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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Find the sum of 48/56 and 95/23:

First, we need to find a common denominator for the two fractions. The least common multiple of 56 and 23 is 1624. So, we can convert both fractions to have a denominator of 1624:

48/56 = (48*29)/(56*29) = 1392/1624
95/23 = (95*71)/(23*71) = 6765/1624

Now, we can add the two fractions:

(1392/1624) + (6765/1624) = (1392 + 6765)/1624 = 8157/1624

2. Subtract 34/26 from the result:

Again, we need to find a common denominator. The least common multiple of 1624 and 26 is 42176. So, we can convert both fractions to have a denominator of 42176:

8157/1624 = (8157*26)/(1624*26) = 212082/42176
34/26 = (34*1624)/(26*1624) = 55336/42176

Now, we can subtract the two fractions:

(212082/42176) - (55336/42176) = (212082 - 55336)/42176 = 156746/42176

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

156746/42176 = (156746/2)/(42176/2) = 78373/21088

So, John found that the value of the operation is 78373/21088.

### Answer: 78373/21088

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?

Llama 3 70B:

To add the fractions 88/9 and 28/65, we need to find a common denominator, which is 585. So, we can rewrite the fractions as:

88/9 = 520/585
28/65 = 196/585

Now, we can add them:

520/585 + 196/585 = 716/585

Next, we need to subtract 18/37 from the result. Again, we need to find a common denominator, which is 2165. So, we can rewrite the fractions as:

716/585 = 2596/2165
18/37 = 468/2165

Now, we can subtract:

2596/2165 - 468/2165 = 2128/2165

So, the result expressed as a simple fraction is:

### Answer: 2128/2165

Expected answer: 210434/21645

Correct? No

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

Llama 3 70B:

To simplify the expression, we need to evaluate the fractions and then add them.

First, let's evaluate the fractions:

(63 / 41) = 63 ÷ 41 = 1 22/41
(44 / 50) = 44 ÷ 50 = 0.88 = 22/25

Now, let's add the fractions:

1 22/41 + 22/25 = 1 + (22/41 + 22/25)

To add the fractions, we need to find the least common multiple (LCM) of 41 and 25, which is 205.

So, we can rewrite the fractions with the LCM as the denominator:

22/41 = 110/205
22/25 = 88/205

Now, we can add the fractions:

1 + (110/205 + 88/205) = 1 + 198/205 = 1 198/205

### Answer: 1 198/205

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.

Llama 3 70B:

Reasoning: To add these fractions, we need to find a common denominator. The least common multiple of 41 and 77 is 3187. So, we can convert both fractions to have a denominator of 3187:

71/41 = (71*77)/(41*77) = 5487/3187
41/77 = (41*41)/(77*41) = 1681/3187

Now we can add:

5487/3187 + 1681/3187 = (5487 + 1681)/3187 = 7168/3187

This fraction is already in its simplest form.

### Answer: 7168/3187

Expected answer: 7148/3157

Correct? No

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

Llama 3 70B:

To calculate the result, we need to find a common denominator for the two fractions. The least common multiple of 65 and 35 is 455. So, we can convert both fractions to have a denominator of 455:

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

Now we can add the two fractions:

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

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 13:

798/455 = (798/13)/(455/13) = 66/35

### Answer: 66/35

Expected answer: 114/65

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 81 and 47 is 3789. So, we can convert both fractions to have a denominator of 3789:

75/81 = (75*47)/(81*47) = 3525/3789
97/47 = (97*81)/(47*81) = 7847/3789

Now we can add:

3525/3789 + 7847/3789 = (3525 + 7847)/3789 = 11372/3789

### Answer: 11372/3789

Expected answer: 3794/1269

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 88 by 1: 88/1 = 88
2. Divide 38 by 53: 38/53 = 38/53 (this is already a simplified fraction)
3. Subtract 38/53 from 88: 88 - 38/53

To subtract a fraction from a whole number, we need to convert the whole number to a fraction with a denominator of 53:

88 = 88/1 = (88 × 53)/53 = 4696/53

Now we can subtract:

4696/53 - 38/53 = (4696 - 38)/53 = 4658/53

So, the result is:

### Answer: 4658/53

Expected answer: 4626/53

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 80 by 94: 80 / 94 = 80/94
2. Divide 78 by 59: 78 / 59 = 78/59
3. Add the two results: (80/94) + (78/59)

To add these fractions, we need to find a common denominator. The least common multiple of 94 and 59 is 5518. So, we can convert both fractions to have a denominator of 5518:

(80/94) = (440/5518)
(78/59) = (738/5518)

Now we can add:

(440/5518) + (738/5518) = (1178/5518)

This is the simplified form of the expression.

### Answer: 1178/5518

Expected answer: 6026/2773

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 56 and 50 is 1400. So, we can convert both fractions to have a denominator of 1400:

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

Now we can add:

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

This fraction is already in simplest form.

### 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.

Llama 3 70B:

First, let's find the sum of 96/11 and 12/5:

96/11 = 96/11
12/5 = (12*11)/(5*11) = 132/55

Now, add them:

(96/11) + (132/55) = (528+132)/55 = 660/55

Next, subtract 38/87 from the sum:

(660/55) - (38/87) = (660*87 - 38*55)/(55*87) = (57540 - 2090)/4795 = 55450/4795

### Answer: 55450/4795

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.

Llama 3 70B:

Let's break it down step by step:

1. 82 divided by 9: 82 ÷ 9 = 9 1/9 = 91/9
2. 82 divided by 63: 82 ÷ 63 = 1 19/63
3. Subtract the two results: 91/9 - 1 19/63 = 91/9 - 82/63

To subtract these fractions, we need a common denominator, which is 567 (9 × 63). So, we can rewrite the fractions as:

91/9 = 567/63
82/63 = 82/63

Now, subtract:

567/63 - 82/63 = 485/63

So, the resulting value is 485/63.

