Claude-3 Sonnet 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 Sonnet:
To solve this problem, we need to find the sum of the two fractions (74/63) and (91/78). First, we need to find the least common denominator (LCD) of 63 and 78. The LCD is the smallest positive number that is divisible by both denominators. To find the LCD, we can use the prime factorization method: 63 = 3^2 × 7 78 = 2 × 3^2 × 13 The LCD is the product of the highest powers of each prime factor present in either denominator: LCD = 2 × 3^2 × 7 × 13 = 1,386 Now, we need to convert both fractions to equivalent fractions with the LCD as the denominator. (74/63) = (74 × 22/63 × 22) = 1,628/1,386 (91/78) = (91 × 17/78 × 17) = 1,547/1,386 Now, we can add the numerators and keep the denominator the same: (1,628/1,386) + (1,547/1,386) = (1,628 + 1,547)/1,386 = 3,175/1,386 To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 3,175 and 1,386 is 1. Therefore, the sum of (74/63) and (91/78) is 3,175/1,386. ### Answer: 3,175/1,386
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
Claude-3 Sonnet:
To add fractions with different denominators, we need to find a common denominator and convert the fractions to equivalent fractions with the same denominator. The least common multiple (LCM) of 5 and 25 is 25. Converting 94/5 to an equivalent fraction with denominator 25: 94/5 = (94 × 5)/25 = 470/25 Now we can add the fractions: 470/25 + 1/25 = (470 + 1)/25 = 471/25 To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 1. Therefore, the result is: 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 Sonnet:
Okay, let's solve this step-by-step: 1. From the previous problem, we have 471/25. 2. We need to add 73/89 to 471/25. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with the same denominator. The LCM of 25 and 89 is 2225. Converting 471/25 to an equivalent fraction with denominator 2225: 471/25 = (471 × 89)/2225 = 41,859/2225 Converting 73/89 to an equivalent fraction with denominator 2225: 73/89 = (73 × 25)/2225 = 1,825/2225 Now we can add the fractions: 41,859/2225 + 1,825/2225 = (41,859 + 1,825)/2225 = 43,684/2225 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD. The GCD of 43,684 and 2225 is 17. 43,684/2225 = (43,684/17) / (2225/17) = 2,575 / 131 Therefore, the final result is: 2,575/131 ### Answer: 2,575/131
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 Sonnet:
Okay, let's solve this step-by-step: Given: - First fraction: 94/89 - Second fraction: 1/25 To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with the same denominator. The LCM of 89 and 25 is 2225. Converting the fractions to equivalent fractions with denominator 2225: - 94/89 = (94 × 25)/2225 = 2350/2225 - 1/25 = (1 × 89)/2225 = 89/2225 Now we can add the fractions: 2350/2225 + 89/2225 = (2350 + 89)/2225 = 2439/2225 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD. The GCD of 2439 and 2225 is 1. Therefore, the simplified result is: 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 Sonnet:
To subtract fractions, we need to find a common denominator for both fractions. The least common multiple of 20 and 8 is 40. So, we convert both fractions to have a denominator of 40: 48/20 = 48/20 * 2/2 = 96/40 49/8 = 49/8 * 5/5 = 245/40 Now we can subtract: 245/40 - 96/40 = 149/40 To simplify 149/40, we divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified fraction is 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 Sonnet:
Okay, let's solve this new problem: We need to subtract 48/14 from 49/8. First, we need to find the least common multiple (LCM) of 14 and 8 to get a common denominator. The LCM of 14 and 8 is 56. So, we convert both fractions to have a denominator of 56: 48/14 = 48/14 * 4/4 = 192/56 49/8 = 49/8 * 7/7 = 343/56 Now we can subtract: 343/56 - 192/56 = 151/56 To simplify 151/56, we divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified fraction is 151/56. ### Answer: 151/56
Expected answer: 151/56
Correct? Yes
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
Claude-3 Sonnet:
To calculate the value of the expression ((45 / 5) - (6 / 47)), we need to perform the following steps: 1. Calculate (45 / 5) 45 / 5 = 9 2. Calculate (6 / 47) 6 / 47 = 0.1276595744680851 (rounded to 10 decimal places) 3. Subtract (6 / 47) from (45 / 5) 9 - 0.1276595744680851 = 8.8723404255319149 Therefore, the value of the expression ((45 / 5) - (6 / 47)) is 8.8723404255319149. ### Answer: 8.8723404255319149
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 Sonnet:
Okay, let's calculate this step-by-step: 1. First, we need to find the value of ((45 / 5) - (6 / 47)): (45 / 5) = 9 (6 / 47) = 0.1276595744680851 (rounded to 10 decimal places) ((45 / 5) - (6 / 47)) = 9 - 0.1276595744680851 = 8.8723404255319149 2. Now, we need to add this value to itself: 8.8723404255319149 + 8.8723404255319149 = 17.7446808510638298 Therefore, if we add the value of ((45 / 5) - (6 / 47)) to itself, the result is 17.7446808510638298. ### Answer: 17.7446808510638298
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 Sonnet:
Okay, let's recalculate the value of the expression with the new information that there are 63 oranges instead of 45. To calculate the value of the expression ((63 / 5) - (6 / 47)), we need to perform the following steps: 1. Calculate (63 / 5) 63 / 5 = 12.6 2. Calculate (6 / 47) (same as before) 6 / 47 = 0.1276595744680851 (rounded to 10 decimal places) 3. Subtract (6 / 47) from (63 / 5) 12.6 - 0.1276595744680851 = 12.4723404255319149 Therefore, the value of the expression ((63 / 5) - (6 / 47)) is 12.4723404255319149. ### Answer: 12.4723404255319149
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 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 49 and 35. The LCM of 49 and 35 is 1715. Step 2: Convert the fractions to equivalent fractions with the common denominator of 1715. 22/49 = (22 × 35)/1715 = 770/1715 72/35 = (72 × 49)/1715 = 3528/1715 Step 3: Add the fractions with the common denominator. (770/1715) + (3528/1715) = 4298/1715 Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator. The GCF of 4298 and 1715 is 7. 4298/1715 = (4298/7)/(1715/7) = 613/245 Therefore, the sum of 22/49 and 72/35 as a simplified fraction is 613/245. ### Answer: 613/245
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations first and then subtract the results. Given: - (39 / 9) - (44 / 69) Step 1: Calculate (39 / 9) 39 / 9 = 4.33333... (repeating decimal) Step 2: Calculate (44 / 69) 44 / 69 = 0.63768... (repeating decimal) Step 3: Subtract the results (39 / 9) - (44 / 69) = 4.33333... - 0.63768... = 4.33333... + (-0.63768...) = 3.69565... (repeating decimal) Therefore, the result of (39 / 9) - (44 / 69) is 3.69565... (repeating decimal). ### Answer: 3.69565...
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
Claude-3 Sonnet:
To calculate the sum of 49/79 and 18/21, we need to find a common denominator for both fractions. The least common multiple (LCM) of 79 and 21 is 1659. So, we convert both fractions to have a denominator of 1659. 49/79 = (49 × 21)/1659 = 1029/1659 18/21 = (18 × 79)/1659 = 1422/1659 Now we can add the fractions: 1029/1659 + 1422/1659 = 2451/1659 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 3. 2451/1659 = (2451/3)/(1659/3) = 817/553 Therefore, the sum of 49/79 and 18/21 is 817/553. ### Answer: 817/553
Expected answer: 817/553
Correct? Yes
Problem: After getting the sum of 49/79 and 18/21 from the previous problem, let's denote this sum as n. Calculate the result of adding 71/97 to n.
Claude-3 Sonnet:
In the previous problem, we found that the sum of 49/79 and 18/21 is 817/553. Let's denote this sum as n: n = 817/553 Now, we need to add 71/97 to n. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. The LCM of 553 and 97 is 53641. So, we convert both fractions to have a denominator of 53641. n = 817/553 = (817 × 97)/53641 = 79049/53641 71/97 = (71 × 553)/53641 = 39323/53641 Now we can add the fractions: 79049/53641 + 39323/53641 = 118372/53641 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 7. 118372/53641 = (118372/7)/(53641/7) = 16910/7661 Therefore, the result of adding 71/97 to n (the sum of 49/79 and 18/21) is 16910/7661. ### Answer: 16910/7661
Expected answer: 118512/53641
Correct? No
Problem: In the previous problem, we found the sum of 49/79 and 18/21. Now, let's alter the scenario a bit. Instead of having 49/79 part, let's say we have 49/3 part. Keeping the 18/21 part the same, what would be the new total? Calculate the sum of 49/3 and 18/21.
Claude-3 Sonnet:
To calculate the sum of 49/3 and 18/21, we need to find a common denominator for both fractions. The least common multiple (LCM) of 3 and 21 is 63. So, we convert both fractions to have a denominator of 63. 49/3 = (49 × 21)/63 = 1029/63 18/21 = (18 × 3)/63 = 54/63 Now we can add the fractions: 1029/63 + 54/63 = 1083/63 Therefore, the sum of 49/3 and 18/21 is 1083/63. ### Answer: 1083/63
Expected answer: 361/21
Correct? Yes
Problem: What is the sum of 95/46 and 65/31?
Claude-3 Sonnet:
To find the sum of 95/46 and 65/31, we need to find a common denominator for both fractions. The least common multiple (LCM) of 46 and 31 is 1426. So, we convert both fractions to have a denominator of 1426. 95/46 = (95 × 31)/1426 = 2945/1426 65/31 = (65 × 46)/1426 = 2990/1426 Now we can add the fractions: 2945/1426 + 2990/1426 = 5935/1426 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 7. 5935/1426 = (847 × 7)/(203 × 7) = 847/203 Therefore, the sum of 95/46 and 65/31 is 847/203. ### Answer: 847/203
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 63 and 6. The LCM of 63 and 6 is 189. Step 2: Convert the fractions to equivalent fractions with the common denominator of 189. 25/63 = (25 × 3)/189 74/6 = (74 × 31.5)/189 Step 3: Add the fractions. (25 × 3)/189 + (74 × 31.5)/189 = 75/189 + 2337/189 = 2412/189 Step 4: Simplify the fraction if possible. 2412/189 = 12.76 (rounded to two decimal places) ### Answer: 12.76
Expected answer: 802/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 91 and 47. The LCM of 91 and 47 is 4277. Step 2: Convert the fractions to equivalent fractions with the common denominator 4277. 79/91 = (79 × 47)/4277 = 3713/4277 100/47 = (100 × 91)/4277 = 9100/4277 Step 3: Add the fractions with the common denominator. (3713/4277) + (9100/4277) = 12813/4277 Step 4: Simplify the fraction if possible. 12813/4277 = 3 (The fraction is already in its simplest form) Therefore, the sum of 79/91 and 100/47 is 3. ### Answer: 3
Expected answer: 12813/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations first and then add the results. Given: - (55 / 47) - (72 / 21) Step 1: Calculate (55 / 47) 55 / 47 = 1.170212765957447 Step 2: Calculate (72 / 21) 72 / 21 = 3.4285714285714284 Step 3: Add the results from Step 1 and Step 2 (55 / 47) + (72 / 21) = 1.170212765957447 + 3.4285714285714284 = 4.598784194289275 Therefore, the result of ((55 / 47) + (72 / 21)) is approximately 4.598784194289275. ### Answer: 4.598784194289275
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
Claude-3 Sonnet:
To find the sum of 86/62 and 99/41, we need to first find a common denominator for both fractions. The least common multiple (LCM) of 62 and 41 is 1262. So, we convert both fractions to have a denominator of 1262. 86/62 = (86 × 20.3548)/1262 = 1749/1262 99/41 = (99 × 30.7804)/1262 = 3047/1262 Now we can add the fractions: 1749/1262 + 3047/1262 = 4796/1262 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 2. 4796/1262 = (4796/2)/(1262/2) = 2398/631 ### Answer: 2398/631
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
Claude-3 Sonnet:
To calculate the sum of 87/88 and 24/13, we need to find a common denominator for both fractions. The least common multiple (LCM) of 88 and 13 is 1144. So, we convert both fractions to have a denominator of 1144. 87/88 = (87 × 13)/1144 = 1131/1144 24/13 = (24 × 88)/1144 = 2112/1144 Now we can add the fractions: 1131/1144 + 2112/1144 = 3243/1144 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 9. 3243/1144 = (3243/9)/(1144/9) = 361/127 Therefore, the sum of 87/88 and 24/13 is 361/127. ### Answer: 361/127
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
Claude-3 Sonnet:
To calculate ((68 / 33) + (70 / 25)), we need to first find the values of 68 / 33 and 70 / 25.
68 / 33 = 2.0606... (repeating decimal)
70 / 25 = 2.8
Now, we can add these two values together:
2.0606... + 2.8 = 4.8606...
To express the answer in its simplest form, we need to convert the repeating decimal to a fraction.
4.8606... = 4 + 0.8606...
0.8606... = 8606/9999 (the repeating part is 06, so we have 86 over 99)
Therefore, 4.8606... = 4 + (8606/9999)
= (39999 + 8606) / 9999
= 48605 / 9999
Thus, the simplest form of the answer is 48605 / 9999.
### Answer: 48605 / 9999
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 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 97 and 9. LCM of 97 and 9 = 873 Step 2: Convert the fractions to equivalent fractions with the common denominator of 873. 35/97 = (35 × 9)/873 11/9 = (11 × 97)/873 Step 3: Add the numerators of the equivalent fractions. (35 × 9)/873 + (11 × 97)/873 = 315/873 + 1067/873 = 1382/873 Step 4: Simplify the resulting fraction by finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by the GCF. GCF of 1382 and 873 = 1 1382/873 = 1382/1 × 1/873 = 1382/873 Therefore, the sum of 35/97 and 11/9 in simplest form is 1382/873. ### Answer: 1382/873
Expected answer: 1382/873
Correct? Yes
Problem: After finding the summation of 35/97 and 11/9, what would be the result if you add 11/25 to that sum? Express the result as a simplified fraction.
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 35/97 and 11/9, which we calculated earlier as 1382/873. 2. Now, we need to add 11/25 to this sum. To add fractions with different denominators, we need to find the least common denominator (LCD) and convert all fractions to equivalent fractions with the LCD as the denominator. The LCD of 873 and 25 is 21825. So, we convert the fractions as follows: 1382/873 = (1382 × 25)/21825 11/25 = (11 × 873)/21825 3. Now we can add the numerators: (1382 × 25)/21825 + (11 × 873)/21825 = 34550/21825 + 9603/21825 = 44153/21825 4. Finally, we simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. The GCF of 44153 and 21825 is 1. Therefore, the simplified fraction is 44153/21825. ### Answer: 44153/21825
Expected answer: 44153/21825
Correct? Yes
Problem: Suppose instead of adding 35/97 and 11/9, we change the problem slightly to adding 35/97 and 11/15. What would be the result of the sum? Express it in simplest form.
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 97 and 15. LCM of 97 and 15 = 1455 Step 2: Convert the fractions to equivalent fractions with the common denominator of 1455. 35/97 = (35 × 15)/1455 11/15 = (11 × 97)/1455 Step 3: Add the numerators of the equivalent fractions. (35 × 15)/1455 + (11 × 97)/1455 = 525/1455 + 1067/1455 = 1592/1455 Step 4: Simplify the resulting fraction by finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by the GCF. GCF of 1592 and 1455 = 1 1592/1455 = 1592/1 × 1/1455 = 1592/1455 Therefore, the sum of 35/97 and 11/15 in simplest form is 1592/1455. ### Answer: 1592/1455
Expected answer: 1592/1455
Correct? Yes
Problem: What is the result of subtracting 79/70 from 11/5?
Claude-3 Sonnet:
To subtract fractions, we need to find a common denominator for both fractions. The least common multiple of 5 and 70 is 70. So, we convert 11/5 to an equivalent fraction with a denominator of 70: 11/5 = (11 * 14)/70 = 154/70 Now we can subtract the fractions: 154/70 - 79/70 = (154 - 79)/70 = 75/70 To convert the fraction to a mixed number, we divide the numerator by the denominator: 75/70 = 1 + 5/70 Therefore, the result of subtracting 79/70 from 11/5 is 1 5/70. ### Answer: 1 5/70
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 Sonnet:
Okay, let's break this down step-by-step: 1. The previous answer from subtracting 79/70 from 11/5 was 1 5/70. 2. To add 62/46 to 1 5/70, we need to find a common denominator for 70 and 46. The least common multiple of 70 and 46 is 1610. 3. Convert 1 5/70 to an equivalent fraction with denominator 1610: 1 5/70 = (1 * 23)/70 + 5/70 = 23/1610 + 5/1610 = 28/1610 4. Convert 62/46 to an equivalent fraction with denominator 1610: 62/46 = (62 * 35)/1610 = 2170/1610 5. Add the fractions: 28/1610 + 2170/1610 = 2198/1610 6. Convert the fraction to a mixed number: 2198/1610 = 1 + 588/1610 Therefore, the result of adding 62/46 to the previous answer of 1 5/70 is 1 588/1610. ### Answer: 1 588/1610
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 Sonnet:
Okay, let's solve this step-by-step: 1) We are given 61/5 and need to subtract 79/70 from it. 2) First, we need to convert both fractions to have a common denominator. The least common multiple of 5 and 70 is 70. 3) To convert 61/5 to an equivalent fraction with denominator 70: 61/5 = (61 * 14)/70 = 854/70 4) Now we can subtract: 854/70 - 79/70 = (854 - 79)/70 = 775/70 5) To convert 775/70 to a mixed number: 775/70 = 11 5/70 Therefore, the result of subtracting 79/70 from 61/5 is 11 5/70. ### Answer: 11 5/70
Expected answer: 155/14
Correct? Yes
Problem: What is the sum of 68/16 and 52/78?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 16 and 78. The LCM of 16 and 78 is 312. Step 2: Convert the fractions to equivalent fractions with the common denominator of 312. 68/16 = (68 × 19.5)/312 = 1326/312 52/78 = (52 × 4)/312 = 208/312 Step 3: Add the fractions with the common denominator. (1326/312) + (208/312) = 1534/312 Step 4: Simplify the fraction if possible. 1534/312 = 4.91025641025641 Therefore, the sum of 68/16 and 52/78 is 4.91025641025641. ### Answer: 4.91025641025641
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 75 and 47. The LCM of 75 and 47 is 1125. Step 2: Convert the fractions to equivalent fractions with the common denominator 1125. 21/75 = (21 × 15)/1125 = 315/1125 44/47 = (44 × 24)/1125 = 1056/1125 Step 3: Add the fractions with the common denominator. (315/1125) + (1056/1125) = 1371/1125 Step 4: Simplify the fraction if possible. 1371/1125 = 1.219 (approximately) Therefore, the sum of 21/75 and 44/47 is 1.219. ### Answer: 1.219
Expected answer: 1429/1175
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
Claude-3 Sonnet:
To calculate the result of (77/5 + 4/11), we need to find a common denominator for the fractions and then add them. Step 1: Find the least common multiple (LCM) of 5 and 11 to get the common denominator. LCM of 5 and 11 = 55 Step 2: Convert the fractions to equivalent fractions with the common denominator of 55. 77/5 = (77 × 11)/55 = 847/55 4/11 = (4 × 5)/55 = 20/55 Step 3: Add the fractions with the common denominator. (847/55) + (20/55) = 867/55 Step 4: Simplify the fraction if possible. 867/55 = 15.7636... Therefore, the result of (77/5 + 4/11) is approximately 15.7636. ### Answer: 15.7636
Expected answer: 867/55
Correct? No
Problem: What's the sum of 60/48 and 37/47?
Claude-3 Sonnet:
To find the sum of 60/48 and 37/47, we need to first find a common denominator for both fractions. The least common multiple (LCM) of 48 and 47 is 1128. So, we convert both fractions to have a denominator of 1128. 60/48 = (60 × 23.5)/1128 = 1410/1128 37/47 = (37 × 24)/1128 = 888/1128 Now we can add the fractions: 1410/1128 + 888/1128 = 2298/1128 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 2. 2298/1128 = 1149/564 Therefore, the sum of 60/48 and 37/47 is 1149/564. ### Answer: 1149/564
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 Sonnet:
Okay, let's solve this step-by-step: 1) First, we found the sum of 60/48 and 37/47, which is 1149/564. 2) Now, we need to add 35/35 to 1149/564. To add fractions with different denominators, we need to find the least common denominator (LCD). The LCD of 564 and 35 is 19740 (564 x 35 = 19740). 3) Convert the fractions to have a denominator of 19740: 1149/564 = (1149 x 35)/19740 = 40215/19740 35/35 = (35 x 564)/19740 = 19740/19740 = 1 4) Add the fractions: 40215/19740 + 1/1 = 40216/19740 5) Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 4: 40216/19740 = 10054/4935 Therefore, the sum of 60/48, 37/47, and 35/35 is 10054/4935. ### Answer: 10054/4935
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 Sonnet:
To solve this problem, we need to find the sum of the weights of apples and oranges that Jane will buy. Given information: - Jane will buy 60/45 kilograms of apples. - Jane will buy 37/47 kilograms of oranges. Step 1: Find a common denominator for the fractions. The least common multiple (LCM) of 45 and 47 is 945. Step 2: Convert the fractions to have the same denominator of 945. 60/45 = (60 × 21)/945 = 1260/945 kilograms of apples 37/47 = (37 × 20)/945 = 740/945 kilograms of oranges Step 3: Add the weights of apples and oranges. Weight of apples + Weight of oranges = Total weight 1260/945 + 740/945 = 2000/945 kilograms Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 5. 2000/945 = 400/189 kilograms Therefore, the total weight of the apples and oranges that Jane will buy is 400/189 kilograms. ### Answer: 400/189
Expected answer: 299/141
Correct? No
Problem: Solve ((14 / 72) + (25 / 6)).
Claude-3 Sonnet:
To solve this expression, we need to perform the division operations first, and then add the results. Given expression: ((14 / 72) + (25 / 6)) Step 1: Evaluate 14 / 72 14 / 72 = 0.194444... Step 2: Evaluate 25 / 6 25 / 6 = 4.166666... Step 3: Add the results from Step 1 and Step 2 (14 / 72) + (25 / 6) = 0.194444... + 4.166666... = 4.361111... Therefore, the solution to the given expression ((14 / 72) + (25 / 6)) is approximately 4.361111. ### Answer: 4.361111
Expected answer: 157/36
Correct? No
Problem: What is the sum of 84/97 and 25/2?
Claude-3 Sonnet:
To find the sum of 84/97 and 25/2, we need to first find a common denominator for both fractions. The least common multiple (LCM) of 97 and 2 is 194. So, we convert both fractions to have a denominator of 194. 84/97 = (84 × 2)/194 = 168/194 25/2 = (25 × 97)/194 = 2425/194 Now we can add the fractions: 168/194 + 2425/194 = (168 + 2425)/194 = 2593/194 To simplify the fraction, we divide the numerator and denominator by their greatest common factor (GCF), which is 1. Therefore, the sum of 84/97 and 25/2 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we found the sum of 84/97 and 25/2, which is 2593/194. 2. Now, we need to subtract 100/71 from 2593/194. To do this, we need to find a common denominator for 2593/194 and 100/71. The LCM of 194 and 71 is 13774. So, we convert both fractions to have a denominator of 13774. 2593/194 = (2593 × 71)/13774 = 183083/13774 100/71 = (100 × 194)/13774 = 19400/13774 Now we can subtract: 183083/13774 - 19400/13774 = (183083 - 19400)/13774 = 163683/13774 To simplify the fraction, we divide the numerator and denominator by their GCF, which is 3. 163683/13774 = (163683/3)/(13774/3) = 54561/4591 Therefore, after subtracting 100/71 from the sum of 84/97 and 25/2, the new result is 54561/4591. ### Answer: 54561/4591
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 Sonnet:
Okay, let's solve this new scenario. Given: - The first fraction is 84/96 (instead of 84/97) - The second fraction is still 25/2 To find the sum, we need to find a common denominator for both fractions. The least common multiple (LCM) of 96 and 2 is 96. So, we can convert the second fraction to have a denominator of 96. 84/96 (no need to convert) 25/2 = (25 × 48)/96 = 1200/96 Now we can add the fractions: 84/96 + 1200/96 = (84 + 1200)/96 = 1284/96 To simplify the fraction, we divide the numerator and denominator by their greatest common factor (GCF), which is 4. 1284/96 = (1284/4)/24 = 321/24 Therefore, the sum of 84/96 and 25/2 is 321/24. ### Answer: 321/24
Expected answer: 107/8
Correct? Yes
Problem: What is the difference between the fractions 66/20 and 4/78?
Claude-3 Sonnet:
To find the difference between two fractions, we need to first find a common denominator and then convert both fractions to equivalent fractions with that common denominator. Then, we can subtract the numerators and keep the denominator the same. Given fractions: 66/20 and 4/78 Step 1: Find the least common multiple (LCM) of the denominators 20 and 78. LCM of 20 and 78 = 780 Step 2: Convert both fractions to equivalent fractions with the denominator 780. 66/20 = (66 × 39)/780 = 2574/780 4/78 = (4 × 10)/780 = 40/780 Step 3: Subtract the numerators and keep the denominator the same. (2574/780) - (40/780) = 2534/780 Therefore, the difference between the fractions 66/20 and 4/78 is 2534/780. ### Answer: 2534/780
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 Sonnet:
Okay, let's solve this step-by-step: 1. We previously found that the difference between 66/20 and 4/78 is 2534/780. 2. Now we need to add 6/15 to this result. 3. To add fractions with different denominators, we need to find the least common denominator (LCD) and convert the fractions to equivalent fractions with the same denominator. 4. The LCD of 780 and 15 is 3900. 5. Converting the fractions: 2534/780 = (2534 × 5)/3900 = 12670/3900 6/15 = (6 × 260)/3900 = 1560/3900 6. Adding the fractions: 12670/3900 + 1560/3900 = 14230/3900 Therefore, the result of adding 6/15 to the difference between 66/20 and 4/78 is 14230/3900. ### Answer: 14230/3900
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 Sonnet:
Okay, let's find the difference between the fractions 66/21 and 4/78. Given fractions: 66/21 and 4/78 Step 1: Find the least common multiple (LCM) of the denominators 21 and 78. LCM of 21 and 78 = 1638 Step 2: Convert both fractions to equivalent fractions with the denominator 1638. 66/21 = (66 × 78)/1638 = 5148/1638 4/78 = (4 × 21)/1638 = 84/1638 Step 3: Subtract the numerators and keep the denominator the same. (5148/1638) - (84/1638) = 5064/1638 Therefore, the difference between the fractions 66/21 and 4/78 is 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 Sonnet:
To calculate the expression 83 divided by 37 minus 12 divided by 14, we need to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Given: - 83 divided by 37 = 83/37 = 2.24324324... ≈ 2.24 - 12 divided by 14 = 12/14 = 0.85714286... ≈ 0.86 Subtracting the second value from the first: 2.24 - 0.86 = 1.38 Therefore, the expression 83 divided by 37 minus 12 divided by 14 is equal to 1.38. ### Answer: 1.38
Expected answer: 359/259
Correct? No
Problem: What is the sum of 95/57 and 28/80?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 57 and 80. The LCM of 57 and 80 is 3,040. Step 2: Convert the fractions to equivalent fractions with the common denominator of 3,040. 95/57 = (95 × 53)/3,040 = 5,035/3,040 28/80 = (28 × 38)/3,040 = 1,064/3,040 Step 3: Add the fractions with the common denominator. (5,035/3,040) + (1,064/3,040) = 6,099/3,040 Step 4: Simplify the fraction, if possible. 6,099/3,040 = 2.0065 (rounded to 4 decimal places) Therefore, the sum of 95/57 and 28/80 is 2.0065. ### Answer: 2.0065
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
Claude-3 Sonnet:
To calculate the sum of 14/57 and 92/42, we need to find a common denominator for both fractions. The least common multiple (LCM) of 57 and 42 is 1194. So, we convert both fractions to have a denominator of 1194. 14/57 = (14 × 21)/1194 = 294/1194 92/42 = (92 × 28.5)/1194 = 2622/1194 Now we can add the fractions: 294/1194 + 2622/1194 = (294 + 2622)/1194 = 2916/1194 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 6. 2916/1194 = (2916/6)/(1194/6) = 486/199 Therefore, the sum of 14/57 and 92/42 is 486/199. ### Answer: 486/199
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations first and then add the results. Given: - (77 / 55) - (6 / 5) Step 1: Calculate (77 / 55) 77 / 55 = 1.4 Step 2: Calculate (6 / 5) 6 / 5 = 1.2 Step 3: Add the results from Step 1 and Step 2 (77 / 55) + (6 / 5) = 1.4 + 1.2 = 2.6 Therefore, the result of ((77 / 55) + (6 / 5)) is 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 Sonnet:
Okay, let's solve this step-by-step:
Given:
* The previously calculated result: ((77 / 55) + (6 / 5)) = 2.6
* We need to add 39/64 to this result
Step 1: Convert 2.6 to an improper fraction
2.6 = (2 × 64 + 38) / 64
= 166 / 64
Step 2: Add 39/64 to 166/64
(166 / 64) + (39 / 64) = (166 + 39) / 64
= 205 / 64
Therefore, if we add the previously calculated result (2.6) to 39/64, we get the fraction 205/64.
### Answer: 205/64
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 Sonnet:
Okay, let's solve this modified problem. Given: - (77 / 55) + (6 / 79) Step 1: Calculate (77 / 55) 77 / 55 = 1.4 Step 2: Calculate (6 / 79) 6 / 79 = 0.0759493670886076 (rounded to 10 decimal places) Step 3: Add the results from Step 1 and Step 2 (77 / 55) + (6 / 79) = 1.4 + 0.0759493670886076 = 1.4759493670886076 To express the result as a fraction, we need to find the least common denominator (LCD) of 55 and 79, which is 4335. Step 4: Convert the decimal to a fraction with the denominator 4335 1.4759493670886076 = 6385/4335 Therefore, the result of ((77 / 55) + (6 / 79)) expressed as a fraction is 6385/4335. ### Answer: 6385/4335
Expected answer: 583/395
Correct? No
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
Claude-3 Sonnet:
To calculate the value of (56 / 8) + (90 / 86), we need to perform the following steps: 1. Calculate 56 / 8 56 / 8 = 7 2. Calculate 90 / 86 90 / 86 = 1.0465116279069767 (rounded to 10 decimal places) 3. Add the two results 7 + 1.0465116279069767 = 8.0465116279069767 Therefore, the value of (56 / 8) + (90 / 86) is 8.0465116279069767. ### Answer: 8.0465116279069767
Expected answer: 346/43
Correct? Yes
Problem: Following the previous calculation of (56 / 8) + (90 / 86), what would the result be if you then subtracted (41 / 76) from that sum?
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. We previously calculated (56 / 8) + (90 / 86) = 8.0465116279069767 2. Now we need to subtract (41 / 76) from this result. 41 / 76 = 0.5394736842105263 (rounded to 10 decimal places) 3. Subtracting: 8.0465116279069767 - 0.5394736842105263 = 7.5070379436964504 Therefore, if we subtract (41 / 76) from the sum of (56 / 8) + (90 / 86), the result is 7.5070379436964504. ### Answer: 7.5070379436964504
Expected answer: 24533/3268
Correct? No
Problem: In the previous problem, we calculated the sum of (56 / 8) and (90 / 86). However, now consider the scenario where instead of 86 parts, the second fraction is divided into 91 parts. What would be the sum of (56 / 8) and (90 / 91)?
Claude-3 Sonnet:
Okay, let's calculate the sum of (56 / 8) and (90 / 91). 1. Calculate 56 / 8 56 / 8 = 7 2. Calculate 90 / 91 90 / 91 = 0.9890109890109891 (rounded to 10 decimal places) 3. Add the two results 7 + 0.9890109890109891 = 7.9890109890109891 Therefore, the sum of (56 / 8) and (90 / 91) is 7.9890109890109891. ### Answer: 7.9890109890109891
Expected answer: 727/91
Correct? No
Problem: What is the sum of 23/20 and 82/97?
Claude-3 Sonnet:
To find the sum of 23/20 and 82/97, we need to find a common denominator for both fractions. The least common multiple (LCM) of 20 and 97 is 1940. So, we convert both fractions to have a denominator of 1940. 23/20 = (23 × 97)/1940 = 2231/1940 82/97 = (82 × 20)/1940 = 1640/1940 Now we can add the fractions: (2231/1940) + (1640/1940) = (2231 + 1640)/1940 = 3871/1940 To simplify the fraction, we divide the numerator and denominator by their greatest common factor (GCF), which is 11. 3871/1940 = (3871/11)/(1940/11) = 352/176 Therefore, the sum of 23/20 and 82/97 is 352/176. ### Answer: 352/176
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
Claude-3 Sonnet:
To calculate the sum of 54/88 and 28/10, we need to find a common denominator for both fractions. The least common multiple (LCM) of 88 and 10 is 880. So, we convert both fractions to have a denominator of 880: 54/88 = (54 × 10)/880 = 540/880 28/10 = (28 × 88)/880 = 2464/880 Now we can add the fractions: 540/880 + 2464/880 = 3004/880 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 4. 3004/880 = (3004/4)/(880/4) = 751/220 Therefore, the sum of 54/88 and 28/10 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we found the sum of 54/88 and 28/10, which is 751/220. 2. Now, we need to add 751/220 to 21/13. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators, which is 780 (220 × 13 × 3). 3. Convert the fractions to have a denominator of 780: 751/220 = (751 × 3)/780 = 2253/780 21/13 = (21 × 60)/780 = 1260/780 4. Add the fractions: 2253/780 + 1260/780 = 3513/780 5. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3. 3513/780 = (3513/3)/(780/3) = 1171/260 Therefore, the sum of 54/88, 28/10, and 21/13 is 1171/260. ### Answer: 1171/260
Expected answer: 14383/2860
Correct? No
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations first, and then add the results. Given: - 7 / 69 (division of 7 by 69) - 71 / 47 (division of 71 by 47) Step 1: Calculate 7 / 69 7 / 69 = 0.1014492753623188 (rounded to 10 decimal places) Step 2: Calculate 71 / 47 71 / 47 = 1.5106382978723404 (rounded to 10 decimal places) Step 3: Add the results from Step 1 and Step 2 0.1014492753623188 + 1.5106382978723404 = 1.6120875732346592 (rounded to 10 decimal places) Therefore, the result of the operation 7 / 69 + 71 / 47 is: ### Answer: 1.6120875732346592
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
Claude-3 Sonnet:
To find the sum of two fractions with different denominators, we need to find a common denominator and then convert both fractions to equivalent fractions with that common denominator. Then, we can add the numerators and keep the common denominator. Step 1: Find the least common multiple (LCM) of the denominators 32 and 15. The LCM of 32 and 15 is 480. Step 2: Convert the fractions to equivalent fractions with the common denominator of 480. 15/32 = (15 × 15)/480 = 225/480 65/15 = (65 × 32)/480 = 2080/480 Step 3: Add the numerators and keep the common denominator. (225/480) + (2080/480) = (225 + 2080)/480 = 2305/480 Therefore, the sum of 15/32 and 65/15 is 2305/480. ### Answer: 2305/480
Expected answer: 461/96
Correct? Yes
Problem: What is the sum of 87/26 and the result of the previous problem ((15/32) + (65/15))?
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. In the previous problem, we found that (15/32) + (65/15) = 2305/480 2. Now we need to add 87/26 to 2305/480 To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with the same denominator. The LCM of 26 and 480 is 3120. 3. Convert the fractions to equivalent fractions with the denominator 3120: 87/26 = (87 × 120)/3120 = 10440/3120 2305/480 = (2305 × 6.5)/3120 = 14982.5/3120 4. Add the numerators and keep the common denominator: (10440/3120) + (14982.5/3120) = 25422.5/3120 Therefore, the sum of 87/26 and (15/32) + (65/15) is 25422.5/3120. ### Answer: 25422.5/3120
Expected answer: 10169/1248
Correct? Yes
Problem: What is the sum of 4/31 and 76/11?
Claude-3 Sonnet:
To find the sum of two fractions with different denominators, we need to first find the least common denominator (LCD) and then convert both fractions to equivalent fractions with the LCD as the denominator. Then, we can add the numerators and keep the LCD as the denominator.
Given fractions: 4/31 and 76/11
Step 1: Find the LCD of 31 and 11.
LCD = 31 × 11 = 341
Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
4/31 = (4 × 11)/341
76/11 = (76 × 31)/341
Step 3: Add the numerators and keep the LCD as the denominator.
(4 × 11)/341 + (76 × 31)/341 = (44 + 2356)/341
= 2400/341
Step 4: Simplify the fraction if possible.
2400/341 = 7 (The fraction is already in its simplest form)
Therefore, the sum of 4/31 and 76/11 is 7.
### Answer: 7
Expected answer: 2400/341
Correct? No
Problem: What is the sum when you add 82/15 to 100/12?
Claude-3 Sonnet:
To add fractions with different denominators, we need to find a common denominator and convert the fractions to equivalent fractions with the same denominator. The least common multiple (LCM) of 15 and 12 is 60. Step 1: Convert 82/15 to an equivalent fraction with the denominator 60. 82/15 = (82 × 4)/60 = 328/60 Step 2: Convert 100/12 to an equivalent fraction with the denominator 60. 100/12 = (100 × 5)/60 = 500/60 Step 3: Add the fractions with the common denominator. 328/60 + 500/60 = (328 + 500)/60 = 828/60 Step 4: Simplify the fraction if possible. 828/60 = 13 + (28/60) = 13 + (14/30) = 13 + (7/15) Therefore, the sum of 82/15 and 100/12 is 13 + (7/15). ### Answer: 13 + (7/15)
Expected answer: 69/5
Correct? No
Problem: Calculate the result of the expression ((92 / 29) + (41 / 33)). Write your answer as a simplified fraction or a whole number.
Claude-3 Sonnet:
To calculate the result of the expression ((92 / 29) + (41 / 33)), we need to perform the following steps: 1. Calculate 92 / 29: 92 / 29 = 3.172413793... (repeating decimal) Converting to a fraction: 92 / 29 = 3 11/29 2. Calculate 41 / 33: 41 / 33 = 1.242424... (repeating decimal) Converting to a fraction: 41 / 33 = 1 8/33 3. Add the fractions: (3 11/29) + (1 8/33) = (3 + 1) + (11/29 + 8/33) = 4 + (11/29 + 8/33) To add the fractions 11/29 and 8/33, we need to find the least common denominator (LCD). The LCD of 29 and 33 is 957. 11/29 = 380/957 8/33 = 232/957 380/957 + 232/957 = 612/957 Therefore, (11/29 + 8/33) = 612/957 4. Combine the whole number and the fraction: 4 + 612/957 = 4 612/957 ### Answer: 4 612/957
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 29 and 98. The LCM of 29 and 98 is 2,794. Step 2: Convert the fractions to equivalent fractions with the common denominator of 2,794. 57/29 = (57 × 96)/2,794 = 5,472/2,794 14/98 = (14 × 28)/2,794 = 392/2,794 Step 3: Add the fractions with the common denominator. (5,472/2,794) + (392/2,794) = (5,472 + 392)/2,794 = 5,864/2,794 Step 4: Simplify the fraction if possible. 5,864/2,794 = 2.1 (approximately) ### Answer: 2.1
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
Claude-3 Sonnet:
To solve the given expression, we need to find a common denominator for the fractions and then add them. Step 1: Find the least common multiple (LCM) of 25 and 28 to get the common denominator. LCM of 25 and 28 = 700 Step 2: Convert the fractions to equivalent fractions with the common denominator of 700. 70/25 = (70 × 28)/700 = 1960/700 83/28 = (83 × 25)/700 = 2075/700 Step 3: Add the fractions with the common denominator. (1960/700) + (2075/700) = (1960 + 2075)/700 = 4035/700 Step 4: Simplify the fraction, if possible. 4035/700 = 5.765 Therefore, the solution to the given expression 70/25 + 83/28 is 5.765. ### Answer: 5.765
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
Claude-3 Sonnet:
To add fractions, we need to find a common denominator for both fractions. The least common multiple (LCM) of 73 and 23 is 1679. First, we convert both fractions to have the same denominator of 1679: 50/73 = (50 × 23)/1679 = 1150/1679 20/23 = (20 × 73)/1679 = 1460/1679 Now we can add the numerators: 1150/1679 + 1460/1679 = 2610/1679 To simplify the fraction, we need to find the greatest common divisor (GCD) of 2610 and 1679, which is 1. Therefore, the simplified fraction is: 2610/1679 = (2610/1)/1679 = 2610/1679 ### Answer: 2610/1679
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 Sonnet:
Okay, let's break this down step-by-step:
1. First, we need to find the result of adding 50/73 and 20/23:
* We found this in the previous question: 50/73 + 20/23 = 2610/1679
2. Next, we need to add 83/35 to 2610/1679:
* To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
* The LCM of 1679 and 35 is 58765.
* So we convert both fractions to have a denominator of 58765:
- 2610/1679 = (2610 × 35)/58765 = 91350/58765
- 83/35 = (83 × 1679)/58765 = 139577/58765
* Now we can add the numerators:
91350/58765 + 139577/58765 = 230927/58765
3. Finally, we simplify the fraction 230927/58765:
* The greatest common divisor (GCD) of 230927 and 58765 is 1.
* Therefore, the simplified fraction is: 230927/58765
### Answer: 230927/58765
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 Sonnet:
To solve this problem, we need to add the fractions 50/57 and 20/23. First, we need to find the least common multiple (LCM) of 57 and 23, which is 1311. Next, we convert both fractions to have the same denominator of 1311: 50/57 = (50 × 23)/1311 = 1150/1311 20/23 = (20 × 57)/1311 = 1140/1311 Now, we can add the numerators: 1150/1311 + 1140/1311 = 2290/1311 To simplify the fraction, we need to find the greatest common divisor (GCD) of 2290 and 1311, which is 1. Therefore, the simplified fraction is: 2290/1311 ### Answer: 2290/1311
Expected answer: 2290/1311
Correct? Yes
Problem: What is the value of ((49 / 57) + (89 / 99))?
Claude-3 Sonnet:
To find the value of ((49 / 57) + (89 / 99)), we need to perform the following steps: 1. Calculate 49 / 57 49 / 57 = 0.8596491228070175 2. Calculate 89 / 99 89 / 99 = 0.8989898989898989 3. Add the two results 0.8596491228070175 + 0.8989898989898989 = 1.7586390217969164 Therefore, the value of ((49 / 57) + (89 / 99)) is 1.7586390217969164. ### Answer: 1.7586390217969164
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
Claude-3 Sonnet:
To calculate 94/35 - 23/49, we need to first find a common denominator for the fractions. The least common multiple of 35 and 49 is 1715. So, we convert the fractions to have a denominator of 1715: 94/35 = (94 * 49)/1715 = 4606/1715 23/49 = (23 * 35)/1715 = 805/1715 Now we can subtract: 4606/1715 - 805/1715 = 3801/1715 To simplify the fraction 3801/1715, we need to find the greatest common factor (GCF) of 3801 and 1715. The GCF of 3801 and 1715 is 37. Therefore, the simplified fraction is: 3801/1715 = (3801/37) / (1715/37) = 103/47 ### Answer: 103/47
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 Sonnet:
To calculate the sum of 58/30 and 49/37, we need to find a common denominator for both fractions. The least common multiple (LCM) of 30 and 37 is 1110. So, we convert both fractions to have a denominator of 1110. 58/30 = (58 × 37)/1110 = 2146/1110 49/37 = (49 × 30)/1110 = 1470/1110 Now we can add the fractions: 2146/1110 + 1470/1110 = 3616/1110 Therefore, the sum of 58/30 and 49/37 is 3616/1110. ### Answer: 3616/1110
Expected answer: 1808/555
Correct? Yes
Problem: If the sum of 58/30 and 49/37 is represented by the variable 't', what would be the value of 't' added to 't'?
Claude-3 Sonnet:
Okay, let's think through this step-by-step: 1) We are told that the sum of 58/30 and 49/37 is represented by the variable 't'. 2) We calculated this sum in the previous question, and it is 3616/1110. 3) So we can substitute this value for 't': t = 3616/1110 4) The question asks for the value of 't' added to 't'. 5) Adding a fraction to itself is the same as multiplying the fraction by 2. 6) So 't' added to 't' is the same as (3616/1110) + (3616/1110) = (3616 + 3616)/1110 = 7232/1110. Therefore, the value of 't' added to 't' is 7232/1110. ### Answer: 7232/1110
Expected answer: 3616/555
Correct? Yes
Problem: Calculate the sum of 45/53 and 71/50.
Claude-3 Sonnet:
To calculate the sum of 45/53 and 71/50, we need to find a common denominator for both fractions. The least common multiple (LCM) of 53 and 50 is 2650. So, we convert both fractions to have a denominator of 2650. 45/53 = (45 × 50)/2650 = 2250/2650 71/50 = (71 × 53)/2650 = 3763/2650 Now we can add the fractions: (2250/2650) + (3763/2650) = 6013/2650 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 7. 6013/2650 = (6013/7)/(2650/7) = 859/379 Therefore, the sum of 45/53 and 71/50 is 859/379. ### Answer: 859/379
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
Claude-3 Sonnet:
To calculate the sum of 36/72 and 49/1, we need to first convert the fractions to have a common denominator. The least common multiple of 72 and 1 is 72. 36/72 = 36/72 = 1/2 49/1 = 49/72 Now we can add the fractions: 1/2 + 49/72 = (36 + 49)/72 = 85/72 To convert the fraction to a mixed number: 85/72 = 1 + 13/72 Therefore, the sum of 36/72 and 49/1 is 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 Sonnet:
To find the sum of two fractions with different denominators, we need to find a common denominator and then convert both fractions to equivalent fractions with that common denominator. Then, we can add the numerators and keep the common denominator. Given fractions: 61/20 and 29/15 Step 1: Find the least common multiple (LCM) of the denominators 20 and 15. LCM of 20 and 15 = 60 Step 2: Convert both fractions to equivalent fractions with the denominator 60. 61/20 = (61 × 3)/60 = 183/60 29/15 = (29 × 4)/60 = 116/60 Step 3: Add the numerators and keep the common denominator. (183/60) + (116/60) = (183 + 116)/60 = 299/60 Therefore, the sum of 61/20 and 29/15 is 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 Sonnet:
Okay, let's solve this step-by-step: First, we need to find the sum of 61/20 and 29/15: * The least common multiple (LCM) of 20 and 15 is 60 * 61/20 = (61 × 3)/60 = 183/60 * 29/15 = (29 × 4)/60 = 116/60 * 183/60 + 116/60 = 299/60 Now, we need to add 299/60 to 58/31: * The LCM of 60 and 31 is 930 * 299/60 = (299 × 15.5)/930 = 4635.5/930 * 58/31 = (58 × 30)/930 = 1740/930 * 4635.5/930 + 1740/930 = 6375.5/930 Therefore, the sum of 61/20, 29/15, and 58/31 is 6375.5/930. ### Answer: 6375.5/930
Expected answer: 12749/1860
Correct? No
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 Sonnet:
Okay, let's find the sum of 61/20 and 29/67. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and convert both fractions to equivalent fractions with the same denominator. Given fractions: 61/20 and 29/67 Step 1: Find the LCM of 20 and 67. LCM of 20 and 67 = 1340 Step 2: Convert both fractions to equivalent fractions with the denominator 1340. 61/20 = (61 × 67)/1340 = 4087/1340 29/67 = (29 × 20)/1340 = 580/1340 Step 3: Add the numerators and keep the common denominator. (4087/1340) + (580/1340) = (4087 + 580)/1340 = 4667/1340 Therefore, the sum of 61/20 and 29/67 is 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 Sonnet:
To solve this expression, we need to find the common denominator for the two fractions and then add the fractions. Step 1: Find the least common multiple (LCM) of 90 and 79. The LCM of 90 and 79 is 7110 (90 × 79 = 7110). Step 2: Convert the fractions to equivalent fractions with the common denominator of 7110. 33/90 = (33 × 79)/7110 = 2607/7110 77/79 = (77 × 90)/7110 = 6930/7110 Step 3: Add the fractions. (2607/7110) + (6930/7110) = 9537/7110 Therefore, the unsimplified fraction is 9537/7110. ### Answer: 9537/7110
Expected answer: 3179/2370
Correct? Yes
Problem: In continuation of the previous question, what would you get if you subtract 7/89 from the result of ((33 / 90) + (77 / 79))? Please give your answer as an unsimplified fraction.
Claude-3 Sonnet:
Okay, let's continue from the previous question. We had: (33/90) + (77/79) = 9537/7110 Now, we need to subtract 7/89 from this result. Step 1: Convert 7/89 to an equivalent fraction with the denominator of 7110. 7/89 = (7 × 79)/7110 = 553/7110 Step 2: Subtract the fractions. (9537/7110) - (553/7110) = (9537 - 553)/7110 = 8984/7110 Therefore, the unsimplified fraction after subtracting 7/89 from the result of ((33/90) + (77/79)) is 8984/7110. ### Answer: 8984/7110
Expected answer: 266341/210930
Correct? No
Problem: Taking the previous problem into consideration, what if the fraction you were initially adding to 33/90 was 98/79 instead of 77/79? Solve the expression ((33 / 90) + (98 / 79)) and give your answer as an unsimplified fraction.
Claude-3 Sonnet:
Okay, let's solve the expression ((33/90) + (98/79)) and give the answer as an unsimplified fraction. Step 1: Find the least common multiple (LCM) of 90 and 79. The LCM of 90 and 79 is 7110 (90 × 79 = 7110). Step 2: Convert the fractions to equivalent fractions with the common denominator of 7110. 33/90 = (33 × 79)/7110 = 2607/7110 98/79 = (98 × 90)/7110 = 8820/7110 Step 3: Add the fractions. (2607/7110) + (8820/7110) = 11427/7110 Therefore, the unsimplified fraction is 11427/7110. ### Answer: 11427/7110
Expected answer: 3809/2370
Correct? Yes
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
Claude-3 Sonnet:
To find the sum of two fractions with different denominators, we need to find a common denominator and then add the fractions with the same denominator. Step 1: Find the least common multiple (LCM) of the denominators 79 and 6. The LCM of 79 and 6 is 474. Step 2: Convert the fractions to equivalent fractions with the common denominator of 474. 30/79 = (30 × 6)/474 = 180/474 29/6 = (29 × 79)/474 = 2291/474 Step 3: Add the fractions with the same denominator. (180/474) + (2291/474) = (180 + 2291)/474 = 2471/474 Therefore, the sum of 30/79 and 29/6 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 30/79 and 29/6: 30/79 + 29/6 = 2471/474 (as calculated in the previous question) 2. Next, we need to subtract 44/75 from 2471/474. To do this, we need to find a common denominator for 2471/474 and 44/75. The least common multiple (LCM) of 474 and 75 is 19950. 3. Convert the fractions to equivalent fractions with the common denominator of 19950: 2471/474 = (2471 × 42)/19950 = 103782/19950 44/75 = (44 × 266)/19950 = 11704/19950 4. Subtract the fractions: 103782/19950 - 11704/19950 = 92078/19950 Therefore, after subtracting 44/75 from the sum of 30/79 and 29/6, the result is 92078/19950. ### Answer: 92078/19950
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 Sonnet:
Okay, let's recalculate the sum with the correct fraction 30/97 instead of 30/79. To find the sum of 30/97 and 29/6, we need to find a common denominator and then add the fractions with the same denominator. Step 1: Find the least common multiple (LCM) of the denominators 97 and 6. The LCM of 97 and 6 is 582. Step 2: Convert the fractions to equivalent fractions with the common denominator of 582. 30/97 = (30 × 6)/582 = 180/582 29/6 = (29 × 97)/582 = 2813/582 Step 3: Add the fractions with the same denominator. (180/582) + (2813/582) = (180 + 2813)/582 = 2993/582 Therefore, the sum of 30/97 and 29/6 is 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 Sonnet:
To solve this problem, we need to convert the fractions to have a common denominator, and then perform the subtraction. Step 1: Find the least common multiple (LCM) of the denominators 66 and 2. LCM of 66 and 2 = 132 Step 2: Convert the fractions to have a denominator of 132. 59/2 = 59 × (66/66) = 3894/132 11/66 = 11 × (2/2) = 22/132 Step 3: Subtract the fractions. 3894/132 - 22/132 = (3894 - 22)/132 = 3872/132 Step 4: Simplify the fraction if possible. 3872/132 = 29.333 (rounded to 3 decimal places) Therefore, the answer when subtracting 11/66 from 59/2 is 29.333. ### Answer: 29.333
Expected answer: 88/3
Correct? No
Problem: Consider these two fractions: 58/23 and 25/26. What is the sum when those two fractions are added together?
Claude-3 Sonnet:
To add fractions, we need to find a common denominator for both fractions. The least common multiple (LCM) of 23 and 26 is 598. So, we convert both fractions to have a denominator of 598: 58/23 = (58 × 26)/598 = 1508/598 25/26 = (25 × 23)/598 = 575/598 Now we can add the numerators: 1508/598 + 575/598 = 2083/598 To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the sum of 58/23 and 25/26 is 2083/598. ### Answer: 2083/598
Expected answer: 2083/598
Correct? Yes
Problem: We previously calculated the sum of the fractions 58/23 and 25/26. Now, suppose we had started with 45/23 instead of 58/23. How does the sum of 45/23 and 25/26 compare to the original calculation?
Claude-3 Sonnet:
Okay, let's calculate the sum of 45/23 and 25/26. First, we need to find the least common multiple (LCM) of 23 and 26, which is 598. Then, we convert both fractions to have a denominator of 598: 45/23 = (45 × 26)/598 = 1170/598 25/26 = (25 × 23)/598 = 575/598 Now we can add the numerators: 1170/598 + 575/598 = 1745/598 To compare this sum to the original calculation of 58/23 + 25/26, we can subtract: 2083/598 - 1745/598 = 338/598 Therefore, the sum of 45/23 and 25/26 is 338/598 less than the sum of 58/23 and 25/26. ### Answer: 338/598 less
Expected answer: 1745/598
Correct? No
Problem: Calculate the sum of the fractions 70/13 and 17/52.
Claude-3 Sonnet:
To calculate the sum of two fractions, we need to find a common denominator and then add the fractions with the same denominator.
Step 1: Find the least common multiple (LCM) of the denominators 13 and 52.
The LCM of 13 and 52 is 156.
Step 2: Convert the fractions to equivalent fractions with the common denominator of 156.
70/13 = (70 × 12)/156 = 840/156
17/52 = (17 × 3)/156 = 51/156
Step 3: Add the fractions with the same denominator.
(840/156) + (51/156) = 891/156
Step 4: Simplify the fraction if possible.
891/156 = 5 (with a remainder of 131/156)
= 5 + 131/156
Therefore, the sum of the fractions 70/13 and 17/52 is 5 + 131/156.
### Answer: 5 + 131/156
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
Claude-3 Sonnet:
To find the sum of 78/44 and 17/91, we need to find a common denominator for both fractions. The least common multiple (LCM) of 44 and 91 is 1,292. So, we convert both fractions to have a denominator of 1,292. 78/44 = (78 × 29)/1,292 = 2,262/1,292 17/91 = (17 × 14)/1,292 = 238/1,292 Now we can add the fractions: 2,262/1,292 + 238/1,292 = (2,262 + 238)/1,292 = 2,500/1,292 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 4. 2,500/1,292 = (2,500/4)/(1,292/4) = 625/323 Therefore, the sum of 78/44 and 17/91 is 625/323. ### Answer: 625/323
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
Claude-3 Sonnet:
To find the sum of 43/4 and 71/4, we need to first find a common denominator for both fractions. The least common denominator (LCD) of 4 and 4 is 4.
Now, we can convert both fractions to have the same denominator of 4:
43/4 = 43/4 (no need to change)
71/4 = 71/4 (no need to change)
Next, we add the numerators and keep the denominator the same:
43/4 + 71/4 = (43 + 71)/4
= 114/4
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 2.
114/4 = (114/2) / (4/2)
= 57/2
Therefore, the sum of 43/4 and 71/4 is 57/2.
### Answer: 57/2
Expected answer: 57/2
Correct? Yes
Problem: What is the sum of 43/4 and 71/4 plus 92/79?
Claude-3 Sonnet:
To find the sum of 43/4, 71/4, and 92/79, we need to first find a common denominator for all three fractions. The least common denominator (LCD) of 4, 4, and 79 is 316.
Now, we can convert all three fractions to have the same denominator of 316:
43/4 = (43 × 79)/316 = 3397/316
71/4 = (71 × 79)/316 = 5609/316
92/79 = (92 × 4)/316 = 368/316
Next, we add the numerators and keep the denominator the same:
3397/316 + 5609/316 + 368/316 = (3397 + 5609 + 368)/316
= 9374/316
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 2.
9374/316 = (9374/2) / (316/2)
= 4687/158
Therefore, the sum of 43/4, 71/4, and 92/79 is 4687/158.
### Answer: 4687/158
Expected answer: 4687/158
Correct? Yes
Problem: What if instead of adding 71/4, we added 71/89 to 43/4? What would be the new total?
Claude-3 Sonnet:
Okay, let's find the sum of 43/4 and 71/89.
First, we need to find the least common denominator (LCD) of 4 and 89. The LCD is 356 (4 × 89 = 356).
Now, we convert both fractions to have the denominator of 356:
43/4 = (43 × 89)/356 = 3827/356
71/89 = (71 × 4)/356 = 284/356
Next, we add the numerators and keep the denominator the same:
3827/356 + 284/356 = (3827 + 284)/356
= 4111/356
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 3.
4111/356 = (4111/3) / (356/3)
= 1370/119
Therefore, the sum of 43/4 and 71/89 is 1370/119.
### Answer: 1370/119
Expected answer: 4111/356
Correct? No
Problem: What is the result of adding the fractions 17/74 and 53/27?
Claude-3 Sonnet:
To add fractions with different denominators, we need to find a common denominator and convert the fractions to equivalent fractions with the same denominator. Then, we can add the numerators and keep the common denominator. Step 1: Find the least common multiple (LCM) of the denominators 74 and 27. LCM of 74 and 27 = 1998 Step 2: Convert the fractions to equivalent fractions with the denominator 1998. 17/74 = (17 × 27)/1998 = 459/1998 53/27 = (53 × 74)/1998 = 3922/1998 Step 3: Add the numerators and keep the common denominator. (459/1998) + (3922/1998) = (459 + 3922)/1998 = 4381/1998 Step 4: Simplify the fraction if possible. 4381/1998 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. 4381/1998 = (4381/3)/(1998/3) = 1460/666 Therefore, the result of adding the fractions 17/74 and 53/27 is 1460/666. ### Answer: 1460/666
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
Claude-3 Sonnet:
To compute the value of (76/76) + (96/16), we need to perform the following steps: 1. Evaluate (76/76): 76/76 = 1 2. Evaluate (96/16): 96/16 = 6 3. Add the two values: (76/76) + (96/16) = 1 + 6 = 7 Therefore, the value of (76/76) + (96/16) is 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 Sonnet:
Okay, let's solve this step-by-step: 1. We first need to find the value of (76/76) + (96/16) (76/76) = 1 (96/16) = 6 1 + 6 = 7 2. So the value of (76/76) + (96/16) is 7 3. Now we need to add this value (7) to itself 7 + 7 = 14 Therefore, after finding the value of (76/76) + (96/16), which is 7, and then adding that solution (7) to itself, the result is 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 Sonnet:
Okay, let's recalculate the expression with the new fraction (96/33) instead of (96/16). Given: - The first fraction is (76/76) - The second fraction is now (96/33) Step 1: Evaluate (76/76) (76/76) = 1 Step 2: Evaluate (96/33) (96/33) = 2.909090909... (rounded to 2.91) Step 3: Add the two values (76/76) + (96/33) = 1 + 2.91 = 3.91 Therefore, the new total with the second fraction as (96/33) is 3.91. ### Answer: 3.91
Expected answer: 43/11
Correct? No
Problem: What is the result of ((94 / 14) - (50 / 90))? Answer as a simplified fraction.
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations and then subtract the resulting values. Given: - (94 / 14) - (50 / 90) Step 1: Divide 94 by 14. 94 / 14 = 6 (with a remainder of 8) Step 2: Divide 50 by 90. 50 / 90 = 5 / 9 Step 3: Subtract the two values. (94 / 14) - (50 / 90) = 6 - (5 / 9) To subtract a fraction from a whole number, we need to convert the whole number to an improper fraction. 6 = 6 × (9 / 9) = 54 / 9 Now, we can subtract the fractions. (54 / 9) - (5 / 9) = (54 - 5) / 9 = 49 / 9 Therefore, the result of ((94 / 14) - (50 / 90)) as a simplified fraction is: ### Answer: 49/9
Expected answer: 388/63
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
Claude-3 Sonnet:
To solve this problem, we need to find a common denominator for the fractions and then subtract them. Given: - 33/7 - 29/79 Step 1: Find the least common multiple (LCM) of the denominators 7 and 79. LCM of 7 and 79 = 553 Step 2: Convert the fractions to equivalent fractions with the common denominator of 553. 33/7 = (33 × 79)/553 = 2607/553 29/79 = (29 × 7)/553 = 203/553 Step 3: Subtract the fractions. (2607/553) - (203/553) = 2404/553 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). GCD of 2404 and 553 = 1 2404/553 = (2404/1) / (553/1) = 2404/553 Therefore, the result of subtracting 29/79 from 33/7 is 2404/553. ### Answer: 2404/553
Expected answer: 2404/553
Correct? Yes
Problem: Now, after you found the result of subtracting 29/79 from 33/7, what would you get if you subtract 61/76 from that earlier result?
Claude-3 Sonnet:
Okay, let's solve this step-by-step: Given: - The result of subtracting 29/79 from 33/7 is 2404/553 - We need to subtract 61/76 from 2404/553 Step 1: Find the least common multiple (LCM) of the denominators 553 and 76. LCM of 553 and 76 = 21,008 Step 2: Convert the fractions to equivalent fractions with the common denominator of 21,008. 2404/553 = (2404 × 38)/21,008 = 91,352/21,008 61/76 = (61 × 276)/21,008 = 16,836/21,008 Step 3: Subtract the fractions. (91,352/21,008) - (16,836/21,008) = 74,516/21,008 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). GCD of 74,516 and 21,008 = 4 74,516/21,008 = (74,516/4) / (21,008/4) = 18,629/5,252 Therefore, the result of subtracting 61/76 from the earlier result of 2404/553 is 18,629/5,252. ### Answer: 18,629/5,252
Expected answer: 148971/42028
Correct? No
Problem: Suppose in the previous problem, instead of subtracting 29/79 from 33/7, we subtract 11/79 from 33/7. What would be the new result?
Claude-3 Sonnet:
To solve this problem, we need to find a common denominator for the fractions and then subtract them. Given: - 33/7 - 11/79 Step 1: Find the least common multiple (LCM) of the denominators 7 and 79. LCM of 7 and 79 = 553 Step 2: Convert the fractions to equivalent fractions with the common denominator of 553. 33/7 = (33 × 79)/553 = 2607/553 11/79 = (11 × 7)/553 = 77/553 Step 3: Subtract the fractions. (2607/553) - (77/553) = 2530/553 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). GCD of 2530 and 553 = 1 2530/553 = (2530/1) / (553/1) = 2530/553 Therefore, the result of subtracting 11/79 from 33/7 is 2530/553. ### Answer: 2530/553
Expected answer: 2530/553
Correct? Yes
Problem: What is the sum of 60/79 and 53/38?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 79 and 38. The LCM of 79 and 38 is 3002. Step 2: Convert the fractions to equivalent fractions with the common denominator of 3002. 60/79 = (60 × 38)/3002 = 2280/3002 53/38 = (53 × 79)/3002 = 4187/3002 Step 3: Add the fractions with the common denominator. (2280/3002) + (4187/3002) = 6467/3002 Step 4: Simplify the fraction if possible. 6467/3002 = 2.155 (rounded to 3 decimal places) Therefore, the sum of 60/79 and 53/38 is 2.155. ### Answer: 2.155
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
Claude-3 Sonnet:
To solve this fraction equation, we need to find a common denominator for both fractions and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 48 and 84. The LCM of 48 and 84 is 336. Step 2: Convert the fractions to equivalent fractions with the common denominator of 336. 39/48 = (39 × 7)/336 = 273/336 19/84 = (19 × 4)/336 = 76/336 Step 3: Add the fractions with the common denominator. 273/336 + 76/336 = (273 + 76)/336 = 349/336 Step 4: Simplify the fraction if possible. 349/336 = 1 + 13/336 Therefore, the solution to the fraction equation 39/48 + 19/84 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. We first calculated the value of 39/48 + 19/84, which is 1 + 13/336. 2. Now, we need to add this result to itself. (1 + 13/336) + (1 + 13/336) = 1 + 1 + 13/336 + 13/336 = 2 + 26/336 = 2 + 1/12 (since 26/336 = 1/12) = 2 + 1/12 Therefore, if we add the obtained result of 39/48 + 19/84 (which is 1 + 13/336) to itself, the final result would be: ### Answer: 2 + 1/12
Expected answer: 349/168
Correct? No
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 Sonnet:
To solve the fraction equation 39/48 + 19/13, we need to find a common denominator for both fractions and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 48 and 13. The LCM of 48 and 13 is 624. Step 2: Convert the fractions to equivalent fractions with the common denominator of 624. 39/48 = (39 × 13)/624 = 507/624 19/13 = (19 × 48)/624 = 912/624 Step 3: Add the fractions with the common denominator. 507/624 + 912/624 = (507 + 912)/624 = 1419/624 Step 4: Simplify the fraction if possible. 1419/624 = 2 + 171/624 Therefore, the solution to the fraction equation 39/48 + 19/13 is 2 + 171/624. ### Answer: 2 + 171/624
Expected answer: 473/208
Correct? Yes
Problem: What is the sum of 16/86 and 60/3?
Claude-3 Sonnet:
To find the sum of 16/86 and 60/3, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of 86 and 3 to get the common denominator. LCM of 86 and 3 = 258 Step 2: Convert the fractions to equivalent fractions with the common denominator of 258. 16/86 = (16 × 3)/258 = 48/258 60/3 = (60 × 86)/258 = 5160/258 Step 3: Add the fractions with the common denominator. 48/258 + 5160/258 = 5208/258 Step 4: Simplify the fraction if possible. 5208/258 = 20.18/1 = 20 18/100 Therefore, the sum of 16/86 and 60/3 is 20 18/100. ### Answer: 20 18/100
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
Claude-3 Sonnet:
To solve the equation ((95 / 69) + (67 / 9)), we need to perform the division operations first, and then add the results. Given: - (95 / 69) represents the division of 95 by 69. - (67 / 9) represents the division of 67 by 9. Step 1: Divide 95 by 69. 95 / 69 = 1.376811594202899 (rounded to 9 decimal places) Step 2: Divide 67 by 9. 67 / 9 = 7.444444444444445 (rounded to 9 decimal places) Step 3: Add the results from Step 1 and Step 2. (95 / 69) + (67 / 9) = 1.376811594202899 + 7.444444444444445 = 8.821256038647344 (rounded to 9 decimal places) Therefore, the solution to the equation ((95 / 69) + (67 / 9)) is: ### Answer: 8.821256038647344
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
Claude-3 Sonnet:
To calculate 95 / 16 - 43 / 60, we need to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). First, we calculate the divisions: 95 / 16 = 5.9375 43 / 60 = 0.7166666... Next, we subtract the two results: 5.9375 - 0.7166666... = 5.2208333... Therefore, the result of 95 / 16 - 43 / 60 is: ### Answer: 5.2208333...
Expected answer: 1253/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the numerators. The common denominator of 8 and 16 is 16 (the least common multiple of 8 and 16). So, we need to convert 38/8 to an equivalent fraction with a denominator of 16. 38/8 = (38 × 2)/16 = 76/16 Now we can add the fractions: 76/16 + 4/16 = (76 + 4)/16 = 80/16 To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 16. 80/16 = (80/16) / (16/16) = 5/1 = 5 Therefore, the sum of 38/8 and 4/16 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. In the previous problem, we found that the sum of 38/8 and 4/16 is 5. 2. To add 32/64 to this sum, we need to convert 5 to an equivalent fraction with a denominator of 64. 5 = (5 × 8)/8 = 40/8 40/8 = (40 × 8)/64 = 320/64 3. Now we can add 32/64 to 320/64: 320/64 + 32/64 = (320 + 32)/64 = 352/64 4. To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 32. 352/64 = (352/32) / (64/32) = 11/2 Therefore, if we add 32/64 to the sum of 38/8 and 4/16, the new total is 11/2. ### Answer: 11/2
Expected answer: 11/2
Correct? Yes
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 Sonnet:
Okay, let's solve this step-by-step: Given fractions: 12/8 and 4/16 Step 1: Find the least common denominator (LCD) of 8 and 16. The LCD of 8 and 16 is 16. Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator. 12/8 = (12 × 2)/16 = 24/16 4/16 (no need to convert as the denominator is already 16) Step 3: Add the numerators and keep the denominator the same. 24/16 + 4/16 = (24 + 4)/16 = 28/16 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 28 and 16 is 4. 28/16 = (28/4) / (16/4) = 7/4 Therefore, the sum of 12/8 and 4/16 is 7/4. ### Answer: 7/4
Expected answer: 7/4
Correct? Yes
Problem: Calculate the result of 67 / 15 - 27 / 12.
Claude-3 Sonnet:
To calculate the result of 67 / 15 - 27 / 12, we need to perform the following steps: 1. Calculate 67 / 15: 67 / 15 = 4.47 (rounded to two decimal places) 2. Calculate 27 / 12: 27 / 12 = 2.25 3. Subtract 2.25 from 4.47: 4.47 - 2.25 = 2.22 Therefore, the result of 67 / 15 - 27 / 12 is 2.22. ### Answer: 2.22
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
Claude-3 Sonnet:
To calculate the sum of 38/59 and 80/94, we need to find a common denominator for both fractions. The least common multiple (LCM) of 59 and 94 is 5546. So, we convert both fractions to have a denominator of 5546. 38/59 = (38 × 94)/5546 = 3572/5546 80/94 = (80 × 59)/5546 = 4720/5546 Now we can add the fractions: 3572/5546 + 4720/5546 = 8292/5546 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 2. 8292/5546 = (8292/2)/(5546/2) = 4146/2773 Therefore, the sum of 38/59 and 80/94 is 4146/2773. ### Answer: 4146/2773
Expected answer: 4146/2773
Correct? Yes
Problem: If you add 84/30 to the sum of 38/59 and 80/94, what is the resultant value?
Claude-3 Sonnet:
To find the resultant value, we need to first calculate the sum of 38/59 and 80/94, and then add 84/30 to it. From the previous question, we know that the sum of 38/59 and 80/94 is 4146/2773. Now, we need to find a common denominator for 4146/2773 and 84/30. The LCM of 2773 and 30 is 83190. So, we convert both fractions to have a denominator of 83190. 4146/2773 = (4146 × 30)/83190 = 124380/83190 84/30 = (84 × 2773)/83190 = 233532/83190 Now we can add the fractions: 124380/83190 + 233532/83190 = 357912/83190 To simplify the fraction, we divide the numerator and denominator by their GCD, which is 6. 357912/83190 = (357912/6)/(83190/6) = 59652/13865 Therefore, the resultant value after adding 84/30 to the sum of 38/59 and 80/94 is 59652/13865. ### Answer: 59652/13865
Expected answer: 59552/13865
Correct? No
Problem: If instead of 38/59, the fraction was 38/39, what would be the new sum when combined with 80/94?
Claude-3 Sonnet:
Okay, let's calculate the sum of 38/39 and 80/94. First, we need to find the least common multiple (LCM) of 39 and 94 to get a common denominator. The LCM of 39 and 94 is 3666. Now, we convert both fractions to have a denominator of 3666. 38/39 = (38 × 94)/3666 = 3572/3666 80/94 = (80 × 39)/3666 = 3120/3666 Next, we add the fractions: 3572/3666 + 3120/3666 = 6692/3666 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 2. 6692/3666 = (6692/2)/(3666/2) = 3346/1833 Therefore, the sum of 38/39 and 80/94 is 3346/1833. ### Answer: 3346/1833
Expected answer: 3346/1833
Correct? Yes
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
Claude-3 Sonnet:
To calculate the sum of 10/14 and 70/20, we need to find a common denominator for both fractions. The least common multiple of 14 and 20 is 140. So, we convert both fractions to have a denominator of 140: 10/14 = (10 × 10)/140 = 100/140 70/20 = (70 × 7)/140 = 490/140 Now we can add the fractions: 100/140 + 490/140 = 590/140 To convert the fraction to a decimal, we divide the numerator by the denominator: 590/140 = 4.2142857142857144 Therefore, the sum of 10/14 and 70/20 as a decimal is 4.2142857142857144. ### Answer: 4.2142857142857144
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 Sonnet:
Okay, let's solve this step-by-step: 1. Calculate the sum of 10/14 and 70/20: Common denominator = 140 10/14 = 100/140 70/20 = 490/140 100/140 + 490/140 = 590/140 2. Convert 590/140 to a decimal: 590/140 = 4.2142857142857144 3. Add 100/20 to 4.2142857142857144: 100/20 = 5 (when converted to a decimal) 4.2142857142857144 + 5 = 9.2142857142857144 Therefore, the new total after adding the sum of 10/14 and 70/20 to 100/20 is 9.2142857142857144. ### Answer: 9.2142857142857144
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 Sonnet:
Okay, let's recalculate the sum with the corrected first fraction, 10/18, and the second fraction, 70/20. To find the sum, we need to find the least common multiple (LCM) of 18 and 20, which is 180. Converting the fractions to have a denominator of 180: 10/18 = (10 × 10)/180 = 100/180 70/20 = (70 × 9)/180 = 630/180 Now, we can add the fractions: 100/180 + 630/180 = 730/180 To convert the fraction to a decimal, we divide the numerator by the denominator: 730/180 = 4.0555555555555554 Therefore, the sum of 10/18 and 70/20 as a decimal is 4.0555555555555554. ### Answer: 4.0555555555555554
Expected answer: 73/18
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
Claude-3 Sonnet:
To subtract fractions, we need to find a common denominator for both fractions. The least common multiple of 44 and 5 is 220. So, we convert both fractions to have a denominator of 220: 19/44 = (19 × 5)/220 = 95/220 33/5 = (33 × 44)/220 = 1452/220 Now we can subtract: 1452/220 - 95/220 = 1357/220 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 13: 1357/220 = (1357/13)/(220/13) = 105/17 Therefore, the result of subtracting 19/44 from 33/5 is 105/17. ### Answer: 105/17
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 Sonnet:
To solve this problem, we need to perform the following steps: 1. Calculate (97 / 13) 97 / 13 = 7.46153846... 2. Calculate (62 / 22) 62 / 22 = 2.81818181... 3. Add the two results 7.46153846... + 2.81818181... = 10.27972027... 4. Round the result to the nearest hundredth 10.27972027... rounds to 10.28 Therefore, the result of (97 / 13) + (62 / 22), rounded to the nearest hundredth, 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 Sonnet:
To solve this problem, we need to find the values of 78 divided by 35 and 30 divided by 60, and then add them together. Given information: - 78 divided by 35 - 30 divided by 60 Step 1: Find the value of 78 divided by 35. 78 ÷ 35 = 2.2285714285714286 Step 2: Find the value of 30 divided by 60. 30 ÷ 60 = 0.5 Step 3: Find the sum of the two values. Sum = 2.2285714285714286 + 0.5 Sum = 2.7285714285714286 Therefore, the sum of 78 divided by 35 and 30 divided by 60 is 2.7285714285714286. ### Answer: 2.7285714285714286
Expected answer: 191/70
Correct? Yes
Problem: What is the sum of 49/75 and 88/58?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 75 and 58. The LCM of 75 and 58 is 1450. Step 2: Convert the fractions to equivalent fractions with the common denominator 1450. 49/75 = (49 × 19.3333)/1450 = 946/1450 88/58 = (88 × 25)/1450 = 2200/1450 Step 3: Add the numerators of the equivalent fractions. 946/1450 + 2200/1450 = (946 + 2200)/1450 = 3146/1450 Step 4: Simplify the fraction if possible. 3146/1450 = 2.17 Therefore, the sum of 49/75 and 88/58 is 2.17. ### Answer: 2.17
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
Claude-3 Sonnet:
To solve this problem, we need to perform the following operations: 1. Calculate 50 / 2 2. Calculate 50 / 32 3. Subtract the result of step 2 from the result of step 1 Step 1: 50 / 2 = 25 Step 2: 50 / 32 = 1.5625 Step 3: 25 - 1.5625 = 23.4375 Therefore, the result of ((50 / 2) - (50 / 32)) is 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 Sonnet:
Okay, let's solve this step-by-step: 1. Calculate the difference between (50 / 2) and (50 / 32): (50 / 2) = 25 (50 / 32) = 1.5625 25 - 1.5625 = 23.4375 2. Calculate (72 / 81): 72 / 81 = 0.8888888888888888 3. Add the results from steps 1 and 2: 23.4375 + 0.8888888888888888 = 24.3263888888888888 Therefore, the result when you add (72 / 81) to the difference between (50 / 2) and (50 / 32) is 24.3263888888888888. ### Answer: 24.3263888888888888
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 Sonnet:
Okay, let's solve this step-by-step: 1. Calculate 50 / 2 50 / 2 = 25 2. Calculate 50 / 91 50 / 91 = 0.5494505494505495 3. Subtract the result of step 2 from the result of step 1 25 - 0.5494505494505495 = 24.4505494505494505 Therefore, the result of ((50 / 2) - (50 / 91)) is 24.4505494505494505. ### Answer: 24.4505494505494505
Expected answer: 2225/91
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
Claude-3 Sonnet:
To solve this problem, we need to perform the following steps: 1. Calculate 77 / 30 77 / 30 = 2.5666... 2. Calculate 18 / 51 18 / 51 = 0.3529... 3. Add the two results 2.5666... + 0.3529... = 2.9195... Therefore, the result of ((77 / 30) + (18 / 51)) is approximately 2.9195. ### Answer: 2.9195
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
Claude-3 Sonnet:
To solve this problem, we need to perform the division operations first and then add the results. Given: - (36 / 37) represents the division of 36 by 37. - (8 / 4) represents the division of 8 by 4. Step 1: Calculate (36 / 37) 36 / 37 = 0.972972972972973 (rounded to 9 decimal places) Step 2: Calculate (8 / 4) 8 / 4 = 2 Step 3: Add the results from Step 1 and Step 2 (36 / 37) + (8 / 4) = 0.972972972972973 + 2 = 2.972972972972973 Therefore, the result of (36 / 37) + (8 / 4) is 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 Sonnet:
Okay, let's solve this step-by-step: Step 1: Calculate (36 / 37) + (8 / 4) (36 / 37) = 0.972972972972973 (rounded to 9 decimal places) (8 / 4) = 2 (36 / 37) + (8 / 4) = 0.972972972972973 + 2 = 2.972972972972973 Step 2: Add the result from Step 1 to itself 2.972972972972973 + 2.972972972972973 = 5.945945945945946 Therefore, the final result is 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 Sonnet:
Okay, let's recalculate with the new expression (36 / 37) + (8 / 56). Given: - (36 / 37) represents the division of 36 by 37. - (8 / 56) represents the division of 8 by 56. Step 1: Calculate (36 / 37) 36 / 37 = 0.972972972972973 (rounded to 9 decimal places) Step 2: Calculate (8 / 56) 8 / 56 = 0.142857142857143 (rounded to 9 decimal places) Step 3: Add the results from Step 1 and Step 2 (36 / 37) + (8 / 56) = 0.972972972972973 + 0.142857142857143 = 1.115830115830116 Therefore, the result of (36 / 37) + (8 / 56) is 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 Sonnet:
To calculate (57 / 22) - (72 / 48), we first need to find the values of each fraction: 57 / 22 = 2.59090909... 72 / 48 = 1.5 Now we subtract: 2.59090909... - 1.5 = 1.09090909... To express this as a fraction in simplest form, we need to convert the decimal to a fraction. 1.09090909... = 1 + 0.09090909... 0.09090909... = 9/99 (repeating decimal) So, 1.09090909... = 1 + 9/99 = 108/99 Therefore, the result of (57 / 22) - (72 / 48) expressed as a fraction in simplest form is: ### Answer: 108/99
Expected answer: 12/11
Correct? Yes
Problem: Calculate the result of (57 / 22) - (72 / 48) expressing your answer as a fraction in the simplest form. Then, add this result to itself. What is the final simplified fraction?
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. Calculate (57 / 22) - (72 / 48) 57 / 22 = 2.59090909... 72 / 48 = 1.5 2.59090909... - 1.5 = 1.09090909... 2. Convert the decimal to a fraction in simplest form 1.09090909... = 1 + 0.09090909... 0.09090909... = 9/99 (repeating decimal) 1.09090909... = 1 + 9/99 = 108/99 So, (57 / 22) - (72 / 48) = 108/99 3. Add this result to itself 108/99 + 108/99 = 216/99 4. Simplify the fraction 216/99 216/99 = 2 * (108/99) = 2 * (27/25) = 54/25 Therefore, the final simplified fraction is: ### Answer: 54/25
Expected answer: 24/11
Correct? No
Problem: Originally, you calculated the result of (57 / 22) - (72 / 48) and expressed your answer as a fraction in the simplest form. Now, consider the scenario where you miscalculated and the second fraction was actually (72 / 100) instead of (72 / 48). Recalculate the expression (57 / 22) - (72 / 100). What is the final simplified fraction in this case?
Claude-3 Sonnet:
Okay, let's recalculate the expression (57 / 22) - (72 / 100) with the corrected second fraction. First, we find the values of the fractions: 57 / 22 = 2.59090909... 72 / 100 = 0.72 Now we subtract: 2.59090909... - 0.72 = 1.87090909... To convert the decimal to a fraction, we follow the same process as before: 1.87090909... = 1 + 0.87090909... 0.87090909... = 87/99 (repeating decimal) So, 1.87090909... = 1 + 87/99 = 186/99 Therefore, the result of (57 / 22) - (72 / 100) expressed as a simplified fraction is: ### Answer: 186/99
Expected answer: 1029/550
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
Claude-3 Sonnet:
To solve this problem, we need to find the values of 48 divided by 16 and 12 divided by 29, and then add them together. Given information: - 48 divided by 16 - 12 divided by 29 Step 1: Find the value of 48 divided by 16. 48 ÷ 16 = 3 Step 2: Find the value of 12 divided by 29. 12 ÷ 29 = 0.4137931... (repeating decimal) Step 3: Add the two values together. 3 + 0.4137931... = 3.4137931... Therefore, the sum of 48 divided by 16 and 12 divided by 29 is 3.4137931... ### Answer: 3.4137931...
Expected answer: 99/29
Correct? No
Problem: What is the sum of 37/20 and 16/75? Write your answer as a simplified fraction.
Claude-3 Sonnet:
To find the sum of two fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator. Then, we can add the numerators and keep the LCD as the denominator. Given fractions: 37/20 and 16/75 Step 1: Find the LCD of 20 and 75. The LCD is the least common multiple of 20 and 75, which is 300. Step 2: Convert both fractions to equivalent fractions with the denominator 300. 37/20 = (37 × 15)/300 = 555/300 16/75 = (16 × 4)/300 = 64/300 Step 3: Add the numerators and keep the denominator as 300. 555/300 + 64/300 = (555 + 64)/300 = 619/300 Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. The GCF of 619 and 300 is 1. 619/300 = (619/1) / (300/1) = 619/300 Therefore, the sum of 37/20 and 16/75 as a simplified fraction is 619/300. ### Answer: 619/300
Expected answer: 619/300
Correct? Yes
Problem: In addition to the previously computed sum of 37/20 and 16/75, now add the fraction 61/80 to this sum. What is the total when all three fractions are added together?
Claude-3 Sonnet:
Okay, let's add 61/80 to the previously computed sum of 37/20 and 16/75, which was 619/300. Given: - Sum of 37/20 and 16/75 = 619/300 - Additional fraction to add: 61/80 Step 1: Find the LCD of 300 and 80. The LCD is the least common multiple of 300 and 80, which is 1200. Step 2: Convert all fractions to equivalent fractions with the denominator 1200. 619/300 = (619 × 4)/1200 = 2476/1200 61/80 = (61 × 15)/1200 = 915/1200 Step 3: Add the numerators and keep the denominator as 1200. 2476/1200 + 915/1200 = (2476 + 915)/1200 = 3391/1200 Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. The GCF of 3391 and 1200 is 1. 3391/1200 = (3391/1) / (1200/1) = 3391/1200 Therefore, the sum of 37/20, 16/75, and 61/80 is 3391/1200. ### Answer: 3391/1200
Expected answer: 3391/1200
Correct? Yes
Problem: If there originally were 60/20 portions of a cake and you added 16/75 portions of another cake to it, how much cake would you have in total? Please write your answer as a simplified fraction.
Claude-3 Sonnet:
To solve this problem, we need to find the sum of the two fractions representing the portions of cake. Given information: - There were originally 60/20 portions of a cake. - 16/75 portions of another cake were added. Step 1: Find the least common denominator (LCD) of 20 and 75. The LCD of 20 and 75 is 300. Step 2: Convert both fractions to equivalent fractions with the denominator 300. 60/20 = (60 × 15)/300 = 900/300 16/75 = (16 × 4)/300 = 64/300 Step 3: Add the numerators and keep the denominator as 300. 900/300 + 64/300 = (900 + 64)/300 = 964/300 Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. The GCF of 964 and 300 is 4. 964/300 = (964/4) / (300/4) = 241/75 Therefore, the total amount of cake after adding 16/75 portions to the original 60/20 portions is 241/75. ### Answer: 241/75
Expected answer: 241/75
Correct? Yes
Problem: Calculate the summation: 83/40 + 6/8.
Claude-3 Sonnet:
To calculate the summation of 83/40 and 6/8, we need to find a common denominator for both fractions. The least common multiple (LCM) of 40 and 8 is 80. So, we convert both fractions to have a denominator of 80: 83/40 = (83 × 2)/80 = 166/80 6/8 = (6 × 10)/80 = 60/80 Now we can add the fractions: 166/80 + 60/80 = (166 + 60)/80 = 226/80 To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2. 226/80 = (226/2)/(80/2) = 113/40 Therefore, the summation of 83/40 and 6/8 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the result of 83/40 + 6/8: Common denominator = 80 83/40 = (83 × 2)/80 = 166/80 6/8 = (6 × 10)/80 = 60/80 166/80 + 60/80 = 226/80 226/80 = (226/2)/(80/2) = 113/40 2. Now, we need to subtract 24/64 from 113/40: Common denominator = 640 113/40 = (113 × 16)/640 = 1808/640 24/64 = (24 × 10)/640 = 240/640 1808/640 - 240/640 = 1568/640 3. To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 32. 1568/640 = (1568/32)/(640/32) = 49/20 Therefore, after finding the result of 83/40 + 6/8 and then subtracting 24/64 from it, we get 49/20. ### Answer: 49/20
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 Sonnet:
Okay, let's recalculate the summation with the new fraction 83/18 instead of 83/40. To find the sum of 83/18 and 6/8, we need to find the least common multiple (LCM) of 18 and 8, which is 72. Converting the fractions to have a denominator of 72: 83/18 = (83 × 4)/72 = 332/72 6/8 = (6 × 9)/72 = 54/72 Now we can add the fractions: 332/72 + 54/72 = (332 + 54)/72 = 386/72 To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2. 386/72 = (386/2)/(72/2) = 193/36 Therefore, the summation of 83/18 and 6/8 is 193/36. ### Answer: 193/36
Expected answer: 193/36
Correct? Yes
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
Claude-3 Sonnet:
To add fractions with different denominators, we need to find a common denominator and convert the fractions to equivalent fractions with the same denominator. Then, we can add the numerators and keep the common denominator. Step 1: Find the least common multiple (LCM) of the denominators 69 and 61. LCM of 69 and 61 = 4189 Step 2: Convert the fractions to equivalent fractions with the common denominator 4189. 37/69 = (37 × 61)/4189 67/61 = (67 × 69)/4189 Step 3: Add the numerators and keep the common denominator. (37 × 61)/4189 + (67 × 69)/4189 = (2257 + 4623)/4189 = 6880/4189 Step 4: Simplify the fraction if possible. 6880/4189 = 1.64 (approximately) Therefore, the result of the addition of the fractions 37/69 and 67/61 is approximately 1.64. ### Answer: 1.64
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
Claude-3 Sonnet:
To find the sum of 89/84 and 75/34, we need to find a common denominator for both fractions. The least common multiple (LCM) of 84 and 34 is 252. So, we convert both fractions to have a denominator of 252. 89/84 = (89 × 3)/252 = 267/252 75/34 = (75 × 7)/238 = 525/252 Now we can add the fractions: 267/252 + 525/252 = (267 + 525)/252 = 792/252 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 12. 792/252 = (792/12)/(252/12) = 66/21 Therefore, the sum of 89/84 and 75/34 is 66/21. ### Answer: 66/21
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
Claude-3 Sonnet:
To add fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator. Then, we can add the numerators and keep the LCD as the denominator. Step 1: Find the LCD of 78 and 83. The LCD is the least common multiple of 78 and 83, which is 6,534. Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator. 51/78 = (51 × 84)/6,534 44/83 = (44 × 79)/6,534 Step 3: Add the numerators and keep the LCD as the denominator. (51 × 84)/6,534 + (44 × 79)/6,534 = (4,284 + 3,476)/6,534 = 7,760/6,534 Step 4: Simplify the fraction, if possible. 7,760/6,534 = 1 19/6,534 Therefore, the result of adding 51/78 and 44/83 is 1 19/6,534. ### Answer: 1 19/6,534
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
Claude-3 Sonnet:
To calculate the sum of two fractions, we need to find a common denominator and then add the numerators. The least common multiple (LCM) of 85 and 55 is 1105. So, we convert the fractions to equivalent fractions with a denominator of 1105: 99/85 = (99/85) * (13/13) = 1287/1105 77/55 = (77/55) * (20/20) = 1540/1105 Now we can add the numerators: 1287/1105 + 1540/1105 = 2827/1105 To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 7. 2827/7 = 404 1105/7 = 158 Therefore, the sum of 99/85 and 77/55 is 404/158. ### Answer: 404/158
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 Sonnet:
To solve this problem, we need to perform the division operations and then subtract the resulting values. Given: - 97 / 56 - 31 / 52 Step 1: Divide 97 by 56. 97 / 56 = 1.732142857 (repeating decimal) Step 2: Divide 31 by 52. 31 / 52 = 0.596153846 (repeating decimal) Step 3: Subtract the second value from the first value. 1.732142857 - 0.596153846 = 1.135989011 (repeating decimal) Step 4: Convert the repeating decimal to a fraction. To convert a repeating decimal to a fraction, we can use the following steps: a) Let x = 1.135989011... b) Multiply both sides by 10^n, where n is the number of digits in the repeating block (in this case, n = 6). 10^6 x = 1135989.011... c) Subtract the original equation from the new equation. 10^6 x - x = 1135989 - 1.135989011... (10^6 - 1) x = 1135988 d) Divide both sides by (10^6 - 1) to find x. x = 1135988 / (10^6 - 1) x = 1135988 / 999999 x = 1135 / 999 Therefore, the value of 97 / 56 - 31 / 52 can be represented as the simplified fraction 1135 / 999. ### Answer: 1135/999
Expected answer: 827/728
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
Claude-3 Sonnet:
To calculate the result of (78 / 74) + (72 / 51), we need to find a common denominator for the fractions and then add the fractions.
Step 1: Find the least common multiple (LCM) of 74 and 51 to get the common denominator.
LCM of 74 and 51 = 3774
Step 2: Convert the fractions to equivalent fractions with the common denominator of 3774.
78/74 = (78 × 51)/3774
72/51 = (72 × 74)/3774
Step 3: Add the fractions.
(78 × 51)/3774 + (72 × 74)/3774 = (3978 + 5328)/3774
= 9306/3774
Step 4: Simplify the fraction if possible.
9306/3774 = 2.467 (rounded to 3 decimal places)
### Answer: 2.467
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 Sonnet:
To solve this problem, we need to perform the division operations and then subtract the results. Given: - (33 / 23) - (12 / 75) Step 1: Perform the division operations. 33 / 23 = 1.43478... 12 / 75 = 0.16 Step 2: Subtract the results. (33 / 23) - (12 / 75) = 1.43478... - 0.16 = 1.27478... To express the answer as a fraction, we need to convert the decimal value to a fraction. Step 3: Convert the decimal value to a fraction. 1.27478... = 1 + 27478/100000 = 1 + (27478 × 4) / 400000 = 1 + 109912/400000 = 509912/400000 Therefore, the result of the operation (33 / 23) - (12 / 75) expressed as a fraction is: ### Answer: 509912/400000
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 Sonnet:
To solve this problem, we need to perform the division operations and then subtract the results. Given: - 85/42 - 98/99 Step 1: Divide 85 by 42. 85/42 = 2.02380952380952 Step 2: Divide 98 by 99. 98/99 = 0.989898989898989 Step 3: Subtract the second result from the first result. 2.02380952380952 - 0.989898989898989 = 1.03391053391053 Step 4: Round the result to the nearest hundredth. 1.03391053391053 rounded to the nearest hundredth is 1.03 Therefore, the result of the operation 85/42 - 98/99, simplified 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 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of 30 and 77 to get the common denominator. LCM of 30 and 77 = 1770 Step 2: Convert the fractions to equivalent fractions with the common denominator of 1770. 19/30 = (19 × 59)/1770 = 1121/1770 75/77 = (75 × 23)/1770 = 1725/1770 Step 3: Add the fractions with the common denominator. (1121/1770) + (1725/1770) = (1121 + 1725)/1770 = 2846/1770 Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by the GCF. GCF of 2846 and 1770 = 2 2846/1770 = (2846/2) / (1770/2) = 1423/885 Therefore, the sum of 19/30 and 75/77 expressed as a simplified fraction is 1423/885. ### Answer: 1423/885
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 Sonnet:
To find the sum of two fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator. Then, we can add the numerators and keep the LCD as the denominator. Given fractions: 57/66 and 39/64 Step 1: Find the LCD of 66 and 64. The LCD is the least common multiple of 66 and 64, which is 1056. Step 2: Convert both fractions to equivalent fractions with the LCD as the denominator. 57/66 = (57 × 16)/1056 = 912/1056 39/64 = (39 × 16.5)/1056 = 643.5/1056 Step 3: Add the numerators and keep the LCD as the denominator. (912/1056) + (643.5/1056) = (912 + 643.5)/1056 = 1555.5/1056 Therefore, the sum of 57/66 and 39/64 is 1555.5/1056. ### Answer: 1555.5/1056
Expected answer: 1037/704
Correct? Yes
Problem: After finding the sum of 57/66 and 39/64, what is its sum with 10/29? Please express your answer as a fraction.
Claude-3 Sonnet:
Okay, let's find the sum of 1555.5/1056 and 10/29. First, we need to find the LCD of 1056 and 29. The LCD is the least common multiple of 1056 and 29, which is 30624. Next, we convert both fractions to equivalent fractions with the LCD as the denominator. 1555.5/1056 = (1555.5 × 29)/30624 = 45109.5/30624 10/29 = (10 × 1056)/30624 = 10560/30624 Now, we can add the numerators and keep the LCD as the denominator. (45109.5/30624) + (10560/30624) = (45109.5 + 10560)/30624 = 55669.5/30624 Therefore, the sum of 1555.5/1056 and 10/29 is 55669.5/30624. ### Answer: 55669.5/30624
Expected answer: 37113/20416
Correct? No
Problem: When we earlier calculated the sum of two fractions, we used 57/66 and 39/64. However, there was a mistake in our calculation and the second fraction should have been 49/64 instead. Could you please recalculate and find the correct sum of the fractions 57/66 and 49/64?
Claude-3 Sonnet:
Sure, let's recalculate the sum of 57/66 and 49/64. Given fractions: 57/66 and 49/64 Step 1: Find the LCD of 66 and 64. The LCD is the least common multiple of 66 and 64, which is 1056. Step 2: Convert both fractions to equivalent fractions with the LCD as the denominator. 57/66 = (57 × 16)/1056 = 912/1056 49/64 = (49 × 16.5)/1056 = 807/1056 Step 3: Add the numerators and keep the LCD as the denominator. (912/1056) + (807/1056) = (912 + 807)/1056 = 1719/1056 Therefore, the sum of 57/66 and 49/64 is 1719/1056. ### Answer: 1719/1056
Expected answer: 1147/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
Claude-3 Sonnet:
To find the sum of 80/13 and 2/48, we need to find a common denominator for both fractions. The least common multiple (LCM) of 13 and 48 is 624. So, we convert both fractions to have a denominator of 624. 80/13 = (80 × 48)/624 = 3840/624 2/48 = (2 × 13)/624 = 26/624 Now we can add the fractions: 3840/624 + 26/624 = 3866/624 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 2. 3866/624 = 1933/312 Therefore, the sum of 80/13 and 2/48 is 1933/312. ### Answer: 1933/312
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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 80/13 and 2/48: 80/13 = 6.15384615... (repeating decimal) 2/48 = 0.04166666... (repeating decimal) Sum = 6.15384615... + 0.04166666... = 6.19551282... (repeating decimal) 2. Now, we need to add this result to itself: 6.19551282... + 6.19551282... = 12.39102564... (repeating decimal) To express the final answer as a fraction: 12.39102564... = 12 + 39/99 (converting the repeating decimal to a fraction) Therefore, the sum of (80/13 + 2/48) added to itself is 12 + 39/99. ### Answer: 12 + 39/99
Expected answer: 1933/156
Correct? No
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 Sonnet:
To find the sum of 80/5 and 2/48, we need to find a common denominator for both fractions. The least common multiple (LCM) of 5 and 48 is 240. So, we convert both fractions to have a denominator of 240. 80/5 = (80 × 48)/240 = 3840/240 2/48 = (2 × 5)/240 = 10/240 Now we can add the fractions: 3840/240 + 10/240 = 3850/240 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 10. 3850/240 = 385/24 Therefore, the sum of 80/5 and 2/48 is 385/24. ### Answer: 385/24
Expected answer: 385/24
Correct? Yes
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
Claude-3 Sonnet:
To calculate the result of the operation ((55 / 30) - (1 / 72)), we need to perform the following steps: 1. Calculate 55 / 30 55 / 30 = 1.83333... 2. Calculate 1 / 72 1 / 72 = 0.01388... 3. Subtract the second result from the first result 1.83333... - 0.01388... = 1.81945... Therefore, the result of the operation ((55 / 30) - (1 / 72)) is approximately 1.81945. ### Answer: 1.81945
Expected answer: 131/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
Claude-3 Sonnet:
To calculate the sum of two fractions, we need to find a common denominator and then add the numerators. Step 1: Find the least common multiple (LCM) of the denominators 21 and 86. The LCM of 21 and 86 is 1806. Step 2: Convert the fractions to equivalent fractions with the common denominator 1806. 69/21 = (69 × 86)/1806 = 5934/1806 71/86 = (71 × 21)/1806 = 1491/1806 Step 3: Add the numerators of the equivalent fractions. 5934/1806 + 1491/1806 = 7425/1806 Step 4: Simplify the resulting fraction, if possible. 7425/1806 = (7425/1806) × (1/1) = (7425/1) / (1806/1) = 7425/1806 Therefore, the sum of the fractions 69/21 and 71/86 is 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 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 69/21 and 71/86: LCM of 21 and 86 = 1806 69/21 = (69 × 86)/1806 = 5934/1806 71/86 = (71 × 21)/1806 = 1491/1806 5934/1806 + 1491/1806 = 7425/1806 2. Now we need to add 86/62 to 7425/1806: LCM of 1806 and 62 = 112172 7425/1806 = (7425 × 62)/112172 = 461350/112172 86/62 = (86 × 1806)/112172 = 154716/112172 461350/112172 + 154716/112172 = 616066/112172 3. Simplifying the resulting fraction: 616066/112172 = (616066/112172) × (1/1) = (616066/2) / (112172/2) = 308033/56086 Therefore, the result of adding the sum of 69/21 and 71/86 to 86/62 is 308033/56086. ### Answer: 308033/56086
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 Sonnet:
To calculate the sum of the fractions 69/60 and 71/86, we need to find a common denominator and then add the numerators. Step 1: Find the least common multiple (LCM) of the denominators 60 and 86. The LCM of 60 and 86 is 1720. Step 2: Convert the fractions to equivalent fractions with the common denominator 1720. 69/60 = (69 × 28.67)/1720 = 1977/1720 (where 28.67 = 1720/60) 71/86 = (71 × 20)/1720 = 1420/1720 Step 3: Add the numerators of the equivalent fractions. 1977/1720 + 1420/1720 = 3397/1720 Step 4: Simplify the resulting fraction, if possible. 3397/1720 is already in its simplest form. Therefore, the sum of the fractions 69/60 and 71/86 is 3397/1720. ### Answer: 3397/1720
Expected answer: 1699/860
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 60 and 45. The LCM of 60 and 45 is 180. Step 2: Convert the fractions to equivalent fractions with the common denominator of 180. 24/60 = (24/60) × (3/3) = 72/180 42/45 = (42/45) × (4/4) = 168/180 Step 3: Add the fractions with the common denominator. (72/180) + (168/180) = 240/180 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 240 and 180 is 60. 240/180 = (240/60) / (180/60) = 4/3 Therefore, the sum of 24/60 and 42/45 as a simplified fraction is 4/3. ### Answer: 4/3
Expected answer: 4/3
Correct? Yes
Problem: If we take the sum of 24/60 and 42/45 from the previous problem, and add it to the fraction 66/12, what is the new total? Answer as a simplified fraction.
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. We know from the previous problem that the sum of 24/60 and 42/45 is 4/3. 2. Now we need to add 4/3 to 66/12. 3. To add fractions with different denominators, we need to find the least common denominator (LCD). The LCD of 3 and 12 is 12. 4. Convert 4/3 to an equivalent fraction with the denominator of 12: 4/3 = (4/3) × (4/4) = 16/12 5. Now we can add the fractions: 16/12 + 66/12 = 82/12 6. Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 82 and 12 is 2. 82/12 = (82/2) / (12/2) = 41/6 Therefore, the sum of 4/3 and 66/12 as a simplified fraction is 41/6. ### Answer: 41/6
Expected answer: 41/6
Correct? Yes
Problem: In the previous problem, suppose the fraction we added to 24/60 was actually 42/67, not 42/45. What would the new total be? Answer as a simplified fraction.
Claude-3 Sonnet:
Okay, let's solve this new problem. We need to find the sum of 24/60 and 42/67. Step 1: Find the least common multiple (LCM) of the denominators 60 and 67. The LCM of 60 and 67 is 1340. Step 2: Convert the fractions to equivalent fractions with the common denominator of 1340. 24/60 = (24/60) × (22/22) = 528/1340 42/67 = (42/67) × (20/20) = 840/1340 Step 3: Add the fractions with the common denominator. (528/1340) + (840/1340) = 1368/1340 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 1368 and 1340 is 4. 1368/1340 = (1368/4) / (1340/4) = 342/335 Therefore, the sum of 24/60 and 42/67 as a simplified fraction is 342/335. ### Answer: 342/335
Expected answer: 344/335
Correct? No
Problem: What is the sum of 64/76 and 35/33?
Claude-3 Sonnet:
To find the sum of 64/76 and 35/33, we need to find a common denominator for both fractions. The least common multiple (LCM) of 76 and 33 is 2508. So, we convert both fractions to have a denominator of 2508. 64/76 = (64 × 33)/2508 = 2112/2508 35/33 = (35 × 76)/2508 = 2660/2508 Now we can add the fractions: 2112/2508 + 2660/2508 = 4772/2508 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 4. 4772/2508 = (4772/4)/(2508/4) = 1193/627 Therefore, the sum of 64/76 and 35/33 is 1193/627. ### Answer: 1193/627
Expected answer: 1193/627
Correct? Yes
Problem: After finding the sum of 64/76 and 35/33, what is the result when you add 47/38 to that sum?
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the sum of 64/76 and 35/33: * We found this in the previous question to be 1193/627 2. Now we need to add 47/38 to 1193/627 * To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators * The LCM of 627 and 38 is 23826 * So we convert both fractions to have a denominator of 23826 * 1193/627 = (1193 * 38)/23826 = 45334/23826 * 47/38 = (47 * 627)/23826 = 29469/23826 * Now we can add: 45334/23826 + 29469/23826 = 74803/23826 3. To simplify the fraction 74803/23826, we divide the numerator and denominator by their greatest common factor, which is 7 * 74803/23826 = (74803/7)/(23826/7) = 10686/3404 Therefore, the sum of 64/76, 35/33, and 47/38 is 10686/3404. ### Answer: 10686/3404
Expected answer: 3937/1254
Correct? No
Problem: After reconsidering the previous problem, suppose initially there were 43/76 of an orange instead of 64/76. What will be the new sum when you add it to the same 35/33 of an apple?
Claude-3 Sonnet:
Okay, let's recalculate the sum with the new fraction 43/76 instead of 64/76. We need to find a common denominator for 43/76 and 35/33. The least common multiple (LCM) of 76 and 33 is 2508. So, we convert both fractions to have a denominator of 2508. 43/76 = (43 × 33)/2508 = 1419/2508 35/33 = (35 × 76)/2508 = 2660/2508 Now we can add the fractions: 1419/2508 + 2660/2508 = 4079/2508 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 7. 4079/2508 = (4079/7)/(2508/7) = 583/358 Therefore, the sum of 43/76 and 35/33 is 583/358. ### Answer: 583/358
Expected answer: 4079/2508
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 Sonnet:
To solve this problem, we need to find a common denominator for the two fractions and then add the fractions. Step 1: Find the least common multiple (LCM) of 16 and 10 to get the common denominator. LCM of 16 and 10 = 80 Step 2: Convert the fractions to equivalent fractions with the common denominator of 80. 47/16 = (47 × 5)/80 = 235/80 96/10 = (96 × 8)/80 = 768/80 Step 3: Add the fractions. (235/80) + (768/80) = 1003/80 Step 4: Express the result as a mixed fraction if necessary. 1003/80 = 12 + (23/80) Therefore, the sum of 47/16 and 96/10 expressed as a mixed fraction is 12 23/80. ### Answer: 12 23/80
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
Claude-3 Sonnet:
To solve this problem, we need to perform the following steps: 1. Evaluate the expression (58 / 2) 58 / 2 = 29 2. Evaluate the expression (31 / 32) 31 / 32 = 0.96875 3. Add the results of the two expressions 29 + 0.96875 = 29.96875 Therefore, the result of the operation (58 / 2) + (31 / 32) is 29.96875. ### 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 Sonnet:
Okay, let's solve this step-by-step: 1. Calculate (58 / 2) + (31 / 32) (58 / 2) = 29 (31 / 32) = 0.96875 29 + 0.96875 = 29.96875 2. Calculate 90 / 58 90 / 58 = 1.55172413793103 3. Subtract 90 / 58 from the previous result 29.96875 - 1.55172413793103 = 28.41702586206897 Therefore, the final result after subtracting 90 / 58 from the operation (58 / 2) + (31 / 32) is 28.41702586206897. ### 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 Sonnet:
Okay, let's solve this new problem step-by-step: 1. Evaluate the expression (58 / 2) 58 / 2 = 29 2. Evaluate the expression (10 / 32) 10 / 32 = 0.3125 3. Add the results of the two expressions 29 + 0.3125 = 29.3125 Therefore, the result of the operation (58 / 2) + (10 / 32) is 29.3125. ### 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 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 90 and 26. The LCM of 90 and 26 is 90 × 26 = 2340. Step 2: Convert the fractions to equivalent fractions with the common denominator of 2340. 26/90 = (26/90) × (26/26) = 676/2340 50/26 = (50/26) × (90/90) = 1700/2340 Step 3: Add the fractions with the common denominator. (676/2340) + (1700/2340) = 2376/2340 Step 4: Simplify the fraction if possible. 2376/2340 = 1188/1170 Therefore, the sum of 26/90 and 50/26 as a fraction is 1188/1170. ### Answer: 1188/1170
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
Claude-3 Sonnet:
To calculate the sum of 80/98 and 92/82, we need to find a common denominator for both fractions. The least common multiple (LCM) of 98 and 82 is 8006. So, we convert both fractions to have a denominator of 8006. 80/98 = (80 × 81)/8006 = 6480/8006 92/82 = (92 × 97)/8006 = 8924/8006 Now we can add the fractions: 6480/8006 + 8924/8006 = 15404/8006 To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 2. 15404/8006 = (15404/2)/(8006/2) = 7702/4003 Therefore, the sum of 80/98 and 92/82 is 7702/4003. ### Answer: 7702/4003
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
Claude-3 Sonnet:
To calculate the sum of 89/44 and 69/5, we need to find a common denominator for both fractions. The least common multiple (LCM) of 44 and 5 is 220. So, we convert both fractions to have a denominator of 220. 89/44 = (89 × 5)/220 = 445/220 69/5 = (69 × 44)/220 = 3036/220 Now we can add the fractions: 445/220 + 3036/220 = 3481/220 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 1. Therefore, the sum of 89/44 and 69/5 is 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 Sonnet:
Okay, let's calculate this step-by-step: 1. First, we need to find the sum of 89/44 and 69/5: 89/44 + 69/5 = (89 × 5 + 69 × 44) / (44 × 5) = (445 + 3036) / 220 = 3481 / 220 2. Now, we need to add this sum (3481/220) to itself: (3481/220) + (3481/220) = (3481 + 3481) / 220 = 6962 / 220 = 31.6454545... To simplify the fraction: The greatest common divisor (GCD) of 6962 and 220 is 2. 6962 / 2 = 3481 220 / 2 = 110 Therefore, the result of adding the sum of 89/44 and 69/5 to itself is: 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 Sonnet:
Okay, let's calculate the sum of 89/44 and 69/38. First, we need to find the least common multiple (LCM) of 44 and 38 to get a common denominator. The LCM of 44 and 38 is 532. Now, we convert both fractions to have a denominator of 532: 89/44 = (89 × 12)/532 = 1068/532 69/38 = (69 × 14)/532 = 966/532 Next, we add the fractions: 1068/532 + 966/532 = 2034/532 To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 2. 2034/532 = (2034/2)/(532/2) = 1017/266 Therefore, the sum of 89/44 and 69/38 is 1017/266. ### Answer: 1017/266
Expected answer: 3209/836
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
Claude-3 Sonnet:
To calculate the given expression, we need to perform the following steps: Step 1: Calculate 79/32 79/32 = 2.46875 Step 2: Calculate 52/55 52/55 = 0.945454545... Step 3: Subtract 52/55 from 79/32 79/32 - 52/55 = 2.46875 - 0.945454545... = 1.523295455... Therefore, the value of the expression 79/32 - 52/55 is approximately 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 Sonnet:
To solve this problem, we need to find the usual length of the pieces and then subtract 18/90 feet from it. Given information: - Each piece of wood is 45/2 feet long. - The piece they sold is 18/90 feet shorter than the usual length. Step 1: Find the usual length of the pieces. Usual length = 45/2 feet Usual length = 22.5 feet Step 2: Subtract 18/90 feet from the usual length to find the length of the piece they sold. Length of the piece sold = Usual length - 18/90 feet Length of the piece sold = 22.5 feet - (18/90) feet Length of the piece sold = 22.5 feet - 0.2 feet Length of the piece sold = 22.3 feet Therefore, the length of the piece of wood that Wooden Treasures sold is 22.3 feet. ### Answer: 22.3
Expected answer: 223/10
Correct? Yes
Problem: Now, suppose Wooden Treasures had initially cut their log into piece of lengths (45/2) feet. After, they sold a piece that was 62/90 feet shorter than the standard length. How long was the piece they sold this time?
Claude-3 Sonnet:
To solve this problem, we need to find the standard length of the pieces and then subtract 62/90 feet from it. Given information: - The standard length of each piece is (45/2) feet. - The piece they sold is 62/90 feet shorter than the standard length. Step 1: Find the standard length of the pieces. Standard length = 45/2 feet Standard length = 22.5 feet Step 2: Subtract 62/90 feet from the standard length to find the length of the piece they sold. Length of the piece sold = Standard length - 62/90 feet Length of the piece sold = 22.5 feet - (62/90) feet Length of the piece sold = 22.5 feet - 0.689 feet Length of the piece sold = 21.811 feet Therefore, the length of the piece of wood that Wooden Treasures sold this time is 21.811 feet. ### Answer: 21.811
Expected answer: 1963/90
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
Claude-3 Sonnet:
To find the sum of two fractions, we need to find a common denominator and then add the fractions. Step 1: Find the least common multiple (LCM) of the denominators 92 and 74. The LCM of 92 and 74 is 1036. Step 2: Convert the fractions to equivalent fractions with the common denominator 1036. 99/92 = (99 × 11)/1036 15/74 = (15 × 14)/1036 Step 3: Add the fractions. (99 × 11)/1036 + (15 × 14)/1036 = (1089 + 210)/1036 = 1299/1036 Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). The GCD of 1299 and 1036 is 7. 1299/1036 = (1299/7)/(1036/7) = 185/148 Therefore, the sum of 99/92 and 15/74 as a simplified fraction is 185/148. ### Answer: 185/148
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
Claude-3 Sonnet:
To calculate 54/1 + 62/30, we first need to find the common denominator for the fractions. The common denominator is the least common multiple (LCM) of the denominators, which in this case is 30. So, we need to convert 54/1 to an equivalent fraction with a denominator of 30. 54/1 = 54/1 * 30/30 = 1620/30 Now we can add the fractions: 1620/30 + 62/30 = (1620 + 62)/30 = 1682/30 To express the answer in simplest terms, we need to find the greatest common factor (GCF) of the numerator and denominator and divide both by that number. The GCF of 1682 and 30 is 2. 1682/2 = 841 30/2 = 15 Therefore, the simplest form of the answer is 841/15. ### Answer: 841/15
Expected answer: 841/15
Correct? Yes
Problem: If we subtract 53/41 from the result of 54/1 + 62/30, what is the new result? Express your answer in simplest terms.
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1. First, we need to find the result of 54/1 + 62/30 (as we did in the previous question): 54/1 + 62/30 = 1620/30 + 62/30 = 1682/30 = 841/15 2. Now, we need to subtract 53/41 from 841/15. To do this, we need to find a common denominator for 841/15 and 53/41. The least common multiple (LCM) of 15 and 41 is 615. 3. Convert the fractions to equivalent fractions with a denominator of 615: 841/15 = 841/15 * 41/41 = 34481/615 53/41 = 53/41 * 15/15 = 795/615 4. Subtract the fractions: 34481/615 - 795/615 = 33686/615 5. Express the result in simplest terms by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by that number. The GCF of 33686 and 615 is 1. Therefore, the simplest form is 33686/615. ### Answer: 33686/615
Expected answer: 33686/615
Correct? Yes
Problem: If we had originally started with 93 instead of 54, and added 62/30 to that, what would be the new result? Express the answer in simplest terms.
Claude-3 Sonnet:
Okay, let's solve this step-by-step: 1) We start with 93/1 instead of 54/1 2) We need to convert 93/1 to an equivalent fraction with a denominator of 30 93/1 = 93/1 * 30/30 = 2790/30 3) Now we add 62/30 to 2790/30 2790/30 + 62/30 = (2790 + 62)/30 = 2852/30 4) To express the answer in simplest terms, we need to find the greatest common factor (GCF) of the numerator and denominator and divide both by that number. 5) The GCF of 2852 and 30 is 2. 2852/2 = 1426 30/2 = 15 6) Therefore, the simplest form of the answer is 1426/15. ### Answer: 1426/15
Expected answer: 1426/15
Correct? Yes
Problem: What value do you get by adding 85/29 and 47/7?
Claude-3 Sonnet:
To add fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator. Then, we can add the numerators and keep the denominator the same. Given fractions: 85/29 and 47/7 Step 1: Find the LCD of 29 and 7. LCD = 29 × 7 = 203 Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator. 85/29 = (85 × 7)/203 47/7 = (47 × 29)/203 Step 3: Add the numerators and keep the denominator the same. (85 × 7)/203 + (47 × 29)/203 = (595 + 1363)/203 = 1958/203 Therefore, the sum of 85/29 and 47/7 is 1958/203. ### Answer: 1958/203
Expected answer: 1958/203
Correct? Yes
Problem: After finding the result of adding 85/29 and 47/7, what is the new total if you also add 81/42?
Claude-3 Sonnet:
Okay, let's add 81/42 to the previous result of 1958/203. First, we need to find the LCD of 203 and 42. LCD = 203 × 42 = 8526 Now, we convert all fractions to equivalent fractions with the LCD as the denominator. 1958/203 = (1958 × 42)/8526 81/42 = (81 × 203)/8526 Then, we add the numerators and keep the denominator the same. (1958 × 42)/8526 + (81 × 203)/8526 = (82236 + 16443)/8526 = 98679/8526 Therefore, the sum of 85/29, 47/7, and 81/42 is 98679/8526. ### Answer: 98679/8526
Expected answer: 4699/406
Correct? Yes
Problem: After calculating the result from the previous problem, consider a new situation: You have now 85/64 of a pound of oranges and 47/7 pounds of apples. What is the new total weight of your fruits in pounds?
Claude-3 Sonnet:
To solve this problem, we need to convert both fractions to have the same denominator, and then add the numerators while keeping the denominator the same. Given: - Weight of oranges = 85/64 pounds - Weight of apples = 47/7 pounds Step 1: Find the least common denominator (LCD) of 64 and 7. LCD = 64 × 7 = 448 Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator. 85/64 = (85 × 7)/448 47/7 = (47 × 64)/448 Step 3: Add the numerators and keep the denominator the same. (85 × 7)/448 + (47 × 64)/448 = (595 + 3008)/448 = 3603/448 Step 4: Convert the resulting fraction to a mixed number (if possible). 3603/448 = 8 1/448 pounds Therefore, the total weight of your fruits is 8 1/448 pounds. ### Answer: 8 1/448
Expected answer: 3603/448
Correct? No