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 Sonnet:

To solve this problem, we need to follow these steps:

1. Find the least common denominator (LCD) for all the fractions involved.
2. Convert all the fractions to equivalent fractions with the LCD as the denominator.
3. Add the numerators of the first two fractions and subtract the numerator of the third fraction.
4. Simplify the resulting fraction if possible.

Step 1: Find the LCD
The LCD for 56, 23, and 26 is 1288 (the least common multiple of 56, 23, and 26).

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
48/56 = (48 × 23)/1288
95/23 = (95 × 56)/1288
34/26 = (34 × 49)/1288

Step 3: Add the numerators of the first two fractions and subtract the numerator of the third fraction.
(48 × 23) + (95 × 56) - (34 × 49) = 1104 + 5320 - 1666 = 4758

Step 4: Simplify the resulting fraction if possible.
4758/1288 = 3694/1000

Therefore, the value that John found for the given operation is 3694/1000.

### Answer: 3694/1000

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 Sonnet:

To solve this problem, we need to follow these steps:

1. Find the least common denominator (LCD) for the fractions 88/9, 28/65, and 18/37.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the first two fractions.
4. Subtract the third fraction from the sum.
5. Simplify the resulting fraction, if possible.

Step 1: Find the LCD.
The LCD is the least common multiple of 9, 65, and 37, which is 1885.

Step 2: Convert each fraction to an equivalent fraction with the LCD as the denominator.
88/9 = (88 × 209)/1885 = 18432/1885
28/65 = (28 × 29)/1885 = 812/1885
18/37 = (18 × 51)/1885 = 918/1885

Step 3: Add the first two fractions.
18432/1885 + 812/1885 = 19244/1885

Step 4: Subtract the third fraction from the sum.
19244/1885 - 918/1885 = 18326/1885

Step 5: Simplify the resulting fraction, if possible.
18326/1885 = 9163/945 (by dividing both the numerator and denominator by 2)

Therefore, the result expressed as a simple fraction is 9163/945.

### Answer: 9163/945

Expected answer: 210434/21645

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the sum of the two fractions and then simplify the result to the lowest terms.

Given:
- (63 / 41) + (44 / 50)

Step 1: Find the least common denominator (LCD) of 41 and 50.
The LCD of 41 and 50 is 410 (41 × 10 = 410, 50 × 8 = 400).

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
63 / 41 = (63 × 10) / 410 = 630 / 410
44 / 50 = (44 × 8) / 400 = 352 / 410

Step 3: Add the fractions with the same denominator.
(630 / 410) + (352 / 410) = (630 + 352) / 410 = 982 / 410

Step 4: Simplify the fraction to the lowest terms by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 982 and 410 is 41.
982 / 41 = 24
410 / 41 = 10

Therefore, the simplified fraction is 24 / 10 = 2 (2/5).

### Answer: 2 (2/5)

Expected answer: 2477/1025

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find a common denominator for the two fractions and then add the numerators.

Given information:
- John had 71/41 of a cake left.
- Emily added 41/77 of another cake to it.

Step 1: Find the least common multiple (LCM) of 41 and 77 to get the common denominator.
LCM of 41 and 77 = 3137

Step 2: Convert the fractions to equivalent fractions with the common denominator of 3137.
71/41 = (71 × 77) / (41 × 77) = 5447 / 3137
41/77 = (41 × 41) / (77 × 41) = 1681 / 3137

Step 3: Add the numerators of the equivalent fractions.
(5447 + 1681) / 3137

Step 4: Simplify the fraction, if possible.
7128 / 3137 = 2264 / 997 (simplified by dividing both numerator and denominator by 3)

Therefore, the total amount of cake is 2264/997.

### Answer: 2264/997

Expected answer: 7148/3157

Correct? No

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

Claude-3 Sonnet:

To calculate 10/65 + 56/35, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 65 and 35 is 455.

So, we convert both fractions to have a denominator of 455:
10/65 = (10 × 7)/455
56/35 = (56 × 13)/455

Now we can add the fractions:
(10 × 7)/455 + (56 × 13)/455 = (70 + 728)/455 = 798/455

To simplify the fraction 798/455, we divide both the numerator and denominator by their greatest common divisor, which is 7.

798/455 = (798/7)/(455/7) = 114/65

Therefore, the result of 10/65 + 56/35 as a simple fraction is:
### 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 Sonnet:

To add fractions with different denominators, we need to find the least common denominator (LCD) and convert both fractions to have the same denominator.

The LCD of 81 and 47 is 81 × 47 = 3807.

Converting 75/81 to have the denominator 3807:
75/81 = (75 × 47)/3807 = 3525/3807

Converting 97/47 to have the denominator 3807:
97/47 = (97 × 81)/3807 = 7857/3807

Now we can add the fractions:
3525/3807 + 7857/3807 = (3525 + 7857)/3807 = 11382/3807

Therefore, the result of adding 75/81 and 97/47 as an unsimplified fraction is:
### 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 Sonnet:

To solve this problem, we need to find a common denominator for the fractions and then subtract them.

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

Step 2: Convert the fractions to equivalent fractions with the common denominator of 53.
88/1 = 88/1 × 53/53 = 4664/53
38/53 = 38/53 × 1/1 = 38/53

Step 3: Subtract the fractions.
(4664/53) - (38/53) = (4664 - 38)/53 = 4626/53

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
GCF of 4626 and 53 = 1
4626/53 ÷ 1/1 = 4626/53

Therefore, the simplified fraction is 4626/53.

### 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 Sonnet:

To evaluate the expression ((80 / 94) + (78 / 59)), we need to perform the following steps:

1. Divide 80 by 94:
   80 / 94 = 0.851063829787234

2. Divide 78 by 59:
   78 / 59 = 1.322033898305085

3. Add the two results:
   0.851063829787234 + 1.322033898305085 = 2.173097728092319

To simplify the answer, we can express it as an improper fraction:
2.173097728092319 = 2 + 173/997

Therefore, the simplified form of the expression ((80 / 94) + (78 / 59)) is:

### Answer: 2 + 173/997

Expected answer: 6026/2773

Correct? No

Problem: What is the sum of 89/56 and 48/50? 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 56 and 50.
The LCM of 56 and 50 is 1400.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 1400.
89/56 = (89 × 25)/1400 = 2225/1400
48/50 = (48 × 28)/1400 = 1344/1400

Step 3: Add the fractions with the common denominator.
(2225/1400) + (1344/1400) = (2225 + 1344)/1400 = 3569/1400

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 3569 and 1400 is 1.
3569/1400 = (3569/1)/1400 = 3569/1400

Therefore, the sum of 89/56 and 48/50 as a simplified fraction is:
### Answer: 3569/1400

Expected answer: 3569/1400

Correct? Yes

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 Sonnet:

To solve this problem, we need to find the sum of 96/11 and 12/5, and then subtract 38/87 from the result.

Given:
- 96/11 = 8 72/11
- 12/5 = 2 2/5
- 38/87

Step 1: Find the least common denominator (LCD) for 72/11, 2/5, and 38/87.
LCD = 435

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
96/11 = 8 72/11 = 8 (40/1) = 320/435
12/5 = 2 2/5 = 2 (87/87) = 174/435
38/87 = 38/87 = 38/435

Step 3: Add the fractions with the same denominator.
(320/435) + (174/435) = 494/435

Step 4: Subtract 38/435 from the sum.
(494/435) - (38/435) = 456/435

Therefore, the result when you subtract 38/87 from the sum of 96/11 and 12/5 is 456/435.

### Answer: 456/435

Expected answer: 51154/4785

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate 82 divided by 9
2. Calculate 82 divided by 63
3. Subtract the second result from the first result
4. Simplify the resulting fraction

Step 1: 82 divided by 9
82 ÷ 9 = 9 + 1/9

Step 2: 82 divided by 63
82 ÷ 63 = 1 + 19/63

Step 3: Subtract the second result from the first result
(9 + 1/9) - (1 + 19/63)
= (9 - 1) + (1/9 - 19/63)
= 8 + (-18/63 + 1/9)
= 8 + (-162/567 + 63/567)
= 8 + (-99/567)

Step 4: Simplify the resulting fraction
-99/567 = -33/189

Therefore, the resulting value is 8 - 33/189.

### Answer: 8 - 33/189

Expected answer: 164/21

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate 23/3
2. Calculate 80/91 + 26/24
3. Subtract the sum from 23/3

Step 1: Calculate 23/3
23/3 = 7 (2/3)

Step 2: Calculate 80/91 + 26/24
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.

LCD of 91 and 24 = 1092
80/91 = (80 × 12)/1092 = 960/1092
26/24 = (26 × 45.5)/1092 = 1183/1092

960/1092 + 1183/1092 = 2143/1092

Step 3: Subtract the sum from 23/3
23/3 = 7 (2/3) = 23/3
2143/1092 = 1 (1051/1092)

23/3 - 2143/1092 = (23 × 364 - 2143 × 1)/1092
= 8372/1092 - 2143/1092
= 6229/1092

Therefore, the value of 23/3 minus the sum of 80/91 and 26/24 is 6229/1092.