### Answer: 485/63

Expected answer: 164/21

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Calculate the value of 23/3:
23/3 = 23 ÷ 3 = 7 2/3 = 23/3

2. Calculate the sum of 80/91 and 26/24:
80/91 + 26/24 = 80/91 + 13/12 (since 26/24 = 13/12)

To add these fractions, we need a common denominator, which is 1092. So, we can rewrite the fractions as:
80/91 = 880/1092
13/12 = 953/1092

Now, we can add them:
880/1092 + 953/1092 = 1833/1092

3. Subtract the sum from 23/3:
23/3 - 1833/1092 = ?

To subtract these fractions, we need a common denominator, which is 1092. So, we can rewrite 23/3 as:
23/3 = 2531/1092

Now, we can subtract:
2531/1092 - 1833/1092 = 698/1092

So, the final answer is:
### Answer: 698/1092

Expected answer: 6229/1092

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 18 and 60 is 180. So, we can convert both fractions to have a denominator of 180:

37/18 = (37*10)/(18*10) = 370/180
24/60 = (24*3)/(60*3) = 72/180

Now we can add:

370/180 + 72/180 = (370+72)/180 = 442/180

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 2:

442/180 = (442/2)/(180/2) = 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.

Llama 3 70B:

To find the sum of 33/41 and 95/62, we need to find a common denominator between 41 and 62. The least common multiple (LCM) of 41 and 62 is 2542. So, we can convert both fractions to have a denominator of 2542:

33/41 = (33*62)/(41*62) = 2058/2542
95/62 = (95*41)/(62*41) = 3905/2542

Now we can add the two fractions:

2058/2542 + 3905/2542 = (2058 + 3905)/2542 = 5963/2542

So, the sum of 33/41 and 95/62 is 5963/2542.

### Answer: 5963/2542

Expected answer: 5941/2542

Correct? No

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

Llama 3 70B:

To evaluate the expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   ((30 / 11) + (72 / 38)) = (30/11) + (72/38)
   = (270/11*38) + (792/11*38)  (common denominator)
   = (270 + 792) / (11*38)
   = 1062 / 418
   = 253 / 101  (simplified)

2. Add the result to (81 / 34):
   (253 / 101) + (81 / 34)
   = (253*34) / (101*34) + (81*101) / (34*101)  (common denominator)
   = (8582 + 8181) / (101*34)
   = 16763 / 3434
   = 16763/3434  (already simplified)

### Answer: 16763/3434

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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   (64 / 34) = 64/34 = 32/17
   (3 / 24) = 3/24 = 1/8

2. Add the results:
   (32/17) + (1/8) = (32*8 + 1*17) / (17*8) = (256 + 17) / 136 = 273 / 136

3. Evaluate the last expression:
   (41 / 96)

4. Add the results:
   (273 / 136) + (41 / 96) = (273*96 + 41*136) / (136*96) = (26208 + 5606) / 13056 = 31814 / 13056

To simplify the fraction, we can find the greatest common divisor (GCD) of 31814 and 13056, which is 2. Divide both numerator and denominator by 2:
   (31814 / 2) / (13056 / 2) = 15907 / 6528

### Answer: 15907/6528

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?

Llama 3 70B:

To calculate the final answer, we need to follow the order of operations.

First, let's add 83/73 and 53/77:

w = 83/73 + 53/77

To add these fractions, we need to find a common denominator, which is 73 × 77 = 5621. So, we can rewrite the fractions with this denominator:

w = (83 × 77) / 5621 + (53 × 73) / 5621
w = 6401 / 5621 + 3879 / 5621
w = (6401 + 3879) / 5621
w = 10280 / 5621

Now, we need to add 80/76 to w:

Final answer = w + 80/76

Again, we need to find a common denominator, which is 5621 × 76 = 426596. So, we can rewrite the fractions with this denominator:

Final answer = (10280 × 76) / 426596 + (80 × 5621) / 426596
Final answer = 781280 / 426596 + 449680 / 426596
Final answer = (781280 + 449680) / 426596
Final answer = 1230960 / 426596

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

Final answer = 307740 / 106649

### Answer: 307740/106649

Expected answer: 307360/106799

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 20 and 66 is 660. So, we can convert both fractions to have a denominator of 660:

27/20 = (27*33)/(20*33) = 891/660
14/66 = (14*10)/(66*10) = 140/660

Now we can add:

891/660 + 140/660 = 1031/660

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 11:

1031/660 = (1031/11)/(660/11) = 93/60

We can simplify further by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

93/60 = (93/3)/(60/3) = 31/20

### Answer: 31/20

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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 32 by 14: 32 ÷ 14 = 32/14 = 16/7
2. Divide 22 by 47: 22 ÷ 47 = 22/47
3. Subtract the two results: (16/7) - (22/47)

To subtract these fractions, we need to find a common denominator, which is 329. So, we can rewrite the fractions as:

(16/7) = (736/329)
(22/47) = (176/329)

Now, subtract:

(736/329) - (176/329) = (736 - 176)/329 = 560/329

So, the result of the expression is:

### Answer: 560/329

Expected answer: 598/329

Correct? No

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

Llama 3 70B:

To find the sum of 74/61 and 41/53, we need to find a common denominator between 61 and 53. The least common multiple (LCM) of 61 and 53 is 3233.

So, we can convert both fractions to have a denominator of 3233:

74/61 = (74 × 53) / (61 × 53) = 3922 / 3233
41/53 = (41 × 61) / (53 × 61) = 2511 / 3233

Now, we can add the two fractions:

3922 / 3233 + 2511 / 3233 = (3922 + 2511) / 3233 = 6433 / 3233

### Answer: 6433/3233

Expected answer: 6423/3233

Correct? No

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

Llama 3 70B:

Let's break it down step by step:

1. Evaluate the expression inside the parentheses:
94 / 2 = 47
74 / 57 = 1 (approximately, since 74 is not exactly divisible by 57)

So, the expression becomes:
47 - 1 = 46

2. Now, add the result to 56 / 97:
46 + 56 / 97

To add these two numbers, we need to convert 46 to a fraction with a denominator of 97:
46 = 4492 / 97

Now, add the fractions:
4492 / 97 + 56 / 97 = 4548 / 97

### Answer: 4548/97

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.

Llama 3 70B:

To find the sum, we need to follow the order of operations (PEMDAS):

1. Calculate the sum of 24/34 and 44/87:
   To add these fractions, we need a common denominator, which is 2856. So, we can rewrite the fractions as:
   24/34 = 696/2856
   44/87 = 1372/2856
   Now, we can add them:
   696/2856 + 1372/2856 = 2068/2856

2. Calculate the sum of 14/89 and the result from step 1:
   Again, we need a common denominator, which is 25104. So, we can rewrite the fractions as:
   14/89 = 2816/25104
   2068/2856 = 20680/25104
   Now, we can add them:
   2816/25104 + 20680/25104 = 23496/25104

We can simplify the fraction 23496/25104 by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
   23496 ÷ 4 = 5874
   25104 ÷ 4 = 6276
   So, the simplified fraction is:
### Answer: 5874/6276

Expected answer: 180194/131631

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 30 and 60 is 60. So, we can convert 73/30 to 146/60.

