Problem: Suppose we had made a mistake in the original problem and it was actually 48/14 we were to subtract from 49/8. What would the result have been in that case? Please answer as a simplified fraction.

Llama 3 70B:

To subtract 48/14 from 49/8, we need to find a common denominator. The least common multiple of 14 and 8 is 56. So, we can convert both fractions to have a denominator of 56:

48/14 = 168/56
49/8 = 343/56

Now we can subtract:

343/56 - 168/56 = 175/56

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

175 ÷ 7 = 25
56 ÷ 7 = 8

So, the result is:

### Answer: 25/8

Expected answer: 151/56

Correct? No

Problem: After getting the sum of 49/79 and 18/21 from the previous problem, let's denote this sum as n. Calculate the result of adding 71/97 to n.

Llama 3 70B:

We already calculated the sum of 49/79 and 18/21, which is:

n = 2451/1659

Now, we need to add 71/97 to n. To do this, we need to find a common denominator for 1659 and 97. The least common multiple (LCM) of 1659 and 97 is 160943. So, we can convert both fractions to have a denominator of 160943:

n = 2451/1659 = (2451 × 97) / (1659 × 97) = 237547 / 160943
71/97 = (71 × 1659) / (97 × 1659) = 117289 / 160943

Now we can add the two fractions:

237547 / 160943 + 117289 / 160943 = (237547 + 117289) / 160943 = 354836 / 160943

### Answer: 354836/160943

Expected answer: 118512/53641

Correct? No

Problem: In the previous problem, we found the sum of 49/79 and 18/21. Now, let's alter the scenario a bit. Instead of having 49/79 part, let's say we have 49/3 part. Keeping the 18/21 part the same, what would be the new total? Calculate the sum of 49/3 and 18/21.

Llama 3 70B:

To calculate the sum, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 3 and 21 is 21. So, we can convert the first fraction to have a denominator of 21:

49/3 = (49 × 7) / (3 × 7) = 343 / 21

Now we can add the two fractions:

343 / 21 + 18 / 21 = (343 + 18) / 21 = 361 / 21

### Answer: 361/21

Expected answer: 361/21

Correct? Yes

Problem: After you calculated the sum of 87/88 and 24/13, find the result when you add this sum to 36/9.

Llama 3 70B:

We already calculated the sum of 87/88 and 24/13:

1131/1144 + 2112/1144 = 3243/1144

Now, we need to add 36/9 to this sum. To do this, we need to find a common denominator for 1144 and 9. The least common multiple (LCM) of 1144 and 9 is 10308. So, we can convert both fractions to have a denominator of 10308:

3243/1144 = (3243*9)/(1144*9) = 29157/10308
36/9 = (36*1144)/(9*1144) = 4104/10308

Now we can add the two fractions:

29157/10308 + 4104/10308 = (29157 + 4104)/10308 = 33261/10308

### Answer: 33261/10308

Expected answer: 7819/1144

Correct? No

Problem: After you calculated the sum of 87/88 and 24/13 and added 36/9 to this sum, reconsider the problem. This time, let's say we started with 87/83 instead of 87/88. What would be the sum of 87/83 and 24/13?

Llama 3 70B:

Let's recalculate the sum with the new fraction 87/83.

To calculate the sum, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 83 and 13 is 1079. So, we can convert both fractions to have a denominator of 1079:

87/83 = (87*13)/(83*13) = 1131/1079
24/13 = (24*83)/(13*83) = 1992/1079

Now we can add the two fractions:

1131/1079 + 1992/1079 = (1131 + 1992)/1079 = 3123/1079

### Answer: 3123/1079

Expected answer: 3123/1079

Correct? Yes

Problem: What is the result when you add 62/46 to your previous answer from subtracting 79/70 from 11/5?

Llama 3 70B:

We need to add 62/46 to 15/14. To do this, we need to find a common denominator. The least common multiple of 46 and 14 is 322. So, we can rewrite 15/14 as 225/322 and 62/46 as 134/322.

Now, we can add:

225/322 + 134/322 = (225 + 134)/322 = 359/322

### Answer: 359/322

Expected answer: 779/322

Correct? No

Problem: Previously, we solved for the difference when you subtracted 79/70 from 11/5. Now, consider what happens if you originally started with 61/5 instead of 11/5. What would be the result when you subtract 79/70 from this new value?

Llama 3 70B:

Let's follow the same steps as before. We need to find a common denominator, which is still 70. So, we can rewrite 61/5 as 854/70.

Now, we can subtract:

854/70 - 79/70 = (854 - 79)/70 = 775/70

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

775/70 = 311/14

### Answer: 311/14

Expected answer: 155/14

Correct? No

Problem: Now that you calculated the sum of 21/75 and 44/47, can you find out what would be the total of two such sums added together?

Llama 3 70B:

To find the total of two such sums added together, we can multiply the sum by 2:

4287/3525 × 2 = 8574/3525

### Answer: 8574/3525

Expected answer: 2858/1175

Correct? Yes

Problem: Previously, you computed the sum of 21/75 and 44/47. Now, imagine instead that the fraction was 21/63 rather than 21/75. What would the sum of 21/63 and 44/47 be?

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple (LCM) of 63 and 47 is 2961. So, we can convert both fractions to have a denominator of 2961:

21/63 = (21*47)/(63*47) = 987/2961
44/47 = (44*63)/(47*63) = 2772/2961

Now we can add the fractions:

987/2961 + 2772/2961 = (987+2772)/2961 = 3759/2961

### Answer: 3759/2961

Expected answer: 179/141

Correct? Yes

Problem: In addition to the calculation you did in the last question, let's add another operation. Solve ((14 / 24) + ((14 / 72) + (25 / 6))).

Llama 3 70B:

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

1. Divide 14 by 24: 14 ÷ 24 = 7/12
2. Evaluate the expression inside the parentheses: ((14 / 72) + (25 / 6))
   - Divide 14 by 72: 14 ÷ 72 = 7/36
   - Divide 25 by 6: 25 ÷ 6 = 25/6
   - Add the two fractions: (7/36) + (25/6)
     - Convert 25/6 to 150/36 (common denominator is 36)
     - (7/36) + (150/36) = 157/36
3. Add the two results: (7/12) + (157/36)

To add these fractions, we need to find a common denominator. The least common multiple of 12 and 36 is 36. So, we can convert 7/12 to 21/36:

(21/36) + (157/36) = 178/36

### Answer: 178/36

Expected answer: 89/18

Correct? Yes

Problem: In the previous problem, we calculated the sum ((14 / 72) + (25 / 6)). But what if we made a mistake and it wasn't 25/6 of something added, but it was actually 90/6? Given this new information, what would be the new value of ((14 / 72) + (90 / 6))?

Llama 3 70B:

Let's recalculate the expression with the new information:

1. Divide 14 by 72: 14 ÷ 72 = 7/36
2. Divide 90 by 6: 90 ÷ 6 = 15
3. Add the two values: (7/36) + 15

To add a fraction and a whole number, we can convert the whole number to a fraction with a denominator of 36:

(7/36) + (540/36) = 547/36

### Answer: 547/36

Expected answer: 547/36

Correct? Yes

Problem: After finding the sum of 84/97 and 25/2, subtract 100/71 from your result. What is the new result?

Llama 3 70B:

We already found the sum of 84/97 and 25/2:

2593/194

Now, we need to subtract 100/71 from this result. To do this, we need to find the least common multiple (LCM) of 194 and 71, which is 13838. So, we can convert the fractions as follows:

2593/194 = (2593*71)/(194*71) = 183383/13838
100/71 = (100*194)/(71*194) = 19400/13838

Now, we can subtract the fractions:

183383/13838 - 19400/13838 = (183383 - 19400)/13838 = 163983/13838

### Answer: 163983/13838

Expected answer: 164703/13774

Correct? No

Problem: After previously finding the sum of 84/97 and 25/2, now consider a new scenario. What if, instead of having 84 parts out of 97, we had 84 parts out of 96? What then would be the sum of these fractions: 84/96 and 25/2?

Llama 3 70B:

Let's recalculate the sum with the new fraction 84/96.

First, we can simplify 84/96 by dividing both numerator and denominator by their greatest common divisor, which is 12:

84/96 = (84 ÷ 12)/(96 ÷ 12) = 7/8

Now, we can add 7/8 and 25/2:

7/8 = (7*1)/(8*1) = 7/8
25/2 = (25*4)/(2*4) = 100/8

Now, we can add the fractions:

7/8 + 100/8 = (7 + 100)/8 = 107/8

### Answer: 107/8

Expected answer: 107/8

Correct? Yes

Problem: After finding the difference between the fractions 66/20 and 4/78, what would the result be if you add 6/15 to your answer?

Llama 3 70B:

To add 6/15 to the result, we need to find a common denominator. The least common multiple of 1560 and 15 is 1560. So, we can convert 6/15 to have a denominator of 1560:

6/15 = (6*104)/(15*104) = 624/1560

Now we can add the two fractions:

5068/1560 + 624/1560 = (5068+624)/1560 = 5692/1560

### Answer: 5692/1560

Expected answer: 1423/390

Correct? Yes

Problem: Suppose that instead of having 66/20 in the original problem, we have 66/21. What would be the difference between the fractions 66/21 and 4/78?

Llama 3 70B:

To find the difference between the fractions 66/21 and 4/78, we need to first find a common denominator. The least common multiple of 21 and 78 is 1638. So, we can convert both fractions to have a denominator of 1638:

66/21 = (66*78)/(21*78) = 5148/1638
4/78 = (4*21)/(78*21) = 84/1638

Now we can subtract the two fractions:

5148/1638 - 84/1638 = (5148-84)/1638 = 5064/1638

### Answer: 5064/1638

Expected answer: 844/273

Correct? Yes

Problem: If you subtract 38/65 from the sum of 14/57 and 92/42, what would be the result?

Llama 3 70B:

First, let's calculate the sum of 14/57 and 92/42:

14/57 = (14*42)/(57*42) = 588/2394
92/42 = (92*57)/(42*57) = 5244/2394

Now we can add the two fractions:

588/2394 + 5244/2394 = (588 + 5244)/2394 = 5832/2394

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6:

5832/2394 = (5832 ÷ 6)/(2394 ÷ 6) = 972/399

Now, let's subtract 38/65 from the result:

972/399 - 38/65 = ?

To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 399 and 65 is 25935. So, we can convert both fractions to have a denominator of 25935:

972/399 = (972*65)/(399*65) = 63380/25935
38/65 = (38*399)/(65*399) = 15162/25935

Now we can subtract the two fractions:

63380/25935 - 15162/25935 = (63380 - 15162)/25935 = 48218/25935

### Answer: 48218/25935

Expected answer: 16006/8645

Correct? No

Problem: In the previous problem, you found the result of adding 14/57 and 92/42. Now consider a different scenario where instead of adding 92/42 you add 32/42 to 14/57. What would be the new result?

Llama 3 70B:

To calculate the sum, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 57 and 42 is 2394. So, we can convert both fractions to have a denominator of 2394:

14/57 = (14*42)/(57*42) = 588/2394
32/42 = (32*57)/(42*57) = 1816/2394

Now we can add the two fractions:

588/2394 + 1816/2394 = (588 + 1816)/2394 = 2404/2394

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

2404/2394 = (2404 ÷ 2)/(2394 ÷ 2) = 1202/1197

### Answer: 1202/1197

Expected answer: 134/133

Correct? No

Problem: If we add the previously calculated result to 39/64, what fraction do we get?

Llama 3 70B:

To add the result to 39/64, we need to convert the result to a fraction with the same denominator as 39/64, which is 64.

2.6 = 2 24/64 (convert 0.6 to a fraction with denominator 64)

Now, add 2 24/64 to 39/64:

2 24/64 + 39/64 = 2 + (24 + 39)/64 = 2 + 63/64 = 2 63/64

### Answer: 2 63/64

Expected answer: 1027/320

Correct? No

Problem: Let's change the previous problem a bit. Instead of adding 6/5, what if we added 6/79 to 77/55? What fraction would we get then?

Llama 3 70B:

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

1. Divide 77 by 55: 77 ÷ 55 = 1.4
2. Divide 6 by 79: 6 ÷ 79 = 0.076
3. Add the results: 1.4 + 0.076 = 1.476

To convert the result to a fraction, we can write:

1.476 = 148/100 = 74/50 = 37/25

### Answer: 37/25

Expected answer: 583/395

Correct? No

Problem: Previously, you found the sum of 23/20 and 82/97. Now, take that result and subtract 7/44 from it. What's the answer?

Llama 3 70B:

We need to subtract 7/44 from 3871/1940. To do this, we need to find a common denominator. The least common multiple of 1940 and 44 is 85960. So, we can convert both fractions to have a denominator of 85960:

3871/1940 = (3871 x 44) / (1940 x 44) = 170284 / 85960
7/44 = (7 x 1940) / (44 x 1940) = 13780 / 85960

Now we can subtract:

170284 / 85960 - 13780 / 85960 = (170284 - 13780) / 85960 = 156504 / 85960

### Answer: 156504/85960

Expected answer: 19593/10670

Correct? No

Problem: Previously, you found the sum of 23/20 and 82/97. Now imagine instead of 23/20, you have 23/43. What would be the new result if you add 23/43 and 82/97?

Llama 3 70B:

To add these two fractions, we need to find a common denominator. The least common multiple of 43 and 97 is 4181. So, we can convert both fractions to have a denominator of 4181:

23/43 = (23 x 97) / (43 x 97) = 2231 / 4181
82/97 = (82 x 43) / (97 x 43) = 3546 / 4181

Now we can add:

2231 / 4181 + 3546 / 4181 = (2231 + 3546) / 4181 = 5777 / 4181

### Answer: 5777/4181

Expected answer: 5757/4171

Correct? No

Problem: After finding the sum of 54/88 and 28/10, add this to 21/13 and find the resulting value.

Llama 3 70B:

We already found the sum of 54/88 and 28/10:

375.5/110

To add this to 21/13, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 110 and 13 is 1430. So, we can convert both fractions to have a denominator of 1430:

375.5/110 = (375.5*13)/(110*13) = 4881.5/1430
21/13 = (21*110)/(13*110) = 2310/1430

Now we can add the two fractions:

4881.5/1430 + 2310/1430 = (4881.5 + 2310)/1430 = 7191.5/1430

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

7191.5 ÷ 1 = 7191.5
1430 ÷ 1 = 1430

So, the resulting value is:

7191.5/1430

### Answer: 7191.5/1430

Expected answer: 14383/2860

Correct? No

Problem: What is the sum of 87/26 and the result of the previous problem ((15/32) + (65/15))?

Llama 3 70B:

First, let's find the sum of 15/32 and 65/15:

15/32 = (15*15)/(32*15) = 225/480
65/15 = (65*32)/(15*32) = 2080/480

Now we can add:

225/480 + 2080/480 = 2305/480

Now, let's add 87/26 to this result. To do this, we need to find a common denominator. The least common multiple of 26 and 480 is 12480. So, we can convert both fractions to have a denominator of 12480:

87/26 = (87*480)/(26*480) = 4180/12480
2305/480 = (2305*26)/(480*26) = 59930/12480

Now we can add:

4180/12480 + 59930/12480 = 64110/12480

### Answer: 64110/12480

Expected answer: 10169/1248

Correct? No

Problem: Now, in addition to the previous question, what is the sum when you add the fraction 46/83 to the result of adding 82/15 and 100/12?

Llama 3 70B:

First, let's recall the result of adding 82/15 and 100/12:

82/15 + 100/12 = 69/5

Now, we want to add 46/83 to this result. To do this, we need to find a common denominator. The least common multiple of 5 and 83 is 415. So, we can convert both fractions to have a denominator of 415:

69/5 = (69*83)/(5*83) = 5697/415
46/83 = (46*5)/(83*5) = 230/415

Now we can add:

5697/415 + 230/415 = 5927/415

### Answer: 5927/415

Expected answer: 5957/415

Correct? No

Problem: Now suppose we made an adjustment. Instead of adding 82/15 to 100/12, we are going to add 61/15 to 100/12. What would be the new sum?

Llama 3 70B:

To add these two fractions, we need to find a common denominator. The least common multiple of 15 and 12 is 60. So, we can convert both fractions to have a denominator of 60:

61/15 = (61*4)/(15*4) = 244/60
100/12 = (100*5)/(12*5) = 500/60

Now we can add:

244/60 + 500/60 = 744/60

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

744/60 = (744/4)/(60/4) = 186/15

### Answer: 186/15

Expected answer: 62/5

Correct? Yes

Problem: If you add 83/35 to the result of adding the fractions 50/73 and 20/23, what is the total value?

Llama 3 70B:

First, let's find the result of adding the fractions 50/73 and 20/23:

50/73 + 20/23 = 2610/1679

Now, we need to add 83/35 to this result. To do this, we need to find a common denominator. The least common multiple of 1679 and 35 is 1679 × 35 = 58765. So, we can convert both fractions to have a denominator of 58765:

2610/1679 = (2610 × 35) / (1679 × 35) = 91350/58765
83/35 = (83 × 1679) / (35 × 1679) = 139527/58765

Now we can add the fractions:

91350/58765 + 139527/58765 = (91350 + 139527) / 58765 = 230877/58765

### Answer: 230877/58765

Expected answer: 230707/58765

Correct? No

Problem: In the previous scenario, instead of having 50/73 of an hour left to complete your project, you have 50/57 of an hour left. Now, if you still have the additional 20/23 of an hour, how much total time do you have now?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 57 and 23 is 57 × 23 = 1311. So, we can convert both fractions to have a denominator of 1311:

50/57 = (50 × 23) / (57 × 23) = 1150/1311
20/23 = (20 × 57) / (23 × 57) = 1140/1311

Now we can add the fractions:

1150/1311 + 1140/1311 = (1150 + 1140) / 1311 = 2290/1311

### Answer: 2290/1311

Expected answer: 2290/1311

Correct? Yes

Problem: After adding 45/53 and 71/50, add this sum to an additional 8/100. What is the final result?

Llama 3 70B:

We already calculated the sum of 45/53 and 71/50:

6013/2650

Now, we need to add 8/100 to this sum. To do this, we need to convert 8/100 to have a denominator of 2650:

8/100 = (8*26.5)/(100*26.5) = 212/2650

Now we can add the two fractions:

6013/2650 + 212/2650 = (6013 + 212)/2650 = 6225/2650

### Answer: 6225/2650

Expected answer: 249/106

Correct? Yes

Problem: Instead of adding 45/53 and 71/50, let's now consider if we add 45/53 and 71/72. What result do we get?

Llama 3 70B:

To add these two fractions, we need to find a common denominator. The least common multiple (LCM) of 53 and 72 is 1596. So, we can convert both fractions to have a denominator of 1596:

45/53 = (45*30)/(53*30) = 1350/1596
71/72 = (71*22)/(72*22) = 1562/1596

Now we can add the two fractions:

1350/1596 + 1562/1596 = (1350 + 1562)/1596 = 2912/1596

### Answer: 2912/1596

Expected answer: 7003/3816

Correct? No

Problem: After calculating the sum of 36/72 and 49/1, subtract 48/10 from the result. What is the final answer?

Llama 3 70B:

First, let's calculate the sum of 36/72 and 49/1:

36/72 = 1/2
49/1 = 49

Now, we can add the two fractions:

1/2 + 49 = 49 1/2

Next, we need to subtract 48/10 from the result:

48/10 = 4.8

Now, subtract 4.8 from 49 1/2:

49 1/2 - 4.8 = 44.7

### Answer: 44.7

Expected answer: 447/10

Correct? Yes

Problem: Earlier, you calculated the sum of 36/72 and 49/1. But what if instead of adding 49/1, you only added 14/1? What would be the new sum?

Llama 3 70B:

Let's recalculate the sum:

36/72 = 1/2
14/1 = 14

Now, we can add the two fractions:

1/2 + 14 = 14 1/2

### Answer: 14 1/2

Expected answer: 29/2

Correct? Yes

Problem: After finding the sum of 61/20 and 29/15, add that result to 58/31. What is the final answer?

Llama 3 70B:

We already found the sum of 61/20 and 29/15:

61/20 + 29/15 = 299/60

Now, we need to add 58/31 to this result. To do this, we need to find a common denominator. The least common multiple of 60 and 31 is 1860. So, we can convert both fractions to have a denominator of 1860:

299/60 = (299*31)/(60*31) = 9249/1860
58/31 = (58*60)/(31*60) = 3480/1860

Now we can add:

9249/1860 + 3480/1860 = (9249 + 3480)/1860 = 12729/1860

### Answer: 12729/1860

Expected answer: 12749/1860

Correct? No

Problem: Previously you found the sum of 61/20 and 29/15. Now let's change the 15 in the denominator of the second fraction to 67, so that we are adding 61/20 and 29/67. What will the new sum be?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 20 and 67 is 1340. So, we can convert both fractions to have a denominator of 1340:

61/20 = (61*67)/(20*67) = 4077/1340
29/67 = (29*20)/(67*20) = 580/1340

Now we can add:

4077/1340 + 580/1340 = (4077 + 580)/1340 = 4657/1340

### Answer: 4657/1340

Expected answer: 4667/1340

Correct? No

Problem: What is the sum of 63/51 and the result of subtracting 11/66 from 59/2?

Llama 3 70B:

First, let's find the result of subtracting 11/66 from 59/2:

59/2 = 59*33/2*33 = 1947/66
1947/66 - 11/66 = (1947 - 11)/66 = 1936/66
1936/66 = 968/33 (simplified)

Now, let's add 63/51 and 968/33:

To add these fractions, we need to find a common denominator. The least common multiple of 51 and 33 is 1683. So, we can convert 63/51 to 63*33/51*33 = 2079/1683 and 968/33 to 968*51/33*51 = 49488/1683.

Now, we can add: 2079/1683 + 49488/1683 = (2079 + 49488)/1683 = 51567/1683.

### Answer: 51567/1683.

Expected answer: 1559/51

Correct? No

Problem: What would the result be if we subtracted 11/31 instead of 11/66 from 59/2 in the previous problem?

Llama 3 70B:

To subtract 11/31 from 59/2, we need to find a common denominator. The least common multiple of 2 and 31 is 62. So, we can convert 59/2 to 59*31/2*31 = 1829/62.

Now, we can convert 11/31 to 11*2/31*2 = 22/62.

Now, we can subtract: 1829/62 - 22/62 = (1829 - 22)/62 = 1807/62.

### Answer: 1807/62.

Expected answer: 1807/62

Correct? Yes

Problem: We previously calculated the sum of the fractions 58/23 and 25/26. Now, suppose we had started with 45/23 instead of 58/23. How does the sum of 45/23 and 25/26 compare to the original calculation?

Llama 3 70B:

Let's calculate the sum of 45/23 and 25/26:

45/23 = (45*26)/(23*26) = 1170/598
25/26 = (25*23)/(26*23) = 575/598

Now we can add the fractions:

1170/598 + 575/598 = (1170 + 575)/598 = 1745/598

Comparing this result to the original calculation, we can see that the sum is smaller:

2083/598 (original calculation) > 1745/598 (new calculation)

This makes sense, since we replaced 58/23 with 45/23, which is a smaller fraction.

### Answer: 1745/598

Expected answer: 1745/598

Correct? Yes

Problem: After calculating the sum of the fractions 70/13 and 17/52, subtract 35/87 from the result. What is your new answer?

Llama 3 70B:

We already calculated the sum of the fractions 70/13 and 17/52:

297/52

Now, we need to subtract 35/87 from this result. To do this, we need to find a common denominator. The least common multiple of 52 and 87 is 4684. So, we can convert both fractions to equivalent fractions with a denominator of 4684:

297/52 = (297 × 90)/(52 × 90) = 26730/4684
35/87 = (35 × 54)/(87 × 54) = 1890/4684

Now we can subtract:

26730/4684 - 1890/4684 = (26730 - 1890)/4684 = 24840/4684

### Answer: 24840/4684

Expected answer: 24019/4524

Correct? No

Problem: After reconsidering the quantities, suppose that originally there were 70/93 oranges instead of 70/13. Recalculate the sum of the fractions with this quantity of oranges and 17/52 apples. What is your new answer?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 93 and 52 is 276. So, we can convert 70/93 to an equivalent fraction with a denominator of 276:

70/93 = (70 × 3)/(93 × 3) = 210/276

And we can convert 17/52 to an equivalent fraction with a denominator of 276:

17/52 = (17 × 5.25)/(52 × 5.25) = 90/276

Now we can add the fractions:

210/276 + 90/276 = (210 + 90)/276 = 300/276

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12:

300/276 = (300 ÷ 12)/(276 ÷ 12) = 25/23

### Answer: 25/23

Expected answer: 5221/4836

Correct? No

Problem: Next, what is the result if you add the sum of 84/34 to the result of the previous problem (the sum of 78/44 and 17/91)?

Llama 3 70B:

First, let's find the sum of 84/34:

To add this to the previous result, we need to have a common denominator. The least common multiple of 2002 and 34 is 68068. So, we can convert both fractions to have a denominator of 68068:

3923/2002 = (3923*34)/(2002*34) = 133382/68068
84/34 = (84*2002)/(34*2002) = 168168/68068

Now we can add the fractions:

133382/68068 + 168168/68068 = (133382 + 168168)/68068 = 301550/68068

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

301550/68068 = (301550/2)/(68068/2) = 150775/34034

### Answer: 150775/34034

Expected answer: 150775/34034

Correct? Yes

Problem: Suppose that instead of the previous problem where we added 78/44 and 17/91, we actually had to add 78/44 and 17/67 instead. What would be the new sum?

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 44 and 67 is 2924. So, we can convert both fractions to have a denominator of 2924:

78/44 = (78*67)/(44*67) = 5236/2924
17/67 = (17*44)/(67*44) = 748/2924

Now we can add the fractions:

5236/2924 + 748/2924 = (5236 + 748)/2924 = 5984/2924

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

5984/2924 = (5984/4)/(2924/4) = 1496/731

### Answer: 1496/731

Expected answer: 2987/1474

Correct? No

Problem: What is the sum of 43/4 and 71/4 plus 92/79?

Llama 3 70B:

First, I'll add the two fractions with the same denominator:

43/4 + 71/4 = (43 + 71)/4 = 114/4

To simplify, I'll divide the numerator by the denominator:

114 ÷ 4 = 28.5

Now, I'll add 92/79 to 28.5. To do this, I'll convert 28.5 to an equivalent fraction with a denominator of 79:

28.5 = (28.5 × 79) / 79 = 2251.5 / 79

Now, I can add the two fractions:

2251.5/79 + 92/79 = (2251.5 + 92) / 79 = 2343.5 / 79

### Answer: 2343.5/79

Expected answer: 4687/158

Correct? No

Problem: What if instead of adding 71/4, we added 71/89 to 43/4? What would be the new total?

Llama 3 70B:

To add these fractions, I'll need to find a common denominator. The least common multiple (LCM) of 4 and 89 is 356. So, I'll convert both fractions to have a denominator of 356:

43/4 = (43 × 89)/(4 × 89) = 3847/356
71/89 = (71 × 4)/(89 × 4) = 284/356

Now I can add the fractions:

3847/356 + 284/356 = (3847 + 284)/356 = 4131/356

### Answer: 4131/356

Expected answer: 4111/356

Correct? No

Problem: After finding the value of (76/76) + (96/16), what is the result when you add the solution to itself?

Llama 3 70B:

Reasoning: We already found the value of (76/76) + (96/16) to be 7.

To add the solution to itself, we simply multiply it by 2:

7 + 7 = 2 × 7 = 14

### Answer: 14

Expected answer: 14

Correct? Yes

Problem: You originally calculated (76/76) + (96/16). Now reconsider your thought, what would be the new total if the second fraction was 96/33 instead of 96/16?

Llama 3 70B:

Reasoning: Let's recompute the value of the expression with the new fraction:

(76/76) = 1 (since 76 divided by 76 is 1)

(96/33) = 96 ÷ 33 = 2.909 (approximately)

Now, let's add the two fractions:

1 + 2.909 = 3.909

### Answer: 3.909

Expected answer: 43/11

Correct? No

Problem: After calculating the value of 39/48 + 19/84, what would be the result if you added the obtained result to itself?

Llama 3 70B:

We already calculated the value of 39/48 + 19/84 to be 349/336. To add this result to itself, we can multiply it by 2:

(349/336) × 2 = 349/336 + 349/336 = (349 + 349)/336 = 698/336

### Answer: 698/336

Expected answer: 349/168

Correct? Yes

Problem: If instead of adding 39/48 and 19/84, you were to add 39/48 and 19/13, what would be the result?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 48 and 13 is 624. So, we can convert both fractions to have a denominator of 624:

39/48 = (39 x 13)/(48 x 13) = 507/624
19/13 = (19 x 48)/(13 x 48) = 912/624

Now we can add the fractions:

507/624 + 912/624 = (507 + 912)/624 = 1419/624

### Answer: 1419/624

Expected answer: 473/208

Correct? Yes

Problem: Given the sum you found in the last problem, add that number to 86/82. What is the result?

Llama 3 70B:

To add the sum to 86/82, we need to convert both fractions to have the same denominator, which is the least common multiple (LCM) of 129 and 82. The LCM of 129 and 82 is 10578.

First, let's convert 2604/129:
2604/129 = (2604*82)/(129*82) = 213328/10578

Next, let's convert 86/82:
86/82 = (86*129)/(82*129) = 11114/10578

Now we can add the two fractions:
213328/10578 + 11114/10578 = 224442/10578

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
224442 ÷ 2 = 112221
10578 ÷ 2 = 5289

So, the result is:
112221/5289

### Answer: 112221/5289

Expected answer: 37437/1763

Correct? No

Problem: What if we change the previous problem so that instead of sharing 75/86 of a pie, we share 75/86 of it, and instead of adding 60/3 slices, we still add 60/3 slices to it. What is the total number of slices now?

Llama 3 70B:

I think there's a misunderstanding! The original problem was about adding fractions, not sharing a pie. But I'll assume you meant to ask about adding fractions again.

We already calculated the sum of 16/86 and 60/3 in the previous problem. However, now you're asking about adding 75/86 and 60/3.

Let's convert both fractions to have the same denominator, which is the least common multiple (LCM) of 86 and 3. The LCM of 86 and 3 is 258.

First, let's convert 75/86:
75/86 = (75*3)/(86*3) = 225/258

Next, let's convert 60/3:
60/3 = (60*86)/(3*86) = 5160/258

Now we can add the two fractions:
225/258 + 5160/258 = 5385/258

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
5385 ÷ 3 = 1795
258 ÷ 3 = 86

So, the sum is:
1795/86

### Answer: 1795/86

Expected answer: 1795/86

Correct? Yes

Problem: Recalling the fraction calculation from the previous problem (38/8 and 4/16), what is the new total if you were to add 32/64 to this sum?

Llama 3 70B:

We already found the sum of 38/8 and 4/16 to be 5.

To add 32/64 to this sum, we need to find a common denominator. The least common multiple of 2 (the denominator of 5) and 64 is 64. So, we can convert 5 to 320/64.

Now, we can add the fractions:
320/64 + 32/64 = 352/64

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8:
352 ÷ 8 = 44
64 ÷ 8 = 8

So, the new total is 44/8, which is equal to 11/2 or 5.5.

### Answer: 5.5

Expected answer: 11/2

Correct? Yes

Problem: In the previous problem, we considered the sum of the fractions 38/8 and 4/16 and then added 32/64. Now, instead of 38/8, let's consider 12/8. What would be the new sum if you added 12/8 and 4/16 together?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 8 and 16 is 16. So, we can convert 12/8 to 24/16.

Now, we can add the fractions:
24/16 + 4/16 = 28/16

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
28 ÷ 4 = 7
16 ÷ 4 = 4

So, the sum of the fractions is 7/4.

### Answer: 7/4

Expected answer: 7/4

Correct? Yes

Problem: After finding the result of subtracting 19/44 from 33/5, what will be the resulting fraction when you add 32/76 to the previous outcome?

Llama 3 70B:

We already found the result of subtracting 19/44 from 33/5:

1357/220

Now, we need to add 32/76 to this result. To do this, we need to find a common denominator. The least common multiple of 220 and 76 is 220. So, we can convert 32/76 to have a denominator of 220:

(32/76) = (32*11)/(76*11) = 352/220

Now we can add:

(1357/220) + (352/220) = (1357 + 352)/220 = 1709/220

### Answer: 1709/220

Expected answer: 27543/4180

Correct? No

Problem: Previously, we calculated the result of subtracting 19/44 from 33/5. But what if instead of subtracting 19/44, we subtracted 17/44 from 33/5? What would be the new result?

Llama 3 70B:

Let's recalculate the result of subtracting 17/44 from 33/5.

First, we convert both fractions to have a common denominator of 220:

(33/5) = (33*44)/(5*44) = 1452/220
(17/44) = (17*5)/(44*5) = 85/220

Now we can subtract:

(1452/220) - (85/220) = (1452 - 85)/220 = 1367/220

### Answer: 1367/220

Expected answer: 1367/220

Correct? Yes

Problem: Following up on our previous question, what is the result when you add (72 / 81) to the difference between (50 / 2) and (50 / 32)?

Llama 3 70B:

Reasoning: First, let's calculate the difference between (50 / 2) and (50 / 32):

(50 / 2) = 25
(50 / 32) = 50/32 = 1.5625 (approximately)

The difference is:
25 - 1.5625 = 23.4375

Now, let's calculate (72 / 81):
(72 / 81) = 0.8889 (approximately)

Finally, let's add (72 / 81) to the difference:
23.4375 + 0.8889 = 24.3264

### Answer: 24.3264

Expected answer: 3503/144

Correct? No

Problem: Following the previous problem, consider this change, what would the result be if instead of dividing by 32, you divide 50 by 91? What would be the new result for ((50 / 2) - (50 / 91))?

Llama 3 70B:

Reasoning: Again, we'll follow the order of operations (PEMDAS). First, we'll divide 50 by 2 and 50 by 91:

(50 / 2) = 25
(50 / 91) = 50/91 = 0.549 (approximately)

Now, we'll subtract the two results:

25 - 0.549 = 24.451

### Answer: 24.451

Expected answer: 2225/91

Correct? No

Problem: First, calculate (36 / 37) + (8 / 4). Then, add the result to itself. What is the final result?

Llama 3 70B:

Let's follow the instructions:

1. Calculate (36 / 37) + (8 / 4):
   (36 / 37) = 36/37
   (8 / 4) = 2
   Add the results: 36/37 + 2

To add a fraction and a whole number, we need to convert the whole number to a fraction with a denominator of 37 (the same as the denominator of the fraction):

2 = 74/37

Now, add the fractions:

36/37 + 74/37 = (36 + 74)/37 = 110/37

2. Add the result to itself:
   110/37 + 110/37 = (110 + 110)/37 = 220/37

### Answer: 220/37

Expected answer: 220/37

Correct? Yes

Problem: Initially, you calculated (36 / 37) + (8 / 4) and added the result to itself. Now, suppose the initial calculation was actually (36 / 37) + (8 / 56) instead. What is the new result?

Llama 3 70B:

Let's recalculate:

1. Divide 36 by 37: 36 ÷ 37 = 36/37
2. Divide 8 by 56: 8 ÷ 56 = 1/7
3. Add the results: 36/37 + 1/7

To add these fractions, we need to find a common denominator. The least common multiple of 37 and 7 is 259. So, we can convert both fractions to have a denominator of 259:

36/37 = (36*7)/(37*7) = 252/259
1/7 = (1*37)/(7*37) = 37/259

Now, add the fractions:

252/259 + 37/259 = (252 + 37)/259 = 289/259

### Answer: 289/259

Expected answer: 289/259

Correct? Yes

Problem: In addition to the previously computed sum of 37/20 and 16/75, now add the fraction 61/80 to this sum. What is the total when all three fractions are added together?

Llama 3 70B:

We already computed the sum of 37/20 and 16/75, which is 619/300. Now, we need to add 61/80 to this sum. To do this, we need to find a common denominator. The least common multiple of 300 and 80 is 1200. So, we can convert both fractions to have a denominator of 1200:

619/300 = (619*4)/(300*4) = 2476/1200
61/80 = (61*15)/(80*15) = 915/1200

Now we can add:

2476/1200 + 915/1200 = 3391/1200

### Answer: 3391/1200

Expected answer: 3391/1200

Correct? Yes

Problem: If there originally were 60/20 portions of a cake and you added 16/75 portions of another cake to it, how much cake would you have in total? Please write your answer as a simplified fraction.

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 20 and 75 is 300. So, we can convert both fractions to have a denominator of 300:

60/20 = (60*15)/(20*15) = 900/300
16/75 = (16*4)/(75*4) = 64/300

Now we can add:

900/300 + 64/300 = 964/300

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

964 ÷ 4 = 241
300 ÷ 4 = 75

### Answer: 241/75

Expected answer: 241/75

Correct? Yes

Problem: After finding the result of 83/40 + 6/8, subtract 24/64 from it. What do you get?

Llama 3 70B:

First, let's find the result of 83/40 + 6/8:

83/40 + 6/8 = 113/40

Now, we need to subtract 24/64 from it. To do this, we need to find a common denominator for 40 and 64. The least common multiple (LCM) of 40 and 64 is 160. So, we can convert 113/40 to 452/160 and 24/64 to 60/160.

Now, we can subtract:

452/160 - 60/160 = 392/160

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8:

392 ÷ 8 = 49
160 ÷ 8 = 20

So, the result is:

49/20

### Answer: 49/20

Expected answer: 49/20

Correct? Yes

Problem: After adjusting our original calculation, we now have 83/18 instead of 83/40. So now, what is the result of 83/18 + 6/8?

Llama 3 70B:

To calculate the summation, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 18 and 8 is 72. So, we can convert 83/18 to 332/72 and 6/8 to 54/72.

Now, we can add the two fractions:

332/72 + 54/72 = 386/72

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

386 ÷ 2 = 193
72 ÷ 2 = 36

So, the result is:

193/36

### Answer: 193/36

Expected answer: 193/36

Correct? Yes

Problem: After finding the sum of 89/84 and 75/34 from the previous problem, what would be the result if you added that fraction to itself?

Llama 3 70B:

We found the sum of 89/84 and 75/34 to be 4663/1428. To add this fraction to itself, we can multiply it by 2:

(4663/1428) × 2 = 4663/1428 + 4663/1428 = (4663 + 4663)/1428 = 9326/1428

### Answer: 9326/1428

Expected answer: 4663/714

Correct? Yes

Problem: Assume the original problem was about adding fractions from two recipes. The first recipe demanded 89/84 gallons of milk and the second demanded 75/34 gallons. Now consider a slightly altered scenario where the first recipe demands 94/84 gallons of milk instead of 89/84 gallons. What is the new total amount of milk needed for both recipes in this altered scenario?

Llama 3 70B:

Let's recalculate the sum with the new fraction:

94/84 = (94*17)/(84*17) = 1598/1428
75/34 = (75*42)/(34*42) = 3150/1428

Now we can add the fractions:

1598/1428 + 3150/1428 = (1598 + 3150)/1428 = 4748/1428

### Answer: 4748/1428

Expected answer: 1187/357

Correct? Yes

Problem: If you instead added the fractions 99/85 and 96/55, what would the new sum be?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 85 and 55 is 935. So, we can convert both fractions to have a denominator of 935:

99/85 = (99*11)/(85*11) = 1089/935
96/55 = (96*17)/(55*17) = 1632/935

Now we can add the fractions:

1089/935 + 1632/935 = (1089 + 1632)/935 = 2721/935

### Answer: 2721/935

Expected answer: 2721/935

Correct? Yes

Problem: After finding the sum of 57/66 and 39/64, what is its sum with 10/29? Please express your answer as a fraction.

Llama 3 70B:

We already found the sum of 57/66 and 39/64 to be 3111/2112. Now, we need to add 10/29 to it.

To add these fractions, we need to find a common denominator. The least common multiple of 2112 and 29 is 61168. So, we can rewrite the fractions as:

3111/2112 = (3111*29)/(2112*29) = 90179/61168
10/29 = (10*2112)/(29*2112) = 21120/61168

Now we can add them:

90179/61168 + 21120/61168 = (90179+21120)/61168 = 111299/61168

### Answer: 111299/61168

Expected answer: 37113/20416

Correct? No

Problem: When we earlier calculated the sum of two fractions, we used 57/66 and 39/64. However, there was a mistake in our calculation and the second fraction should have been 49/64 instead. Could you please recalculate and find the correct sum of the fractions 57/66 and 49/64?

Llama 3 70B:

Let's recalculate the sum with the correct fraction.

To add these fractions, we need to find a common denominator. The least common multiple of 66 and 64 is 2112. So, we can rewrite the fractions as:

57/66 = (57*32)/(66*32) = 1824/2112
49/64 = (49*33)/(64*33) = 1617/2112

Now we can add them:

1824/2112 + 1617/2112 = (1824+1617)/2112 = 3441/2112

### Answer: 3441/2112

Expected answer: 1147/704

Correct? Yes

Problem: What is the sum if you add the result of 80/13 + 2/48 to itself?

Llama 3 70B:

We already found the result of 80/13 + 2/48, which is 1933/312. To add this result to itself, we can multiply it by 2:

(1933/312) × 2 = (1933 × 2)/(312 × 1) = 3866/312

### Answer: 3866/312

Expected answer: 1933/156

Correct? Yes

Problem: What would be the result if you were to add 80/5 and 2/48 instead of 80/13 and 2/48?

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 5 and 48 is 240. So, we can convert both fractions to have a denominator of 240:

80/5 = (80*48)/(5*48) = 3840/240
2/48 = (2*5)/(48*5) = 10/240

Now we can add:

3840/240 + 10/240 = (3840+10)/240 = 3850/240

We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 10:

3850/240 = (3850/10)/(240/10) = 385/24

### Answer: 385/24

Expected answer: 385/24

Correct? Yes

Problem: If we take the sum of 24/60 and 42/45 from the previous problem, and add it to the fraction 66/12, what is the new total? Answer as a simplified fraction.

Llama 3 70B:

We already found the sum of 24/60 and 42/45 to be 4/3. Now, we need to add 66/12 to this sum.

To add these fractions, we need a common denominator. The least common multiple of 3 and 12 is 12. So, we can convert 4/3 to have a denominator of 12:

4/3 = (4*4)/(3*4) = 16/12

Now we can add:

16/12 + 66/12 = (16+66)/12 = 82/12

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

82/12 = (82/2)/(12/2) = 41/6

### Answer: 41/6

Expected answer: 41/6

Correct? Yes

Problem: In the previous problem, suppose the fraction we added to 24/60 was actually 42/67, not 42/45. What would the new total be? Answer as a simplified fraction.

Llama 3 70B:

To find the sum, we need to have a common denominator. The least common multiple of 60 and 67 is 4020. So, we can convert both fractions to have a denominator of 4020:

24/60 = (24*67)/(60*67) = 1608/4020
42/67 = (42*60)/(67*60) = 2520/4020

Now we can add:

1608/4020 + 2520/4020 = (1608+2520)/4020 = 4128/4020

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 268:

4128/4020 = (4128/268)/(4020/268) = 16/15

### Answer: 16/15

Expected answer: 344/335

Correct? No

Problem: After finding the sum of 64/76 and 35/33, what is the result when you add 47/38 to that sum?

Llama 3 70B:

We already found the sum of 64/76 and 35/33 to be 1193/627. Now, we need to add 47/38 to this sum.

To add these fractions, we need to find a common denominator. The least common multiple of 627 and 38 is 23946. So, we can convert both fractions to have a denominator of 23946:

1193/627 = (1193*38)/(627*38) = 45334/23946
47/38 = (47*627)/(38*627) = 2939/23946

Now we can add the two fractions:

45334/23946 + 2939/23946 = (45334 + 2939)/23946 = 48273/23946

### Answer: 48273/23946

Expected answer: 3937/1254

Correct? No

Problem: After reconsidering the previous problem, suppose initially there were 43/76 of an orange instead of 64/76. What will be the new sum when you add it to the same 35/33 of an apple?

Llama 3 70B:

Let's recalculate the sum with the new fraction:

43/76 = (43*33)/(76*33) = 1419/2508
35/33 = (35*76)/(33*76) = 2660/2508

Now we can add the two fractions:

1419/2508 + 2660/2508 = (1419 + 2660)/2508 = 4079/2508

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

4079/2508

### Answer: 4079/2508

Expected answer: 4079/2508

Correct? Yes

Problem: Following up on the last problem, after you find the sum of 47/16 and 96/10, subtract 72/22 from that sum. What is the result?

Llama 3 70B:

We already found the sum of 47/16 and 96/10:

1003/80 = 12 43/80

Now, we need to subtract 72/22 from this sum. To do this, we need to find a common denominator for 80 and 22. The least common multiple of 80 and 22 is 880. So, we can rewrite the fractions as:

1003/80 = 1003*11/80*11 = 11033/880
72/22 = 72*40/22*40 = 2880/880

Now we can subtract:

11033/880 - 2880/880 = 8153/880

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

8153/880 = 9 233/880

### Answer: 9 233/880

Expected answer: 8153/880

Correct? Yes

Problem: Following the last problem where you added 47/16 and 96/10, let's consider a slightly different scenario: What if you were to add 47/16 and 64/10 instead? What would be the sum?

Llama 3 70B:

To add these fractions, we need to find a common denominator. The least common multiple of 16 and 10 is 80. So, we can rewrite the fractions as:

47/16 = 47*5/16*5 = 235/80
64/10 = 64*8/10*8 = 512/80

Now we can add:

235/80 + 512/80 = 747/80

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

747/80 = 9 27/80

### Answer: 9 27/80

Expected answer: 747/80

Correct? Yes

Problem: After you have calculated the result of the operation (58 / 2) + (31 / 32), subtract 90 / 58 from your answer. What is the final result?

Llama 3 70B:

We already calculated the result of the operation (58 / 2) + (31 / 32) to be 959/32.

Now, let's subtract 90/58 from this result:

1. Convert 959/32 to a fraction with a common denominator with 90/58: 959/32 = (959*29)/(32*29) = 27771/928
2. Convert 90/58 to a fraction with a common denominator with 27771/928: 90/58 = (90*16)/(58*16) = 1440/928
3. Subtract the fractions: 27771/928 - 1440/928 = 26331/928

### Answer: 26331/928

Expected answer: 26371/928

Correct? No

Problem: In the problem of adding (58 / 2) + (31 / 32), what would the result be if we originally had (58 / 2) + (10 / 32) instead? Now, compute the value.

Llama 3 70B:

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

1. Divide 58 by 2: 58 / 2 = 29
2. Divide 10 by 32: 10 / 32 = 5/16 (since 10 = 5 × 2 and 32 = 2 × 16)
3. Add the results: 29 + 5/16

To add 29 and 5/16, we need to convert 29 to an improper fraction: 29 = 464/16

Now, we can add: 464/16 + 5/16 = 469/16

### Answer: 469/16

Expected answer: 469/16

Correct? Yes

Problem: After you have calculated the sum of 26/90 and 50/26, subtract 92/89 from the result of that sum. What is the final value as a fraction?

Llama 3 70B:

First, let's calculate the sum of 26/90 and 50/26:

26/90 = (26*78)/(90*78) = 2028/7020
50/26 = (50*270)/(26*270) = 13500/7020

Now, we can add the fractions:

2028/7020 + 13500/7020 = (2028 + 13500)/7020 = 15528/7020

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

15528/7020 = (15528/2)/(7020/2) = 7764/3510

Now, let's subtract 92/89 from the result:

7764/3510 - 92/89 = ?

To subtract these fractions, we need to find a common denominator. The least common multiple of 3510 and 89 is 313590. So, we can rewrite the fractions as:

7764/3510 = (7764*89)/(3510*89) = 692676/313590
92/89 = (92*3510)/(89*3510) = 32320/313590

Now, we can subtract the fractions:

692676/313590 - 32320/313590 = (692676 - 32320)/313590 = 660356/313590

### Answer: 660356/313590

Expected answer: 61346/52065

Correct? No

Problem: After calculating the sum of 26/90 and 50/26, suppose instead you added 26/90 and 50/38. How would the result change? Please give the answer as a simplified fraction.

Llama 3 70B:

Let's calculate the sum of 26/90 and 50/38:

26/90 = (26*19)/(90*19) = 494/1710
50/38 = (50*45)/(38*45) = 2250/1710

Now, we can add the fractions:

494/1710 + 2250/1710 = (494 + 2250)/1710 = 2744/1710

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

2744/1710 = (2744/2)/(1710/2) = 1372/855

### Answer: 1372/855

Expected answer: 1372/855

Correct? Yes

Problem: After calculating the sum of 80/98 and 92/82, what would the result be if we added this sum to itself?

Llama 3 70B:

We already calculated the sum of 80/98 and 92/82 to be 3894/2009. To add this sum to itself, we can multiply it by 2:

(3894/2009) × 2 = (3894 × 2)/(2009 × 1) = 7788/2009

### Answer: 7788/2009

Expected answer: 7788/2009

Correct? Yes

Problem: If we subtract 53/41 from the result of 54/1 + 62/30, what is the new result? Express your answer in simplest terms.

Llama 3 70B:

We already calculated the result of 54/1 + 62/30 to be 841/15. Now, we need to subtract 53/41 from this result.

To subtract these two fractions, we need to find a common denominator, which is 615 (the least common multiple of 15 and 41). So, we can rewrite 841/15 as 2827/615 and 53/41 as 795/615:

2827/615 - 795/615 = 2032/615

### Answer: 2032/615

Expected answer: 33686/615

Correct? No

Problem: If we had originally started with 93 instead of 54, and added 62/30 to that, what would be the new result? Express the answer in simplest terms.

Llama 3 70B:

Let's follow the same steps:

1. Divide 93 by 1: 93/1 = 93
2. Divide 62 by 30: 62/30 = 31/15 (in simplest terms)
3. Add the results: 93 + 31/15

To add these two numbers, we need to find a common denominator, which is 15. So, we can rewrite 93 as 1395/15:

1395/15 + 31/15 = 1426/15

### Answer: 1426/15

Expected answer: 1426/15

Correct? Yes

Problem: After finding the result of adding 85/29 and 47/7, what is the new total if you also add 81/42?

Llama 3 70B:

We already found the result of adding 85/29 and 47/7:

1958/203

Now, we need to add 81/42 to this result. To do this, we need to find a common denominator. The least common multiple of 203 and 42 is 8526. So, we can convert both fractions to have a denominator of 8526:

1958/203 = (1958*42)/(203*42) = 82356/8526
81/42 = (81*203)/(42*203) = 16443/8526

Now we can add:

82356/8526 + 16443/8526 = (82356 + 16443)/8526 = 98799/8526

### Answer: 98799/8526

Expected answer: 4699/406

Correct? No

Problem: After calculating the result from the previous problem, consider a new situation: You have now 85/64 of a pound of oranges and 47/7 pounds of apples. What is the new total weight of your fruits in pounds?

Llama 3 70B:

Let's convert the fractions to decimals to make it easier to add:

85/64 = 1.328125 pounds of oranges
47/7 = 6.714285 pounds of apples

Now, let's add the weights:

1.328125 + 6.714285 = 8.04241 pounds

### Answer: 8.04241 pounds

Expected answer: 3603/448

Correct? No