### Answer: 6229/1092

Expected answer: 6229/1092

Correct? Yes

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

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 18 and 60 to get the common denominator.
LCM of 18 and 60 = 180

Step 2: Convert the fractions to equivalent fractions with the common denominator of 180.
37/18 = (37 × 10)/180 = 370/180
24/60 = (24 × 3)/180 = 72/180

Step 3: Add the fractions with the common denominator.
(370/180) + (72/180) = 442/180

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
GCF of 442 and 180 = 2
442/180 = (442/2) / (180/2) = 221/90

Therefore, the sum of 37/18 and 24/60 when simplified to the lowest terms is 221/90.

### Answer: 221/90

Expected answer: 221/90

Correct? Yes

Problem: Determine the sum of 33/41 and 95/62. 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: 33/41 and 95/62

Step 1: Find the LCD of 41 and 62.
LCD = 41 × 62 = 2542

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
33/41 = (33 × 62)/2542 = 2046/2542
95/62 = (95 × 41)/2542 = 3895/2542

Step 3: Add the numerators and keep the LCD as the denominator.
(2046/2542) + (3895/2542) = (2046 + 3895)/2542 = 5941/2542

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 5941 and 2542 = 1
5941/2542 = (5941/1) / (2542/1) = 5941/2542

Therefore, the sum of 33/41 and 95/62 is 5941/2542.

### 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 Sonnet:

To solve this problem, we need to perform the following steps:

1. Solve the expression inside the first parentheses: (30 / 11) + (72 / 38)
   a. Convert the fractions to have a common denominator: (30 × 38 / 418) + (72 × 11 / 418)
   b. Simplify: (1140 / 418) + (792 / 418)
   c. Add the numerators: 1140 + 792 = 1932
   d. Result: 1932 / 418

2. Solve the expression inside the second parentheses: (81 / 34)

3. Add the results from steps 1 and 2:
   a. Convert the fractions to have a common denominator: (1932 × 34 / 14188) + (81 × 418 / 14188)
   b. Simplify: (65688 / 14188) + (33918 / 14188)
   c. Add the numerators: 65688 + 33918 = 99606
   d. Result: 99606 / 14188

4. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator:
   a. GCD of 99606 and 14188 is 6
   b. Divide the numerator and denominator by the GCD: (99606 / 6) / (14188 / 6)
   c. Result: 16601 / 2364

### Answer: 16601 / 2364

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 Sonnet:

To solve this problem, we need to follow these steps:

1. Simplify the fractions (64/34) and (3/24) by finding their common denominators and adding them.
2. Simplify the fraction (41/96).
3. Add the results from steps 1 and 2.

Step 1: Finding the common denominator for (64/34) and (3/24)
The least common multiple of 34 and 24 is 102.
(64/34) = (64 × 3/102) = 192/102
(3/24) = (3 × 4/96) = 12/102
(192/102) + (12/102) = 204/102

Step 2: Simplifying (41/96)
(41/96) = (41/96)

Step 3: Adding the results from steps 1 and 2
(204/102) + (41/96) = (204/102) + (41 × (102/102)/96) = (204 + 41 × (102/96))/102 = (204 + 4284/96)/102 = 4488/102 = 44/1

Therefore, the simplified fraction is 44/1.

### Answer: 44/1

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 Sonnet:

To solve this problem, we need to follow these steps:

Step 1: Find the least common denominator (LCD) for the fractions 83/73 and 53/77.
The LCD is the least common multiple of 73 and 77, which is 5641.

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
83/73 = (83 × 77)/5641 = 6391/5641
53/77 = (53 × 73)/5641 = 3869/5641

Step 3: Add the fractions with the same denominator.
6391/5641 + 3869/5641 = 10260/5641 = 'w'

Step 4: Find the LCD for 'w' and 80/76.
The LCD is the least common multiple of 5641 and 76, which is 428716.

Step 5: Convert the fractions to equivalent fractions with the LCD as the denominator.
'w' = 10260/5641 = (10260 × 76)/428716 = 779760/428716
80/76 = (80 × 5641)/428716 = 451280/428716

Step 6: Add the fractions with the same denominator.
779760/428716 + 451280/428716 = 1231040/428716

Step 7: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator, and dividing both by the GCD.
The GCD of 1231040 and 428716 is 4.
1231040/428716 = (1231040/4)/(428716/4) = 307760/107179

Therefore, the final answer in simplified fraction form is 307760/107179.

### Answer: 307760/107179

Expected answer: 307360/106799

Correct? No

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

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 20 and 66 is 660.

Step 1: Convert 27/20 to an equivalent fraction with the denominator 660.
27/20 = (27 × 33)/660 = 891/660

Step 2: Convert 14/66 to an equivalent fraction with the denominator 660.
14/66 = (14 × 10)/660 = 140/660

Step 3: Add the fractions with the common denominator.
891/660 + 140/660 = 1031/660

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
The GCD of 1031 and 660 is 1.
1031/660 = 1031/660

Therefore, the sum of 27/20 and 14/66 is 1031/660.

### Answer: 1031/660

Expected answer: 1031/660

Correct? Yes

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

Claude-3 Sonnet:

To solve this expression, we need to perform the division operations first, and then subtract the results.

Given expression: ((32 / 14) - (22 / 47))

Step 1: Divide 32 by 14
32 / 14 = 2.285714286 (repeating decimal)
We can express this as the fraction 16/7

Step 2: Divide 22 by 47
22 / 47 = 0.468085106 (repeating decimal)
We can express this as the fraction 22/47

Step 3: Subtract the fractions
(16/7) - (22/47)
To subtract 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.

LCD of 7 and 47 = 329

(16/7) = (16 × 47/7 × 47) = 752/329
(22/47) = (22 × 7/47 × 7) = 154/329

Now, we can subtract:
(752/329) - (154/329) = 598/329

To simplify the fraction 598/329, we need to find the greatest common divisor (GCD) of 598 and 329, and then divide both the numerator and denominator by the GCD.

GCD of 598 and 329 = 1

Therefore, the simplified fraction is 598/329.

### 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 Sonnet:

To find 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 61 and 53 to get the common denominator.
LCM of 61 and 53 = 3233

Step 2: Convert the fractions to equivalent fractions with the common denominator of 3233.
74/61 = (74 × 53)/3233 = 3922/3233
41/53 = (41 × 61)/3233 = 2501/3233

Step 3: Add the fractions with the same denominator.
(3922/3233) + (2501/3233) = 6423/3233

Therefore, the sum of 74/61 and 41/53 expressed in fractions 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 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate 94 / 2 - 74 / 57
   94 / 2 = 47
   74 / 57 = 1.298245614035088 (rounded to 9 decimal places)
   47 - 1.298245614035088 = 45.701754385964912 (rounded to 9 decimal places)

2. Calculate 56 / 97
   56 / 97 = 0.577319587628866 (rounded to 9 decimal places)

3. Add the results from steps 1 and 2
   45.701754385964912 + 0.577319587628866 = 46.279073973593778 (rounded to 9 decimal places)

To express the final result as a fraction, we can use a calculator or a computer program to find the closest fraction approximation.

Using an online fraction calculator, the closest fraction approximation to 46.279073973593778 is 1517/33.

Therefore, the final fraction is 1517/33.

### Answer: 1517/33

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 Sonnet:

To solve this problem, we need to find the sum of the fractions 14/89 and (24/34 + 44/87), and then simplify the resulting fraction.

Step 1: Find the least common denominator (LCD) for 14/89, 24/34, and 44/87.
The LCD is the least common multiple of 89, 34, and 87, which is 26326.

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
14/89 = (14 × 296)/26326
24/34 = (24 × 774)/26326
44/87 = (44 × 302)/26326

Step 3: Add the numerators of the equivalent fractions.
(14 × 296)/26326 + (24 × 774)/26326 + (44 × 302)/26326
= 4144/26326 + 18576/26326 + 13288/26326
= 36008/26326

Step 4: Simplify the resulting fraction by finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both the numerator and denominator by the GCF.
The GCF of 36008 and 26326 is 2.
36008/26326 = (36008/2) / (26326/2)
= 18004/13163

Therefore, the sum of 14/89 and (24/34 + 44/87) is 18004/13163.

### Answer: 18004/13163

Expected answer: 180194/131631

Correct? No

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

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 30 and 60 is 60.

Converting 73/30 to an equivalent fraction with denominator 60:
73/30 = (73 × 2)/60 = 146/60

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

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2.

154/60 = (154/2)/(60/2) = 77/30

Therefore, the sum of 73/30 and 8/60 is 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 Sonnet:

To solve this problem, we need to follow these steps:

1. Find a common denominator for the fractions 82/49 and 45/60.
2. Convert the fractions to equivalent fractions with the common denominator.
3. Add the numerators of the equivalent fractions.
4. Find a common denominator for the result from step 3 and the fraction 99/59.
5. Convert the fractions to equivalent fractions with the common denominator.
6. Add the numerators of the equivalent fractions.
7. Simplify the resulting fraction.

Step 1: The least common multiple (LCM) of 49 and 60 is 1470.

Step 2: Convert the fractions to equivalent fractions with the denominator 1470.
82/49 = (82 × 30)/1470 = 2460/1470
45/60 = (45 × 24.5)/1470 = 1102.5/1470

Step 3: Add the numerators of the equivalent fractions.
d = 2460/1470 + 1102.5/1470 = 3562.5/1470

Step 4: The LCM of 1470 and 59 is 86730.

Step 5: Convert the fractions to equivalent fractions with the denominator 86730.
3562.5/1470 = (3562.5 × 59)/86730 = 209937.5/86730
99/59 = (99 × 1470)/86730 = 145530/86730

Step 6: Add the numerators of the equivalent fractions.
209937.5/86730 + 145530/86730 = 355467.5/86730

Step 7: Simplify the resulting fraction.
355467.5/86730 = 4.1/1

Therefore, the resulting sum is 4.1.

### Answer: 4.1

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 Sonnet:

To solve this problem, we need to follow the given steps:

Step 1: Subtract 76/30 from 91/16
First, we need to find a common denominator for 91/16 and 76/30. The least common multiple of 16 and 30 is 480.

91/16 = (91 × 30)/480 = 2730/480
76/30 = (76 × 16)/480 = 1216/480

Now, we can subtract:
2730/480 - 1216/480 = 1514/480

Step 2: Add the answer from Step 1 to 18/44
To add fractions with different denominators, we need to find a common denominator again. The least common multiple of 480 and 44 is 2640.

1514/480 = (1514 × 5.5)/2640 = 8327/2640
18/44 = (18 × 60)/2640 = 1080/2640

Now, we can add:
8327/2640 + 1080/2640 = 9407/2640

To round the final answer to the nearest hundredth, we need to convert the fraction to a decimal:
9407/2640 = 3.5626515151515154

Rounding to the nearest hundredth, we get:
### 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 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate (8 / 91) + (49 / 5)
   * (8 / 91) = 0.087912087912...
   * (49 / 5) = 9.8
   * (8 / 91) + (49 / 5) = 0.087912087912... + 9.8 = 9.887912087912...

2. Calculate (32 / 76)
   * (32 / 76) = 0.421052631578...

3. Subtract (32 / 76) from the result obtained in step 1
   * 9.887912087912... - 0.421052631578... = 9.466859456334...

4. Simplify the fraction
   * 9.466859456334... can be written as 1249/132

Therefore, the simplified fraction is 1249/132.

### Answer: 1249/132

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 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate the value of (75 / 45) + (5 / 49)
   75 / 45 = 5 / 3
   5 / 49 = 0.102040816326531 (approximately)
   (75 / 45) + (5 / 49) = (5 / 3) + 0.102040816326531 = 1.702040816326531

2. Add the value obtained in step 1 with 3 / 58
   1.702040816326531 + (3 / 58) = 1.702040816326531 + 0.051724137931034 = 1.753764954257565

3. Convert the final value to a simple fraction
   1.753764954257565 = 101 / 58 (approximately)

Therefore, the final answer as a simple fraction is:
### Answer: 101/58

Expected answer: 15521/8526

Correct? No

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

Claude-3 Sonnet:

To calculate ((43 / 15) - (33 / 95)), we need to first find the values of 43 / 15 and 33 / 95, and then subtract them.

43 / 15 = 2.8666...
33 / 95 = 0.3473...

Subtracting these two values:
2.8666... - 0.3473... = 2.5193...

To simplify this to its lowest terms, we need to convert the decimal to a fraction.

2.5193... = 2.5193 (repeating decimal)
= 2 + 5193/10000

Simplifying the fraction 5193/10000:
5193/10000 = 259/500

Therefore, the simplified form of 2.5193... is:
2 + 259/500
= 2259/500

### Answer: 2259/500

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 Sonnet:

To solve this problem, we need to find the sum of (78/45) + (89/36) and then add it to itself.

Step 1: Find the common denominator for 45 and 36.
The least common multiple (LCM) of 45 and 36 is 180.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 180.
78/45 = (78 × 4)/180 = 312/180
89/36 = (89 × 5)/180 = 445/180

Step 3: Add the fractions with the common denominator.
(312/180) + (445/180) = 757/180

Step 4: Add the sum to itself.
(757/180) + (757/180) = 1514/180

Step 5: Simplify the fraction if possible.
1514/180 = (1514 ÷ 2)/180 = 757/90

Therefore, the sum of ((78/45) + (89/36)) added to itself is 757/90.

### Answer: 757/90

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 Sonnet:

To solve this problem, we need to follow these steps:

1. Divide 93 by 34 to get the first fraction.
2. Subtract 77/74 from the first fraction.
3. Simplify the resulting fraction.

Step 1: Divide 93 by 34 to get the first fraction.
93 ÷ 34 = 2 with a remainder of 25
25/34 = 25/34

So, the first fraction is 2 + 25/34 = 93/34

Step 2: Subtract 77/74 from 93/34.
93/34 - 77/74 = (93 × 74 - 77 × 34) / (34 × 74)
             = (6882 - 2618) / 2516
             = 4264 / 2516

Step 3: Simplify the resulting fraction 4264/2516.
The greatest common divisor (GCD) of 4264 and 2516 is 4.
4264 ÷ 4 = 1066
2516 ÷ 4 = 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 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 35 and 85.
The LCM of 35 and 85 is 1785.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 1785.
86/35 = (86 × 51)/1785 = 4386/1785
68/85 = (68 × 21)/1785 = 1428/1785

Step 3: Add the fractions with the common denominator.
(4386/1785) + (1428/1785) = 5814/1785

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 5814 and 1785 is 3.
5814/1785 = (5814/3)/(1785/3) = 1938/595

Therefore, the sum of 86/35 and 68/85 expressed as a simplified fraction is 1938/595.

### Answer: 1938/595

Expected answer: 114/35

Correct? Yes

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

Claude-3 Sonnet:

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

Step 1: Find the least common multiple (LCM) of 53 and 94.
The LCM of 53 and 94 is 1486.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 1486.
99/53 = (99/53) × (28/28) = (2772/1486)
67/94 = (67/94) × (16/16) = (1072/1486)

Step 3: Add the fractions with the common denominator.
(2772/1486) + (1072/1486) = 3844/1486

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 3844 and 1486 is 2.
3844/1486 = (3844/2) / (1486/2) = 1922/743

Therefore, the sum of 99/53 and 67/94 in simplest form is 1922/743.

### Answer: 1922/743

Expected answer: 12857/4982

Correct? No

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

Claude-3 Sonnet:

To find the simplified form of the fraction that results from 74/27 minus 56/33, we need to follow these steps:

1. Find the least common denominator (LCD) of 27 and 33.
   The LCD of 27 and 33 is 891 (27 × 33 = 891).

2. Convert the fractions to equivalent fractions with the LCD as the denominator.
   74/27 = (74 × 33)/891 = 2442/891
   56/33 = (56 × 27)/891 = 1512/891

3. Subtract the fractions.
   (2442/891) - (1512/891) = 930/891

4. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor (GCF).
   The GCF of 930 and 891 is 31.
   930/891 = (930/31) / (891/31) = 30/29

Therefore, the simplified form of the fraction that results from 74/27 minus 56/33 is 30/29.

### Answer: 30/29

Expected answer: 310/297

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to follow these steps:

1. Find the sum of 96/40 and 11/99
2. Convert the fractions to have a common denominator
3. Add the numerators
4. Subtract 91/65 from the sum
5. Simplify the resulting fraction

Step 1: Find the sum of 96/40 and 11/99
Sum = 96/40 + 11/99

Step 2: Convert the fractions to have a common denominator
The least common multiple of 40 and 99 is 3960.
96/40 = (96 × 99)/3960 = 9504/3960
11/99 = (11 × 40)/3960 = 440/3960

Step 3: Add the numerators
Sum = 9504/3960 + 440/3960 = (9504 + 440)/3960 = 9944/3960

Step 4: Subtract 91/65 from the sum
91/65 = (91 × 61)/3965 = 5551/3965
Sum - 91/65 = 9944/3960 - 5551/3965 = (9944 × 3965 - 5551 × 3960)/15684600 = 4393/15684600

Step 5: Simplify the resulting fraction
4393/15684600 = 1/3565

Therefore, the result when you subtract 91/65 from the sum of 96/40 and 11/99 is 1/3565.

### Answer: 1/3565

Expected answer: 10/9

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to follow the given steps and perform the calculations.

Step 1: Divide 10 by 5 and add that result to 35 divided by 27. This will give us the value of h.
10 ÷ 5 = 2
35 ÷ 27 = 1.296296296...
h = 2 + 1.296296296... = 3.296296296...

Step 2: Add 47 divided by 99 to h. This will give us the value of p.
47 ÷ 99 = 0.474747474...
p = 3.296296296... + 0.474747474... = 3.771043770...

Therefore, the value of p is approximately 3.771043770.

### Answer: 3.771043770

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 Sonnet:

To solve this problem, we need to find a common denominator for the two fractions and then add their numerators.

The least common multiple (LCM) of 81 and 66 is 2,646.

So, we can convert the fractions to equivalent fractions with a common denominator of 2,646.

90/81 = (90 × 33)/2,646 = 2,970/2,646
2/66 = (2 × 40)/2,646 = 80/2,646

Now, we can add the numerators:
2,970/2,646 + 80/2,646 = 3,050/2,646

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 3,050 and 2,646 is 2.

Therefore, the simplified fraction is:
3,050/2,646 ÷ 2/2 = 1,525/1,323

### Answer: 1,525/1,323

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 Sonnet:

To solve this problem, we need to find the length of one piece of ribbon and then multiply it by 2 to find the total length of both pieces together.

Given information:
- Oliver has a piece of ribbon that is 56/41 yards long.
- He gets another piece of the same length.

Step 1: Convert the fraction 56/41 to a decimal.
56/41 = 1.3658536585365854 yards

Step 2: Find the length of both pieces of ribbon together.
Length of one piece of ribbon = 1.3658536585365854 yards
Length of both pieces together = 1.3658536585365854 yards × 2
Length of both pieces together = 2.7317073170731707 yards

Therefore, both pieces of ribbon together would be 2.7317073170731707 yards long.

### Answer: 2.7317073170731707

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 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 75 and 92.
The LCM of 75 and 92 is 3,700.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 3,700.
92/75 = (92/75) × (49/49) = (4,508/3,700)
66/92 = (66/92) × (40/40) = (2,640/3,700)

Step 3: Add the fractions.
(4,508/3,700) + (2,640/3,700) = 7,148/3,700

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
The GCF of 7,148 and 3,700 is 4.
7,148/3,700 = (7,148/4) / (3,700/4) = 1,787/925

Therefore, the result of 92/75 + 66/92 as a simplified fraction is 1,787/925.

### Answer: 1,787/925

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 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: 32/65 and 73/22

Step 1: Find the LCD of 65 and 22.
LCD = 65 × 22 = 1430

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
32/65 = (32 × 22)/1430 = 704/1430
73/22 = (73 × 65)/1430 = 4745/1430

Step 3: Add the numerators and keep the LCD as the denominator.
704/1430 + 4745/1430 = (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 Sonnet:

To find the difference between 51/34 and 12/86, we need to first find a common denominator for both fractions.

The least common multiple (LCM) of 34 and 86 is 1054.

So, we convert both fractions to have a denominator of 1054:
51/34 = (51 × 31)/1054 = 1581/1054
12/86 = (12 × 12)/1054 = 144/1054

Now we can subtract:
1581/1054 - 144/1054 = 1437/1054

To express the answer in its simplest form, we need to find the greatest common factor (GCF) of the numerator and denominator.
The GCF of 1437 and 1054 is 1.

Therefore, the simplest form of the answer is:
1437/1054

### Answer: 1437/1054

Expected answer: 117/86

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to follow these steps:

1. Convert the whole number 51 to an improper fraction: 51 = (51 × 8)/8 = 408/8
2. Add the fractions 408/8 and 93/8: (408/8) + (93/8) = 501/8
3. Convert the fraction 58/44 to an equivalent fraction with a denominator of 8: 58/44 = (58 × 8)/(44 × 8) = 464/352 = 33/24
4. Add the fractions 501/8 and 33/24: (501/8) + (33/24) = (501 × 3 + 33 × 1)/24 = 1536/24
5. Simplify the fraction 1536/24 by dividing the numerator and denominator by their greatest common divisor (GCD), which is 24: 1536/24 = 64/1 = 64

Therefore, the final result as a simplified fraction is 64.

### Answer: 64

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 Sonnet:

To subtract fractions, we need to find a common denominator for both fractions. The least common multiple of 5 and 25 is 25.

First, we convert 82/5 to an equivalent fraction with a denominator of 25:
82/5 = (82 × 5)/25 = 410/25

Now we can subtract the fractions:
410/25 - 98/25 = (410 - 98)/25 = 312/25

To simplify the fraction 312/25, we divide both the numerator and denominator by their greatest common factor, which is 4:
312/25 = (312/4)/(25/4) = 78/6.25

The fraction 78/6.25 can be written as a mixed number:
78/6.25 = 12 + 3/6.25 = 12 + 0.48 = 12.48

Therefore, the simplest form of the result is 12.48.

### Answer: 12.48

Expected answer: 312/25

Correct? Yes

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

Claude-3 Sonnet:

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

The least common multiple (LCM) of 50 and 22 is 550.

So, we need to convert both fractions to have a denominator of 550.

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

Now we can add the fractions:
704/550 + 1750/550 = 2454/550

Therefore, the unsimplified fraction is:
### 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 Sonnet:

To solve this problem, we need to find the value of s first, and then calculate b using the given information.

Given information:
- s = (24/6) + (40/53)
- b = s + s

Step 1: Find the value of s.
s = (24/6) + (40/53)
s = 4 + 0.7547... (rounded to four decimal places)
s = 4.7547

Step 2: Find the value of b.
b = s + s
b = 4.7547 + 4.7547
b = 9.5094

Therefore, the value of b is 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 Sonnet:

To calculate ((80 / 90) + (52 / 11)), we need to first find the values of 80 / 90 and 52 / 11.

80 / 90 = 8/9
52 / 11 = 4 (with a remainder of 8)
            = 4 + 8/11

Now, we can add these two fractions:
(8/9) + (4 + 8/11)
= (8/9) + (44/11 + 8/11)
= (8/9) + (52/11)
= (88/9 + 52/11)
= (88*11 + 52*9) / (9*11)
= (968 + 468) / 99
= 1436 / 99

To express this as a mixed number, we divide 1436 by 99 to get the whole number part:
1436 / 99 = 14 with a remainder of 50

Therefore, the mixed number representation is:
14 + 50/99

### Answer: 14 + 50/99

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 Sonnet:

To calculate the sum of 12/18 and 91/74, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 18 and 74 is 1332.

So, we convert both fractions to have a denominator of 1332.

12/18 = (12 × 74)/1332 = 888/1332
91/74 = (91 × 18)/1332 = 1638/1332

Now we can add the fractions:
888/1332 + 1638/1332 = 2526/1332

To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator.
The GCF of 2526 and 1332 is 6.

2526/1332 = (2526/6)/(1332/6) = 421/222

Therefore, the sum of 12/18 and 91/74 expressed as a simplified fraction is 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 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 2 and 25.
The LCM of 2 and 25 is 50.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 50.
7/2 = (7 × 25)/50 = 175/50
51/25 = (51 × 2)/50 = 102/50

Step 3: Add the numerators and keep the common denominator.
(175/50) + (102/50) = (175 + 102)/50 = 277/50

Therefore, the sum of the fractions 7/2 and 51/25 is 277/50.

### 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 Sonnet:

To solve this problem, we need to perform the following steps:

1. Evaluate the expression ((68 / 69) + (93 / 7))
   68 / 69 = 0.985507246376812
   93 / 7 = 13.285714285714286
   (0.985507246376812) + (13.285714285714286) = 14.271221532091098

2. Check if the expression ((68 / 69) + (93 / 7)) is a monomial
   A monomial is a single term with variables raised to non-negative integer powers.
   The given expression is not a monomial as it is a sum of two fractions.

3. Add (3 / 46) to the result obtained in step 1
   14.271221532091098 + (3 / 46) = 14.271221532091098 + 0.065217391304348 = 14.336438923395446

4. Express the final result as a simple fraction
   To convert a decimal to a fraction, we need to find the closest fraction with a small denominator.
   14.336438923395446 ≈ 327 / 23

Therefore, the resulting value as a simple fraction is 327 / 23.

### Answer: 327 / 23

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 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.

The LCD of 98 and 4 is 196 (the least common multiple of 98 and 4).

Converting 31/98 to an equivalent fraction with denominator 196:
31/98 = (31 × 2)/196 = 62/196

Converting 60/4 to an equivalent fraction with denominator 196:
60/4 = (60 × 49)/196 = 2940/196

Now we can add the fractions:
62/196 + 2940/196 = 3002/196

To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.

The GCF of 3002 and 196 is 2.

3002/196 = (3002/2)/(196/2) = 1501/98

Therefore, the result of adding 31/98 to 60/4 as a simplified fraction is:
### 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 Sonnet:

To calculate ((3/2) + (24/36)), we need to find a common denominator for the fractions.

The least common multiple of 2 and 36 is 36.

So, we convert 3/2 to an equivalent fraction with a denominator of 36:
3/2 = (3 × 18)/36 = 54/36

Now we can add the fractions:
(54/36) + (24/36) = (54 + 24)/36 = 78/36

To simplify the fraction 78/36, we divide both the numerator and denominator by their greatest common factor, which is 6.

78/36 = (78/6)/(36/6) = 13/6

### 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 Sonnet:

To solve this problem, we need to follow these steps:

1. Find the least common denominator (LCD) for the fractions 92/54, 90/13, and 46/41.
2. Convert all fractions to equivalent fractions with the LCD as the denominator.
3. Add the first two fractions.
4. Subtract the third fraction from the sum.
5. Simplify the resulting fraction if possible.

Step 1: The LCD for 54, 13, and 41 is 1722 (the least common multiple of 54, 13, and 41).

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
92/54 = (92/54) × (32/32) = 1664/1722
90/13 = (90/13) × (132/132) = 11880/1722
46/41 = (46/41) × (42/42) = 1932/1722

Step 3: Add the first two fractions.
(1664/1722) + (11880/1722) = 13544/1722

Step 4: Subtract the third fraction from the sum.
(13544/1722) - (1932/1722) = 11612/1722

Step 5: Simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
The GCD of 11612 and 1722 is 2.
11612/1722 = (11612/2) / (1722/2) = 5806/861

Therefore, the result as a simplified fraction is 5806/861.

### Answer: 5806/861

Expected answer: 108002/14391

Correct? No

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

Claude-3 Sonnet:

To find twice the value of 29/23, we first need to calculate the value of 29/23.

29/23 = 1.26086956521739

Now, to find twice the value, we multiply it by 2:

2 × (29/23) = 2 × 1.26086956521739 = 2.52173913043478

To simplify this fraction, we need to find the greatest common factor (GCF) of the numerator and denominator, and then divide both by the GCF.

The GCF of 2521 and 1000 is 1.

Therefore, the simplified form of 2.52173913043478 is:

2521/1000

### Answer: 2521/1000

Expected answer: 58/23

Correct? No

Problem: What is the sum of 29/20 and 17/72? 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: 29/20 and 17/72

Step 1: Find the LCD of 20 and 72.
The LCD is the least common multiple of 20 and 72, which is 360.

Step 2: Convert both fractions to equivalent fractions with the denominator 360.
29/20 = (29 × 18)/360 = 522/360
17/72 = (17 × 5)/360 = 85/360

Step 3: Add the numerators and keep the denominator as 360.
(522/360) + (85/360) = (522 + 85)/360 = 607/360

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 607 and 360 is 1.
607/360 = (607/1) / (360/1) = 607/360

Therefore, the sum of 29/20 and 17/72 as a simplified fraction is 607/360.

### 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 Sonnet:

To calculate the value of the given expression, we need to perform the operations in the correct order, following the PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) rule.

Given expression: ((36 / 27) + (80 / 10)) - (73 / 79)

Step 1: Calculate the divisions inside the parentheses.
36 / 27 = 1.333...
80 / 10 = 8

Step 2: Calculate the expressions inside the parentheses by adding the results from Step 1.
(1.333... + 8) = 9.333...

Step 3: Calculate the division outside the parentheses.
73 / 79 = 0.924...

Step 4: Subtract the result from Step 3 from the result in Step 2.
9.333... - 0.924... = 8.409...

To simplify the answer, we can express it as a mixed fraction or a decimal value.

As a mixed fraction: 8 + 409/1000
As a decimal value: 8.409

### Answer: 8.409

Expected answer: 1993/237

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to perform the following steps:

1. Calculate (86 / 71)
   86 / 71 = 1.21126760563380...

2. Calculate (91 / 75)
   91 / 75 = 1.21333333333333...

3. Add the two results
   1.21126760563380... + 1.21333333333333... = 2.42460093896713...

4. Round the result to the nearest hundredth
   2.42460093896713... rounds to 2.42

Therefore, the answer to (86 / 71) + (91 / 75), rounded to the nearest hundredth, is:

### Answer: 2.42

Expected answer: 12911/5325

Correct? No

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

Claude-3 Sonnet:

To calculate ((21/75) + (74/43)) + (10/62), we need to find a common denominator for all the fractions involved. The least common multiple of 75, 43, and 62 is 10,290.

Step 1: Convert all fractions to equivalent fractions with the common denominator of 10,290.
21/75 = (21 × 137)/10,290 = 2,877/10,290
74/43 = (74 × 239)/10,290 = 17,686/10,290
10/62 = (10 × 166)/10,290 = 1,660/10,290

Step 2: Add the numerators of the equivalent fractions.
(2,877/10,290) + (17,686/10,290) + (1,660/10,290) = (2,877 + 17,686 + 1,660)/10,290 = 22,223/10,290

Step 3: Simplify the resulting fraction by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF.
The GCF of 22,223 and 10,290 is 3.
22,223/10,290 = (22,223/3)/(10,290/3) = 7,407/3,430

Therefore, the simplified result of ((21/75) + (74/43)) + (10/62) is 7,407/3,430.

### Answer: 7,407/3,430

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 Sonnet:

To compute ((75 / 66) + (81 / 61)), we need to find a common denominator for the fractions 75/66 and 81/61.

The least common multiple (LCM) of 66 and 61 is 2006.

So, we can convert the fractions to equivalent fractions with a common denominator of 2006:
75/66 = (75 × 30)/2006 = 2250/2006
81/61 = (81 × 33)/2006 = 2673/2006

Now, we can add the fractions:
(2250/2006) + (2673/2006) = 4923/2006

To reduce the fraction 4923/2006 to its lowest term, we need to find the greatest common divisor (GCD) of 4923 and 2006, and then divide both the numerator and denominator by the GCD.

The GCD of 4923 and 2006 is 1.

Therefore, the reduced fraction is 4923/2006.

### Answer: 4923/2006

Expected answer: 3307/1342

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the value of the fraction t and then add it to itself to find the total sum l.

Given information:
- t = 53/18 + 21/99
- We need to find the total sum l of two identical fractions t.

Step 1: Find the value of the fraction t.
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.

LCD of 18 and 99 = 198

53/18 = (53 × 11)/198 = 583/198
21/99 = (21 × 2)/198 = 42/198

t = 583/198 + 42/198
t = 625/198

Step 2: Find the total sum l of two identical fractions t.
l = t + t
l = 625/198 + 625/198
l = 1250/198

Step 3: Simplify the fraction l by dividing the numerator and denominator by their greatest common divisor (GCD).
GCD of 1250 and 198 = 2

l = (1250/2) / (198/2)
l = 625/99

Therefore, the total sum l of two identical fractions t is 625/99.

### Answer: 625/99

Expected answer: 625/99

Correct? Yes

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 Sonnet:

To solve this problem, we need to follow these steps:

1. Calculate 58/49 + 31/34
   * First, we need to find the least common denominator (LCD) of 49 and 34, which is 1666.
   * 58/49 = (58 × 34)/1666 = 1972/1666
   * 31/34 = (31 × 49)/1666 = 1519/1666
   * 1972/1666 + 1519/1666 = 3491/1666

2. Add 3491/1666 to 74/38
   * We need to find the LCD of 1666 and 38, which is 63108.
   * 3491/1666 = (3491 × 38)/63108 = 132658/63108
   * 74/38 = (74 × 1666)/63108 = 123484/63108
   * 132658/63108 + 123484/63108 = 256142/63108

3. Simplify the fraction 256142/63108
   * The greatest common divisor (GCD) of 256142 and 63108 is 6.
   * 256142/63108 = (256142/6)/(63108/6) = 42690/10518

Therefore, the final result as a simple fraction is 42690/10518.

### Answer: 42690/10518

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 Sonnet:

To solve this problem, we need to calculate the two fractions separately and then add them together.

Given information:
- 100 divided by 76
- 29 divided by 14

Step 1: Calculate 100 divided by 76.
100 ÷ 76 = 1.315789... (repeating decimal)

Step 2: Calculate 29 divided by 14.
29 ÷ 14 = 2.071428... (repeating decimal)

Step 3: Add the two fractions together.
1.315789... + 2.071428... = 3.387217... (repeating decimal)

To simplify the answer, we can convert the repeating decimal to a fraction.

3.387217... = 3 + 0.387217...
0.387217... = 387217/1000000 (repeating decimal)
= 387217/999999 (converting to a fraction)

Therefore, the sum of 100 divided by 76 and 29 divided by 14 can be expressed as:
3 + 387217/999999

### Answer: 3 + 387217/999999

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 Sonnet:

To solve this problem, we need to find a common denominator for the fractions 51/18 and 8/42, and then express them as equivalent fractions with the same denominator.

The least common multiple (LCM) of 18 and 42 is 126.

Step 1: Express 51/18 as an equivalent fraction with denominator 126.
51/18 = (51 × 7)/126 = 357/126

Step 2: Express 8/42 as an equivalent fraction with denominator 126.
8/42 = (8 × 3)/126 = 24/126

Since Evan has read 51/18 of the novel, and Olivia has read the same amount as Evan, which is 24/126, the total amount of the novel that Olivia has read is:

Total amount read by Olivia = 24/126 + 24/126 = 48/126

To simplify the fraction 48/126, we divide both the numerator and denominator by their greatest common divisor, which is 6.

48/126 = (48/6) / (126/6) = 8/21

Therefore, Olivia has read 8/21 of the novel in total.

### Answer: 8/21

Expected answer: 127/42

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the values of 48/13 and 31/22, and then add them together.

48/13 = 3.6923076923076925
31/22 = 1.4090909090909092

Adding these two values:
3.6923076923076925 + 1.4090909090909092 = 5.1013986013986017

Therefore, the sum of 48/13 and 31/22 is 5.1013986013986017.

To express the answer as a fraction, we can convert the decimal to a fraction by finding the closest fraction approximation.

The closest fraction approximation to 5.1013986013986017 is 103/20.

### Answer: 103/20

Expected answer: 1459/286

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to follow these steps:

Step 1: Find the value of 24/86 + 76/77
24/86 = 0.2790697674... (rounded to 4 decimal places)
76/77 = 0.9870129870... (rounded to 4 decimal places)
24/86 + 76/77 = 0.2790697674 + 0.9870129870 = 1.2660827544 (rounded to 4 decimal places)

Step 2: Find the value of 27/6
27/6 = 4.5

Step 3: Subtract the value obtained in Step 1 from the value obtained in Step 2
27/6 - (24/86 + 76/77) = 4.5 - 1.2660827544 = 3.2339172456 (rounded to 4 decimal places)

Therefore, the final answer is:
### Answer: 3.2339

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 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 39 and 14.
The LCM of 39 and 14 is 546.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 546.
73/39 = (73 × 14)/546
49/14 = (49 × 39)/546

Step 3: Add the numerators of the equivalent fractions.
(73 × 14)/546 + (49 × 39)/546 = 1022/546 + 1911/546 = 2933/546

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 2933 and 546 is 1.

Therefore, the simplified fraction 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 Sonnet:

To find the sum of 75/65 and 7/39, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 65 and 39 is 1365.

So, we convert both fractions to have a denominator of 1365.

75/65 = (75 × 21)/1365 = 1575/1365
7/39 = (7 × 35)/1365 = 245/1365

Now we can add the fractions:
1575/1365 + 245/1365 = 1820/1365

To simplify the fraction, we divide the numerator and denominator by their greatest common factor (GCF), which is 5.

1820/1365 = (1820/5) / (1365/5) = 364/273

Therefore, the sum of 75/65 and 7/39, simplified, is 364/273.

### Answer: 364/273

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 Sonnet:

To solve this problem, we need to perform the following steps:

Step 1: Calculate 79/1 - 30/92
79/1 = 79
30/92 = 0.326086956521739

79 - 0.326086956521739 = 78.673913043478261

Step 2: Subtract 61/63 from the result obtained in Step 1
61/63 = 0.968253968253968

78.673913043478261 - 0.968253968253968 = 77.705659075224293

Therefore, the final value is 77.705659075224293.

### Answer: 77.705659075224293

Expected answer: 225191/2898

Correct? No

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

Claude-3 Sonnet:

To calculate (58 / 26) + (58 / 26), we need to first find the value of 58 / 26.

58 / 26 = 2.23076923...

Now, we can add this value to itself:
(58 / 26) + (58 / 26) = 2.23076923... + 2.23076923... = 4.46153846...

To express the answer in simplest form, we can convert the decimal to a fraction.

4.46153846... = 446/100

The simplest form of 446/100 is 223/50.

Therefore, the simplest form of (58 / 26) + (58 / 26) is 223/50.

### Answer: 223/50

Expected answer: 58/13

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the value of 'k' first, and then add the additional 47/71 gallons to it.

Given information:
- Alex initially had 69/63 gallons of orange juice.
- Alex bought an additional 77/5 gallons of orange juice.
- The total amount of orange juice after the purchase is 'k' gallons.
- Alex received another 47/71 gallons of orange juice from Sally.

Step 1: Find the value of 'k' gallons.
69/63 + 77/5 = (69 × 5 + 77 × 63) / (63 × 5)
= (345 + 4851) / 315
= 5196 / 315
= 16.49 gallons

Therefore, 'k' = 16.49 gallons.

Step 2: Add the additional 47/71 gallons from Sally to 'k'.
'k' + 47/71 = 16.49 + (47 / 71)
= 16.49 + 0.66197183
= 17.15197183 gallons

Therefore, Alex had a total of 17.15197183 gallons of orange juice after receiving the additional amount from Sally.

### Answer: 17.15197183

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 Sonnet:

To solve this problem, we need to perform the operations inside the parentheses first, and then combine the results.

Given expression: ((100 / 61) + ((39 / 6) + (67 / 49)))

Step 1: Simplify the fractions inside the inner parentheses.
(39 / 6) = 6.5
(67 / 49) = 1.367346939...

Step 2: Add the fractions inside the inner parentheses.
(39 / 6) + (67 / 49) = 6.5 + 1.367346939... = 7.867346939...

Step 3: Simplify the fractions outside the parentheses.
(100 / 61) = 1.639344262...

Step 4: Add the results from Steps 2 and 3.
(100 / 61) + (7.867346939...) = 1.639344262... + 7.867346939... = 9.506691201...

To express the final result as a simplified fraction, we need to convert the decimal to a fraction.

9.506691201... = 9 + 506691201/1000000000
= 9 + (506691201 / 1000000000)
= (9000000000 + 506691201) / 1000000000
= 9506691201 / 1000000000

Therefore, the simplified fraction is:
### Answer: 9506691201/1000000000

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 Sonnet:

To find the sum of 85/1 and 83/69, we need to first convert them to equivalent fractions with the same denominator.

The least common multiple (LCM) of 1 and 69 is 69.

85/1 = 85/1 * 69/69 = 5865/69
83/69 = 83/69

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 factor (GCF) of 5948 and 69.
The GCF of 5948 and 69 is 1.

Therefore, the simplified fraction is 5948/69.

### 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 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 13 and 86.
The LCM of 13 and 86 is 1118.

Step 2: Convert the fractions to equivalent fractions with the common denominator 1118.
92/13 = (92 × 86)/1118 = 7912/1118
43/86 = (43 × 13)/1118 = 559/1118

Step 3: Add the fractions with the common denominator.
(7912/1118) + (559/1118) = 8471/1118

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 8471 and 1118 is 7.
8471/1118 = (8471/7)/(1118/7) = 1209/159

Therefore, the sum of 92/13 and 43/86 as a simplified fraction is 1209/159.

### Answer: 1209/159

Expected answer: 197/26

Correct? No

Problem: What is the sum of 67/32 and 10/98, expressed 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 32 and 98.
The LCM of 32 and 98 is 3136.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 3136.
67/32 = (67 × 98)/3136 = 6586/3136
10/98 = (10 × 32)/3136 = 320/3136

Step 3: Add the fractions with the common denominator.
(6586/3136) + (320/3136) = (6586 + 320)/3136 = 6906/3136

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 6906 and 3136 is 2.

Step 5: Divide the numerator and denominator by the GCF to simplify the fraction.
6906/3136 = (6906/2)/(3136/2) = 3453/1568

Therefore, the sum of 67/32 and 10/98, expressed as a simplified fraction, is 3453/1568.

### Answer: 3453/1568

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 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: 59/52 and 70/32

Step 1: Find the LCD of 52 and 32.
LCD = 52 × 32 / GCD(52, 32)
LCD = 52 × 32 / 4
LCD = 416

Step 2: Convert the fractions to equivalent fractions with the LCD as the denominator.
59/52 = (59 × 8)/416
59/52 = 472/416

70/32 = (70 × 13)/416
70/32 = 910/416

Step 3: Add the numerators and keep the LCD as the denominator.
Sum = (472 + 910)/416
Sum = 1382/416

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
GCD of 1382 and 416 is 2
1382/416 = (1382/2) / (416/2)
1382/416 = 691/208

Therefore, the sum of 59/52 and 70/32 as a simplified fraction 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 Sonnet:

To solve this problem, we need to follow the given order of operations.

Step 1: Calculate 48 divided by 5
48 ÷ 5 = 9.6

Step 2: Calculate 11 divided by 65
11 ÷ 65 = 0.1692307692307692

Step 3: Subtract the result of Step 2 from the result of Step 1
9.6 - 0.1692307692307692 = 9.4307692307692308

Step 4: Calculate 28 divided by 2
28 ÷ 2 = 14

Step 5: Add the result of Step 4 to the result of Step 3
9.4307692307692308 + 14 = 23.4307692307692308

### Answer: 23.4307692307692308

Expected answer: 1523/65

Correct? Yes

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

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.

The LCD of 52 and 82 is 1642 (the least common multiple of 52 and 82).

Converting 20/52 to an equivalent fraction with the denominator 1642:
20/52 = (20 × 31)/1642 = 620/1642

Converting 75/82 to an equivalent fraction with the denominator 1642:
75/82 = (75 × 20)/1642 = 1500/1642

Now we can add the fractions:
620/1642 + 1500/1642 = 2120/1642

To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.

The GCF of 2120 and 1642 is 2.

2120/1642 = (2120/2) / (1642/2) = 1060/821

Therefore, the simplified result is 1060/821.

### Answer: 1060/821

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 Sonnet:

To subtract fractions, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 84 and 5 is 420.

So, we convert both fractions to have a denominator of 420.

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

Now we can subtract:
(2604/420) - (460/420) = 2144/420

To simplify the fraction 2144/420, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 84.

2144/84 = 25.5
420/84 = 5

Therefore, the simplified fraction is 25.5/5 or 51/10.

### Answer: 51/10

Expected answer: 536/105

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the sum of 81/90 and 94/49, and then double the result.

Given:
- 81/90
- 94/49

Step 1: Find the common denominator for 81/90 and 94/49.
The least common multiple (LCM) of 90 and 49 is 1890.

Step 2: Convert the fractions to equivalent fractions with the common denominator of 1890.
81/90 = (81 × 21)/1890 = 1701/1890
94/49 = (94 × 38.57142857)/1890 = 3625/1890

Step 3: Find the sum of the equivalent fractions.
(1701/1890) + (3625/1890) = 5326/1890

Step 4: Double the sum.
Double of (5326/1890) = (5326 × 2)/1890 = 10652/1890

Therefore, the double of the sum of 81/90 and 94/49 is 10652/1890.

### Answer: 10652/1890

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 Sonnet:

To find the difference between 69/21 and 10/92, we need to first find a common denominator for both fractions.

The least common multiple (LCM) of 21 and 92 is 1092.

So, we convert both fractions to have a denominator of 1092.

69/21 = (69 × 52)/1092 = 3588/1092
10/92 = (10 × 12)/1092 = 120/1092

Now we can subtract:
3588/1092 - 120/1092 = 3468/1092

To write the answer as a simple fraction, we need to divide the numerator and denominator by their greatest common factor (GCF).

The GCF of 3468 and 1092 is 12.

3468/1092 = (3468/12) / (1092/12) = 289/91

### Answer: 289/91

Expected answer: 1023/322

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to perform the following steps:

Step 1: Calculate (26 / 87) + (92 / 88)
(26 / 87) = 0.2988505747126437
(92 / 88) = 1.0454545454545454
(26 / 87) + (92 / 88) = 0.2988505747126437 + 1.0454545454545454 = 1.3443051201671891

Step 2: Calculate (26 / 57)
(26 / 57) = 0.45614035087719296

Step 3: Add the results from Step 1 and Step 2
1.3443051201671891 + 0.45614035087719296 = 1.8004454710443821

### Answer: 1.8004454710443821

Expected answer: 21825/12122

Correct? Yes

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 Sonnet:

To solve this problem, we need to find a common denominator for all the fractions and then add the fractions by converting them to equivalent fractions with the common denominator.

Given fractions:
78/66
28/6
90/34

Step 1: Find the least common multiple (LCM) of the denominators 66, 6, and 34.
LCM of 66, 6, and 34 = 1122

Step 2: Convert each fraction to an equivalent fraction with the denominator 1122.
78/66 = (78 × 17)/1122 = 1326/1122
28/6 = (28 × 187)/1122 = 5236/1122
90/34 = (90 × 33)/1122 = 2970/1122

Step 3: Add the numerators of the equivalent fractions.
1326/1122 + 5236/1122 + 2970/1122 = 9532/1122

Step 4: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by the GCF.
GCF of 9532 and 1122 = 2
9532/1122 = (9532/2) / (1122/2) = 4766/561

Therefore, the result of adding 78/66, 28/6, and 90/34 together as a simplified fraction is:
### 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 Sonnet:

To calculate (12/7) - (9/23), we need to find a common denominator for the fractions and then subtract the second fraction from the first.

Step 1: Find the least common multiple (LCM) of 7 and 23 to get the common denominator.
LCM of 7 and 23 = 161

Step 2: Convert the fractions to equivalent fractions with the common denominator of 161.
12/7 = (12 × 23)/161 = 276/161
9/23 = (9 × 7)/161 = 63/161

Step 3: Subtract the fractions.
(276/161) - (63/161) = 213/161

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor (GCF).
GCF of 213 and 161 = 1
213/161 = (213/1) / (161/1) = 213/161

Therefore, the simplified answer is:
### Answer: 213/161

Expected answer: 213/161

Correct? Yes

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

Claude-3 Sonnet:

To calculate the sum of 95/18 and 51/61, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 18 and 61 is 1098.

So, we convert both fractions to have a denominator of 1098:
95/18 = (95 × 61)/1098 = 5795/1098
51/61 = (51 × 18)/1098 = 918/1098

Now we can add the fractions:
5795/1098 + 918/1098 = 6713/1098

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 6713 and 1098 is 7.

Therefore, the simplified fraction is:
6713/1098 = (6713/7)/(1098/7) = 959/157

### Answer: 959/157

Expected answer: 6713/1098

Correct? No

Problem: Calculate the following subtraction of fractions: (93 / 46) - (51 / 84). 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 (LCM) of 46 and 84 is 1932.

Step 1: Convert both fractions to equivalent fractions with the same denominator (1932).
(93/46) = (93 × 42/46 × 42) = 1953/1932
(51/84) = (51 × 23/84 × 23) = 1173/1932

Step 2: Subtract the numerators.
(1953/1932) - (1173/1932) = (1953 - 1173)/1932 = 780/1932

Step 3: Simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
The GCF of 780 and 1932 is 12.
780/1932 = (780/12) / (1932/12) = 65/161

Therefore, the simplified fraction for (93/46) - (51/84) is 65/161.

### Answer: 65/161

Expected answer: 911/644

Correct? No

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

Claude-3 Sonnet:

To calculate the sum of the fractions 12/70 and 84/9, we need to find a common denominator and then add the fractions.

Step 1: Find the least common multiple (LCM) of 70 and 9 to get the common denominator.
LCM of 70 and 9 = 630

Step 2: Convert the fractions to equivalent fractions with the common denominator of 630.
12/70 = (12 × 9)/630 = 108/630
84/9 = (84 × 70)/630 = 5880/630

Step 3: Add the fractions with the common denominator.
(108/630) + (5880/630) = 5988/630

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
GCD of 5988 and 630 = 6
5988/630 = (5988/6) / (630/6) = 998/105

Therefore, the sum of the fractions 12/70 and 84/9 in simplified form is 998/105.

### Answer: 998/105

Expected answer: 998/105

Correct? Yes

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

Claude-3 Sonnet:

To solve this problem, we need to follow these steps:

1. Convert the fractions to have a common denominator.
   40/92 = 120/276
   32/3 = 9408/276

2. Subtract 120/276 from 9408/276.
   9408/276 - 120/276 = 9288/276

3. Simplify the fraction 9288/276.
   9288/276 = 33.6 (rounded to 1 decimal place)

4. Double the result.
   33.6 × 2 = 67.2

Therefore, if you subtract 40/92 from 32/3 and double the result, you would get 67.2.

### Answer: 67.2

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 Sonnet:

To find the sum of 79/24 and 79/24, we need to add the fractions.

79/24 + 79/24 = (79 + 79)/24
            = 158/24
            = 6 6/24 (Dividing the numerator by the denominator)
            = 6 1/4 (Simplifying the fraction)

Therefore, the sum of 79/24 and 79/24 is 6 1/4.

### Answer: 6 1/4

Expected answer: 79/12

Correct? No

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

Claude-3 Sonnet:

To find the sum of 91/76 and 12/22, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 76 and 22 is 532.

So, we convert both fractions to have a denominator of 532:
91/76 = (91 × 7)/532 = 637/532
12/22 = (12 × 24)/532 = 288/532

Now we can add the fractions:
637/532 + 288/532 = 925/532

To simplify the fraction 925/532, we need to find the greatest common factor (GCF) of 925 and 532.
The GCF of 925 and 532 is 5.

925/532 = (925/5)/(532/5) = 185/106

Therefore, the simplified sum of 91/76 and 12/22 is 185/106.

### Answer: 185/106

Expected answer: 1457/836

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to follow these steps:

1. Find a common denominator for 88/93 and 6/47
2. Convert both fractions to equivalent fractions with the common denominator
3. Add the numerators of the equivalent fractions
4. Simplify the resulting fraction
5. Add the simplified fraction to 92/4
6. Simplify the final result

Step 1: The least common multiple of 93 and 47 is 4371. This will be our common denominator.

Step 2: Convert the fractions to equivalent fractions with the denominator 4371.
88/93 = (88 × 47)/4371 = 4136/4371
6/47 = (6 × 93)/4371 = 558/4371

Step 3: Add the numerators of the equivalent fractions.
4136/4371 + 558/4371 = 4694/4371

Step 4: Simplify the resulting fraction.
4694/4371 = 1074/1001

Step 5: Add the simplified fraction to 92/4.
1074/1001 + 92/4 = (1074 × 4 + 92 × 1001)/4004 = 4368/4004

Step 6: Simplify the final result.
4368/4004 = 1092/1001

Therefore, the final answer is 1092/1001.

### Answer: 1092/1001

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 Sonnet:

To solve this problem, we need to find the sum of the fractions 95/83 and (52/21 + 75/67).

First, let's find the sum of 52/21 and 75/67.
We need to find the least common denominator (LCD) of 21 and 67, which is 201 (21 × 9 = 189, 67 × 3 = 201).

52/21 = (52 × 9)/189 = 468/189
75/67 = (75 × 3)/201 = 225/201

468/189 + 225/201 = (468 × 201 + 225 × 189) / (189 × 201)
                  = 93768 + 42525 / 37989
                  = 136293 / 37989
                  = 3 58/37989

Now, we need to add 95/83 and 3 58/37989.
The LCD of 83 and 37989 is 83 × 457 = 37989.

95/83 = (95 × 457) / 37989 = 43415 / 37989
3 58/37989 = 3 58/37989

43415/37989 + 3 58/37989 = (43415 + 3 × 37989 + 58) / 37989
                          = 43415 + 113967 + 58 / 37989
                          = 157440 / 37989
                          = 4 5/37989

Therefore, the sum of 95/83 and (52/21 + 75/67) as a simplified fraction is 4 5/37989.

### Answer: 4 5/37989

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 Sonnet:

To solve this problem, we need to perform the division operations and then subtract the resulting values.

Given expression: ((73 / 27) - (23 / 48))

Step 1: Simplify the fraction 73 / 27
73 / 27 = 2 (with a remainder of 19)
73 / 27 = 2 + (19 / 27)
73 / 27 = 2 + (19 × 4 / 108)
73 / 27 = 2 + (76 / 108)
73 / 27 = 2 69/108

Step 2: Simplify the fraction 23 / 48
23 / 48 = 23 × 2 / 96
23 / 48 = 46 / 96
23 / 48 = 23 / 48

Step 3: Subtract the fractions
(2 69/108) - (23 / 48)
= (2 69/108) - (46 / 96)
= (2 69/108) - (23 / 48)
= (264 / 108) - (46 / 96)
= (264 × 4 / 432) - (46 × 4 / 384)
= 1056 / 432 - 184 / 384
= 1056 / 432 - 552 / 1152
= 504 / 1152

Therefore, the value of the expression ((73 / 27) - (23 / 48)) as a simplified fraction is 7/16.

### Answer: 7/16

Expected answer: 961/432

Correct? No

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

Claude-3 Sonnet:

To solve this expression, we need to perform the division operations first, and then subtract the results.

Given expression: (78 / 2) - (70 / 23)

Step 1: Perform the division operations.
78 / 2 = 39
70 / 23 = 3.043478261 (rounded to 9 decimal places)

Step 2: Subtract the results.
39 - 3.043478261 = 35.956521739

Therefore, the simplified decimal answer is:

### Answer: 35.956521739

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 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.

The LCD of 1 and 4 is 4.

34/1 = 34/1 * 4/4 = 136/4
53/4 = 53/4

Now we can add the fractions:
136/4 + 53/4 = (136 + 53)/4 = 189/4

To express the answer as a mixed number, we divide 189 by 4 to get the whole number part and the remainder as the fractional part.

189/4 = 47 with a remainder of 1

Therefore, the mixed number representation is 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 Sonnet:

To find the sum of two fractions, we need to find a common denominator and then add the numerators.

The least common multiple of 36 and 96 is 288.

So, we convert the fractions to have a denominator of 288:
3/36 = 24/288
97/96 = 242/288

Now we can add the numerators:
24/288 + 242/288 = 266/288

To simplify the fraction, we divide the numerator and denominator by their greatest common factor, which is 2:
266/288 = 133/144

Therefore, the sum of 3/36 and 97/96 as a simplified fraction is:
### Answer: 133/144

Expected answer: 35/32

Correct? No

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

Claude-3 Sonnet:

To calculate ((92 / 95) + (4 / 74)), we need to find a common denominator for the fractions and then add the fractions.

Step 1: Find the least common multiple (LCM) of 95 and 74 to get the common denominator.
LCM of 95 and 74 = 6,630

Step 2: Convert the fractions to equivalent fractions with the common denominator of 6,630.
92/95 = (92 × 69.8947...)/6,630 = 6,430/6,630
4/74 = (4 × 89.5945...)/6,630 = 358/6,630

Step 3: Add the fractions.
(6,430/6,630) + (358/6,630) = 6,788/6,630

Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
GCD of 6,788 and 6,630 = 2
6,788/6,630 = (6,788/2) / (6,630/2) = 3,394/3,315

Therefore, the simplified fraction for ((92 / 95) + (4 / 74)) is 3,394/3,315.

### Answer: 3,394/3,315

Expected answer: 3594/3515

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to find the value of 'v' first, and then add it to 88/72.

Given information:
- v = 69/47
- d = 88/72 + v

Step 1: Find the value of v.
v = 69/47

Step 2: Find the value of 88/72.
88/72 = 1.22222...

Step 3: Add v to 88/72 to find the value of d.
d = 88/72 + v
d = 1.22222... + 69/47
d = 1.22222... + 1.46808...
d = 2.69030...

To express the final answer as a fraction, we need to find the common denominator for 1.22222... and 1.46808....

The common denominator is 144 (since 72 × 2 = 144 and 47 × 3 = 141).

d = (88 + 69) / 144
d = 157 / 144

Therefore, the value of d is 157/144.

### Answer: 157/144

Expected answer: 1138/423

Correct? No

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

Claude-3 Sonnet:

To solve this problem, we need to convert the mixed fractions to improper fractions, perform the subtraction, and then convert the result back to a mixed fraction or a simple fraction, if possible.

Given information:
- The wholesaler initially has 41/26 barrels of olive oil.
- They sell 41/72 barrels of olive oil.

Step 1: Convert the mixed fractions to improper fractions.
41/26 = (41 × 1 + 0) / 26 = 41/26
41/72 = (41 × 0 + 0) / 72 = 0 + 41/72 = 41/72

Step 2: Perform the subtraction.
(41/26) - (41/72) = (41 × 72/72 - 41 × 26/72) / 72
= (2952/72 - 1066/72) / 72
= 1886/72

Step 3: Convert the result to a simple fraction, if possible.
1886/72 = (1886 × 1/72) / 1
= 26 + (14/72)

Therefore, the amount of olive oil the wholesaler has now is 14/72 barrels.

### Answer: 14/72

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 Sonnet:

To find the sum of 85/75 and 88/56, we need to first convert the fractions to have a common denominator.

The least common multiple of 75 and 56 is 1200.

85/75 = (85 × 16)/1200 = 1360/1200 = 1.133333...
88/56 = (88 × 21.428571...)/1200 = 1885.714286/1200 = 1.571428...

Now we can add the converted fractions:
1.133333... + 1.571428... = 2.704761...

Therefore, the sum of 85/75 and 88/56 in decimal form is 2.705.

### Answer: 2.705

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 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.

The LCD of 33 and 2 is 66.

Converting the fractions:
12/33 = (12 × 2)/66 = 24/66
49/2 = (49 × 33)/66 = 1617/66

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

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

Therefore, the mixed fraction is 24 57/66.

### Answer: 24 57/66

Expected answer: 547/22

Correct? Yes

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

Claude-3 Sonnet:

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

Given fractions:
78/65 + 78/65

Step 1: Add the numerators.
78 + 78 = 156

Step 2: Keep the denominator the same.
The denominator is 65.

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

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 156 and 65 is 13.

156/13 = 12
65/13 = 5

Therefore, the simplified fraction is:
12/5

### Answer: 12/5

Expected answer: 12/5

Correct? Yes

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

Claude-3 Sonnet:

To calculate the sum of 16/7 and 11/90, we need to find a common denominator for both fractions.

The least common multiple (LCM) of 7 and 90 is 630.

So, we convert both fractions to have a denominator of 630.

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

Now we can add the fractions:
1440/630 + 77/630 = 1517/630

To simplify the fraction 1517/630, we need to find the greatest common factor (GCF) of 1517 and 630.

The GCF of 1517 and 630 is 7.

1517/630 = (1517/7)/(630/7) = 217/90

### Answer: 217/90

Expected answer: 1517/630

Correct? No