Problem: John has been learning to add and subtract fractions at school. He was given a problem during his homework that puzzled him. He had to take the sum of 48/56 and 95/23 and then subtract 34/26 from the result. What was the value that John found for this operation? Answer in simplest form.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, we need to find the sum of 48/56 and 95/23.
   To add fractions, we need to find the least common denominator (LCD).
   The LCD of 56 and 23 is 1288 (56 × 23 = 1288).

   Now, we convert the fractions to equivalent fractions with the LCD:
   48/56 = (48 × 23) / 1288 = 1104/1288
   95/23 = (95 × 56) / 1288 = 5320/1288

   Add the fractions: 1104/1288 + 5320/1288 = 6424/1288

2. Next, we subtract 34/26 from the result.
   The LCD of 1288 and 26 is 1288 (1288 is already divisible by 26).

   Convert 34/26 to an equivalent fraction with the LCD:
   34/26 = (34 × 49) / 1288 = 1666/1288

   Subtract the fractions: 6424/1288 - 1666/1288 = 4758/1288

3. Simplify the result:
   4758/1288 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF).
   The GCF of 4758 and 1288 is 14.

   4758/1288 = (4758 ÷ 14) / (1288 ÷ 14) = 339/92

Therefore, the value John found for this operation, in simplest form, is 339/92.

### Answer: 339/92

Expected answer: 7702/2093

Correct? No

Problem: First, add the fractions 88/9 and 28/65. Then subtract the fraction 18/37 from the result. What is the result expressed as a simple fraction?

Claude-3 Opus:

Okay, let's solve this problem step by step:

1. Add the fractions 88/9 and 28/65:
   To add fractions with different denominators, we need to find the least common denominator (LCD).
   LCD of 9 and 65 = 9 × 65 = 585
   Now, we convert both fractions to equivalent fractions with the LCD:
   88/9 = 88 × 65/9 × 65 = 5720/585
   28/65 = 28 × 9/65 × 9 = 252/585
   Add the numerators: 5720/585 + 252/585 = 5972/585

2. Subtract the fraction 18/37 from the result:
   The result from step 1 is 5972/585. Now we need to subtract 18/37 from this fraction.
   First, find the LCD of 585 and 37:
   LCD of 585 and 37 = 21645
   Convert both fractions to equivalent fractions with the LCD:
   5972/585 = 5972 × 37/585 × 37 = 220964/21645
   18/37 = 18 × 585/37 × 585 = 10530/21645
   Subtract the numerators: 220964/21645 - 10530/21645 = 210434/21645

3. Simplify the resulting fraction:
   210434/21645 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF).
   GCF of 210434 and 21645 = 1
   Therefore, the fraction cannot be simplified further.

### Answer: 210434/21645

Expected answer: 210434/21645

Correct? Yes

Problem: What is the result of (63 / 41) + (44 / 50) when simplified to the lowest terms?

Claude-3 Opus:

To simplify (63 / 41) + (44 / 50) to the lowest terms, we need to perform the division and addition, and then find a common denominator to add the fractions.

1. Simplify 63 / 41:
   63 / 41 = 1.536585... (rounded)
   This cannot be simplified further as the result is not a rational number.

2. Simplify 44 / 50:
   44 / 50 = 22 / 25 (divide both numerator and denominator by their common factor of 2)

3. Add the fractions:
   (63 / 41) + (22 / 25)

   To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 41 and 25.
   LCM(41, 25) = 1025

   Now, we convert both fractions to equivalent fractions with the common denominator:

   (63 / 41) = (63 * 25) / (41 * 25) = 1575 / 1025
   (22 / 25) = (22 * 41) / (25 * 41) = 902 / 1025

   Add the fractions:
   (1575 / 1025) + (902 / 1025) = (1575 + 902) / 1025 = 2477 / 1025

   This fraction cannot be simplified further as the numerator and denominator have no common factors other than 1.

### Answer: 2477 / 1025

Expected answer: 2477/1025

Correct? Yes

Problem: John had 71/41 of a cake left and Emily added 41/77 of another cake to it. How much cake is there in total? Give your answer as a simplified fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. John had 71/41 of a cake left.
2. Emily added 41/77 of another cake to it.
3. To find the total amount of cake, we need to add these two fractions:

   71/41 + 41/77

4. To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
   LCM(41, 77) = 3157

5. Now, we can convert both fractions to equivalent fractions with the common denominator of 3157:

   71/41 = (71 × 77) / (41 × 77) = 5467/3157
   41/77 = (41 × 41) / (77 × 41) = 1681/3157

6. Add the fractions:

   5467/3157 + 1681/3157 = (5467 + 1681) / 3157 = 7148/3157

7. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
   GCD(7148, 3157) = 1

   The fraction 7148/3157 is already in its simplest form.

### Answer: 7148/3157

Expected answer: 7148/3157

Correct? Yes

Problem: Calculate the result of 10/65 + 56/35. Answer as a simple fraction.

Claude-3 Opus:

To calculate 10/65 + 56/35, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 35.

LCM(65, 35) = 455

Now, we convert both fractions to equivalent fractions with the common denominator:

10/65 = (10 × 7) / (65 × 7) = 70/455
56/35 = (56 × 13) / (35 × 13) = 728/455

Add the numerators and keep the common denominator:

70/455 + 728/455 = (70 + 728) / 455 = 798/455

Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF):

GCF(798, 455) = 7

(798 ÷ 7) / (455 ÷ 7) = 114/65

### Answer: 114/65

Expected answer: 114/65

Correct? Yes

Problem: What is the result of adding 75/81 and 97/47? Leave your answer as an unsimplified fraction.

Claude-3 Opus:

To add fractions with different denominators, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators.

The LCM of 81 and 47 is: 81 * 47 = 3807

Now, we need to convert each fraction to an equivalent fraction with the common denominator:

75/81 = (75 * 47) / (81 * 47) = 3525/3807
97/47 = (97 * 81) / (47 * 81) = 7857/3807

Adding the fractions:
(3525/3807) + (7857/3807) = (3525 + 7857) / 3807 = 11382/3807

Therefore, 75/81 + 97/47 = 11382/3807

### Answer: 11382/3807

Expected answer: 3794/1269

Correct? Yes

Problem: What is 88/1 - 38/53? Give your answer as a simplified fraction.

Claude-3 Opus:

To solve 88/1 - 38/53, we need to find a common denominator for the fractions, then subtract the numerators and simplify the result.

The common denominator is the least common multiple (LCM) of 1 and 53, which is 53.

88/1 = (88 × 53) / (1 × 53) = 4664/53
38/53 remains as it is.

Now, we can subtract the numerators:
4664/53 - 38/53 = (4664 - 38) / 53 = 4626/53

To simplify the fraction, we find the greatest common divisor (GCD) of 4626 and 53.
The GCD of 4626 and 53 is 1, so the fraction is already in its simplest form.

### Answer: 4626/53

Expected answer: 4626/53

Correct? Yes

Problem: Evaluate the expression ((80 / 94) + (78 / 59)). What is the answer in simplified form?

Claude-3 Opus:

To evaluate the expression ((80 / 94) + (78 / 59)), we need to perform the division operations and then add the results.

Step 1: Simplify 80 / 94
80 / 94 ≈ 0.8511 (rounded to 4 decimal places)

Step 2: Simplify 78 / 59
78 / 59 ≈ 1.3220 (rounded to 4 decimal places)

Step 3: Add the results from Step 1 and Step 2
0.8511 + 1.3220 ≈ 2.1731

To simplify this further, we can convert the decimal to a fraction:
2.1731 = 21731 / 10000

Simplifying the fraction:
21731 / 10000 = 2 1731/10000

### Answer: 2 1731/10000

Expected answer: 6026/2773

Correct? No

Problem: What is the sum of 89/56 and 48/50? Answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 89/56 and 48/50, we need to find a common denominator. The least common multiple of 56 and 50 is 1400.

89/56 = (89 × 25) / (56 × 25) = 2225/1400
48/50 = (48 × 28) / (50 × 28) = 1344/1400

Now we can add the fractions:

2225/1400 + 1344/1400 = (2225 + 1344) / 1400 = 3569/1400

To simplify this fraction, we divide both the numerator and denominator by their greatest common factor, which is 17.

3569/1400 = (3569 ÷ 17) / (1400 ÷ 17) = 209/82

Therefore, the sum of 89/56 and 48/50, expressed as a simplified fraction, is 209/82.

### Answer: 209/82

Expected answer: 3569/1400

Correct? No

Problem: What is the result when you subtract 38/87 from the sum of 96/11 and 12/5? Please leave your answer as a fraction.

Claude-3 Opus:

To solve this problem, let's break it down into steps:

1. Find the sum of 96/11 and 12/5.
   96/11 + 12/5 = (96 × 5 + 12 × 11) / (11 × 5)
                = (480 + 132) / 55
                = 612 / 55

2. Subtract 38/87 from the result of step 1.
   612/55 - 38/87 = (612 × 87 - 38 × 55) / (55 × 87)
                  = (53244 - 2090) / 4785
                  = 51154 / 4785

Therefore, the result is 51154/4785.

### Answer: 51154/4785

Expected answer: 51154/4785

Correct? Yes

Problem: If you have a number that's 82 divided by 9 and from this you subtract 82 divided by 63, what's the resulting value? Answer as a simplified fraction.

Claude-3 Opus:

Let's solve this step by step:

1) First, let's calculate 82 divided by 9:
   
   82 ÷ 9 = 9.111... (rounded to 3 decimal places)

2) Next, let's calculate 82 divided by 63:
   
   82 ÷ 63 = 1.301... (rounded to 3 decimal places)

3) Now, we subtract the second result from the first:
   
   9.111... - 1.301... = 7.810...

4) To express this as a simplified fraction, we need to write these numbers as fractions:
   
   9.111... = 9 1/9
   1.301... = 1 19/63

5) Now we can subtract these fractions:
   
   9 1/9 - 1 19/63 = (9 * 63 + 1 * 7) / 63 - (1 * 63 + 19 * 1) / 63
                   = (567 + 7) / 63 - (63 + 19) / 63
                   = 574 / 63 - 82 / 63
                   = 492 / 63

6) Simplifying this fraction:
   
   492 ÷ 63 = 7 remainder 51
   51 ÷ 3 = 17
   
   So, 492 / 63 simplifies to 7 17/21

### Answer: 7 17/21

Expected answer: 164/21

Correct? Yes

Problem: Calculate the value of 23/3 minus the sum of 80/91 and 26/24. Answer as a simple fraction.

Claude-3 Opus:

To calculate the value of 23/3 minus the sum of 80/91 and 26/24, we need to:
1. Convert the mixed number 23/3 to an improper fraction.
2. Add 80/91 and 26/24.
3. Subtract the sum from the improper fraction.
4. Simplify the result.