Now, we can add:

146/60 + 8/60 = 154/60

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

154 ÷ 2 = 77
60 ÷ 2 = 30

So, the result 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.

Llama 3 70B:

To find the result, we need to follow the order of operations.

First, let's add the first fraction (82/49) with the second one (45/60):

To add these fractions, we need to find a common denominator, which is 2940. So, we can convert both fractions to have a denominator of 2940:

82/49 = (82*60)/(49*60) = 4920/2940
45/60 = (45*49)/(60*49) = 2205/2940

Now, we can add them:

d = 4920/2940 + 2205/2940 = 7125/2940

Next, we need to add 'd' to the third fraction (99/59):

To add these fractions, we need to find a common denominator, which is 17220. So, we can convert both fractions to have a denominator of 17220:

7125/2940 = (7125*59)/(2940*59) = 42125/17220
99/59 = (99*294)/(59*294) = 29106/17220

Now, we can add them:

result = 42125/17220 + 29106/17220 = 71231/17220

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1722:

result = (71231 ÷ 1722) / (17220 ÷ 1722) = 41/10

### Answer: 41/10

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.

Llama 3 70B:

Let's break it down step by step:

Step 1: Subtract 76/30 from 91/16

To subtract these fractions, we need to find a common denominator. The least common multiple of 16 and 30 is 240. So, we can convert both fractions to have a denominator of 240:

91/16 = (91 × 15) / (16 × 15) = 1365/240
76/30 = (76 × 8) / (30 × 8) = 608/240

Now, we can subtract:

1365/240 - 608/240 = (1365 - 608) / 240 = 757/240

Step 2: Add the answer to 18/44

Again, we need to find a common denominator. The least common multiple of 240 and 44 is 1320. So, we can convert both fractions to have a denominator of 1320:

757/240 = (757 × 5.5) / (240 × 5.5) = 4163.5/1320
18/44 = (18 × 30) / (44 × 30) = 540/1320

Now, we can add:

4163.5/1320 + 540/1320 = (4163.5 + 540) / 1320 = 4703.5/1320

To round the final answer to the nearest hundredth, we can convert the fraction to a decimal:

4703.5/1320 ≈ 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.

Llama 3 70B:

Let's break it down step by step:

1. Calculate the first part: (8 / 91) + (49 / 5)
= (8/91) + (49/5)
= (8/91) + (98.8/10) ( converted 49/5 to a decimal and then to a fraction with a denominator of 10)
= (8/91) + (980/910)
= (72+980)/910
= 1052/910

2. Simplify the fraction: 1052/910
= (2*526)/(2*455)
= 526/455

So, the result of the first part is 526/455.

3. Calculate the second part: (32 / 76)
= (32/76)
= (4*8)/(4*19)
= 8/19

4. Subtract the second part from the first part:
= 526/455 - 8/19
= (526*19)/(455*19) - (8*455)/(19*455)
= 10004/8685 - 3640/8685
= (10004-3640)/8685
= 6364/8685

5. Simplify the fraction: 6364/8685
= (4*15841)/(5*17337)
= 15841/43345

### Answer: 15841/43345

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.

Llama 3 70B:

Let's break it down step by step:

1. Calculate the value of (75 / 45):
(75 / 45) = 5/3

2. Calculate the value of (5 / 49):
(5 / 49) = 5/49

3. Add the values:
(5/3) + (5/49) = (245 + 15) / (3 * 49) = 260 / 147

4. Now, add this value with 3 / 58:
(260 / 147) + (3 / 58) = (260 * 58 + 3 * 147) / (147 * 58) = (15080 + 441) / 8526 = 15521 / 8526

### Answer: 15521/8526

Expected answer: 15521/8526

Correct? Yes

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 43 by 15: 43 ÷ 15 = 43/15 = 2.87 (approximately)
2. Divide 33 by 95: 33 ÷ 95 = 33/95 = 0.35 (approximately)
3. Subtract the two results: 2.87 - 0.35 = 2.52

To simplify the result to its lowest terms, we can convert the decimal to a fraction:

2.52 = 252/100 = 63/25

### Answer: 63/25

Expected answer: 718/285

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the fractions inside the parentheses:
   (78 / 45) = 174 / 90 = 29 / 15
   (89 / 36) = 89 / 36

2. Add the fractions:
   (29 / 15) + (89 / 36) = (1044 + 1335) / 540 = 2379 / 540

3. Add the result to itself:
   (2379 / 540) + (2379 / 540) = (2379 + 2379) / 540 = 4758 / 540

4. Simplify the fraction:
   4758 / 540 = 1586 / 180 = 793 / 90

### Answer: 793 / 90

Expected answer: 757/90

Correct? No

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

Llama 3 70B:

Let's break it down step by step:

1. Divide 93 by 34: 93 ÷ 34 = 93/34
2. Convert the result to a mixed number: 93/34 = 2 29/34
3. Convert the mixed number back to an improper fraction: 2 29/34 = (2 × 34 + 29) / 34 = 87/34
4. Subtract 77/74 from the result: 87/34 - 77/74
5. Find the least common multiple (LCM) of 34 and 74, which is 1424. Convert both fractions to have a denominator of 1424:
   87/34 = (87 × 42) / (34 × 42) = 3654/1424
   77/74 = (77 × 19) / (74 × 19) = 1463/1424
6. Subtract the fractions: 3654/1424 - 1463/1424 = (3654 - 1463) / 1424 = 2191/1424
7. Simplify the fraction: 2191/1424 is already in its simplest form.

### Answer: 2191/1424

Expected answer: 1066/629

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 35 and 85 is 595. So, we can convert both fractions to have a denominator of 595:

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

Now we can add:

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

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 7:

1938/595 = (1938/7)/(595/7) = 278/85

### Answer: 278/85

Expected answer: 114/35

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 53 and 94 is 4978. So, we can convert both fractions to have a denominator of 4978:

99/53 = (99*94)/(53*94) = 9316/4978
67/94 = (67*53)/(94*53) = 3531/4978

Now we can add:

9316/4978 + 3531/4978 = (9316 + 3531)/4978 = 12847/4978

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 1. So, the sum in simplest form is:

### Answer: 12847/4978

Expected answer: 12857/4982

Correct? No

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

Llama 3 70B:

To subtract these fractions, we need to find a common denominator. The least common multiple of 27 and 33 is 297. So, we can rewrite the fractions as:

74/27 = (74*11)/(27*11) = 814/297
56/33 = (56*9)/(33*9) = 504/297

Now we can subtract:

814/297 - 504/297 = (814-504)/297 = 310/297

This fraction is already in its simplest form.

### 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.

Llama 3 70B:

First, let's find the sum of 96/40 and 11/99:

96/40 = 24/10 = 12/5
11/99 = 11/99

To add these fractions, we need a common denominator, which is 495. So, we can convert both fractions to have a denominator of 495:

12/5 = 12*99/5*99 = 2376/495
11/99 = 11*5/99*5 = 55/495

Now, we can add:

2376/495 + 55/495 = 2431/495

Next, let's subtract 91/65 from this result:

91/65 = 91*7.5/65*7.5 = 682.5/487.5

To subtract, we need a common denominator, which is 2437.5. So, we can convert both fractions to have a denominator of 2437.5:

2431/495 = 2431*4.93/495*4.93 = 11993.23/2437.5
682.5/487.5 = 682.5*5/487.5*5 = 3412.5/2437.5

Now, we can subtract:

11993.23/2437.5 - 3412.5/2437.5 = 8580.73/2437.5

To simplify, we can divide both numerator and denominator by their greatest common divisor, which is 73.75:

8580.73 ÷ 73.75 = 116
2437.5 ÷ 73.75 = 33

So, the result is:

### Answer: 116/33

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?

Llama 3 70B:

Let's break it down step by step:

1. Divide 10 by 5 and add that result to 35 divided by 27:

10 ÷ 5 = 2
35 ÷ 27 = 1.30 (approximately)
h = 2 + 1.30 = 3.30

2. Add 47 divided by 99 to h:

47 ÷ 99 = 0.47 (approximately)
p = h + 0.47 = 3.30 + 0.47 = 3.77

### Answer: 3.77

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?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 81 and 66 is 2178. So, we can rewrite the fractions as:

90/81 = 2430/2178
2/66 = 66/2178

Now, we can add them:

2430/2178 + 66/2178 = 2496/2178

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6:

2496 ÷ 6 = 416
2178 ÷ 6 = 363

So, the result is:

416/363

### Answer: 416/363

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?

Llama 3 70B:

Reasoning: If Oliver has two pieces of ribbon, each 56/41 yards long, we can add the lengths together to find the total length.

Total length = 56/41 + 56/41

To add these fractions, we need to have the same denominator, which is 41. So, we can add the numerators (56 + 56) and keep the same denominator.

Total length = (56 + 56)/41
Total length = 112/41

### Answer: 112/41 yards

Expected answer: 112/41

Correct? Yes

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 92 by 75: 92/75 = 92÷75 = 1 17/75
2. Divide 66 by 92: 66/92 = 66÷92 = 2/4 = 1/2
3. Add the two results: 1 17/75 + 1/2

To add these fractions, we need a common denominator. The least common multiple of 75 and 2 is 150. So, we can convert both fractions to have a denominator of 150:

1 17/75 = 122/150 (multiply numerator and denominator by 2)
1/2 = 75/150 (multiply numerator and denominator by 75)

Now we can add:

122/150 + 75/150 = 197/150

### Answer: 197/150

Expected answer: 6707/3450

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 65 and 22 is 1430. So, we can convert both fractions to have a denominator of 1430:

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

Now we can add:

704/1430 + 4745/1430 = (704 + 4745)/1430 = 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.

Llama 3 70B:

To find the difference, we need to subtract the two fractions. However, they have different denominators, so we need to find the least common multiple (LCM) of 34 and 86, which is 1738.

We can rewrite the fractions with the LCM as the denominator:

51/34 = 459/1738
12/86 = 156/1738

Now we can subtract:

459/1738 - 156/1738 = 303/1738

This fraction is already in its simplest form.

### Answer: 303/1738

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?

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS).

First, let's convert the whole number 51 to a fraction: 51 = 408/8

Now, add 51 (as a fraction) to the fraction 93/8:
(408/8) + (93/8) = (408 + 93)/8 = 501/8

Next, add the result to the fraction 58/44:
(501/8) + (58/44)

To add these fractions, we need a common denominator, which is 88. So, we'll convert both fractions:
(501/8) = (5517/88)
(58/44) = (116/88)

Now, add the fractions:
(5517/88) + (116/88) = (5633/88)

The final result is a simplified fraction: 5633/88
### Answer: 5633/88

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.

Llama 3 70B:

To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 25 is 25. So, we can rewrite the first fraction with a denominator of 25:

82/5 = 82 × 5/5 × 5 = 410/25

Now we can subtract:

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

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the result is:

### Answer: 312/25

Expected answer: 312/25

Correct? Yes

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

Llama 3 70B:

To calculate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 64 by 50: 64 / 50 = 64/50
2. Divide 70 by 22: 70 / 22 = 70/22
3. Add the two results: (64/50) + (70/22)

To add these fractions, we need to find a common denominator. The least common multiple of 50 and 22 is 1100. So, we can convert both fractions to have a denominator of 1100:

(64/50) = (1408/1100)
(70/22) = (3500/1100)

Now, we can add:

(1408/1100) + (3500/1100) = (4918/1100)

### Answer: 4918/1100

Expected answer: 1227/275

Correct? No

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

Llama 3 70B:

Let's break it down step by step:

1. John calculated s by adding 24 divided by 6 to 40 divided by 53.

First, let's calculate the divisions:
24 ÷ 6 = 4
40 ÷ 53 = 40/53 (this is a fraction, not a whole number)

Now, add them together:
s = 4 + 40/53

To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction:
s = 4/1 + 40/53
s = (4 × 53)/53 + 40/53
s = 212/53 + 40/53
s = (212 + 40)/53
s = 252/53

2. John then added s to itself to get b.

To add s to itself, we multiply s by 2:
b = 2 × (252/53)
b = (2 × 252)/53
b = 504/53

### Answer: 504/53

Expected answer: 504/53

Correct? Yes

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 80 by 90: 80 ÷ 90 = 8/9
2. Divide 52 by 11: 52 ÷ 11 = 52/11
3. Add the two results: 8/9 + 52/11

To add these fractions, we need a common denominator, which is 99. So, we can convert both fractions:

8/9 = 88/99
52/11 = 52 × 9 / 11 × 9 = 468/99

Now, we can add:

88/99 + 468/99 = 556/99

To express this as a mixed number, we can divide the numerator by the denominator:

556 ÷ 99 = 5 with a remainder of 61

So, the mixed number is:
### Answer: 5 61/99

Expected answer: 556/99

Correct? Yes

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

Llama 3 70B:

To calculate the sum, we need to find a common denominator for the two fractions. The least common multiple of 18 and 74 is 2664. So, we can rewrite the fractions as:

12/18 = 792/2664
91/74 = 1701/2664

Now, we can add the fractions:

792/2664 + 1701/2664 = 2493/2664

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

2493 ÷ 3 = 831
2664 ÷ 3 = 888

So, the simplified fraction is:

831/888

### Answer: 831/888

Expected answer: 421/222

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 2 and 25 is 50. So, we can convert both fractions to have a denominator of 50:

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

Now we can add:

175/50 + 102/50 = (175 + 102) / 50 = 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.

Llama 3 70B:

To evaluate the expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   ((68 / 69) + (93 / 7)) = (68/69) + (93/7)
   = (68/69) + (1329/69) (common denominator)
   = (68 + 1329)/69
   = 1397/69

2. Add the result to (3 / 46):
   (1397/69) + (3/46) = (1397*46 + 3*69)/69*46 (common denominator)
   = (64462 + 207)/3184
   = 64669/3184

### Answer: 64669/3184

Expected answer: 13849/966

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 98 and 4 is 196. So, we can convert both fractions to have a denominator of 196:

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

Now we can add:

62/196 + 2940/196 = 3002/196

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

3002/196 = (3002/2)/(196/2) = 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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the fractions inside the parentheses:
   (3 / 2) = 1.5
   (24 / 36) = 2/3

2. Add the two fractions:
   1.5 + 2/3 = 1.5 + 0.67 = 2.17

To convert 2.17 to a simplified fraction, we can write it as:
   2.17 = 217/100

However, we can simplify this fraction further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1:
   217/100 = 217/100 (already in simplest form)

### Answer: 217/100

Expected answer: 13/6

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Calculate the sum of 92/54 and 90/13:

92/54 = 46/27
90/13 = 90/13

Add the two fractions:

46/27 + 90/13 = (46*13 + 90*27) / (27*13) = (598 + 2430) / 351 = 3028 / 351

2. Take away 46/41 from the result:

3028/351 - 46/41 = (3028*41 - 46*351) / (351*41) = (124468 - 16046) / 14491 = 108422 / 14491

Simplify the fraction:

108422 / 14491 = 7481 / 1037

### Answer: 7481/1037

Expected answer: 108002/14391

Correct? No

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

Llama 3 70B:

To find twice the value of 29/23, we can multiply 29/23 by 2.

(29/23) × 2 = (29 × 2)/23 = 58/23

This fraction is already in its simplest form, as 58 and 23 do not have any common factors.

### 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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 20 and 72 is 360. So, we can convert both fractions to have a denominator of 360:

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

Now we can add:

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

This fraction is already in simplest form, so our answer 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.

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 36 by 27: 36 ÷ 27 = 4/3
2. Divide 80 by 10: 80 ÷ 10 = 8
3. Divide 73 by 79: 73 ÷ 79 = 73/79
4. Add the first two results: (4/3) + 8 = (4/3) + (24/3) = 28/3
5. Subtract the third result from the sum: (28/3) - (73/79)

To subtract fractions with different denominators, we need to find the least common multiple (LCM) of 3 and 79, which is 237. Then, we can convert both fractions to have a denominator of 237:

(28/3) = (1964/237)
(73/79) = (219/237)

Now, we can subtract:

(1964/237) - (219/237) = (1745/237)

So, the simplified answer is:

### Answer: 1745/237

Expected answer: 1993/237

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 86 by 71: 86 ÷ 71 = 1.21
2. Divide 91 by 75: 91 ÷ 75 = 1.21
3. Add the results: 1.21 + 1.21 = 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)

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Calculate the fractions inside the parentheses:
   ((21 / 75) + (74 / 43)) = (0.28 + 1.72) = 2
2. Add the remaining fraction:
   2 + (10 / 62) = 2 + 0.161 = 2.161
3. Convert the decimal to a simplified fraction:
   2.161 = 217/100

### Answer: 217/100

Expected answer: 72056/33325

Correct? No

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

Llama 3 70B:

To compute the expression, we need to follow the order of operations (PEMDAS):

1. Divide 75 by 66: 75 ÷ 66 = 75/66
2. Divide 81 by 61: 81 ÷ 61 = 81/61
3. Add the two fractions: (75/66) + (81/61)

To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 66 and 61 is 4026. So, we can convert both fractions to have a denominator of 4026:

(75/66) = (3075/4026)
(81/61) = (3321/4026)

Now, we can add:

(3075/4026) + (3321/4026) = (6396/4026)

To reduce this fraction to its lowest term, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 6:

(6396 ÷ 6) / (4026 ÷ 6) = 1066/671

### Answer: 1066/671

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.

Llama 3 70B:

To find the sum of the two identical fractions, we need to first find the value of one fraction, t.

t = 53/18 + 21/99

To add these fractions, we need to find a common denominator, which is 198. So, we can rewrite the fractions as:

t = (53*11)/(18*11) + (21*2)/(99*2)
t = 583/198 + 42/198
t = (583 + 42)/198
t = 625/198

Since we have two identical fractions, the total sum, l, is:

l = t + t
l = 625/198 + 625/198
l = (625 + 625)/198
l = 1250/198

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

l = 1250/2 / 198/2
l = 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?

Llama 3 70B:

To calculate the result of 58/49 + 31/34, we need to find a common denominator, which is 1666. So, we can rewrite the fractions as:

58/49 = 1276/1666
31/34 = 899/1666

Now, we can add them:

1276/1666 + 899/1666 = 2175/1666

Next, we need to add this result to the fraction 74/38. Again, we need to find a common denominator, which is 5024. So, we can rewrite the fractions as:

2175/1666 = 8712/5024
74/38 = 1952/5024

Now, we can add them:

8712/5024 + 1952/5024 = 10664/5024

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

10664/5024 = 2666/1256

This is the final result as a simple fraction.

### Answer: 2666/1256

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.

Llama 3 70B:

To calculate the sum, we need to follow the order of operations (PEMDAS):

1. Calculate 100 divided by 76: 100 ÷ 76 = 1.316 (as a decimal) or 79/60 (as a simplified fraction)
2. Calculate 29 divided by 14: 29 ÷ 14 = 2.071 (as a decimal) or 29/14 (as a simplified fraction)
3. Add the two results: 1.316 + 2.071 = 3.387 (as a decimal) or (79/60) + (29/14) = (79/60) + (83/60) = 162/60 = 27/10 (as a simplified fraction)

### Answer: 3.387 or 27/10

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.

Llama 3 70B:

Reasoning: Since Olivia has read the same amount as Evan, Olivia has also read 51/18 of the novel. We can rewrite 8/42 as 4/21, which is the additional amount Olivia has read. To find the total amount Olivia has read, we add the two fractions: 

(51/18) + (4/21) = ((51*7) + (4*6)) / (18*7) = (357 + 24) / 126 = 381 / 126 

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 

381 ÷ 3 = 127 
126 ÷ 3 = 42 

So, the simplified fraction is 127/42.

### Answer: 127/42

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.

Llama 3 70B:

To find the sum, we need to evaluate the expressions inside the parentheses first.

48 divided by 13 is:
48 ÷ 13 = 48/13 = 3 9/13 = 3.6923076923076925 (as a decimal)

31 divided by 22 is:
31 ÷ 22 = 31/22 = 1 9/22 = 1.409090909090909 (as a decimal)

Now, let's add the two results:
3.6923076923076925 + 1.409090909090909 = 5.101398101398101

As a fraction, the result is:
5 101/990

### Answer: 5.101398101398101 or 5 101/990

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.

Llama 3 70B:

To evaluate the expression, I'll follow the order of operations (PEMDAS):

1. Evaluate the fractions inside the parentheses:

24/86 = 0.279 (approximately)
76/77 = 0.987 (approximately)

2. Add the two fractions:

0.279 + 0.987 = 1.266

3. Now, subtract 1.266 from 27/6:

27/6 = 4.5 (exactly)

4.5 - 1.266 = 3.234

### Answer: 3.234

Expected answer: 21415/6622

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 39 and 14 is 546. So, we can convert both fractions to have a denominator of 546:

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

Now we can add:

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

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 7:

2933/7 = 419
546/7 = 78

So, the simplified fraction is:

### Answer: 419/78

Expected answer: 419/78

Correct? Yes

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 65 and 39 is 2535. So, we can convert both fractions to have a denominator of 2535:

75/65 = (75*39)/(65*39) = 2925/2535
7/39 = (7*65)/(39*65) = 455/2535

Now we can add:

2925/2535 + 455/2535 = 3380/2535

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 5:

3380/2535 = (3380/5)/(2535/5) = 676/507

### Answer: 676/507

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?

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Calculate 79/1: 79/1 = 79
2. Calculate 30/92: 30/92 = 15/46
3. Subtract 30/92 from 79/1: 79 - 15/46 = 79 - 0.32609 (approximately) = 78.67391 (approximately)
4. Calculate 61/63: 61/63 = 0.96825 (approximately)
5. Subtract 61/63 from the result: 78.67391 - 0.96825 = 77.70566 (approximately)

### Answer: 77.71 (rounded to two decimal places)

Expected answer: 225191/2898

Correct? No

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

Llama 3 70B:

To calculate the expression, we need to follow the order of operations (PEMDAS):

1. Divide 58 by 26: 58 ÷ 26 = 2 with a remainder of 10, which can be written as a fraction: 58/26 = 2 10/26 = 2 5/13
2. Add the result to itself: (2 5/13) + (2 5/13) = 2 × 2 + 2 × (5/13) = 4 + 10/13 = 4 10/13

So, the result of the expression is 4 10/13.

### Answer: 4 10/13

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?

Llama 3 70B:

Reasoning: Alex initially had 69/63 gallons of orange juice. To add fractions, we need to find a common denominator, which is 63*5 = 315. So, we can convert 69/63 to 345/315 and 77/5 to 462/315. Then, we add them: 345/315 + 462/315 = 807/315. This is the total amount Alex had before receiving more from Sally.

Now, we need to add 807/315 and 47/71. Again, we need to find a common denominator, which is 315*71 = 22305. So, we can convert 807/315 to 807*71/22305 and 47/71 to 47*315/22305. Then, we add them: 807*71/22305 + 47*315/22305 = 57322/22305.

### Answer: 57322/22305.

Expected answer: 127907/7455

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   (100 / 61) = 100/61
   (39 / 6) = 39/6 = 13/2
   (67 / 49) = 67/49

2. Now, add the results:
   (100/61) + (13/2) + (67/49)

To add these fractions, we need a common denominator. The least common multiple of 61, 2, and 49 is 1198. So, we can convert each fraction to have a denominator of 1198:

   (100/61) = (2000/1198)
   (13/2) = (793/1198)
   (67/49) = (174/1198)

Now, add the fractions:
   (2000/1198) + (793/1198) + (174/1198) = (2967/1198)

So, the result of the given expression is 2967/1198.

### Answer: 2967/1198

Expected answer: 56831/5978

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 1 and 69 is 69. So, we can rewrite 85/1 as 85/1 = 85*69/69 = 5925/69.

Now, we can add the two fractions:
5925/69 + 83/69 = (5925 + 83)/69 = 6008/69

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1. So, the simplified answer is:
6008/69

### Answer: 6008/69

Expected answer: 5948/69

Correct? No

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

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 13 and 86 is 2 × 13 × 43 = 1118. So, we can rewrite the fractions as:

92/13 = (92 × 86) / (13 × 86) = 7952 / 1118
43/86 = (43 × 13) / (86 × 13) = 559 / 1118

Now we can add:

7952 / 1118 + 559 / 1118 = (7952 + 559) / 1118 = 8511 / 1118

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 1 (they are coprime). So, the simplified fraction is:

8511 / 1118

### Answer: 8511/1118

Expected answer: 197/26

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 32 and 98 is 1568. So, we can convert both fractions to have a denominator of 1568:

67/32 = (67*49)/(32*49) = 3273/1568
10/98 = (10*16)/(98*16) = 160/1568

Now we can add:

3273/1568 + 160/1568 = (3273+160)/1568 = 3433/1568

This fraction is already in simplest form, so our answer is:

### Answer: 3433/1568

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.

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 52 and 32 is 416. So, we can convert both fractions to have a denominator of 416:

59/52 = (59*8)/(52*8) = 472/416
70/32 = (70*13)/(32*13) = 910/416

Now we can add:

472/416 + 910/416 = 1382/416

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

1382 ÷ 4 = 345.5
416 ÷ 4 = 104

So, the sum is:

### Answer: 345.5/104

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?

Llama 3 70B:

Let's break it down step by step:

1. 48 divided by 5: 48 ÷ 5 = 9.6
2. 11 divided by 65: 11 ÷ 65 = 0.169
3. Subtract 0.169 from 9.6: 9.6 - 0.169 = 9.431
4. 28 divided by 2: 28 ÷ 2 = 14
5. Add 9.431 to 14: 14 + 9.431 = 23.431

### Answer: 23.431

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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 52 and 82 is 676. So, we can convert both fractions to have a denominator of 676:

20/52 = (20*13)/(52*13) = 260/676
75/82 = (75*8)/(82*8) = 600/676

Now we can add:

260/676 + 600/676 = 860/676

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 26:

860/676 = (860/26)/(676/26) = 33/26

### Answer: 33/26

Expected answer: 1385/1066

Correct? No

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

Llama 3 70B:

To subtract 92/84 from 31/5, we need to find a common denominator. The least common multiple of 5 and 84 is 420. So, we can convert both fractions to have a denominator of 420:

31/5 = (31*84)/420 = 2584/420
92/84 = (92*5)/420 = 460/420

Now we can subtract:

2584/420 - 460/420 = (2584 - 460)/420 = 2124/420

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:

2124/420 = (2124 ÷ 4)/(420 ÷ 4) = 531/105

### Answer: 531/105

Expected answer: 536/105

Correct? No

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

Llama 3 70B:

To calculate this, we need to follow the order of operations (PEMDAS):

1. Calculate the sum of 81/90 and 94/49:
   81/90 = 0.9
   94/49 = 1.92
   Sum = 0.9 + 1.92 = 2.82

2. Double the sum:
   2 * 2.82 = 5.64

### Answer: 5.64

Expected answer: 1381/245

Correct? No

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

Llama 3 70B:

To find the difference, we need to subtract the two fractions. However, they have different denominators, so we need to find the least common multiple (LCM) of 21 and 92, which is 6444.

We can rewrite the fractions with the LCM as the denominator:

69/21 = (69*308)/(21*308) = 21252/6444
10/92 = (10*69)/(92*69) = 690/6444

Now we can subtract:

21252/6444 - 690/6444 = (21252 - 690)/6444 = 20562/6444

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

20562/6444 = (20562/2)/(6444/2) = 10281/3222

### Answer: 10281/3222

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?

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses:
   (26 / 87) = 26 ÷ 87 = 0.299
   (92 / 88) = 92 ÷ 88 = 1.045

2. Add the results:
   0.299 + 1.045 = 1.344

3. Now, add the result to (26 / 57):
   (26 / 57) = 26 ÷ 57 = 0.456
   1.344 + 0.456 = 1.8

### Answer: 1.8

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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 66, 6, and 34 is 1326. So, we can convert each fraction to have a denominator of 1326:

78/66 = (78*20)/(66*20) = 1560/1326
28/6 = (28*221)/(6*221) = 6232/1326
90/34 = (90*39)/(34*39) = 3510/1326

Now we can add:

(1560 + 6232 + 3510)/1326 = 11302/1326

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

11302/2 = 5651
1326/2 = 663

So, the result of adding 78/66, 28/6, and 90/34 together is:

### Answer: 5651/663

Expected answer: 4766/561

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 12 by 7: 12 / 7 = 12/7
2. Divide 9 by 23: 9 / 23 = 9/23
3. Subtract the two results: (12/7) - (9/23)

To subtract these fractions, we need to find a common denominator, which is 161. So, we can rewrite the fractions as:

(12/7) = (264/161)
(9/23) = (63/161)

Now, we can subtract:

(264/161) - (63/161) = (264 - 63)/161 = 201/161

So, the result is:

### Answer: 201/161

Expected answer: 213/161

Correct? No

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

Llama 3 70B:

To calculate the sum, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 18 and 61 is 1104. So, we can convert both fractions to have a denominator of 1104:

95/18 = (95 × 61) / (18 × 61) = 5795 / 1104
51/61 = (51 × 18) / (61 × 18) = 918 / 1104

Now we can add the two fractions:

(5795 + 918) / 1104 = 6713 / 1104

This fraction cannot be simplified further, so the answer is:

### Answer: 6713/1104

Expected answer: 6713/1098

Correct? No

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

Llama 3 70B:

To subtract these fractions, we need to find a common denominator. The least common multiple (LCM) of 46 and 84 is 276. So, we can convert both fractions to have a denominator of 276:

(93 / 46) = (93 × 6) / (46 × 6) = 558 / 276
(51 / 84) = (51 × 3) / (84 × 3) = 153 / 276

Now we can subtract:

(558 / 276) - (153 / 276) = (558 - 153) / 276 = 405 / 276

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

405 ÷ 3 = 135
276 ÷ 3 = 92

So, the result of the subtraction is:

### Answer: 135 / 92

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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 70 and 9 is 630. So, we can convert both fractions to have a denominator of 630:

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

Now we can add the fractions:

108/630 + 5880/630 = 5988/630

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6:

5988 ÷ 6 = 996
630 ÷ 6 = 105

So, the sum of the fractions is:

### Answer: 996/105

Expected answer: 998/105

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Subtract 40/92 from 32/3:
First, let's convert the fractions to have a common denominator, which is 276. So, we get:
32/3 = 2816/276
40/92 = 120/276

Now, subtract:
(2816 - 120)/276 = 2696/276

2. Double the result:
Multiply the result by 2:
(2696/276) × 2 = 5392/276

### Answer: 5392/276

Expected answer: 1412/69

Correct? No

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

Llama 3 70B:

To find the sum, I'll add the two fractions:

79/24 + 79/24 = 2 × 79/24 = 158/24

To simplify the fraction, I'll divide both the numerator and the denominator by their greatest common divisor, which is 2:

158 ÷ 2 = 79
24 ÷ 2 = 12

So, the simplified fraction 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.

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 76 and 22 is 836. So, we can convert both fractions to have a denominator of 836:

91/76 = (91*11)/(76*11) = 1001/836
12/22 = (12*38)/(22*38) = 456/836

Now we can add:

1001/836 + 456/836 = 1457/836

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 1. So, the simplified fraction 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?

Llama 3 70B:

To add 88/93 to 6/47, we need to find a common denominator. The least common multiple of 93 and 47 is 4371. So, we can convert both fractions to have a denominator of 4371:

88/93 = (88*47)/(93*47) = 4136/4371
6/47 = (6*93)/(47*93) = 558/4371

Now we can add:

4136/4371 + 558/4371 = 4694/4371

Next, we need to add 4694/4371 to 92/4. To do this, we need to convert 92/4 to have a denominator of 4371:

92/4 = (92*1092)/(4*1092) = 100944/4371

Now we can add:

4694/4371 + 100944/4371 = 105638/4371

### Answer: 105638/4371

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.

Llama 3 70B:

To calculate the sum, we need to follow the order of operations (PEMDAS):

1. Calculate the fractions separately:
   95/83 = 95/83 (cannot be simplified further)
   52/21 = 52/21 (cannot be simplified further)
   75/67 = 75/67 (cannot be simplified further)

2. Calculate the sum of 52/21 and 75/67:
   To add these fractions, we need a common denominator, which is 21*67 = 1407. So, we can rewrite the fractions as:
   52/21 = 364/1407
   75/67 = 825/1407
   Now, we can add them:
   364/1407 + 825/1407 = 1189/1407

3. Calculate the sum of 95/83 and 1189/1407:
   Again, we need a common denominator, which is 83*1407 = 116781. So, we can rewrite the fractions as:
   95/83 = 142445/116781
   1189/1407 = 1189*83/1407*83 = 98747/116781
   Now, we can add them:
   142445/116781 + 98747/116781 = 241192/116781

### Answer: 241192/116781

Expected answer: 553562/116781

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 73 by 27: 73 ÷ 27 = 73/27
2. Divide 23 by 48: 23 ÷ 48 = 23/48
3. Subtract the two results: (73/27) - (23/48)

To subtract these fractions, we need to find a common denominator, which is 432. So, we can rewrite the fractions as:

(2652/432) - (207/432) = (2652 - 207)/432 = 2445/432

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

2445 ÷ 3 = 815
432 ÷ 3 = 144

So, the simplified fraction is:

### Answer: 815/144

Expected answer: 961/432

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 78 by 2: 78 / 2 = 39
2. Divide 70 by 23: 70 / 23 = 3.04 (as a decimal)
3. Subtract the two results: 39 - 3.04 = 35.96

### Answer: 35.96

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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 1 and 4 is 4. So, we can rewrite 34/1 as 136/4. Now we can add:

136/4 + 53/4 = 189/4

To express this as a mixed number, we can divide the numerator by the denominator:

189 ÷ 4 = 47 with a remainder of 1

So, the result 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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 36 and 96 is 288. So, we can convert both fractions to have a denominator of 288:

3/36 = 24/288
97/96 = 259/288

Now we can add:

24/288 + 259/288 = 283/288

### Answer: 283/288

Expected answer: 35/32

Correct? No

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

Llama 3 70B:

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Divide 92 by 95: 92 ÷ 95 = 92/95
2. Divide 4 by 74: 4 ÷ 74 = 4/74
3. Add the two fractions: (92/95) + (4/74)

To add these fractions, we need to find a common denominator. The least common multiple of 95 and 74 is 7030. So, we can convert both fractions to have a denominator of 7030:

(92/95) = (2684/7030)
(4/74) = (148/7030)

Now, we can add:

(2684/7030) + (148/7030) = (2832/7030)

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

(2832 ÷ 2) / (7030 ÷ 2) = 1416/3515

### Answer: 1416/3515

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.

Llama 3 70B:

Reasoning: We are given that v = 69/47. We need to find the value of d, which is equal to 88/72 + v.

First, let's simplify the fraction 88/72 by dividing both numerator and denominator by their greatest common divisor, which is 4:

88/72 = 22/18

Now, we can rewrite the equation as:

d = 22/18 + 69/47

To add these fractions, we need to find a common denominator, which is 846 (the least common multiple of 18 and 47). We can rewrite the fractions with this common denominator:

d = 847/846 + 702/846

Now, we can add the fractions:

d = (847 + 702)/846
d = 1549/846

### Answer: 1549/846

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.

Llama 3 70B:

Reasoning: The wholesaler initially had 41/26 barrels of olive oil.
They sold 41/72 barrels, so we need to subtract this amount from the initial amount:
(41/26) - (41/72) = ?

To subtract these fractions, we need to find a common denominator, which is 72*26 = 1872. So, we can rewrite the fractions with this denominator:

(41*72)/1872 - (41*26)/1872 = ?

Now we can subtract:

(41*72)/1872 - (41*26)/1872 = (41*46)/1872 = 1886/1872

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:

1886/1872 = (1886/2)/(1872/2) = 943/936

### Answer: 943/936

Expected answer: 943/936

Correct? Yes

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

Llama 3 70B:

To find the sum, we need to convert the fractions to decimals and then add them.

85/75 = 1.1333... (divide 85 by 75)
88/56 = 1.5714... (divide 88 by 56)

Now, add the decimals:
1.1333... + 1.5714... = 2.7047...

### Answer: 2.7047...

Expected answer: 284/105

Correct? No

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

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 33 and 2 is 66. So, we can convert both fractions to have a denominator of 66:

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

Now we can add:

24/66 + 1617/66 = 1641/66

To write this as a mixed fraction, we can divide the numerator by the denominator:

1641 ÷ 66 = 24 with a remainder of 53

So, the result is:

24 53/66

### Answer: 24 53/66

Expected answer: 547/22

Correct? No

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

Llama 3 70B:

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

So, we have:

(78/65) + (78/65) = (78 + 78)/65 = 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.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 7 and 90 is 630. So, we can convert both fractions to have a denominator of 630:

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

Now we can add:

1440/630 + 77/630 = (1440+77)/630 = 1517/630

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1. So, the simplified answer is:

### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes