243.44 The denominator is 100 So the simplified fraction is 243/100. ### Answer: 243/100
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?
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Add 83/73 and 53/77 To add fractions, we need to find the least common denominator (LCD) first. The LCD of 73 and 77 is 5621. 83/73 = 5621/5621 53/77 = 4081/5621 Now we can add the numerators: 5621/5621 + 4081/5621 = 9702/5621 This simplified fraction is 'w'. Step 2: Add 80/76 to 'w' The LCD of 5621 and 76 is 426,796. 9702/5621 = 1,726,796/426,796 80/76 = 426,796/426,796 Now we can add the numerators: 1,726,796/426,796 + 426,796/426,796 = 2,153,592/426,796 This final simplified fraction is the answer. ### Answer: 2,153,592/426,796
Expected answer: 307360/106799
Correct? No
Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.
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 20 and 66 is 660. 2) Now we can convert the fractions to have a common denominator of 660: 27/20 = 297/660 14/66 = 140/660 3) Now we can add the fractions: 297/660 + 140/660 = 437/660 4) To simplify the fraction, we need to find the greatest common factor of 437 and 660. The greatest common factor of 437 and 660 is 11. 5) Dividing both the numerator and denominator by 11, we get: 437/660 = 39/60 ### Answer: 39/60
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Evaluate the first part of the expression: (32 / 14) 32 / 14 = 2.2857142857142857 2) Evaluate the second part of the expression: (22 / 47) 22 / 47 = 0.4680851063829787 3) Subtract the two parts: (2.2857142857142857) - (0.4680851063829787) = 1.8176291793313070 4) To write the result as a simplified fraction, we need to find the numerator and denominator. The numerator is 1.8176291793313070 * 100000 = 181762.91793313070 The denominator is 100000 5) Simplifying the fraction, we get: 181762/100000 = 181762/100000 = 181762/100000 = 181762/100000 = 181762/100000 ### Answer: 181762/100000
Expected answer: 598/329
Correct? No
Problem: What is the sum of 74/61 and 41/53 expressed in fractions?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 74/61 and 41/53. 2) To add fractions, we need to find the least common denominator (LCD) of the two fractions. 3) The LCD of 61 and 53 is 3233 (the least common multiple of 61 and 53). 4) Now we need to convert the fractions to have the same denominator of 3233. 5) 74/61 = 3233/3233 * 74/61 = 3874/3233 6) 41/53 = 3233/3233 * 41/53 = 2461/3233 7) Now we can add the fractions: 3874/3233 + 2461/3233 = 6335/3233. ### Answer: 6335/3233
Expected answer: 6423/3233
Correct? No
Problem: First, find out the result of 94 / 2 - 74 / 57. Then add the result to 56 / 97. What fraction do you get?
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Calculate 94 / 2 - 74 / 57 94 / 2 = 47 74 / 57 = 1.2982456140350877 47 - 1.2982456140350877 = 45.7017543859649 Step 2: Add the result to 56 / 97 45.7017543859649 + 56 / 97 = 45.7017543859649 + 0.5773195876288659 = 46.2790739735938 Step 3: Express the final result as a fraction 46.2790739735938 = 46 + 0.2790739735938 The fractional part is 0.2790739735938 To express this as a fraction, we need to find the denominator. The denominator will be 1 followed by the number of decimal places, which is 10 in this case. So the final fraction is 279/1000. ### Answer: 279/1000
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Find the sum of 24/34 and 44/87. 24/34 + 44/87 = (24*87 + 44*34) / (34*87) = (2088 + 1496) / 2958 = 3584 / 2958 = 179/148 Step 2: Find the sum of 14/89 and the result from Step 1. 14/89 + 179/148 = (14*148 + 179*89) / (89*148) = (2072 + 15931) / 13172 = 18003 / 13172 = 137/100 ### Answer: 137/100
Expected answer: 180194/131631
Correct? No
Problem: What would you get if you add 73/30 to 8/60?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for 73/30 and 8/60. 2) The least common denominator is 60 (the least common multiple of 30 and 60). 3) To convert 73/30 to have a denominator of 60, we multiply the numerator and denominator by 2: 73/30 = (73 * 2) / (30 * 2) = 146/60 4) Now we can add the two fractions: 146/60 + 8/60 = 154/60 5) Simplifying the final answer: 154/60 = 2 and 34/60 ### Answer: 2 and 34/60
Expected answer: 77/30
Correct? Yes
Problem: If you take the result of adding 73/30 to 8/60 and then add it to itself again, what fraction do you get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the result of adding 73/30 to 8/60 in the previous problem: 154/60 2) Now we need to add this result to itself: 154/60 + 154/60 = 308/60 3) Simplifying the final answer: 308/60 = 5 and 8/60 ### Answer: 5 and 8/60
Expected answer: 77/15
Correct? Yes
Problem: Suppose you originally had a fraction of 73/30. Now, instead of adding 8/60 to it, you decide to add 49/60. What fraction will you get in this case?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find a common denominator for 73/30 and 49/60. 2) The least common denominator is 60 (the least common multiple of 30 and 60). 3) To convert 73/30 to have a denominator of 60, we multiply the numerator and denominator by 2: 73/30 = (73 * 2) / (30 * 2) = 146/60 4) Now we can add the two fractions: 146/60 + 49/60 = 195/60 5) Simplifying the final answer: 195/60 = 3 and 15/60 ### Answer: 3 and 15/60
Expected answer: 13/4
Correct? Yes
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Add the first fraction (82/49) with the second one (45/60). 82/49 + 45/60 = (82*60 + 49*45) / (49*60) = (4920 + 2205) / 2940 = 7125 / 2940 = 'd' Step 2: Add 'd' to the third fraction (99/59). 'd' + 99/59 = (7125/2940 + 99*2940/59*2940) / 2940 = (7125/2940 + 5940/2940) / 2940 = 13065/2940 = 13/2 + 15/2940 = 13.5 + 0.005 = 13.505 To simplify the final result, we can express it as a fraction: 13.505 = 27011/2000 ### Answer: 27011/2000
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Subtract 76/30 from 91/16 91/16 - 76/30 = (91 * 30 - 76 * 16) / (16 * 30) = (2730 - 1216) / 480 = 1514 / 480 = 3.15 Step 2: Add the answer to 18/44 3.15 + 18/44 = 3.15 + 0.41 = 3.56 Rounding the final answer to the nearest hundredth: ### 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.
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Calculate ((8 / 91) + (49 / 5)) (8 / 91) = 0.0879 (49 / 5) = 9.8 0.0879 + 9.8 = 9.8879 Step 2: Subtract (32 / 76) from the result (32 / 76) = 0.4211 9.8879 - 0.4211 = 9.4668 Step 3: Simplify the result as a fraction The numerator is 9.4668 and the denominator is 1. To simplify, we can convert the decimal to a fraction: 9.4668 = 94668/10000 Therefore, the final simplified answer is: 94668/10000 - 4211/10000 = 90457/10000 ### Answer: 90457/10000
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.
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Calculate the value of ((75 / 45) + (5 / 49)) 75 / 45 = 5/3 5 / 49 = 1/9.8 (5/3) + (1/9.8) = (5/3) + (1/9.8) = (45/9) + (1/9.8) = 5 + 0.102 = 5.102 Step 2: Add this value with 3 / 58 5.102 + (3/58) = 5.102 + 0.0517 = 5.1537 Step 3: Provide the answer as a simple fraction The final answer is 5.1537, which can be expressed as the fraction 295/57. ### Answer: 295/57
Expected answer: 15521/8526
Correct? No
Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Calculate (43 / 15) 43 / 15 = 2.8666666667 2) Calculate (33 / 95) 33 / 95 = 0.3473684211 3) Subtract the two values: 2.8666666667 - 0.3473684211 = 2.5192982456 4) Simplify the result to its lowest terms: The numerator is 2.5192982456 and the denominator is 1. The simplified answer is 2.5192982456. ### Answer: 2.5192982456
Expected answer: 718/285
Correct? No
Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Calculate the first part of the expression: (78 / 45) = 1.73333 2. Calculate the second part of the expression: (89 / 36) = 2.47222 3. Add the two parts together: 1.73333 + 2.47222 = 4.20555 4. Add this sum to itself: 4.20555 + 4.20555 = 8.41110 5. Simplify the fraction: 8.41110 = 841/100 ### Answer: 841/100
Expected answer: 757/90
Correct? No
Problem: Let's consider that 93 is divided by 34 to get a fraction value, from which is subtracted another fraction 77/74. What would be the result as a simplified fraction?
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. Divide 93 by 34 to get a fraction value: 93 / 34 = 2.735294117647059 2. Subtract the fraction 77/74 from the result: 2.735294117647059 - (77/74) = 2.735294117647059 - 1.0405405405405406 = 1.6947535770234184 3. Simplify the result as a fraction: 1.6947535770234184 = 169/100 Therefore, the final result as a simplified fraction is: ### Answer: 169/100
Expected answer: 1066/629
Correct? No
Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions to add: 86/35 and 68/85. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 35 and 85 is 595. 3) Now we need to convert the fractions to have the same denominator of 595: 86/35 = (86 * 17)/595 = 1462/595 68/85 = (68 * 7)/595 = 476/595 4) Now we can add the fractions: 1462/595 + 476/595 = 1938/595 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 1938 and 595 is 17. Dividing both the numerator and denominator by 17, we get: 1938/595 = 114/35 ### Answer: 114/35
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We found the sum of 86/35 and 68/85 to be 114/35 in the previous problem. 2) Now we need to add 86/35 to 114/35. 114/35 + 86/35 = 200/35 3) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 200 and 35 is 5. Dividing both the numerator and denominator by 5, we get: 200/35 = 40/7 ### Answer: 40/7
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.
Claude-3 Haiku:
Okay, let's solve this with the revised fraction 86/75. 1) We have two fractions to add: 86/75 and 68/85. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 75 and 85 is 3825. 3) Now we need to convert the fractions to have the same denominator of 3825: 86/75 = (86 * 51)/3825 = 4386/3825 68/85 = (68 * 45)/3825 = 3060/3825 4) Now we can add the fractions: 4386/3825 + 3060/3825 = 7446/3825 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 7446 and 3825 is 15. Dividing both the numerator and denominator by 15, we get: 7446/3825 = 496/255 ### Answer: 496/255
Expected answer: 146/75
Correct? No
Problem: What is the sum of 99/53 and 67/94 in simplest form?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 99/53 and 67/94. 2) To add fractions, we need to find the least common denominator (LCD). 3) The LCD of 53 and 94 is 4,982 (the least common multiple of 53 and 94). 4) Now we need to convert the fractions to have the same denominator of 4,982. 5) 99/53 = 3,726/4,982 6) 67/94 = 2,844/4,982 7) Now we can add the fractions: 3,726/4,982 + 2,844/4,982 = 6,570/4,982 8) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. 9) The GCF of 6,570 and 4,982 is 2. 10) Dividing both the numerator and denominator by 2, we get 3,285/2,491. ### Answer: 3,285/2,491
Expected answer: 12857/4982
Correct? No
Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the common denominator for the two fractions. The least common multiple of 27 and 33 is 297. 2) Now we can rewrite the fractions with the common denominator of 297: 74/27 = 74 * 11 / 297 56/33 = 56 * 9 / 297 3) Subtract the fractions: 74 * 11 / 297 - 56 * 9 / 297 = (74 * 11 - 56 * 9) / 297 = (814 - 504) / 297 = 310 / 297 4) Simplify the fraction: 310 / 297 = 10 / 9. ### Answer: 10/9
Expected answer: 310/297
Correct? No
Problem: Find the result when you subtract 91/65 from the sum of 96/40 and 11/99. Leave your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Find the sum of 96/40 and 11/99: 96/40 + 11/99 = (96 * 99 + 11 * 40) / (40 * 99) = (9,504 + 440) / 3,960 = 9,944 / 3,960 = 251/100 2. Subtract 91/65 from the sum: 251/100 - 91/65 = (251 * 65 - 91 * 100) / (100 * 65) = (16,315 - 9,100) / 6,500 = 7,215 / 6,500 = 143/130 ### Answer: 143/130
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?
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1) Divide 10 by 5 and add that result to 35 divided by 27. 10 / 5 = 2 35 / 27 = 1.296 2 + 1.296 = 3.296 This gives us the value h = 3.296 Step 2) Add 47 divided by 99 to h. 47 / 99 = 0.475 3.296 + 0.475 = 3.771 Therefore, the value of p is 3.771. ### Answer: 3.771
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fraction 90/81 and we need to add it to 2/66. 2) To add fractions, we need to find the least common denominator (LCD). The LCD of 81 and 66 is 2,646. 3) Now we need to convert the fractions to have the same denominator of 2,646: 90/81 = (90 * 32.67)/2,646 = 2,940/2,646 2/66 = (2 * 40.09)/2,646 = 80.18/2,646 4) Now we can add the fractions: 2,940/2,646 + 80.18/2,646 = 3,020.18/2,646 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 3,020.18 and 2,646 is 2.18. 6) Dividing both the numerator and denominator by 2.18, we get: 3,020.18/2,646 = 1,384/1,214 ### Answer: 1,384/1,214
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?
Claude-3 Haiku:
Okay, let's break this down step-by-step: * Oliver has a piece of ribbon that is 56/41 yards long * He gets another piece of the same length To find the total length of both pieces of ribbon, we need to add the lengths together. The length of the first piece is 56/41 yards. The length of the second piece is also 56/41 yards. To find the total length, we add the two lengths together: * 56/41 + 56/41 = 112/41 yards ### 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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: * Oliver originally had 1 piece of ribbon that was 56/41 yards long * He then got another piece of the same length, so now he has 2 pieces * The total length of the 2 pieces is 56/41 + 56/41 = 112/41 yards * He then received 2 more pieces, each 56/41 yards long * To find the total length of all 4 pieces, we add them together: * 56/41 + 56/41 + 56/41 + 56/41 = 224/41 yards ### 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?
Claude-3 Haiku:
Okay, let's work through this step-by-step: * Oliver initially had a piece of ribbon that was 63/41 yards long * He then received a second piece of the same length To find the total length of both pieces of ribbon, we need to add the lengths together. The length of the first piece is 63/41 yards. The length of the second piece is also 63/41 yards. To find the total length, we add the two lengths together: * 63/41 + 63/41 = 126/41 yards ### 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 92/75 + 66/92 2) First, we need to find a common denominator for the fractions. The least common multiple of 75 and 92 is 6900. 3) So we need to convert the fractions to have a denominator of 6900: 92/75 = 7360/6900 66/92 = 4620/6900 4) Now we can add the fractions: 7360/6900 + 4620/6900 = 11980/6900 5) To simplify the fraction, we can divide both the numerator and denominator by the greatest common factor, which is 20. 11980/6900 = 599/345 ### Answer: 599/345
Expected answer: 6707/3450
Correct? No
Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 32/65 and 73/22. 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 65 and 22 is 1430. 4) We need to convert the fractions to have the LCD of 1430. 5) 32/65 = (32 * 22)/1430 = 704/1430 6) 73/22 = (73 * 65)/1430 = 4745/1430 7) The sum of the fractions is 704/1430 + 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) In the previous problem, the answer was 5449/1430. 2) We now need to add 24/71 to 5449/1430. 3) To find the sum, we need to find a common denominator. 4) The least common denominator (LCD) of 1430 and 71 is 101330. 5) We need to convert the fractions to have the LCD of 101330. 6) 5449/1430 = (5449 * 71)/101330 = 386679/101330 7) 24/71 = (24 * 1430)/101330 = 34320/101330 8) The sum of the fractions is 386679/101330 + 34320/101330 = 421,999/101,330. ### Answer: 421,999/101,330
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 53/65 and 73/22. 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 65 and 22 is 1430. 4) We need to convert the fractions to have the LCD of 1430. 5) 53/65 = (53 * 22)/1430 = 1166/1430 6) 73/22 = (73 * 65)/1430 = 4745/1430 7) The sum of the fractions is 1166/1430 + 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the difference between 51/34 and 12/86. 2) To do this, we need to find a common denominator for the two fractions. 3) The least common denominator (LCD) of 34 and 86 is 2,618 (the least common multiple of 34 and 86). 4) Now we can convert the fractions to have the same denominator of 2,618: 51/34 = (51 * 77)/2,618 = 3,927/2,618 12/86 = (12 * 30)/2,618 = 360/2,618 5) Now we can subtract the fractions: 3,927/2,618 - 360/2,618 = 3,567/2,618 6) To express this in its simplest form, we need to find the greatest common factor (GCF) of the numerator and denominator. 7) The GCF of 3,567 and 2,618 is 1. 8) Therefore, the simplified fraction is 3,567/2,618. ### Answer: 3,567/2,618
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?
Claude-3 Haiku:
Okay, let's break this down step-by-step: Step 1: Take the whole number 51 and add it to the fraction 93/8. 51 + 93/8 = (51 * 8 + 93) / 8 = (408 + 93) / 8 = 501/8 Step 2: Take the sum from Step 1 and add it to the fraction 58/44. 501/8 + 58/44 = (501 * 44 + 58 * 8) / (8 * 44) = (22044 + 464) / 352 = 22508/352 Step 3: Simplify the final result as a fraction. The greatest common factor of 22508 and 352 is 8. Dividing both the numerator and denominator by 8 gives: 22508/352 = 2813.5/44 ### Answer: 2813.5/44
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?
Claude-3 Haiku:
Okay, let's incorporate the additional step: Step 1: Take the whole number 51 and add it to the fraction 93/8. 51 + 93/8 = (51 * 8 + 93) / 8 = (408 + 93) / 8 = 501/8 Step 2: Take the sum from Step 1 and add it to the fraction 58/44. 501/8 + 58/44 = (501 * 44 + 58 * 8) / (8 * 44) = (22044 + 464) / 352 = 22508/352 Step 3: Add the fraction 38/53 to the previous result. 22508/352 + 38/53 = ((22508 * 53) + (38 * 352)) / (352 * 53) = (1192924 + 13376) / 18656 = 1206300/18656 Step 4: Simplify the final result as a fraction. The greatest common factor of 1206300 and 18656 is 4. Dividing both the numerator and denominator by 4 gives: 1206300/18656 = 301575/4664 ### Answer: 301575/4664
Expected answer: 301575/4664
Correct? Yes
Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find a common denominator for the two fractions. The least common multiple of 5 and 25 is 25. 2) Now we can rewrite the fractions with the common denominator of 25: 82/5 = 82 * 5/25 = 410/25 98/25 = 98/25 3) Now we can subtract the fractions: 410/25 - 98/25 = (410 - 98)/25 = 312/25 4) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. 312/25 = 78/5 ### Answer: 78/5
Expected answer: 312/25
Correct? No
Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: (64 / 50) + (70 / 22) First, let's calculate each fraction: 64 / 50 = 1.28 70 / 22 = 3.18 Now, we add the two fractions together: 1.28 + 3.18 = 4.46 To express the answer as an unsimplified fraction, we need to find a common denominator for the two fractions. The least common denominator is 50 * 22 = 1100. So, the unsimplified fraction is: 446/100 ### Answer: 446/100
Expected answer: 1227/275
Correct? No
Problem: John calculated s by adding 24 divided by 6 to 40 divided by 53. He then added s to itself to get b. Can you find the value of b?
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. John calculated s by adding 24 divided by 6 to 40 divided by 53. * 24 divided by 6 = 4 * 40 divided by 53 = 0.7547 * s = 4 + 0.7547 = 4.7547 2. John then added s to itself to get b. * b = s + s * b = 4.7547 + 4.7547 = 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((80 / 90) + (52 / 11)) 2) First, let's calculate the individual fractions: (80 / 90) = 0.8888... (52 / 11) = 4.7272... 3) Now, we add the two fractions: 0.8888... + 4.7272... = 5.6160... 4) To express this as a mixed number, we need to find the whole number part and the fractional part. The whole number part is 5. The fractional part is 0.6160... 5) Simplifying the fractional part, we get: 0.6160... = 6/10 = 3/5 6) Therefore, the final answer expressed as a mixed number is: 5 3/5 ### Answer: 5 3/5
Expected answer: 556/99
Correct? No
Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.
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 18 and 74 is 1332. 2) Convert the fractions to have the common denominator of 1332: 12/18 = 792/1332 91/74 = 1218/1332 3) Now we can add the fractions: 792/1332 + 1218/1332 = 2010/1332 4) Simplify the fraction: 2010/1332 = 5/3.33 = 5/3 ### Answer: 5/3
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 7/2 and 51/25 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 2 and 25 is 50. 4) So we need to convert the fractions to have a denominator of 50: 7/2 = 7 * 25/50 = 175/50 51/25 = 51 * 2/50 = 102/50 5) Now we can add the fractions: 175/50 + 102/50 = 277/50 To write the answer as a simple fraction, we need to simplify the fraction 277/50. The greatest common factor of 277 and 50 is 1, so the fraction cannot be simplified further. ### 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the three fractions: 7/2, 51/25, and 86/39 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 2, 25, and 39 is 390. 4) So we need to convert the fractions to have a denominator of 390: 7/2 = 7 * 195/390 = 1365/390 51/25 = 51 * 16/390 = 816/390 86/39 = 86 * 10/390 = 860/390 5) Now we can add the fractions: 1365/390 + 816/390 + 860/390 = 3041/390 To write the answer as a simple fraction, we need to simplify the fraction 3041/390. The greatest common factor of 3041 and 390 is 13, so the simplified fraction is 233/30. ### Answer: 233/30
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 7/22 and 51/25 2) To find the sum, we need to find a common denominator. 3) The least common denominator (LCD) of 22 and 25 is 550. 4) So we need to convert the fractions to have a denominator of 550: 7/22 = 7 * 25/550 = 175/550 51/25 = 51 * 22/550 = 1122/550 5) Now we can add the fractions: 175/550 + 1122/550 = 1297/550 To write the answer as a simplified fraction, we need to simplify the fraction 1297/550. The greatest common factor of 1297 and 550 is 11, so the simplified fraction is: 1297/550 = 118/50 ### Answer: 118/50
Expected answer: 1297/550
Correct? No
Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.
Claude-3 Haiku:
Okay, let's break this down step-by-step:
1. Calculate the first expression: ((68 / 69) + (93 / 7))
- (68 / 69) = 0.9855072463768116
- (93 / 7) = 13.285714285714286
- (0.9855072463768116) + (13.285714285714286) = 14.271221532091116
2. This first expression is a monomial, so we can add it to the second expression: (3 / 46)
- (3 / 46) = 0.06521739130434783
3. Now we add the two expressions together:
- 14.271221532091116 + 0.06521739130434783 = 14.336438923395464
4. To express the final result as a simple fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
- The numerator is 14336438923395464
- The denominator is 1000000000000000
- The GCD of the numerator and denominator is 1000000000
- Dividing both the numerator and denominator by 1000000000, we get:
- Numerator: 14336.438923395464
- Denominator: 1000
### Answer: 14336/1000
Expected answer: 13849/966
Correct? No
Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to add the fractions 31/98 and 60/4. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 98 and 4 is 392. 3) We need to convert the fractions to have the LCD of 392: 31/98 = 124/392 60/4 = 480/392 4) Now we can add the fractions: 124/392 + 480/392 = 604/392 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. 6) The GCF of 604 and 392 is 4. 7) Dividing both the numerator and denominator by 4, we get: 604/392 = 151/98 ### Answer: 151/98
Expected answer: 1501/98
Correct? No
Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (3 / 2) = 1.5 2) (24 / 36) = 2/3 3) ((3 / 2) + (24 / 36)) = 1.5 + 2/3 = 1.5 + 0.667 = 2.167 To express the answer as a simplified fraction, we need to find the common denominator. The common denominator is 6. 1.5 = 3/2 2/3 = 4/6 So the final expression is: (3/2) + (4/6) = (3 + 4)/6 = 7/6 ### Answer: 7/6
Expected answer: 13/6
Correct? No
Problem: Firstly, calculate the sum of 92/54 and 90/13, then from the result take away 46/41. What's the result as a simplified fraction?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate the sum of 92/54 and 90/13. 92/54 + 90/13 = (92 * 13 + 90 * 54) / (54 * 13) = (1196 + 4860) / 702 = 6056 / 702 = 86/10 Step 2: From the result, take away 46/41. 86/10 - 46/41 = (86 * 41 - 46 * 10) / (10 * 41) = (3526 - 460) / 410 = 3066 / 410 = 153/20 Therefore, the result as a simplified fraction is 153/20. ### Answer: 153/20
Expected answer: 108002/14391
Correct? No
Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the value of 29/23. 2) 29/23 = 1.26086956521739 3) Twice the value of 29/23 is 2 * 1.26086956521739 = 2.52173913043478 4) To simplify the answer to the simplest form, we can reduce the fraction. 5) 2.52173913043478 = 23/9 ### Answer: 23/9
Expected answer: 58/23
Correct? No
Problem: What is the sum of 29/20 and 17/72? 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 20 and 72 is 720. 3) Now we can convert the fractions to have the same denominator of 720: 29/20 = 29 * 36/20 * 36 = 1044/720 17/72 = 17 * 10/72 * 10 = 170/720 4) Now we can add the fractions: 1044/720 + 170/720 = 1214/720 5) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. 1214/720 = 303.5/180 ### Answer: 303/180
Expected answer: 607/360
Correct? No
Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. Evaluate the first part of the expression: (36 / 27) + (80 / 10) - 36 / 27 = 1.333 - 80 / 10 = 8 - 1.333 + 8 = 9.333 2. Evaluate the second part of the expression: 73 / 79 - 73 / 79 = 0.924 3. Subtract the second part from the first part: - 9.333 - 0.924 = 8.409 Therefore, the simplified value of the expression is: ### 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (86 / 71) = 1.21 2) (91 / 75) = 1.21 3) 1.21 + 1.21 = 2.42 Rounding to the nearest hundredth, the final answer is: ### 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)
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate the first term (21 / 75) 21 / 75 = 7 / 25 Step 2: Calculate the second term (74 / 43) 74 / 43 = 74 / 43 Step 3: Add the first two terms (7 / 25) + (74 / 43) = (7 * 43 + 25 * 74) / (25 * 43) = (301 + 1850) / 1075 = 2151 / 1075 Step 4: Add the third term (10 / 62) (2151 / 1075) + (10 / 62) = (2151 * 62 + 1075 * 10) / (1075 * 62) = (133362 + 10750) / 66650 = 144112 / 66650 Step 5: Simplify the fraction 144112 / 66650 = 2176 / 1005 ### Answer: 2176/1005
Expected answer: 72056/33325
Correct? No
Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Compute (75 / 66) 75 / 66 = 5/4.4 = 5/4.4 = 25/22 Step 2: Compute (81 / 61) 81 / 61 = 1.3278688524590164 This can be simplified to 81/61 = 27/20 Step 3: Add the two fractions (25/22) + (27/20) = (25*20 + 22*27) / (22*20) = (500 + 594) / 440 = 1094 / 440 Step 4: Reduce the fraction to its lowest term The greatest common factor of 1094 and 440 is 2. 1094 / 2 = 547 440 / 2 = 220 Therefore, the final answer is 547/220. ### Answer: 547/220
Expected answer: 3307/1342
Correct? No
Problem: Consider two identical fractions, t, each equal to sum of 53/18 and 21/99. Find the total sum, l, of these fractions and present your answer as a simple fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. We have two identical fractions, t, each equal to the sum of 53/18 and 21/99. 2. To find the value of t, we need to add the two fractions: t = 53/18 + 21/99 3. To add the fractions, we need to find the least common denominator (LCD). The LCD of 18 and 99 is 1782. 4. Converting the fractions to have the same denominator of 1782: 53/18 = 295/1782 21/99 = 21/1782 5. Now we can add the fractions: t = 295/1782 + 21/1782 = 316/1782 6. The total sum, l, of the two identical fractions, t, is: l = 2 × t = 2 × 316/1782 = 632/1782 7. To simplify the fraction 632/1782, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 14. 632/1782 = 45/127 ### Answer: 45/127
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate 58/49 + 31/34 58/49 = 1.1836734693877551 31/34 = 0.9117647058823529 1.1836734693877551 + 0.9117647058823529 = 2.0954381752701080 Step 2: Add the result from Step 1 to the fraction 74/38 74/38 = 1.9473684210526315 2.0954381752701080 + 1.9473684210526315 = 4.0428065963227395 Step 3: Simplify the final result as a simple fraction The numerator is 4.0428065963227395 * 100 = 404.28065963227395 The denominator is 100 The simplified fraction is 404/100 = 4.04 ### Answer: 4.04
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate 100 divided by 76. 100 / 76 = 1.3157894736842105 Step 2: Calculate 29 divided by 14. 29 / 14 = 2.0714285714285716 Step 3: Add the two results together. 1.3157894736842105 + 2.0714285714285716 = 3.3872180451127821 Step 4: Simplify the answer as a fraction or decimal. The simplified answer is 3.3872180451127821. ### Answer: 3.3872180451127821
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.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. Evan has read 51/18 of the novel. 2. Olivia has read (8/42) after reading the same amount as Evan. * This means Olivia has read (8/42) + (51/18) of the novel. To simplify this fraction, we need to find a common denominator: * The common denominator is 378 (the least common multiple of 18 and 42). Now we can convert the fractions to have the same denominator: * Evan's fraction: 51/18 = 189/378 * Olivia's fraction: 8/42 = 72/378 Adding these together: * 189/378 + 72/378 = 261/378 Simplifying the fraction: * 261/378 = 87/126 ### Answer: 87/126
Expected answer: 127/42
Correct? No
Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. 48 divided by 13: 48 / 13 = 3.69230769230769 2. 31 divided by 22: 31 / 22 = 1.40909090909091 3. Sum of the two results: 3.69230769230769 + 1.40909090909091 = 5.10139860139860 Therefore, the sum of 48 divided by 13 and 31 divided by 22 is 5.10139860139860. ### Answer: 5.10139860139860
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Find the value of 24/86 + 76/77 24/86 = 0.27906976744186046 76/77 = 0.9870129870129871 0.27906976744186046 + 0.9870129870129871 = 1.26608275445485 Step 2: Subtract the answer from 27/6 27/6 = 4.5 4.5 - 1.26608275445485 = 3.23391724554515 ### Answer: 3.23391724554515
Expected answer: 21415/6622
Correct? No
Problem: Find the sum of 73/39 and 49/14, and 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 73/39 and 49/14. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 39 and 14 is 546. 3) We need to convert the fractions to have the same denominator of 546: 73/39 = (73 * 14)/39 * 14 = 1022/546 49/14 = (49 * 39)/14 * 39 = 1911/546 4) Now we can add the fractions: 1022/546 + 1911/546 = 2933/546 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 2933 and 546 is 3. 6) Dividing both the numerator and denominator by 3, we get: 2933/546 = 977/182 ### Answer: 977/182
Expected answer: 419/78
Correct? No
Problem: What is the sum of 75/65 and 7/39? Simplify your answer.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the sum of two fractions: 75/65 and 7/39. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 65 and 39 is 1,235. 3) Convert the fractions to have the LCD of 1,235: 75/65 = 1,125/1,235 7/39 = 225/1,235 4) Now we can add the fractions: 1,125/1,235 + 225/1,235 = 1,350/1,235 5) To simplify the final answer, we can divide the numerator and denominator by their greatest common factor, which is 5. 1,350/1,235 = 270/247 ### Answer: 270/247
Expected answer: 4/3
Correct? No
Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate 79/1 - 30/92 79/1 = 79 30/92 = 0.326 79 - 0.326 = 78.674 Step 2: Subtract 61/63 from the result 78.674 - 61/63 = 78.674 - 0.968 = 77.706 ### Answer: 77.706
Expected answer: 225191/2898
Correct? No
Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (58 / 26) = 2.23076923076923 2) (58 / 26) + (58 / 26) = 2.23076923076923 + 2.23076923076923 = 4.46153846153846 To express the answer in simplest form, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 4.46153846153846 and 1 is 1. Therefore, the answer in simplest form is: ### Answer: 4.46153846153846
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?
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1) Alex initially had 69/63 gallons of orange juice. 2) He then bought an additional 77/5 gallons. 3) This gave him a total of 'k' gallons. 4) Later, he received 47/71 gallons from Sally. To find the total number of gallons Alex had, we need to first calculate the total amount of orange juice he had after buying the additional 77/5 gallons. Initial amount: 69/63 gallons Additional amount: 77/5 gallons Total after buying additional: 69/63 + 77/5 = (69*5 + 77*63) / (63*5) = (345 + 4851) / 315 = 5196 / 315 = 'k' gallons Now, he received an additional 47/71 gallons from Sally. Total amount: 'k' + 47/71 gallons To find the final total, we need to simplify the fractions and add them together: 'k' + 47/71 = (5196/315) + (47/71) = (5196*71 + 47*315) / (315*71) = (368,916 + 14,805) / 22,365 = 383,721 / 22,365 = 17.16 gallons ### Answer: 17.16 gallons
Expected answer: 127907/7455
Correct? No
Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((100 / 61) + ((39 / 6) + (67 / 49))) 2) First, let's calculate the individual parts: a) 100 / 61 = 1.639344262295082 b) 39 / 6 = 6.5 c) 67 / 49 = 1.3673469387755102 3) Now, let's add them up: 1.639344262295082 + (6.5 + 1.3673469387755102) = 9.406690201070592 4) To simplify the fraction, we need to find the common denominator. The least common multiple of 61, 6, and 49 is 2,646. 5) Multiplying the numerators and denominators to get the simplified fraction: (9.406690201070592 * 2,646) / 2,646 = 24,900 / 2,646 ### Answer: 24,900/2,646
Expected answer: 56831/5978
Correct? No
Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 85/1 = 85 2) 83/69 = 83/69 3) To find the sum, we add the two fractions: 85 + 83/69 = 85 + (83/69) 4) To simplify the result, we need to find a common denominator. The least common denominator of 1 and 69 is 69. 5) 85 + (83/69) = (85*69 + 83)/69 = (5865 + 83)/69 = 5948/69 ### 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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We previously calculated the sum of 85/1 and 83/69 as 5948/69. 2) Now we need to add 21/86 to that sum. 3) To add the fractions, we need to find a common denominator. The least common denominator of 69 and 86 is 5934. 4) 5948/69 = 5934/69 * 86/86 = 511,524/5934 5) 21/86 = 21/86 * 69/69 = 1449/5934 6) Adding the two fractions: 511,524/5934 + 1449/5934 = 512,973/5934 ### Answer: 512,973/5934
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 85/1 = 85 2) 83/52 = 83/52 3) To find the sum, we add the two fractions: 85 + 83/52 = 85 + (83/52) 4) To simplify the result, we need to find a common denominator. The least common denominator of 1 and 52 is 52. 5) 85 + (83/52) = (85*52 + 83)/52 = (4420 + 83)/52 = 4503/52 ### Answer: 4503/52
Expected answer: 4503/52
Correct? Yes
Problem: What is the sum of 92/13 and 43/86 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. The least common multiple of 13 and 86 is 1,118. 2) Now we can convert the fractions to have the same denominator: 92/13 = (92 * 86) / (13 * 86) = 7,912 / 1,118 43/86 = (43 * 13) / (86 * 13) = 559 / 1,118 3) Now we can add the numerators: 7,912 / 1,118 + 559 / 1,118 = 8,471 / 1,118 4) To simplify the fraction, we need to find the greatest common factor of the numerator and denominator. The greatest common factor of 8,471 and 1,118 is 1. 5) Therefore, the simplified fraction is: 8,471 / 1,118 ### Answer: 8,471/1,118
Expected answer: 197/26
Correct? Yes
Problem: You solved the sum of 92/13 and 43/86 in the previous problem. Now, additional 36/72 to that sum. What is the total as a simplified fraction?
Claude-3 Haiku:
Okay, let's continue solving this step-by-step: 1) We already found the sum of 92/13 and 43/86 to be 8,471/1,118. 2) Now we need to add 36/72 to this sum. To do this, we need to convert 36/72 to have the same denominator of 1,118. 36/72 = (36 * 15) / (72 * 15) = 540 / 1,118 3) Now we can add the three fractions together: 8,471/1,118 + 540/1,118 = 9,011/1,118 4) To simplify the fraction, we need to find the greatest common factor of the numerator and denominator. The greatest common factor of 9,011 and 1,118 is 1. 5) Therefore, the simplified fraction is: 9,011/1,118 ### Answer: 9,011/1,118
Expected answer: 105/13
Correct? No
Problem: In the previous problem, you found the sum of 92/13 and 43/86. Now suppose the original problem actually was about adding 61/13, not 92/13, to 43/86. What would be the new sum 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. The least common multiple of 13 and 86 is 1,118. 2) Now we can convert the fractions to have the same denominator: 61/13 = (61 * 86) / (13 * 86) = 5,246 / 1,118 43/86 = (43 * 13) / (86 * 13) = 559 / 1,118 3) Now we can add the numerators: 5,246 / 1,118 + 559 / 1,118 = 5,805 / 1,118 4) To simplify the fraction, we need to find the greatest common factor of the numerator and denominator. The greatest common factor of 5,805 and 1,118 is 1. 5) Therefore, the simplified fraction is: 5,805 / 1,118 ### Answer: 5,805/1,118
Expected answer: 135/26
Correct? Yes
Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 67/32 and 10/98. 2) To add fractions, we need to find the least common denominator (LCD). 3) The LCD of 32 and 98 is 3,136 (the product of the denominators). 4) Now we need to convert the fractions to have the same denominator of 3,136. 5) 67/32 = 67 * 98/32 * 98 = 6,566/3,136 6) 10/98 = 10 * 32/98 * 32 = 320/3,136 7) Now we can add the fractions: 6,566/3,136 + 320/3,136 = 6,886/3,136 8) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. 9) The GCF of 6,886 and 3,136 is 8. 10) Dividing both the numerator and denominator by 8, we get 861/392. ### Answer: 861/392
Expected answer: 3443/1568
Correct? No
Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the sum of 59/52 and 70/32. 2) To add fractions, we need to find the least common denominator (LCD) of the two fractions. 3) The LCD of 52 and 32 is 208. 4) So we need to convert both fractions to have a denominator of 208. 5) 59/52 = 113/208 6) 70/32 = 175/208 7) Now we can add the fractions: 113/208 + 175/208 = 288/208 8) To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 8. 9) 288/208 = 36/26 ### Answer: 36/26
Expected answer: 691/208
Correct? No
Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1. 48 divided by 5: 48 / 5 = 9.6 2. 11 divided by 65: 11 / 65 = 0.169230769 3. Subtract 9.6 from 0.169230769: 0.169230769 - 9.6 = -9.430769231 4. Add 28 divided by 2: 28 / 2 = 14 -9.430769231 + 14 = 4.569230769 ### Answer: 4.569230769
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to add 20/52 and 75/82. 2) To add fractions, we need to find the least common denominator (LCD). The LCD of 52 and 82 is 2,132. 3) Convert the fractions to have the LCD of 2,132: 20/52 = 780/2,132 75/82 = 1,950/2,132 4) Now we can add the fractions: 780/2,132 + 1,950/2,132 = 2,730/2,132 5) To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. 6) The GCF of 2,730 and 2,132 is 2. 7) Dividing both the numerator and denominator by 2, we get: 1,365/1,066. ### Answer: 1,365/1,066
Expected answer: 1385/1066
Correct? No
Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.
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 420. 2) 31/5 = 248/420 3) 92/84 = 420/420 4) Now we can subtract the fractions: 248/420 - 420/420 = (248 - 420)/420 = -172/420 5) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. -172/420 = -43/105 ### Answer: -43/105
Expected answer: 536/105
Correct? No
Problem: Calculate the following: Double the sum of 81/90 and 94/49.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Calculate the sum of 81/90 and 94/49: 81/90 + 94/49 = (81 * 49) / (90 * 49) + (94 * 90) / (49 * 90) = 3,969 / 4,410 + 8,460 / 4,410 = 0.9 + 1.92 = 2.82 2. Double the sum: 2 * 2.82 = 5.64 ### Answer: 5.64
Expected answer: 1381/245
Correct? No
Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to calculate the value of 69/21: 69/21 = 3.285714286 2) Next, we need to calculate the value of 10/92: 10/92 = 0.1086956522 3) Now, we can find the difference between the two values: 3.285714286 - 0.1086956522 = 3.177018634 4) To write the answer as a simple fraction, we need to find the common denominator. The least common denominator is 2,300. 5) 3.177018634 = 7,308/2,300 6) Simplifying the fraction, we get: 7,308/2,300 ### Answer: 7,308/2,300
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate (26 / 87) + (92 / 88) (26 / 87) = 0.2988505747126437 (92 / 88) = 1.0454545454545454 (0.2988505747126437) + (1.0454545454545454) = 1.3443051201671891 Step 2: Add the result to (26 / 57) (26 / 57) = 0.4561403508771929 1.3443051201671891 + 0.4561403508771929 = 1.8004454710443820 ### Answer: 1.8004454710443820
Expected answer: 21825/12122
Correct? Yes
Problem: After you have calculated the result from the previous question, add that sum to (31 / 83). What's the new result?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate the result from the previous question: (26 / 87) + (92 / 88) + (26 / 57) = 1.8004454710443820 Step 2: Add the result to (31 / 83): (31 / 83) = 0.3734939759036145 1.8004454710443820 + 0.3734939759036145 = 2.1739394469479965 ### Answer: 2.1739394469479965
Expected answer: 2187257/1006126
Correct? No
Problem: Recall the previous problem. If you originally had 4 out of 87 oranges instead of 26, and you still have (92 / 88) apples and (26 / 57) peaches, how does the total fruit count change? Compute (4 / 87) + (92 / 88) and then add that to (26 / 57) to find out.
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Calculate (4 / 87) + (92 / 88) (4 / 87) = 0.0459770114942529 (92 / 88) = 1.0454545454545454 (0.0459770114942529) + (1.0454545454545454) = 1.0914315569487783 Step 2: Add the result to (26 / 57) (26 / 57) = 0.4561403508771929 1.0914315569487783 + 0.4561403508771929 = 1.5475719078259712 ### Answer: 1.5475719078259712
Expected answer: 56279/36366
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Add the fractions: 78/66 + 28/6 + 90/34 2) First, we need to find the least common denominator (LCD) of the fractions. The LCD is the least common multiple of the denominators, which is 198. 3) Now we need to convert each fraction to have a denominator of 198: 78/66 = (78 * 3)/198 = 234/198 28/6 = (28 * 33)/198 = 924/198 90/34 = (90 * 6)/198 = 540/198 4) Now we can add the fractions: 234/198 + 924/198 + 540/198 = 1698/198 5) Simplify the fraction: 1698/198 = 17/2 ### Answer: 17/2
Expected answer: 4766/561
Correct? No
Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) (12 / 7) - (9 / 23) 2) First, we need to find a common denominator for the fractions. The least common multiple of 7 and 23 is 161. 3) So we can rewrite the expression as: (12 * 23 / 7 * 23) - (9 * 7 / 23 * 7) 4) Simplifying: (276 / 161) - (63 / 161) 5) Subtracting the fractions: (276 - 63) / 161 6) Simplifying the numerator: 213 / 161 7) Simplifying the fraction to the lowest terms: 213 / 161 = 3 / 23 ### Answer: 3/23
Expected answer: 213/161
Correct? No
Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find the sum of 95/18 and 51/61. 95/18 + 51/61 = (95 * 61 + 51 * 18) / (18 * 61) = (5,795 + 918) / 1,098 = 6,713 / 1,098 = 6.11 2) Now we need to represent the answer as a simplified fraction. To do this, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 6,713 and 1,098 is 3. Dividing both the numerator and denominator by 3, we get: 6,713 / 3 = 2,237 1,098 / 3 = 366 So the simplified fraction is 2,237/366. ### Answer: 2,237/366
Expected answer: 6713/1098
Correct? No
Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) First, we need to find a common denominator for the two fractions. The least common multiple of 46 and 84 is 3,864. 2) Now we can convert the fractions to have the same denominator: (93/46) = (3,864/46 * 93) = 7,920/3,864 (51/84) = (3,864/84 * 51) = 1,938/3,864 3) Now we can subtract the fractions: (7,920/3,864) - (1,938/3,864) = 5,982/3,864 4) Finally, we can simplify the fraction: 5,982/3,864 = 11/7 ### Answer: 11/7
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the two fractions: 12/70 and 84/9 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 70 and 9 is 630. 3) We need to convert the fractions to have the same denominator of 630: 12/70 = (12 * 9) / (70 * 9) = 108/630 84/9 = (84 * 70) / (9 * 70) = 5880/630 4) Now we can add the fractions: 108/630 + 5880/630 = 5988/630 5) To simplify the fraction, we can divide both the numerator and denominator by the greatest common factor, which is 18. 5988/630 = 332/35 ### Answer: 332/35
Expected answer: 998/105
Correct? No
Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Subtract 40/92 from 32/3: 32/3 - 40/92 = (32 * 92 - 40 * 3) / (3 * 92) = (2944 - 120) / 276 = 2824 / 276 = 10.2 2. Double the result: 10.2 * 2 = 20.4 ### Answer: 20.4
Expected answer: 1412/69
Correct? No
Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the expression 79/24 + 79/24 2) To find the sum, we need to find a common denominator for the fractions. 3) The common denominator is 24. 4) 79/24 + 79/24 = (79/24) + (79/24) = 2 * (79/24) = 158/24 5) The simplified fraction is 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) From the previous problem, we found that 79/24 + 79/24 = 158/24 2) Now we need to find the sum of two times this expression: (79/24 + 79/24) + (79/24 + 79/24) = 158/24 + 158/24 = 316/24 3) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. 316/24 = 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the expression 79/20 + 79/20 2) To find the sum, we need to find a common denominator for the fractions. 3) The common denominator is 20. 4) 79/20 + 79/20 = (79/20) + (79/20) = 2 * (79/20) = 158/20 5) The simplified fraction is 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have the fractions 91/76 and 12/22. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 76 and 22 is 1,672. 3) We need to convert the fractions to have the LCD of 1,672: 91/76 = 1,199/1,672 12/22 = 732/1,672 4) Now we can add the fractions: 1,199/1,672 + 732/1,672 = 1,931/1,672 5) To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. 1,931/1,672 = 482.75/418 ### Answer: 482.75/418
Expected answer: 1457/836
Correct? No
Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?
Claude-3 Haiku:
Okay, let's solve this step-by-step: Step 1: Add 88/93 and 6/47 To add fractions, we need to find the least common denominator (LCD). The LCD of 93 and 47 is 4371. 88/93 = (88 * 47) / (93 * 47) = 4136/4371 6/47 = (6 * 93) / (47 * 93) = 558/4371 4136/4371 + 558/4371 = 4694/4371 Step 2: Add the result to 92/4 92/4 = 23 4694/4371 + 23 = 4717/4371 ### Answer: 4717/4371
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1. Calculate 52/21 + 75/67: 52/21 = 2.4761904761904762 75/67 = 1.1194029850746268 2.4761904761904762 + 1.1194029850746268 = 3.5955934612651030 2. Add 95/83 to the result: 95/83 = 1.1445783132530121 1.1445783132530121 + 3.5955934612651030 = 4.7401717745181151 3. Simplify the final result as a fraction: The numerator is 4.7401717745181151 * 100 = 474.0171774518115 The denominator is 100 Simplified fraction: 474/100 ### Answer: 474/100
Expected answer: 553562/116781
Correct? No
Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) Evaluate the first part of the expression: (73 / 27) 73 / 27 = 2.7037037037037037 2) Evaluate the second part of the expression: (23 / 48) 23 / 48 = 0.47916666666666663 3) Subtract the two parts: 2.7037037037037037 - 0.47916666666666663 = 2.22453703703704 4) Simplify the result as a fraction: 2.22453703703704 = 222453703703704/100000000 Therefore, the final simplified answer is: ### Answer: 222453703703704/100000000
Expected answer: 961/432
Correct? No
Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: (78 / 2) - (70 / 23) First, let's calculate the numerators and denominators separately: 78 / 2 = 39 70 / 23 = 3.04347826 Now, we can subtract the two values: 39 - 3.04347826 = 35.95652174 Therefore, the simplified answer is 35.95652174. ### Answer: 35.95652174
Expected answer: 827/23
Correct? No
Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have 34/1 and 53/4 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 1 and 4 is 4. 3) So we need to convert 34/1 to an equivalent fraction with a denominator of 4. 4) 34/1 = 34/1 * 4/4 = 136/4 5) Now we can add the fractions: 136/4 + 53/4 = 189/4 6) To express this as a mixed number, we divide the numerator by the denominator: 189/4 = 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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) In the previous problem, the result of adding 34/1 to 53/4 was 47 1/4. 2) Now we need to add 24/67 to 47 1/4. 3) First, we need to convert 47 1/4 to an improper fraction: 47 1/4 = (47 * 4 + 1) / 4 = 189/4 4) Now we can add the fractions: 189/4 + 24/67 = (189*67 + 24*4) / (4*67) = 12663/268 5) To express this as a mixed number, we divide the numerator by the denominator: 12663/268 = 47 3/268 ### Answer: 47 3/268
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have 34/97 and 53/4 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 97 and 4 is 388. 3) So we need to convert 34/97 and 53/4 to equivalent fractions with a denominator of 388. 4) 34/97 = 34/97 * 4/4 = 136/388 5) 53/4 = 53/4 * 97/97 = 5,141/388 6) Now we can add the fractions: 136/388 + 5,141/388 = 5,277/388 7) To express this as a mixed number, we divide the numerator by the denominator: 5,277/388 = 13 (277/388) ### Answer: 13 (277/388)
Expected answer: 5277/388
Correct? No
Problem: What is the sum of 3/36 and 97/96? 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 3/36 and 97/96. 2) The least common multiple of 36 and 96 is 288. 3) So the common denominator is 288. 4) Now we need to convert the fractions to have a denominator of 288. 5) 3/36 = 24/288 6) 97/96 = 288/288 7) Now we can add the fractions: 24/288 + 288/288 = 312/288 8) Simplifying the fraction, we get: 312/288 = 39/36. ### Answer: 39/36
Expected answer: 35/32
Correct? No
Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) ((92 / 95) + (4 / 74)) 2) First, let's calculate the individual fractions: (92 / 95) = 0.9684210526315789 (4 / 74) = 0.05405405405405406 3) Now, we add the two fractions: 0.9684210526315789 + 0.05405405405405406 = 1.0224751092835441 4) To simplify the fraction, we need to find the common denominator. The least common denominator is 1900. 5) Multiplying the first fraction by 20 and the second fraction by 25 to get the common denominator of 1900: (92 * 20) / (95 * 20) + (4 * 25) / (74 * 25) = 1840/1900 + 100/1850 = 1940/1900 6) Simplifying the fraction, we get: 1940/1900 ### Answer: 1940/1900
Expected answer: 3594/3515
Correct? No
Problem: If the value of a variable 'v' is 69/47, what is the value of 'd' if 'd' equals 88/72 + 'v'? Please write your answer as a fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) The value of the variable 'v' is 69/47. 2) The value of 'd' is given by the equation: d = 88/72 + 'v' 3) Substituting the value of 'v', we get: d = 88/72 + 69/47 4) To simplify this expression, we need to find a common denominator. The least common denominator is 3384 (72 * 47). 5) 88/72 = 1232/3384 6) 69/47 = 1449/3384 7) Combining the terms, we get: d = 1232/3384 + 1449/3384 = 2681/3384 ### Answer: 2681/3384
Expected answer: 1138/423
Correct? No
Problem: Let's say there is a wholesaler who has 41/26 barrels of olive oil in their warehouse. They sell a portion of the oil which is equivalent to 41/72 barrels. How much olive oil do they have now? Express your answer as a simple fraction.
Claude-3 Haiku:
Okay, let's break this down step-by-step: 1) The wholesaler initially has 41/26 barrels of olive oil in their warehouse. 2) They sell a portion of the oil which is equivalent to 41/72 barrels. 3) To find how much olive oil they have now, we need to subtract the amount they sold from the initial amount. The initial amount: 41/26 barrels The amount they sold: 41/72 barrels To subtract fractions, we need to find a common denominator. The least common denominator of 26 and 72 is 312. 41/26 = 156/312 41/72 = 156/312 Now we can subtract: 156/312 - 156/312 = 0/312 Therefore, the amount of olive oil they have now is 0/312, which can be simplified to 0/1. ### Answer: 0/1
Expected answer: 943/936
Correct? No
Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) 85/75 - To convert this to decimal form, we divide 85 by 75: - 85 / 75 = 1.1333 2) 88/56 - To convert this to decimal form, we divide 88 by 56: - 88 / 56 = 1.5714 3) Now we add the two decimal values: - 1.1333 + 1.5714 = 2.7047 ### Answer: 2.7047
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.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to add the fractions 12/33 and 49/2. 2) To add fractions, we need to find a common denominator. The least common denominator (LCD) of 33 and 2 is 66. 3) Convert the fractions to have the LCD of 66: 12/33 = 24/66 49/2 = 1638/66 4) Now we can add the fractions: 24/66 + 1638/66 = 1662/66 5) To write this as a mixed fraction, we need to divide the numerator by the denominator: 1662/66 = 25 12/66 6) Simplifying the fraction 12/66, we get: 12/66 = 2/11 ### Answer: 25 2/11
Expected answer: 547/22
Correct? No
Problem: What is the result of adding two fractions, where each fraction is 78/65?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions, each with a numerator of 78 and a denominator of 65. 2) To add fractions with the same denominators, we add the numerators and keep the same denominator. 3) So, the sum of the two fractions is: (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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) In the previous problem, we found that the sum of two fractions, each equal to 78/65, is 156/65. 2) Now we need to add 156/65 to 71/32. 3) To add fractions with different denominators, we need to find the least common denominator (LCD). 4) The LCD of 65 and 32 is 520. 5) We need to convert both fractions to have the same denominator of 520. 6) 156/65 = 156 * (520/65) = 1248/520 7) 71/32 = 71 * (520/32) = 1160/520 8) Now we can add the fractions: 1248/520 + 1160/520 = 2408/520 ### Answer: 2408/520
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?
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We have two fractions, each with a numerator of 78 and a denominator of 78. 2) To add fractions with the same denominators, we add the numerators and keep the same denominator. 3) So, the sum of the two fractions is: (78/78) + (78/78) = (78 + 78)/78 = 156/78 ### Answer: 156/78
Expected answer: 2
Correct? Yes
Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.
Claude-3 Haiku:
Okay, let's solve this step-by-step: 1) We need to find the common denominator for the two fractions. The least common multiple of 7 and 90 is 630. 2) Convert the fractions to have the common denominator of 630: 16/7 = 144/630 11/90 = 77/630 3) Now we can add the numerators: 144/630 + 77/630 = 221/630 4) Simplify the fraction: The greatest common factor of 221 and 630 is 7. 221/630 = 31/90 ### Answer: 31/90
Expected answer: 1517/630
Correct? No