Step 1: Convert 23/3 to an improper fraction
23/3 = (2 × 3 + 3) / 3 = 9/3 = 3

Step 2: Add 80/91 and 26/24
To add fractions, we need a common denominator. The least common multiple of 91 and 24 is 728.
80/91 = (80 × 8) / (91 × 8) = 640/728
26/24 = (26 × 91) / (24 × 91) = 2366/2184
640/728 + 2366/2184 = (640 × 3) / (728 × 3) + 2366/2184 = 1920/2184 + 2366/2184 = 4286/2184

Step 3: Subtract the sum from the improper fraction
3 - 4286/2184 = (3 × 2184 - 4286) / 2184 = (6552 - 4286) / 2184 = 2266/2184

Step 4: Simplify the result
2266/2184 = 1133/1092

### Answer: 1133/1092

Expected answer: 6229/1092

Correct? No

Problem: What is the sum of 37/18 and 24/60 when simplified to the lowest terms?

Claude-3 Opus:

To find the sum of 37/18 and 24/60, we need to find a common denominator and then add the fractions. Let's solve this step by step.

Step 1: Simplify 24/60 to the lowest terms.
24/60 = 2/5 (divide both numerator and denominator by 12)

Step 2: Find the common denominator for 37/18 and 2/5.
The common denominator is the least common multiple (LCM) of 18 and 5.
LCM(18, 5) = 90

Step 3: Convert both fractions to equivalent fractions with the common denominator of 90.
37/18 = (37 × 5)/(18 × 5) = 185/90
2/5 = (2 × 18)/(5 × 18) = 36/90

Step 4: Add the fractions with the common denominator.
185/90 + 36/90 = (185 + 36)/90 = 221/90

Step 5: Simplify the result to the lowest terms.
221/90 = 17/90 (divide both numerator and denominator by 13)

Therefore, the sum of 37/18 and 24/60, when simplified to the lowest terms, is 17/90.

### Answer: 17/90

Expected answer: 221/90

Correct? No

Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 33/41 and 95/62, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 41 and 62.

LCM(41, 62) = 2542

Now, we convert both fractions to equivalent fractions with the common denominator:

33/41 = (33 × 62) / (41 × 62) = 2046/2542
95/62 = (95 × 41) / (62 × 41) = 3895/2542

Add the numerators and keep the common denominator:

2046/2542 + 3895/2542 = (2046 + 3895) / 2542 = 5941/2542

Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

GCF(5941, 2542) = 1

Since the GCF is 1, the fraction 5941/2542 is already in its simplest form.

### Answer: 5941/2542

Expected answer: 5941/2542

Correct? Yes

Problem: Solve ((30 / 11) + (72 / 38)) and then add the result to (81 / 34). Answer as a simplified fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's solve ((30 / 11) + (72 / 38)):
   
   30 / 11 = 2.727272...
   72 / 38 = 1.894736...
   
   2.727272... + 1.894736... = 4.622008...
   
2. Now, let's add the result to (81 / 34):
   
   81 / 34 = 2.382352...
   
   4.622008... + 2.382352... = 7.004360...
   
3. To express the result as a simplified fraction, we need to find the ratio of the result to 1:
   
   7.004360... / 1 = 7.004360... / 1
   
   Simplifying the fraction:
   
   7.004360... / 1 = 7004360... / 1000000...
   
   Simplifying further:
   
   7004360... / 1000000... = 7004360 / 1000000 (approximately)
   
   Reducing the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
   
   GCD(7004360, 1000000) = 40
   
   (7004360 / 40) / (1000000 / 40) = 175109 / 25000

### Answer: 175109 / 25000

Expected answer: 49773/7106

Correct? No

Problem: What is the result of adding (64 / 34) + (3 / 24) and then adding the result to (41 / 96)? Answer as a simplified fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's add (64 / 34) and (3 / 24):
   
   To add fractions with different denominators, we need to find the least common denominator (LCD). The LCD of 34 and 24 is 408.
   
   (64 / 34) = (64 × 12) / (34 × 12) = 768 / 408
   (3 / 24) = (3 × 17) / (24 × 17) = 51 / 408
   
   Now we can add these fractions:
   (768 / 408) + (51 / 408) = 819 / 408

2. Next, let's add the result (819 / 408) to (41 / 96):
   
   The LCD of 408 and 96 is 1224.
   
   (819 / 408) = (819 × 3) / (408 × 3) = 2457 / 1224
   (41 / 96) = (41 × 12) / (96 × 12) = 492 / 1224
   
   Adding these fractions:
   (2457 / 1224) + (492 / 1224) = 2949 / 1224

3. Now, let's simplify the fraction 2949 / 1224:
   
   2949 and 1224 have a common factor of 3.
   2949 ÷ 3 = 983
   1224 ÷ 3 = 408
   
   The simplified fraction is 983 / 408.

### Answer: 983 / 408

Expected answer: 3973/1632

Correct? No

Problem: Daniel has to solve a math problem for his homework that includes fractions. Initially, he has been asked to add 83/73 and 53/77. The result of this step he saved as 'w'. Then, he needs to add 80/76 to the result 'w'. How would he calculate the final answer in simplified fraction form?

Claude-3 Opus:

Let's solve this problem step by step:

1. First, we need to find the value of 'w' by adding 83/73 and 53/77.
   To add fractions, we need to find the least common multiple (LCM) of the denominators.
   LCM(73, 77) = 5621
   Now, we can convert the fractions to equivalent fractions with the common denominator:
   83/73 = 83 × 77/73 × 77 = 6391/5621
   53/77 = 53 × 73/77 × 73 = 3869/5621
   Adding these fractions:
   w = 6391/5621 + 3869/5621 = 10260/5621

2. Now, we need to add 80/76 to 'w'.
   Again, we need to find the LCM of the denominators:
   LCM(5621, 76) = 427196
   Converting the fractions to equivalent fractions with the common denominator:
   w = 10260/5621 = 10260 × 76/5621 × 76 = 779760/427196
   80/76 = 80 × 5621/76 × 5621 = 449680/427196
   Adding these fractions:
   779760/427196 + 449680/427196 = 1229440/427196

3. Simplifying the final answer:
   1229440/427196 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
   GCD(1229440, 427196) = 4
   1229440/427196 = (1229440 ÷ 4)/(427196 ÷ 4) = 307360/106799

Therefore, the final answer in simplified fraction form is 307360/106799.

### Answer: 307360/106799

Expected answer: 307360/106799

Correct? Yes

Problem: Add the following fractions and simplify your answer: 27/20 and 14/66.

Claude-3 Opus:

To add fractions with different denominators, we first need to find the least common denominator (LCD). The LCD is the least common multiple of the denominators.

Denominators: 20 and 66
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
LCD: 2 × 3 × 5 × 11 = 330

Now, we convert each fraction to an equivalent fraction with the LCD as the denominator:

27/20 = 27 × 330/20 × 330 = 8910/6600
14/66 = 14 × 330/66 × 330 = 4620/21780

Add the fractions:
8910/6600 + 4620/21780 = 8910/6600 + 1540/6600 = 10450/6600

Simplify the result by dividing the numerator and denominator by their greatest common factor (GCF):
Factors of 10450: 1, 2, 5, 10, 19, 22, 25, 38, 50, 95, 110, 190, 209, 418, 475, 550, 1045, 2090, 10450
Factors of 6600: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 25, 30, 33, 44, 50, 55, 60, 66, 75, 100, 110, 132, 150, 165, 200, 220, 264, 275, 300, 330, 440, 550, 600, 660, 825, 1100, 1320, 1650, 2200, 3300, 6600
GCF: 550

10450/6600 ÷ 550/550 = 19/12

### Answer: 19/12

Expected answer: 1031/660

Correct? No

Problem: What is the result of the expression ((32 / 14) - (22 / 47))? Write your answer as a simplified fraction.

Claude-3 Opus:

To simplify the expression ((32 / 14) - (22 / 47)), let's solve it step by step:

1. Simplify 32 / 14:
   32 / 14 = 16 / 7 = 2 2/7

2. Simplify 22 / 47:
   22 / 47 cannot be simplified further

3. Subtract the fractions:
   (2 2/7) - (22 / 47)

   To subtract fractions with different denominators, we need to find the least common denominator (LCD):
   LCD = 7 × 47 = 329

   Convert the fractions to equivalent fractions with the LCD:
   (2 2/7) = (16/7) = (16 × 47) / (7 × 47) = 752 / 329
   (22 / 47) = (22 × 7) / (47 × 7) = 154 / 329

   Now subtract the fractions:
   (752 / 329) - (154 / 329) = (752 - 154) / 329 = 598 / 329

4. Simplify the result:
   598 / 329 = 2 × 13 × 23 / 7 × 47
   The numerator and denominator have no common factors other than 1, so the fraction is already in its simplest form.

### Answer: 598 / 329

Expected answer: 598/329

Correct? Yes

Problem: What is the sum of 74/61 and 41/53 expressed in fractions?

Claude-3 Opus:

To find the sum of 74/61 and 41/53, we need to find a common denominator. The common denominator will be the product of the denominators: 61 * 53 = 3233.

Now, we need to convert each fraction to an equivalent fraction with the common denominator:

74/61 = 74 * 53 / (61 * 53) = 3922/3233
41/53 = 41 * 61 / (53 * 61) = 2501/3233

Now we can add the numerators:

3922/3233 + 2501/3233 = (3922 + 2501)/3233 = 6423/3233

Therefore, the sum of 74/61 and 41/53 is 6423/3233.

### Answer: 6423/3233

Expected answer: 6423/3233

Correct? Yes

Problem: First, find out the result of 94 / 2 - 74 / 57. Then add the result to 56 / 97. What fraction do you get?

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's calculate 94 / 2 - 74 / 57.
   
   94 / 2 = 47
   74 / 57 ≈ 1.2982 (rounded to 4 decimal places)
   
   47 - 1.2982 = 45.7018

2. Now, let's add the result to 56 / 97.
   
   56 / 97 ≈ 0.5773 (rounded to 4 decimal places)
   
   45.7018 + 0.5773 = 46.2791

3. The final result is a decimal, not a fraction. Let's convert it to a fraction.
   
   46.2791 = 462791 / 10000 (as a fraction)
   
   Simplifying the fraction:
   462791 / 10000 = 23139.55 / 500 ≈ 23139 / 500 (rounded down)

### Answer: 23139 / 500

Expected answer: 255877/5529

Correct? No

Problem: What is the sum of 14/89 and the sum of 24/34 and 44/87? Give your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 14/89 and the sum of 24/34 and 44/87, we need to:
1. Add 24/34 and 44/87
2. Add the result to 14/89
3. Simplify the final fraction

Step 1: Adding 24/34 and 44/87
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
LCM of 34 and 87 = 2958
Now, we convert both fractions to equivalent fractions with the LCM as the denominator:
24/34 = 24 × 87/34 × 87 = 2088/2958
44/87 = 44 × 34/87 × 34 = 1496/2958
2088/2958 + 1496/2958 = 3584/2958

Step 2: Adding the result to 14/89
Again, we need to find the LCM of the denominators (2958 and 89).
LCM of 2958 and 89 = 263262
Converting both fractions to equivalent fractions with the LCM as the denominator:
3584/2958 = 3584 × 89/2958 × 89 = 319976/263262
14/89 = 14 × 2958/89 × 2958 = 41412/263262
319976/263262 + 41412/263262 = 361388/263262

Step 3: Simplifying the final fraction
The numerator and denominator have a common factor of 4.
361388 ÷ 4 = 90347
263262 ÷ 4 = 65817
Simplified fraction = 90347/65817

### Answer: 90347/65817

Expected answer: 180194/131631

Correct? No

Problem: What would you get if you add 73/30 to 8/60?

Claude-3 Opus:

To add fractions, we need to find a common denominator. In this case, the common denominator is 60, which is the least common multiple of 30 and 60.

First, let's convert 73/30 to an equivalent fraction with a denominator of 60:
73/30 = (73 * 2)/(30 * 2) = 146/60

Now we can add 146/60 and 8/60:
146/60 + 8/60 = (146 + 8)/60 = 154/60

To simplify the fraction, we divide both the numerator and denominator by their greatest common factor, which is 2:
154/60 = (154 ÷ 2)/(60 ÷ 2) = 77/30

### Answer: 77/30

Expected answer: 77/30

Correct? Yes

Problem: Suppose you have the following three fractions: 82/49, 45/60, and 99/59. If you add the first fraction (82/49) with the second one (45/60), call this result 'd'. Then, add 'd' to the third fraction (99/59). What would be the resulting sum? Please provide your answer as a simplified fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, we need to add the fractions 82/49 and 45/60. To add fractions with different denominators, we need to find the least common denominator (LCD).

   The LCD of 49 and 60 is 1470 (49 * 30 = 1470, 60 * 30 = 1470).

   Now, we convert the fractions to equivalent fractions with the LCD:
   82/49 = (82 * 30) / (49 * 30) = 2460/1470
   45/60 = (45 * 30) / (60 * 30) = 1350/1470

   Adding these fractions:
   2460/1470 + 1350/1470 = 3810/1470

   This result is 'd'.

2. Now, we add 'd' (3810/1470) to the third fraction, 99/59.

   The LCD of 1470 and 59 is 86730 (1470 * 59 = 86730).

   Converting the fractions to equivalent fractions with the LCD:
   3810/1470 = (3810 * 59) / (1470 * 59) = 224790/86730
   99/59 = (99 * 1470) / (59 * 1470) = 145530/86730

   Adding these fractions:
   224790/86730 + 145530/86730 = 370320/86730

3. Simplifying the resulting fraction:
   370320/86730 = 4260/999

Therefore, the resulting sum, simplified, is 4260/999.

### Answer: 4260/999

Expected answer: 47429/11564

Correct? No

Problem: Solve the following two steps: first, subtract 76/30 from 91/16 and second, add the answer to 18/44. Round the final answer to the nearest hundredth.

Claude-3 Opus:

Step 1: Subtract 76/30 from 91/16

To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 30 and 16.

LCM(30, 16) = 240

Now, we convert both fractions to equivalent fractions with the common denominator:

91/16 = 1365/240
76/30 = 608/240

Subtracting the fractions:

1365/240 - 608/240 = 757/240

Step 2: Add the answer from Step 1 to 18/44

First, let's simplify 757/240:

757/240 = 3.154166...

Now, we need to find the common denominator for 3.154166... and 18/44. The common denominator is 44.

3.154166... = 138.783333.../44
18/44 = 18/44

Adding the fractions:

138.783333.../44 + 18/44 = 156.783333.../44

Rounding the final answer to the nearest hundredth:

156.783333.../44 ≈ 3.56

### Answer: 3.56

Expected answer: 9407/2640

Correct? No

Problem: Calculate the result of ((8 / 91) + (49 / 5)) and subtract (32 / 76) from the result. Provide your answer as a simplified fraction.

Claude-3 Opus:

Let's break this down step by step:

1. First, let's calculate (8 / 91) + (49 / 5):
   
   8 / 91 = 8/91 (already in simplified form)
   49 / 5 = 9 4/5

   Now, add these fractions:
   8/91 + 9 4/5 = (8/91) + (484/91) = 492/91

2. Next, we need to subtract (32 / 76) from the result:

   32 / 76 = 8/19 (simplified form)

   492/91 - 8/19 = (492/91) - (8/19)
   
   To subtract these fractions, we need a common denominator. The LCM of 91 and 19 is 1729.
   
   (492 * 19)/(91 * 19) - (8 * 91)/(19 * 91) = 9348/1729 - 728/1729 = 8620/1729

3. Finally, simplify the fraction 8620/1729:
   
   Divide both the numerator and denominator by their GCD, which is 1.
   8620/1729 is already in its simplest form.

### Answer: 8620/1729

Expected answer: 81841/8645

Correct? No

Problem: Calculate the value of ((75 / 45) + (5 / 49)) first. Then add this value with 3 / 58. Provide the answer as a simple fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's calculate the value of ((75 / 45) + (5 / 49)):
   75 / 45 = 5 / 3
   5 / 49 = 5 / 49
   (5 / 3) + (5 / 49) = ((5 * 49) + (5 * 3)) / (3 * 49)
                     = (245 + 15) / 147
                     = 260 / 147

2. Now, let's add (3 / 58) to the result from step 1:
   (260 / 147) + (3 / 58) = ((260 * 58) + (3 * 147)) / (147 * 58)
                          = (15080 + 441) / 8526
                          = 15521 / 8526

3. Simplify the fraction:
   15521 and 8526 have a common factor of 7.
   15521 / 7 = 2217
   8526 / 7 = 1218
   
   So, the simplified fraction is 2217 / 1218.

### Answer: 2217 / 1218

Expected answer: 15521/8526

Correct? No

Problem: Calculate the answer to ((43 / 15) - (33 / 95)) and simplify it to its lowest terms.

Claude-3 Opus:

To calculate ((43 / 15) - (33 / 95)), let's first perform the division operations:

43 / 15 = 2.866666...
33 / 95 = 0.347368...

Now, subtract these values:

2.866666... - 0.347368... = 2.519298...

To simplify this fraction to its lowest terms, we need to convert it to a rational number (a fraction).

2.519298... = 2 + 0.519298...

0.519298... can be written as a fraction by setting up an equation:

Let x = 0.519298...
100x = 51.9298...
100x - x = 51.9298... - 0.519298...
99x = 51.41
x = 51.41 / 99
x = 5141 / 9900

Therefore, 2.519298... = 2 + 5141 / 9900 = 19900 / 9900 + 5141 / 9900 = 25041 / 9900

Simplifying this fraction:
25041 and 9900 have a common factor of 99.
25041 / 99 = 253
9900 / 99 = 100

Therefore, ((43 / 15) - (33 / 95)) simplified to its lowest terms is:
253 / 100

### Answer: 253 / 100

Expected answer: 718/285

Correct? No

Problem: What is the sum of ((78 / 45) + (89 / 36)) added to itself? Answer as a simple fraction.

Claude-3 Opus:

To find the sum of ((78 / 45) + (89 / 36)) added to itself, we need to:
1. Calculate (78 / 45) + (89 / 36)
2. Add the result to itself
3. Simplify the fraction

Step 1: Calculate (78 / 45) + (89 / 36)
- Find a common denominator: 45 × 36 = 1620
- Convert fractions to equivalent fractions with the common denominator:
  - 78 / 45 = (78 × 36) / 1620 = 2808 / 1620
  - 89 / 36 = (89 × 45) / 1620 = 4005 / 1620
- Add the numerators: (2808 + 4005) / 1620 = 6813 / 1620

Step 2: Add the result to itself
- (6813 / 1620) + (6813 / 1620) = (6813 × 2) / 1620 = 13626 / 1620

Step 3: Simplify the fraction
- Divide the numerator and denominator by their greatest common factor (GCF)
- GCF of 13626 and 1620 is 6
- (13626 / 6) / (1620 / 6) = 2271 / 270

### Answer: 2271 / 270

Expected answer: 757/90

Correct? Yes

Problem: Let's consider that 93 is divided by 34 to get a fraction value, from which is subtracted another fraction 77/74. What would be the result as a simplified fraction?

Claude-3 Opus:

Okay, let's solve this problem step by step:

1. First, let's divide 93 by 34 to get a fraction:
   93 ÷ 34 = 93/34

2. Now, we have to subtract 77/74 from 93/34:
   93/34 - 77/74

3. To subtract fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 34 and 74.
   LCM(34, 74) = 1258

4. Now, we convert both fractions to equivalent fractions with the common denominator:
   93/34 = (93 × 37) / (34 × 37) = 3441/1258
   77/74 = (77 × 17) / (74 × 17) = 1309/1258

5. Subtract the fractions:
   3441/1258 - 1309/1258 = (3441 - 1309) / 1258 = 2132/1258

6. Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
   GCD(2132, 1258) = 2
   (2132 ÷ 2) / (1258 ÷ 2) = 1066/629

Therefore, the simplified fraction is 1066/629.

### Answer: 1066/629

Expected answer: 1066/629

Correct? Yes

Problem: Find the sum of 86/35 and 68/85. Express your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 86/35 and 68/85, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 35 and 85.

LCM(35, 85) = 595

Now, we convert both fractions to equivalent fractions with the common denominator:

86/35 = (86 × 17) / (35 × 17) = 1462/595
68/85 = (68 × 7) / (85 × 7) = 476/595

Add the numerators:

1462/595 + 476/595 = (1462 + 476) / 595 = 1938/595

Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

GCF(1938, 595) = 17

(1938/17) / (595/17) = 114/35

### Answer: 114/35

Expected answer: 114/35

Correct? Yes

Problem: What is the sum of 99/53 and 67/94 in simplest form?

Claude-3 Opus:

To find the sum of 99/53 and 67/94 in simplest form, we need to find a common denominator, add the fractions, and then simplify the result.

Step 1: Find the least common multiple (LCM) of the denominators 53 and 94.
LCM(53, 94) = 4982

Step 2: Convert both fractions to equivalent fractions with the common denominator of 4982.
99/53 = 99 × (4982/53) / (4982/53) = 9306/4982
67/94 = 67 × (4982/94) / (4982/94) = 3551/4982

Step 3: Add the numerators of the equivalent fractions.
9306/4982 + 3551/4982 = (9306 + 3551)/4982 = 12857/4982

Step 4: Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).
GCF(12857, 4982) = 1
The fraction 12857/4982 is already in its simplest form.

### Answer: 12857/4982

Expected answer: 12857/4982

Correct? Yes

Problem: What is the simplified form of the fraction that results from 74/27 minus 56/33?

Claude-3 Opus:

To simplify the fraction that results from 74/27 minus 56/33, we need to:
1. Find a common denominator for the fractions
2. Subtract the numerators
3. Simplify the resulting fraction

Step 1: Find the common denominator
- The common denominator is the least common multiple (LCM) of 27 and 33.
- 27 = 3 × 3 × 3
- 33 = 3 × 11
- LCM(27, 33) = 3 × 3 × 3 × 11 = 891

Step 2: Subtract the numerators
- 74/27 = (74 × 33) / 891 = 2442 / 891
- 56/33 = (56 × 27) / 891 = 1512 / 891
- (2442 / 891) - (1512 / 891) = (2442 - 1512) / 891 = 930 / 891

Step 3: Simplify the resulting fraction
- Divide the numerator and denominator by their greatest common factor (GCF).
- GCF(930, 891) = 3
- (930 / 891) ÷ 3 = (310 / 297)

### Answer: 310/297

Expected answer: 310/297

Correct? Yes

Problem: Find the result when you subtract 91/65 from the sum of 96/40 and 11/99. Leave your answer as a simplified fraction.

Claude-3 Opus:

To solve this problem, let's break it down into steps:

1. Find the sum of 96/40 and 11/99.
2. Subtract 91/65 from the result of step 1.
3. Simplify the resulting fraction.

Step 1: Find the sum of 96/40 and 11/99.
To add fractions, we need a common denominator. The least common multiple of 40 and 99 is 3960.

96/40 = 96 × 99 / 40 × 99 = 9504/3960
11/99 = 11 × 40 / 99 × 40 = 440/3960

Now, we can add the fractions:
9504/3960 + 440/3960 = 9944/3960

Step 2: Subtract 91/65 from the result of step 1.
To subtract fractions, we need a common denominator. The least common multiple of 3960 and 65 is 257400.

9944/3960 = 9944 × 65 / 3960 × 65 = 646360/257400
91/65 = 91 × 3960 / 65 × 3960 = 360360/257400

Now, we can subtract the fractions:
646360/257400 - 360360/257400 = 286000/257400

Step 3: Simplify the resulting fraction.
Divide the numerator and denominator by their greatest common factor, which is 28600.

286000/257400 = 10/9

### Answer: 10/9

Expected answer: 10/9

Correct? Yes

Problem: Calculate the sum of the following expressions: 1) Divide 10 by 5 and add that result to 35 divided by 27. This will give you a value h. 2) Then, add 47 divided by 99 to h. This will give you a value p. What is the value of p?

Claude-3 Opus:

Let's solve this problem step by step:

1) First, we need to calculate the value of h.
   - Divide 10 by 5: 10 ÷ 5 = 2
   - Divide 35 by 27: 35 ÷ 27 ≈ 1.2963 (rounded to 4 decimal places)
   - Add the results: 2 + 1.2963 = 3.2963
   So, h = 3.2963

2) Now, we need to calculate the value of p by adding 47 divided by 99 to h.
   - Divide 47 by 99: 47 ÷ 99 ≈ 0.4747 (rounded to 4 decimal places)
   - Add this result to h: 3.2963 + 0.4747 = 3.7710
   So, p = 3.7710

### Answer: 3.7710

Expected answer: 1120/297

Correct? No

Problem: Consider the fraction 90/81. Add it to 2/66 and simplify your answer to the simplest form. What is the result?

Claude-3 Opus:

To add 90/81 and 2/66, we need to find a common denominator. The least common multiple of 81 and 66 is 594.

90/81 = 90/81 * 11/11 = 990/891
2/66 = 2/66 * 9/9 = 18/594

Now we can add the fractions:
990/891 + 18/594 = (990*1 + 18*1)/(594*1) = 1008/594

Simplifying the fraction:
1008/594 = 504/297 = 168/99 = 56/33

Therefore, 90/81 + 2/66 = 56/33.

### Answer: 56/33

Expected answer: 113/99

Correct? No

Problem: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, how long would both pieces of ribbon be together?

Claude-3 Opus:

Let's solve this step by step:

1. Oliver has a piece of ribbon that is 56/41 yards long.
2. He gets another piece of the same length. This means he now has 2 pieces of ribbon, each 56/41 yards long.
3. To find the total length of both pieces together, we need to add the lengths:
   
   56/41 + 56/41 = (56 + 56) / 41
                = 112 / 41
                = <<112/41=2.731707317073171>>2 28/41 yards (or 2.731707317073171 yards as a decimal)

Therefore, both pieces of ribbon together would be 2 28/41 yards long.

### Answer: 2 28/41 yards

Expected answer: 112/41

Correct? No

Problem: What is the result of 92/75 + 66/92? Please give your answer as a simplified fraction.

Claude-3 Opus:

To solve 92/75 + 66/92, we need to find a common denominator. The least common multiple of 75 and 92 is 6900.

92/75 = (92 * 92) / (75 * 92) = 8464/6900
66/92 = (66 * 75) / (92 * 75) = 4950/6900

Now we can add the fractions:

8464/6900 + 4950/6900 = (8464 + 4950) / 6900 = 13414/6900

Simplifying the fraction:

13414/6900 = 1341/690 = 447/230

Therefore, 92/75 + 66/92 = 447/230.

### Answer: 447/230

Expected answer: 6707/3450

Correct? No

Problem: What is the sum of 32/65 and 73/22? Leave your answer as an unsimplified fraction.

Claude-3 Opus:

To find the sum of 32/65 and 73/22, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 22.

LCM(65, 22) = 1430

Now, we convert both fractions to equivalent fractions with the common denominator:

32/65 = (32 × 22) / (65 × 22) = 704 / 1430
73/22 = (73 × 65) / (22 × 65) = 4745 / 1430

Add the numerators and keep the common denominator:

(704 + 4745) / 1430 = 5449 / 1430

Therefore, the sum of 32/65 and 73/22 is 5449/1430.

### Answer: 5449/1430

Expected answer: 5449/1430

Correct? Yes

Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.

Claude-3 Opus:

To find the difference between 51/34 and 12/86, we need to subtract these fractions. However, we can only subtract fractions with the same denominator. So, we first need to find the least common denominator (LCD) of 34 and 86.

The LCD of 34 and 86 is 1462 because 1462 = 2 × 17 × 43, and 34 = 2 × 17, 86 = 2 × 43.

Now, we can express both fractions with the denominator 1462:

51/34 = (51 × 43) / (34 × 43) = 2193/1462
12/86 = (12 × 17) / (86 × 17) = 204/1462

Next, we subtract:

2193/1462 - 204/1462 = (2193 - 204)/1462 = 1989/1462

To simplify this fraction, we find the greatest common factor (GCF) of 1989 and 1462.

The GCF of 1989 and 1462 is 17 because 1989 = 17 × 117 and 1462 = 2 × 17 × 43.

Dividing both the numerator and denominator by 17:

(1989/17) / (1462/17) = 117/86

Therefore, the difference between 51/34 and 12/86 in its simplest form is 117/86.

### Answer: 117/86

Expected answer: 117/86

Correct? Yes

Problem: First take the whole number 51 and add it to the fraction 93/8. Take that sum and add it to the fraction 58/44. What is the final result as a simplified fraction?

Claude-3 Opus:

Let's solve this problem step by step:

1. Add 51 to 93/8:
   51 + 93/8 = 408/8 + 93/8 = 501/8

2. Add the result from step 1 to 58/44:
   501/8 + 58/44 = 5508/88 + 116/88 = 5624/88

3. Simplify the fraction 5624/88:
   Divide both the numerator and denominator by their greatest common factor (GCF).
   The GCF of 5624 and 88 is 8.
   5624 ÷ 8 = 703
   88 ÷ 8 = 11
   
   So, 5624/88 simplifies to 703/11.

### Answer: 703/11

Expected answer: 5627/88

Correct? No

Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.

Claude-3 Opus:

To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.

LCM of 5 and 25 is 25. So, we will convert both fractions to equivalent fractions with a denominator of 25.

82/5 = (82 × 5) / (5 × 5) = 410/25
98/25 remains as it is.

Now, we can subtract the fractions:

410/25 - 98/25 = (410 - 98) / 25 = 312/25

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

GCD of 312 and 25 is 1. So, the fraction 312/25 is already in its simplest form.

### Answer: 312/25

Expected answer: 312/25

Correct? Yes

Problem: Calculate (64 / 50) + (70 / 22) and provide your answer as an unsimplified fraction.

Claude-3 Opus:

To calculate (64 / 50) + (70 / 22), we need to find a common denominator for the fractions and then add the numerators.

The common denominator is the least common multiple (LCM) of 50 and 22.
50 = 2 × 5^2
22 = 2 × 11
LCM(50, 22) = 2 × 5^2 × 11 = 550

Now, we convert both fractions to equivalent fractions with the common denominator:

64 / 50 = (64 × 11) / (50 × 11) = 704 / 550
70 / 22 = (70 × 25) / (22 × 25) = 1750 / 550

Adding the numerators:
(64 / 50) + (70 / 22) = (704 / 550) + (1750 / 550) = (704 + 1750) / 550 = 2454 / 550

### Answer: 2454 / 550

Expected answer: 1227/275

Correct? Yes

Problem: John calculated s by adding 24 divided by 6 to 40 divided by 53. He then added s to itself to get b. Can you find the value of b?

Claude-3 Opus:

Let's solve this problem step by step:

1. Calculate the value of 24 divided by 6:
   24 ÷ 6 = 4

2. Calculate the value of 40 divided by 53:
   40 ÷ 53 ≈ 0.7547

3. Add the results from steps 1 and 2 to get the value of s:
   s = 4 + 0.7547
   s ≈ 4.7547

4. To get the value of b, add s to itself:
   b = s + s
   b ≈ 4.7547 + 4.7547
   b ≈ 9.5094

### Answer: 9.5094

Expected answer: 504/53

Correct? No

Problem: Calculate ((80 / 90) + (52 / 11)) and express your answer as a mixed number.

Claude-3 Opus:

To calculate ((80 / 90) + (52 / 11)), let's break it down into steps:

1. Simplify 80 / 90:
   80 / 90 = 8 / 9 (divide both numerator and denominator by 10)

2. Simplify 52 / 11:
   52 / 11 = 4 8/11 (divide 52 by 11; the quotient is 4 with a remainder of 8)

3. Add the fractions:
   8/9 + 4 8/11
   = (8/9) + ((4 * 11 + 8) / 11) (convert the mixed number to an improper fraction)
   = (8/9) + (52/11) (simplify the numerator)
   = ((8 * 11) / (9 * 11)) + (52 / 11) (find a common denominator by multiplying both denominators)
   = (88 / 99) + (52 / 11) (simplify the first fraction)
   = ((88 * 1) / (99 * 1)) + ((52 * 9) / (11 * 9)) (multiply the numerators and denominators by the reciprocal of the second denominator)
   = (88 / 99) + (468 / 99) (simplify the second fraction)
   = (88 + 468) / 99 (add the numerators)
   = 556 / 99 (simplify the numerator)
   = 5 59/99 (convert the improper fraction to a mixed number)

Therefore, ((80 / 90) + (52 / 11)) = 5 59/99.

### Answer: 5 59/99

Expected answer: 556/99

Correct? No

Problem: Calculate the sum of 12/18 and 91/74. Express your answer as a simplified fraction.

Claude-3 Opus:

To calculate the sum of 12/18 and 91/74, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 18 and 74.

LCM(18, 74) = 2 × 3 × 3 × 37 = 666

Now, we convert both fractions to equivalent fractions with the common denominator:

12/18 = (12 × 37) / (18 × 37) = 444/666
91/74 = (91 × 9) / (74 × 9) = 819/666

Adding the fractions:
444/666 + 819/666 = (444 + 819) / 666 = 1263/666

Simplifying the fraction:
1263/666 = 1 263/666 = 1 + 597/666 = 1 + (3 × 199)/(3 × 222) = 1 + 199/222 = 1 + (199/3) / (222/3) = 1 + 199/222

Therefore, 12/18 + 91/74 = 1 + 199/222 = 421/222

### Answer: 421/222

Expected answer: 421/222

Correct? Yes

Problem: Find the sum of the fractions 7/2 and 51/25. Write your answer as a simple fraction.

Claude-3 Opus:

To find the sum of 7/2 and 51/25, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 2 and 25.

LCM(2, 25) = 2 × 25 = 50

Now, we convert each fraction to an equivalent fraction with the denominator 50:

7/2 = (7 × 25) / (2 × 25) = 175/50
51/25 = (51 × 2) / (25 × 2) = 102/50

Add the numerators:
175/50 + 102/50 = (175 + 102) / 50 = 277/50

Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

GCF(277, 50) = 1

Since the GCF is 1, the fraction 277/50 is already in its simplest form.

### Answer: 277/50

Expected answer: 277/50

Correct? Yes

Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.

Claude-3 Opus:

Let's break this down step by step:

1. First, let's evaluate ((68 / 69) + (93 / 7)).
   
   68 / 69 = 0.9855... (rounded)
   93 / 7 = 13.2857... (rounded)
   
   0.9855... + 13.2857... = 14.2712...

2. Now, we need to determine if 14.2712... is a monomial. A monomial is a single term that can be a number, a variable, or a product of numbers and variables with whole number exponents. In this case, 14.2712... is a number, so it is a monomial.

3. Next, we add this monomial to (3 / 46).
   
   14.2712... + (3 / 46) = 14.2712... + 0.0652... = 14.3364...

4. To provide the resulting value as a simple fraction, we need to convert 14.3364... to a fraction.
   
   14.3364... = 14 + 0.3364...
              = 14 + (0.3364... * 10000) / 10000
              = 14 + 3364 / 10000
              = 140000 / 10000 + 3364 / 10000
              = 143364 / 10000
              = 14591 / 1020 (after simplifying)

### Answer: 14591 / 1020

Expected answer: 13849/966

Correct? No

Problem: What is the result of adding 31/98 to 60/4? Answer as a simplified fraction.

Claude-3 Opus:

To add 31/98 and 60/4, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 98 and 4.

LCM(98, 4) = 196

Now, we convert both fractions to equivalent fractions with the common denominator:

31/98 = (31 × 2)/(98 × 2) = 62/196
60/4 = (60 × 49)/(4 × 49) = 2940/196

Adding the fractions:

62/196 + 2940/196 = (62 + 2940)/196 = 3002/196

Simplifying the fraction:

3002/196 = 1501/98

Therefore, 31/98 + 60/4 = 1501/98.

### Answer: 1501/98

Expected answer: 1501/98

Correct? Yes

Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.

Claude-3 Opus:

To calculate ((3 / 2) + (24 / 36)), let's simplify the fractions and then add them together.

1. Simplify 3 / 2:
   3 / 2 is already in its simplest form.

2. Simplify 24 / 36:
   24 and 36 have a common factor of 12.
   24 ÷ 12 = 2
   36 ÷ 12 = 3
   So, 24 / 36 simplifies to 2 / 3.

3. Add the simplified fractions:
   (3 / 2) + (2 / 3)

   To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 3 is 6.

   Multiply the first fraction by 3/3 and the second fraction by 2/2 to get equivalent fractions with a common denominator of 6:

   (3 / 2) × (3 / 3) = 9 / 6
   (2 / 3) × (2 / 2) = 4 / 6

   Now add the fractions:
   (9 / 6) + (4 / 6) = 13 / 6

4. Simplify the result:
   13 and 6 have no common factors other than 1, so 13 / 6 is already in its simplest form.

### Answer: 13 / 6

Expected answer: 13/6

Correct? Yes

Problem: Firstly, calculate the sum of 92/54 and 90/13, then from the result take away 46/41. What's the result as a simplified fraction?

Claude-3 Opus:

To solve this problem, let's break it down into steps:

1. Calculate the sum of 92/54 and 90/13:
   92/54 + 90/13 = (92 × 13 + 90 × 54) / (54 × 13)
                 = (1196 + 4860) / 702
                 = 6056 / 702
                 = <<6056/702=8 62/702>>8 62/702

2. Subtract 46/41 from the result:
   8 62/702 - 46/41 = (8 62/702 × 41 - 46 × 702) / (702 × 41)
                    = (8 × 41 + 62 × 41 - 46 × 702) / (702 × 41)
                    = (328 + 2542 - 32292) / 28782
                    = -29422 / 28782
                    = <<-29422/28782=-1 640/28782>>-1 640/28782

3. Simplify the fraction:
   -1 640/28782 = <<-1 640/28782=-1 20/1693>>-1 20/1693

### Answer: -1 20/1693

Expected answer: 108002/14391

Correct? No

Problem: What is twice the value of 29/23? Simplify your answer to the simplest form.

Claude-3 Opus:

To find twice the value of 29/23, we need to multiply the fraction by 2.

(29/23) × 2 = (29 × 2)/(23 × 1) = 58/23

Now, let's simplify 58/23 to its simplest form by dividing both the numerator and denominator by their greatest common factor (GCF).

The factors of 58 are 1, 2, 29, and 58.
The factors of 23 are 1 and 23.

The GCF of 58 and 23 is 1. Since the GCF is 1, 58/23 is already in its simplest form.

### Answer: 58/23

Expected answer: 58/23

Correct? Yes

Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 29/20 and 17/72, we need to find a common denominator. The least common multiple of 20 and 72 is 360.

29/20 = (29 * 18) / (20 * 18) = 522/360
17/72 = (17 * 5) / (72 * 5) = 85/360

Now we can add the fractions:

522/360 + 85/360 = (522 + 85) / 360 = 607/360

To simplify this fraction, we divide both the numerator and denominator by their greatest common factor. The greatest common factor of 607 and 360 is 1.

607/360 = 607/360

Therefore, the sum of 29/20 and 17/72 as a simplified fraction is:

### Answer: 607/360

Expected answer: 607/360

Correct? Yes

Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's simplify the fractions within the parentheses:
   (36 / 27) = 1.3333...
   (80 / 10) = 8
   (73 / 79) = 0.9240...

2. Now, let's add the first two terms:
   (36 / 27) + (80 / 10) = 1.3333... + 8 = 9.3333...

3. Finally, let's subtract the third term from the sum:
   9.3333... - (73 / 79) = 9.3333... - 0.9240... = 8.4093...

4. The simplified answer is a repeating decimal, which can be approximated as:
   8.41 (rounded to two decimal places)

### Answer: 8.41

Expected answer: 1993/237

Correct? No

Problem: What is the answer to (86 / 71) + (91 / 75)? Answer as a decimal to the nearest hundredth.

Claude-3 Opus:

To solve (86 / 71) + (91 / 75), let's break it down into steps:

1. Divide 86 by 71:
   86 ÷ 71 ≈ 1.211267605633803

2. Divide 91 by 75:
   91 ÷ 75 = 1.213333333333333

3. Add the results from steps 1 and 2:
   1.211267605633803 + 1.213333333333333 = 2.424600938967136

4. Round the result to the nearest hundredth:
   2.424600938967136 rounded to the nearest hundredth is 2.42

### Answer: 2.42

Expected answer: 12911/5325

Correct? No

Problem: Calculate the following, and express the result as a simplified fraction: ((21 / 75) + (74 / 43)) + (10 / 62)

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's add (21 / 75) and (74 / 43):
   (21 / 75) + (74 / 43) = (21 * 43) / (75 * 43) + (74 * 75) / (43 * 75)
                          = 903 / 3225 + 5550 / 3225
                          = (903 + 5550) / 3225
                          = 6453 / 3225

2. Now, let's add (10 / 62) to the result from step 1:
   (6453 / 3225) + (10 / 62) = (6453 * 62) / (3225 * 62) + (10 * 3225) / (62 * 3225)
                             = 400086 / 200150 + 32250 / 200150
                             = (400086 + 32250) / 200150
                             = 432336 / 200150

3. To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator:
   GCD(432336, 200150) = 2

4. Divide both the numerator and denominator by the GCD:
   (432336 / 2) / (200150 / 2) = 216168 / 100075

Therefore, the simplified fraction is:
### Answer: 216168 / 100075

Expected answer: 72056/33325

Correct? No

Problem: Compute ((75 / 66) + (81 / 61)), and give your answer as a fraction reduced to its lowest term.

Claude-3 Opus:

To compute ((75 / 66) + (81 / 61)), we need to find a common denominator for the fractions, add the numerators, and then reduce the resulting fraction to its lowest term.

Step 1: Find the least common multiple (LCM) of the denominators 66 and 61.
LCM(66, 61) = 4,026

Step 2: Convert both fractions to equivalent fractions with the common denominator of 4,026.
(75 / 66) = (75 × 61) / (66 × 61) = 4,575 / 4,026
(81 / 61) = (81 × 66) / (61 × 66) = 5,346 / 4,026

Step 3: Add the numerators of the equivalent fractions.
(4,575 / 4,026) + (5,346 / 4,026) = (4,575 + 5,346) / 4,026 = 9,921 / 4,026

Step 4: Reduce the resulting fraction to its lowest term by dividing the numerator and denominator by their greatest common factor (GCF).
GCF(9,921, 4,026) = 3
(9,921 / 4,026) = (9,921 ÷ 3) / (4,026 ÷ 3) = 3,307 / 1,342

### Answer: 3,307 / 1,342

Expected answer: 3307/1342

Correct? Yes

Problem: Consider two identical fractions, t, each equal to sum of 53/18 and 21/99. Find the total sum, l, of these fractions and present your answer as a simple fraction.

Claude-3 Opus:

To find the total sum, l, of two identical fractions, t, we first need to calculate the value of t.

Given:
- t = 53/18 + 21/99
- We need to find l, where l = t + t

Step 1: Calculate the value of t by adding 53/18 and 21/99.
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
LCM(18, 99) = 198

Now, we can convert the fractions to equivalent fractions with the common denominator of 198:
53/18 = 583/198 (multiply both numerator and denominator by 11)
21/99 = 42/198 (multiply both numerator and denominator by 2)

t = 583/198 + 42/198
t = 625/198
t = 25/6 (divide both numerator and denominator by 33)

Step 2: Calculate the total sum, l, by adding t to itself.
l = t + t
l = 25/6 + 25/6
l = 50/6
l = 25/3 (divide both numerator and denominator by 2)

Therefore, the total sum, l, of two identical fractions, t, is 25/3.

### Answer: 25/3

Expected answer: 625/99

Correct? No

Problem: First, calculate the result of 58/49 + 31/34. Then, add that result to the fraction 74/38. What is the final result as a simple fraction?

Claude-3 Opus:

Okay, let's solve this problem step by step:

1. Calculate 58/49 + 31/34
   To add fractions, we need a common denominator. The common denominator is 49 × 34 = 1666.
   
   58/49 = 1972/1666 (multiply numerator and denominator by 34)
   31/34 = 1519/1666 (multiply numerator and denominator by 49)
   
   1972/1666 + 1519/1666 = 3491/1666

2. Add the result of step 1 to 74/38
   Again, we need a common denominator. The common denominator is 1666 × 38 = 63308.
   
   3491/1666 = 132658/63308 (multiply numerator and denominator by 38)
   74/38 = 123902/63308 (multiply numerator and denominator by 1666)
   
   132658/63308 + 123902/63308 = 256560/63308

3. Simplify the fraction 256560/63308
   Divide the numerator and denominator by their greatest common divisor (GCD).
   The GCD of 256560 and 63308 is 4.
   
   256560/4 = 64140
   63308/4 = 15827
   
   The simplified fraction is 64140/15827.

### Answer: 64140/15827

Expected answer: 127971/31654

Correct? No

Problem: Calculate the sum of 100 divided by 76 and 29 divided by 14. Please provide your answer as a simplified fraction or decimal.

Claude-3 Opus:

To calculate the sum of 100 divided by 76 and 29 divided by 14, we can follow these steps:

1. Calculate 100 divided by 76:
100 ÷ 76 ≈ 1.3157894736842106

2. Calculate 29 divided by 14:
29 ÷ 14 ≈ 2.0714285714285716

3. Add the results from steps 1 and 2:
1.3157894736842106 + 2.0714285714285716 ≈ 3.387218045112782

Simplified fraction:
100/76 + 29/14 = 700/532 + 406/532 = 1106/532

### Answer: 3.387218045112782 or 1106/532

Expected answer: 901/266

Correct? No

Problem: Given that Evan has read 51/18 of his novel, and Olivia has read (8/42) after reading the same amount of novel as Evan, how much of the novel has Olivia read in total? Answer as a simplified fraction.

Claude-3 Opus:

Let's solve this step by step:

1) First, let's simplify the fraction of the novel that Evan has read:
   51/18 = 17/6 <<51/18 = 17/6>>

2) Now, Olivia has read the same amount as Evan, plus an additional 8/42. 
   To add fractions, we need a common denominator. The common denominator of 6 and 42 is 42.

3) Convert 17/6 to an equivalent fraction with denominator 42:
   17/6 = 17/6 * 7/7 = 119/42 <<17/6 = 17/6 * 7/7 = 119/42>>

4) Now we can add the fractions:
   119/42 + 8/42 = 127/42 <<119/42 + 8/42 = 127/42>>

5) Simplify the fraction:
   127/42 = 3 1/42 <<127/42 = 3 1/42>>

Therefore, Olivia has read 3 1/42 of the novel in total.

### Answer: 3 1/42

Expected answer: 127/42

Correct? Yes

Problem: What is the sum of 48 divided by 13 and 31 divided by 22? Answer as a fraction or a decimal.

Claude-3 Opus:

To find the sum of 48 divided by 13 and 31 divided by 22, we need to perform the divisions and then add the results together.

48 ÷ 13 = 3.692307692... (rounded to 9 decimal places)
31 ÷ 22 = 1.409090909... (rounded to 9 decimal places)

3.692307692... + 1.409090909... = 5.101398601... (rounded to 9 decimal places)

To express the result as a fraction, we need to find a common denominator. The least common multiple of 13 and 22 is 286.

48 ÷ 13 = 48 × (22/286) = 1056/286
31 ÷ 22 = 31 × (13/286) = 403/286

1056/286 + 403/286 = 1459/286

Therefore, the sum of 48 divided by 13 and 31 divided by 22 can be expressed as:

Decimal: 5.101398601 (rounded to 9 decimal places)
Fraction: 1459/286

### Answer: 5.101398601 or 1459/286

Expected answer: 1459/286

Correct? Yes

Problem: First, find the value of 24/86 + 76/77. Subtract your answer from 27/6. Write out your process and show your work.

Claude-3 Opus:

To find the value of 24/86 + 76/77, we need to find a common denominator. The least common multiple of 86 and 77 is 6,622.

24/86 = 24 * (6,622/6,622) = 1,848/6,622
76/77 = 76 * (6,622/6,622) = 6,534/6,622

Now, we can add the fractions:
1,848/6,622 + 6,534/6,622 = (1,848 + 6,534)/6,622 = 8,382/6,622

To subtract this result from 27/6, we need to convert 27/6 to an equivalent fraction with a denominator of 6,622:
27/6 = 27 * (1,103/1,103) = 29,781/6,622

Now, we can subtract:
29,781/6,622 - 8,382/6,622 = (29,781 - 8,382)/6,622 = 21,399/6,622

To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 17:
21,399/6,622 = (21,399/17) / (6,622/17) = 1,259/389

Therefore, the final answer is 1,259/389.

### Answer: 1,259/389

Expected answer: 21415/6622

Correct? No

Problem: Find the sum of 73/39 and 49/14, and express your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 73/39 and 49/14, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 39 and 14.

LCM(39, 14) = 546

Now, we convert each fraction to an equivalent fraction with the common denominator:

73/39 = (73 × 14) / (39 × 14) = 1022/546
49/14 = (49 × 39) / (14 × 39) = 1911/546

Add the fractions:

1022/546 + 1911/546 = (1022 + 1911) / 546 = 2933/546

Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF):

GCF(2933, 546) = 91

(2933/91) / (546/91) = 2933/546

Therefore, the sum of 73/39 and 49/14 is 2933/546.

### Answer: 2933/546

Expected answer: 419/78

Correct? Yes

Problem: What is the sum of 75/65 and 7/39? Simplify your answer.

Claude-3 Opus:

To find the sum of 75/65 and 7/39, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 65 and 39.

LCM(65, 39) = 65 × 39 ÷ GCD(65, 39)
GCD(65, 39) = 13 (using the Euclidean algorithm)
LCM(65, 39) = 65 × 39 ÷ 13 = 195

Now, we can convert both fractions to equivalent fractions with the common denominator of 195:

75/65 = (75 × 3)/(65 × 3) = 225/195
7/39 = (7 × 5)/(39 × 5) = 35/195

Adding the fractions:
225/195 + 35/195 = (225 + 35)/195 = 260/195

Simplifying the result:
260/195 = 4/3 (dividing both numerator and denominator by their GCD, which is 65)

### Answer: 4/3

Expected answer: 4/3

Correct? Yes

Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?

Claude-3 Opus:

Let's solve this problem step by step:

1. Calculate 79/1 - 30/92
   79/1 = 79
   30/92 ≈ 0.326 (rounded to 3 decimal places)
   79 - 0.326 = 78.674

2. Subtract 61/63 from the result (78.674)
   61/63 ≈ 0.968 (rounded to 3 decimal places)
   78.674 - 0.968 = 77.706

Therefore, the final result is approximately 77.706.

### Answer: 77.706

Expected answer: 225191/2898

Correct? No

Problem: Calculate (58 / 26) + (58 / 26), and express your answer in simplest form.

Claude-3 Opus:

To calculate (58 / 26) + (58 / 26), we can follow these steps:

1. Simplify 58 / 26:
   58 ÷ 26 = 2 remainder 6
   58 / 26 = 2 6/26
   Simplify 6/26 by dividing both the numerator and denominator by 2:
   6 ÷ 2 = 3
   26 ÷ 2 = 13
   So, 58 / 26 = 2 3/13

2. Now, we can rewrite the expression as:
   (58 / 26) + (58 / 26) = (2 3/13) + (2 3/13)

3. To add fractions with the same denominator, we simply add the numerators:
   (2 3/13) + (2 3/13) = (2 + 2) + (3/13 + 3/13)
                      = 4 + 6/13
                      = 4 6/13

Therefore, (58 / 26) + (58 / 26) = 4 6/13

### Answer: 4 6/13

Expected answer: 58/13

Correct? Yes

Problem: If Alex has 69/63 gallons of orange juice and he bought additional 77/5 gallons, giving him a total of 'k' gallons. Later, he received another 47/71 gallons of orange juice from Sally. How many gallons did Alex have in total?

Claude-3 Opus:

Let's solve this problem step by step:

1. Alex initially has 69/63 gallons of orange juice.
2. He buys an additional 77/5 gallons.
3. After buying, he has a total of 'k' gallons.
4. Later, he receives another 47/71 gallons from Sally.

To find the total gallons Alex has, we need to add the initial amount, the bought amount, and the received amount.

Initial amount: 69/63 gallons
Bought amount: 77/5 gallons
Received amount: 47/71 gallons

Now, let's add these fractions:
69/63 + 77/5 + 47/71

First, we need to find the least common multiple (LCM) of the denominators:
LCM(63, 5, 71) = 22365

Next, we convert each fraction to have the common denominator:
(69 × 355)/22365 + (77 × 4473)/22365 + (47 × 315)/22365

Simplifying:
24495/22365 + 344421/22365 + 14805/22365

Adding the numerators:
(24495 + 344421 + 14805)/22365 = 383721/22365

Simplifying the fraction:
383721/22365 ≈ 17.16 gallons

### Answer: Alex had approximately 17.16 gallons of orange juice in total.

Expected answer: 127907/7455

Correct? No

Problem: What is the result of ((100 / 61) + ((39 / 6) + (67 / 49)))? Answer as a simplified fraction.

Claude-3 Opus:

Let's solve this problem step by step:

1. First, let's simplify the innermost parentheses (67 / 49):
   67 / 49 = 1 19/49

2. Now, let's simplify (39 / 6) + (1 19/49):
   39 / 6 = 6 3/6 = 6 1/2
   6 1/2 + 1 19/49 = 13/2 + 68/49 = (13 * 49)/(2 * 49) + 68/(2 * 49) = (637 + 68)/(2 * 49) = 705/(2 * 49) = 705/98

3. Finally, let's simplify (100 / 61) + (705/98):
   100 / 61 = 1 39/61
   1 39/61 + 705/98 = (1 * 98 + 39 * 98)/(61 * 98) + (705 * 61)/(98 * 61) = (98 + 3822)/(61 * 98) + 42005/(61 * 98) = 3920/(61 * 98) + 42005/(61 * 98) = (3920 + 42005)/(61 * 98) = 45925/(61 * 98)

Simplifying the fraction:
45925/(61 * 98) = 45925/5978 = 165/22

### Answer: 165/22

Expected answer: 56831/5978

Correct? No

Problem: What is the sum of 85/1 and 83/69? Simplify your answer as much as possible.

Claude-3 Opus:

To find the sum of 85/1 and 83/69, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 1 and 69, which is 69.

85/1 = (85 × 69) / (1 × 69) = 5865/69

Now, we can add the fractions:

5865/69 + 83/69 = (5865 + 83) / 69 = 5948/69

To simplify the fraction, we need to find the greatest common divisor (GCD) of 5948 and 69.

The GCD of 5948 and 69 is 1.

Since the GCD is 1, the fraction 5948/69 is already in its simplest form.

### Answer: 5948/69

Expected answer: 5948/69

Correct? Yes

Problem: What is the sum of 92/13 and 43/86 as a simplified fraction?

Claude-3 Opus:

To find the sum of 92/13 and 43/86, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 13 and 86.

LCM(13, 86) = 13 × 86 = 1118 (since 13 and 86 are relatively prime)

Now, we convert both fractions to equivalent fractions with the common denominator:

92/13 = 92 × (86/86) = 7912/1118
43/86 = 43 × (13/13) = 559/1118

Adding the fractions:

7912/1118 + 559/1118 = (7912 + 559)/1118 = 8471/1118

Simplifying the fraction:
The greatest common divisor (GCD) of 8471 and 1118 is 1 (using the Euclidean algorithm or prime factorization).

Since the GCD is 1, the fraction 8471/1118 is already in its simplest form.

### Answer: 8471/1118

Expected answer: 197/26

Correct? Yes

Problem: What is the sum of 67/32 and 10/98, expressed as a simplified fraction?

Claude-3 Opus:

To find the sum of 67/32 and 10/98, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 32 and 98.

LCM(32, 98) = 2 × 7 × 2 × 7 = 196

Now, we convert both fractions to equivalent fractions with the common denominator:

67/32 = (67 × 6)/(32 × 6) = 402/192
10/98 = (10 × 2)/(98 × 2) = 20/196

Adding the fractions:
402/192 + 20/196 = (402 + 20)/196 = 422/196

Simplifying the fraction:
422/196 = 211/98

### Answer: 211/98

Expected answer: 3443/1568

Correct? No

Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 59/52 and 70/32, we need to find a common denominator. The least common multiple of 52 and 32 is 416.

1. Convert 59/52 to an equivalent fraction with a denominator of 416:
   59/52 × 8/8 = 472/416

2. Convert 70/32 to an equivalent fraction with a denominator of 416:
   70/32 × 13/13 = 910/416

3. Add the numerators of the equivalent fractions:
   472/416 + 910/416 = 1382/416

4. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF). The GCF of 1382 and 416 is 2.
   1382/416 ÷ 2/2 = 691/208

Therefore, the sum of 59/52 and 70/32 is 691/208.

### Answer: 691/208

Expected answer: 691/208

Correct? Yes

Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?

Claude-3 Opus:

Okay, let's break this down step by step:

1. First, we need to calculate 48 divided by 5:
   48 ÷ 5 = 9.6

2. Next, we calculate 11 divided by 65:
   11 ÷ 65 ≈ 0.1692

3. Now, we subtract the result of step 1 from the result of step 2:
   0.1692 - 9.6 = -9.4308

4. Then, we calculate 28 divided by 2:
   28 ÷ 2 = 14

5. Finally, we add the result of step 3 to the result of step 4:
   -9.4308 + 14 = 4.5692

### Answer: 4.5692

Expected answer: 1523/65

Correct? No

Problem: What is the result when you add 20/52 to 75/82? Simplify your answer to the smallest possible fraction.

Claude-3 Opus:

To add 20/52 and 75/82, we need to find a common denominator. The least common multiple of 52 and 82 is 2,706.

20/52 = (20 * 41) / (52 * 41) = 820/2,706
75/82 = (75 * 33) / (82 * 33) = 2,475/2,706

Now we can add the fractions:
820/2,706 + 2,475/2,706 = 3,295/2,706

To simplify this fraction, we find the greatest common factor of the numerator and denominator:
3,295 = 5 * 659
2,706 = 2 * 1,353
The greatest common factor is 1.

Therefore, the simplified fraction is 3,295/2,706.

### Answer: 3,295/2,706

Expected answer: 1385/1066

Correct? No

Problem: What is the result of subtracting 92/84 from 31/5? Answer as a simplified fraction.

Claude-3 Opus:

To subtract 92/84 from 31/5, we need to find a common denominator. The least common multiple of 84 and 5 is 420.

31/5 = (31 × 84) / (5 × 84) = 2604/420
92/84 = (92 × 5) / (84 × 5) = 460/420

Now we can subtract:

2604/420 - 460/420 = (2604 - 460) / 420 = 2144/420

Simplifying the fraction:
2144/420 = 1072/210 = 536/105 = 268/52 = 134/26 = 67/13

### Answer: 67/13

Expected answer: 536/105

Correct? No

Problem: Calculate the following: Double the sum of 81/90 and 94/49.

Claude-3 Opus:

To calculate the given expression, let's break it down into steps:

1. Calculate the sum of 81/90 and 94/49.
   81/90 + 94/49 = (81 × 49 + 94 × 90) / (90 × 49)
                 = (3969 + 8460) / 4410
                 = 12429 / 4410
                 = <<12429/4410=141/50>>141/50

2. Double the sum obtained in step 1.
   2 × 141/50 = 282/50
              = <<282/50=141/25>>141/25

Therefore, double the sum of 81/90 and 94/49 is 141/25.

### Answer: 141/25

Expected answer: 1381/245

Correct? No

Problem: Find the difference between 69/21 and 10/92. Write your answer as a simple fraction.

Claude-3 Opus:

To find the difference between 69/21 and 10/92, we need to subtract these fractions. However, we can only subtract fractions with the same denominator. So, we first need to find the least common denominator (LCD) of 21 and 92.

The LCD of 21 and 92 is 21 × 92 = 1932.

Now, let's convert both fractions to equivalent fractions with the LCD as the denominator:

69/21 = (69 × 92) / (21 × 92) = 6348/1932
10/92 = (10 × 21) / (92 × 21) = 210/1932

Now we can subtract:

6348/1932 - 210/1932 = (6348 - 210)/1932 = 6138/1932

Simplifying the fraction:
6138/1932 = 3069/966 = 3069/966

Therefore, the difference between 69/21 and 10/92 is 3069/966.

### Answer: 3069/966

Expected answer: 1023/322

Correct? Yes

Problem: First, find the result of (26 / 87) + (92 / 88). Then add the result to (26 / 57). What's the answer?

Claude-3 Opus:

Let's solve this problem step by step:

1. Find the result of (26 / 87) + (92 / 88):
   (26 / 87) + (92 / 88) = 0.2988505747126437 + 1.0454545454545454
                         = 1.3443051201671891

2. Add the result from step 1 to (26 / 57):
   1.3443051201671891 + (26 / 57) = 1.3443051201671891 + 0.45614035087719296
                                   = 1.8004454710443821

Therefore, the final result is 1.8004454710443821.

### Answer: 1.8004454710443821

Expected answer: 21825/12122

Correct? No

Problem: What is the result if you add 78/66, 28/6, and 90/34 together? Please provide your answer as a simplified fraction.

Claude-3 Opus:

To add fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators 66, 6, and 34.

LCM(66, 6, 34) = 1122

Now, we convert each fraction to an equivalent fraction with the denominator 1122:

78/66 = (78 × 17) / (66 × 17) = 1326/1122
28/6 = (28 × 187) / (6 × 187) = 5236/1122
90/34 = (90 × 33) / (34 × 33) = 2970/1122

Adding the numerators:
1326/1122 + 5236/1122 + 2970/1122 = (1326 + 5236 + 2970)/1122 = 9532/1122

Simplifying the fraction:
9532/1122 = 4766/561

### Answer: 4766/561

Expected answer: 4766/561

Correct? Yes

Problem: Calculate: (12 / 7) - (9 / 23). Please simplify your answer to the lowest terms.

Claude-3 Opus:

To calculate (12 / 7) - (9 / 23), we need to find a common denominator for the fractions.

The least common multiple (LCM) of 7 and 23 is 7 × 23 = 161.

Now, we can rewrite the fractions with the common denominator:

(12 / 7) = (12 × 23) / (7 × 23) = 276 / 161
(9 / 23) = (9 × 7) / (23 × 7) = 63 / 161

Subtracting the fractions:

(276 / 161) - (63 / 161) = (276 - 63) / 161 = 213 / 161

Simplifying the fraction to the lowest terms:

213 and 161 have a common factor of 3.
(213 / 3) / (161 / 3) = 71 / 53

### Answer: 71 / 53

Expected answer: 213/161

Correct? No

Problem: Calculate the sum of 95/18 and 51/61, and represent your answer as a simplified fraction.

Claude-3 Opus:

To calculate the sum of 95/18 and 51/61, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 18 and 61.

LCM(18, 61) = 1098

Now, we convert both fractions to equivalent fractions with the common denominator:

95/18 = 95 × 61/18 × 61 = 5795/1098
51/61 = 51 × 18/61 × 18 = 918/1098

Adding the fractions:
5795/1098 + 918/1098 = 6713/1098

Simplifying the fraction:
6713/1098 = 6713/1098 ÷ 1 = 6713/1098

The fraction 6713/1098 cannot be simplified further as the greatest common divisor (GCD) of 6713 and 1098 is 1.

### Answer: 6713/1098

Expected answer: 6713/1098

Correct? Yes

Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). Answer as a simplified fraction.

Claude-3 Opus:

To subtract fractions, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of the denominators 46 and 84.

LCM(46, 84) = 2 × 46 = 92 (since 84 is divisible by 46)

Now, we convert both fractions to equivalent fractions with the common denominator:

(93 / 46) = (93 × 2) / (46 × 2) = 186 / 92
(51 / 84) = (51 × 1) / (84 × 1) = 51 / 92

Subtracting the fractions:

(186 / 92) - (51 / 92) = (186 - 51) / 92 = 135 / 92

Simplifying the fraction:

135 / 92 = 45 / 46 (dividing both numerator and denominator by their GCD, which is 3)

### Answer: 45 / 46

Expected answer: 911/644

Correct? No

Problem: Calculate the sum of the fractions 12/70 and 84/9. Please provide your answer in simplified form.

Claude-3 Opus:

To calculate the sum of 12/70 and 84/9, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 70 and 9.

LCM(70, 9) = 630

Now, we convert each fraction to an equivalent fraction with the common denominator:

12/70 = (12 × 9)/(70 × 9) = 108/630
84/9 = (84 × 70)/(9 × 70) = 5880/630

Add the numerators and keep the common denominator:

108/630 + 5880/630 = 5988/630

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):

GCD(5988, 630) = 126

(5988/126)/(630/126) = 47.5/5 = 9.5

### Answer: 9.5

Expected answer: 998/105

Correct? No

Problem: If you subtract 40/92 from 32/3 and double the result, what would you get?

Claude-3 Opus:

Let's solve this problem step by step:

1. First, we need to subtract 40/92 from 32/3.
   32/3 - 40/92 = (32 × 92 - 40 × 3) / (3 × 92)
                = (2944 - 120) / 276
                = 2824 / 276
                = 141/138

2. Now, we need to double the result.
   141/138 × 2 = 282/138
              = 141/69

Therefore, if you subtract 40/92 from 32/3 and double the result, you would get 141/69.

### Answer: 141/69

Expected answer: 1412/69

Correct? No

Problem: What is the sum of 79/24 and 79/24? Keep your answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 79/24 and 79/24, we can follow these steps:

1. Since the fractions have the same denominator, we can simply add the numerators and keep the denominator the same.

   79/24 + 79/24 = (79 + 79) / 24

2. Add the numerators:

   (79 + 79) / 24 = 158 / 24

3. Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). The GCF of 158 and 24 is 2.

   (158 ÷ 2) / (24 ÷ 2) = 79 / 12

Therefore, the sum of 79/24 and 79/24 is 79/12.

### Answer: 79/12

Expected answer: 79/12

Correct? Yes

Problem: What is the sum of 91/76 and 12/22? Please simplify your fraction.

Claude-3 Opus:

To find the sum of 91/76 and 12/22, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 76 and 22.

LCM(76, 22) = 1672

Now, we convert both fractions to equivalent fractions with the common denominator:

91/76 = 91 × 22 / 76 × 22 = 2002/1672
12/22 = 12 × 76 / 22 × 76 = 912/1672

Adding the fractions:

2002/1672 + 912/1672 = 2914/1672

Simplifying the fraction:

2914/1672 = 1457/836

Therefore, the sum of 91/76 and 12/22 is 1457/836.

### Answer: 1457/836

Expected answer: 1457/836

Correct? Yes

Problem: First, add 88/93 to 6/47. Then, add the result to 92/4. What do you get?

Claude-3 Opus:

Let's solve this problem step by step:

1. Add 88/93 to 6/47:
   To add fractions, we need to find a common denominator. The common denominator is 93 * 47 = 4371.
   
   88/93 = 88 * 47 / 4371 = 4136/4371
   6/47 = 6 * 93 / 4371 = 558/4371
   
   4136/4371 + 558/4371 = 4694/4371

2. Add the result (4694/4371) to 92/4:
   Again, we need to find a common denominator. The common denominator is 4 * 4371 = 17484.
   
   4694/4371 = 4694 * 4 / 17484 = 18776/17484
   92/4 = 92 * 4371 / 17484 = 401132/17484
   
   18776/17484 + 401132/17484 = 419908/17484

3. Simplify the result:
   419908/17484 = 24 + 908/17484 = 24 + (227/4371) = 24 227/4371

### Answer: 24 227/4371

Expected answer: 105227/4371

Correct? No

Problem: Calculate the sum of 95/83 and the result of 52/21 + 75/67. Write your answer as a simplified fraction.

Claude-3 Opus:

To calculate the sum of 95/83 and the result of 52/21 + 75/67, let's break it down into steps:

Step 1: Calculate 52/21 + 75/67
52/21 = 52 ÷ 21 = 52 × 1/21 = 52/21
75/67 = 75 ÷ 67 = 75 × 1/67 = 75/67
To add fractions, we need a common denominator. The least common multiple of 21 and 67 is 21 × 67 = 1407.
(52/21) × (67/67) = 3484/1407
(75/67) × (21/21) = 1575/1407
3484/1407 + 1575/1407 = 5059/1407

Step 2: Add 95/83 to the result from Step 1
95/83 = 95 ÷ 83 = 95 × 1/83 = 95/83
The least common multiple of 1407 and 83 is 1407 × 83 = 116781.
(5059/1407) × (83/83) = 419897/116781
(95/83) × (1407/1407) = 133665/116781
419897/116781 + 133665/116781 = 553562/116781

Step 3: Simplify the fraction
553562/116781 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 7.
553562 ÷ 7 = 79080
116781 ÷ 7 = 16683
79080/16683 is the simplified fraction.

### Answer: 79080/16683

Expected answer: 553562/116781

Correct? No

Problem: What is the value of the expression ((73 / 27) - (23 / 48))? Answer as a simplified fraction.

Claude-3 Opus:

To find the value of the expression ((73 / 27) - (23 / 48)), we need to perform the division operations and then subtract the results. Let's solve this step by step.

Step 1: Simplify 73 / 27
73 / 27 = 2 19/27 (divide 73 by 27 to get the mixed number)

Step 2: Simplify 23 / 48
23 / 48 = 23/48 (this fraction cannot be simplified further)

Step 3: Convert 2 19/27 to an improper fraction
2 19/27 = (2 × 27 + 19) / 27 = 73/27

Step 4: Subtract the fractions
(73/27) - (23/48) = (73 × 48 - 23 × 27) / (27 × 48) = (3504 - 621) / 1296 = 2883/1296

Step 5: Simplify the resulting fraction
2883/1296 = 37/16 (divide both the numerator and denominator by 37)

Therefore, the value of the expression ((73 / 27) - (23 / 48)) is 37/16.

### Answer: 37/16

Expected answer: 961/432

Correct? No

Problem: Solve the expression (78 / 2) - (70 / 23). Answer as a simplified decimal or fraction.

Claude-3 Opus:

To solve the expression (78 / 2) - (70 / 23), let's break it down into steps:

1. First, calculate 78 / 2:
   78 / 2 = 39

2. Next, calculate 70 / 23:
   70 / 23 ≈ 3.0434782608695652 (as a decimal)
   or
   70 / 23 = 3 2/23 (as a mixed fraction)

3. Now, subtract the result of step 2 from the result of step 1:
   39 - 3.0434782608695652 ≈ 35.9565217391304348 (as a decimal)
   or
   39 - 3 2/23 = 35 21/23 (as a mixed fraction)

Therefore, the simplified result is:
(78 / 2) - (70 / 23) ≈ 35.9565217391304348 (as a decimal)
or
(78 / 2) - (70 / 23) = 35 21/23 (as a mixed fraction)

### Answer: 35 21/23

Expected answer: 827/23

Correct? No

Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.

Claude-3 Opus:

To add 34/1 and 53/4, we first need to convert 34/1 to an improper fraction.

34/1 = 34

Now, we can add 34 and 53/4:

34 + 53/4 = (34 × 4 + 53) / 4
         = (136 + 53) / 4
         = 189 / 4

To convert 189/4 to a mixed number, we divide 189 by 4:

189 ÷ 4 = 47 remainder 1

This means that 189/4 = 47 1/4

### Answer: 47 1/4

Expected answer: 189/4

Correct? Yes

Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.

Claude-3 Opus:

To find the sum of 3/36 and 97/96, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 36 and 96.

LCM(36, 96) = 2^3 × 3^2 = 288

Now, we convert both fractions to equivalent fractions with the common denominator:

3/36 = (3 × 8)/(36 × 8) = 24/288
97/96 = (97 × 3)/(96 × 3) = 291/288

Adding the fractions:
24/288 + 291/288 = (24 + 291)/288 = 315/288

Simplifying the fraction:
315/288 = (315 ÷ 9)/(288 ÷ 9) = 35/32

### Answer: 35/32

Expected answer: 35/32

Correct? Yes

Problem: Calculate ((92 / 95) + (4 / 74)). Answer as a simplified fraction.

Claude-3 Opus:

To calculate ((92 / 95) + (4 / 74)), let's first perform the division operations and then add the resulting fractions.

Step 1: Simplify 92 / 95
92 and 95 have no common factors other than 1, so this fraction cannot be simplified further.

Step 2: Simplify 4 / 74
4 and 74 have a common factor of 2.
4 ÷ 2 = 2
74 ÷ 2 = 37
So, 4 / 74 = 2 / 37

Step 3: Add the fractions 92 / 95 and 2 / 37
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators.
LCM of 95 and 37 is 3515.

Multiply the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCM:
92 / 95 = (92 × 37) / (95 × 37) = 3404 / 3515
2 / 37 = (2 × 95) / (37 × 95) = 190 / 3515

Now add the numerators and keep the denominator the same:
(3404 / 3515) + (190 / 3515) = (3404 + 190) / 3515 = 3594 / 3515

Step 4: Simplify the resulting fraction
3594 and 3515 have no common factors other than 1, so this fraction cannot be simplified further.

### Answer: 3594 / 3515

Expected answer: 3594/3515

Correct? Yes

Problem: If the value of a variable 'v' is 69/47, what is the value of 'd' if 'd' equals 88/72 + 'v'? Please write your answer as a fraction.

Claude-3 Opus:

To find the value of 'd', we need to add 88/72 and 69/47.

First, let's convert both fractions to a common denominator. The common denominator will be the least common multiple (LCM) of 72 and 47.

LCM(72, 47) = 3384

Now, let's convert each fraction to an equivalent fraction with the denominator 3384:

88/72 = 88 * (3384/72) / 3384 = 4136/3384
69/47 = 69 * (3384/47) / 3384 = 4968/3384

Adding the fractions:

d = 4136/3384 + 4968/3384
d = (4136 + 4968) / 3384
d = 9104/3384

Simplifying the fraction:

9104/3384 = 2276/846 = 1138/423

### Answer: 1138/423

Expected answer: 1138/423

Correct? Yes

Problem: Let's say there is a wholesaler who has 41/26 barrels of olive oil in their warehouse. They sell a portion of the oil which is equivalent to 41/72 barrels. How much olive oil do they have now? Express your answer as a simple fraction.

Claude-3 Opus:

Okay, let's solve this problem step by step:

1. The wholesaler initially has 41/26 barrels of olive oil.
2. They sell a portion equivalent to 41/72 barrels.
3. To find out how much olive oil they have now, we need to subtract the amount sold from the initial amount.

41/26 - 41/72

4. To subtract fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of 26 and 72.
   LCM(26, 72) = 936

5. Now, we convert both fractions to equivalent fractions with the common denominator:

41/26 = (41 × 36)/(26 × 36) = 1476/936
41/72 = (41 × 13)/(72 × 13) = 533/936

6. Subtract the fractions:

1476/936 - 533/936 = (1476 - 533)/936 = 943/936

7. Simplify the fraction:

943/936 = 41/39

Therefore, the wholesaler now has 41/39 barrels of olive oil.

### Answer: 41/39

Expected answer: 943/936

Correct? No

Problem: What is the sum of 85/75 and 88/56? Write your answer in decimal form.

Claude-3 Opus:

To find the sum of 85/75 and 88/56, we need to convert the fractions to a common denominator, add them together, and then convert the result to decimal form.

Converting 85/75 and 88/56 to a common denominator:
85/75 = (85 * 56) / (75 * 56) = 4760/4200
88/56 = (88 * 75) / (56 * 75) = 6600/4200

Adding the fractions:
4760/4200 + 6600/4200 = (4760 + 6600) / 4200 = 11360/4200

Simplifying the result:
11360/4200 = 568/210

Converting 568/210 to decimal form:
568 ÷ 210 ≈ 2.704761904761905

### Answer: 2.704761904761905

Expected answer: 284/105

Correct? No

Problem: What is the result of adding 12 over 33 to 49 over 2? Write your answer as a mixed fraction.

Claude-3 Opus:

To add 12/33 and 49/2, we first need to find a common denominator. The least common multiple of 33 and 2 is 66.

12/33 = (12 × 2)/(33 × 2) = 24/66
49/2 = (49 × 33)/(2 × 33) = 1617/66

Now we can add the fractions:
24/66 + 1617/66 = 1641/66

To convert 1641/66 to a mixed fraction, we divide 1641 by 66:
1641 ÷ 66 = 24 remainder 57

So, 1641/66 = 24 57/66

Simplifying the fraction 57/66 by dividing both the numerator and denominator by 3:
57 ÷ 3 = 19
66 ÷ 3 = 22

Therefore, 57/66 = 19/22

The final answer as a mixed fraction is:
24 19/22

### Answer: 24 19/22

Expected answer: 547/22

Correct? Yes

Problem: What is the result of adding two fractions, where each fraction is 78/65?

Claude-3 Opus:

To add two fractions with the same denominator, we simply add the numerators and keep the denominator the same.

Given fractions: 78/65 and 78/65

Step 1: Add the numerators
78 + 78 = 156

Step 2: Keep the denominator the same
The denominator remains 65

Step 3: Simplify the resulting fraction, if possible
156/65 cannot be simplified further as the numerator and denominator have no common factors other than 1.

Therefore, the sum of the two fractions is 156/65.

### Answer: 156/65

Expected answer: 12/5

Correct? Yes

Problem: Calculate the sum of 16/7 and 11/90. Answer as a simplified fraction.

Claude-3 Opus:

To calculate the sum of 16/7 and 11/90, we need to find a common denominator. The common denominator will be the least common multiple (LCM) of 7 and 90.

LCM(7, 90) = 630

Now, we convert both fractions to equivalent fractions with the common denominator:

16/7 = (16 × 90) / (7 × 90) = 1440/630
11/90 = (11 × 7) / (90 × 7) = 77/630

Add the numerators:

1440/630 + 77/630 = 1517/630

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD):

GCD(1517, 630) = 1

Since the GCD is 1, the fraction 1517/630 is already in its simplest form.

### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes