Problem: After finding the sum of (74 / 63) and (91 / 78), compute what will be the sum if you add the result to itself.

Qwen2-Math 72B:

 Reasoning: The sum of (74 / 63) and (91 / 78) is 2.3412698412698413.
If we add the result to itself, we get 2.3412698412698413 + 2.3412698412698413 = <<2.3412698412698413+2.3412698412698413=4.682539682539683>>4.682539682539683
### Answer: 4.682539682539683

Expected answer: 295/63

Correct? Yes

Problem: In the previous problem you calculated the sum of (74 / 63) and (91 / 78). Now, assume instead of 74 in the first fraction, there were 35. What is the new sum when you add (35 / 63) and (91 / 78)?

Qwen2-Math 72B:

 Reasoning: (35 / 63) = <<35/63=0.5555555555555556>>0.5555555555555556
(91 / 78) = <<91/78=1.1666666666666667>>1.1666666666666667
The sum of (35 / 63) and (91 / 78) is 0.5555555555555556 + 1.1666666666666667 = <<0.5555555555555556+1.1666666666666667=1.7222222222222223>>1.7222222222222223
### Answer: 1.7222222222222223

Expected answer: 31/18

Correct? Yes

Problem: If the sum from the previous problem is then added to 73/89, what is the final result?

Qwen2-Math 72B:

 Reasoning: To add these fractions, we need a common denominator, which is 25 * 89 = 2225.
471/25 = (471 * 89) / (25 * 89) = 41919/2225
73/89 = (73 * 25) / (89 * 25) = 1825/2225
Adding these fractions, we get 41919/2225 + 1825/2225 = 43744/2225
### Answer: 43744/2225

Expected answer: 43744/2225

Correct? Yes

Problem: If instead of adding 94/5 you had added 94/89 to 1/25 in the previous problem, what would have been the result?

Qwen2-Math 72B:

 Reasoning: To add these fractions, we need a common denominator, which is 89 * 25 = 2225.
94/89 = (94 * 25) / (89 * 25) = 2350/2225
1/25 = (1 * 89) / (25 * 89) = 89/2225
Adding these fractions, we get 2350/2225 + 89/2225 = 2439/2225
### Answer: 2439/2225

Expected answer: 2439/2225

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To subtract fractions, we need a common denominator. The least common multiple of 14 and 8 is 56.
49/8 = <<49*7/8*7=343/56>>343/56
48/14 = <<48*4/14*4=192/56>>192/56
343/56 - 192/56 = <<343-192=151>>151/56
### Answer: 151/56

Expected answer: 151/56

Correct? Yes

Problem: After finding the value of ((45 / 5) - (6 / 47)), what would be the result if you add this value to itself?

Qwen2-Math 72B:

 Reasoning: The value of ((45 / 5) - (6 / 47)) is 8.872340425531915.
Adding this value to itself gives 8.872340425531915 + 8.872340425531915 = <<8.872340425531915+8.872340425531915=17.74468085106383>>17.74468085106383
### Answer: 17.74468085106383

Expected answer: 834/47

Correct? Yes

Problem: After reconsideration, suppose there were actually 63 oranges instead of 45. Now calculate the value of the expression ((63 / 5) - (6 / 47)).

Qwen2-Math 72B:

 Reasoning: ((63 / 5) - (6 / 47)) = (<<63/5=12.6>>12.6 - <<6/47=0.1276595744680851>>0.1276595744680851) = <<12.6-0.1276595744680851=12.472340425531915>>12.472340425531915
### Answer: 12.472340425531915

Expected answer: 2931/235

Correct? Yes

Problem: After you've computed the sum of 22/49 and 72/35, add this result to 32/21. What is the final sum, presented as a simplified fraction?

Qwen2-Math 72B:

 Reasoning: We have already computed the sum of 22/49 and 72/35 to be 614/245. Now, we need to add this to 32/21. First, we find a common denominator for 614/245 and 32/21, which is the LCM of 245 and 21. The LCM of 245 and 21 is 735. We convert each fraction to have this common denominator:
614/245 = (614 * 3) / (245 * 3) = 1842/735
32/21 = (32 * 35) / (21 * 35) = 1120/735
Adding these fractions, we get:
1842/735 + 1120/735 = 2962/735
The fraction 2962/735 can be simplified by dividing both the numerator and the denominator by their GCD, which is 1 in this case, so the fraction is already in its simplest form.
### Answer: 2962/735

Expected answer: 2962/735

Correct? Yes

Problem: Imagine you originally had 22/34 of a basket of ripe apples instead of 22/49, and you also have 72/35 of a basket of oranges. How much do you have in total, given these new amounts? Provide your answer in simplified form.

Qwen2-Math 72B:

 Reasoning: To find the total amount of fruit, we need to add the fractions 22/34 and 72/35. First, we find a common denominator, which is the LCM of 34 and 35, which is 1190. We convert each fraction to have this common denominator:
22/34 = (22 * 35) / (34 * 35) = 770/1190
72/35 = (72 * 34) / (35 * 34) = 2448/1190
Adding these fractions, we get:
770/1190 + 2448/1190 = 3218/1190
The fraction 3218/1190 can be simplified by dividing both the numerator and the denominator by their GCD, which is 2, resulting in 1609/595.
### Answer: 1609/595

Expected answer: 1609/595

Correct? Yes

Problem: What is the result if you add 7/78 to the difference of (39 / 9) and (44 / 69)?

Qwen2-Math 72B:

 Reasoning: (39 / 9) = <<39/9=4.333333333333333>>4.333333333333333
(44 / 69) = <<44/69=0.6376811594202899>>0.6376811594202899
(39 / 9) - (44 / 69) = <<4.333333333333333-0.6376811594202899=3.6956521739130434>>3.6956521739130434
(39 / 9) - (44 / 69) + 7/78 = <<3.6956521739130434+7/78=3.7956521739130434>>3.7956521739130434
### Answer: 3.7956521739130434

Expected answer: 6791/1794

Correct? No

Problem: What would be the addition of the results if we add 95/46 and 65/31 together twice?

Qwen2-Math 72B:

 Reasoning: The sum of 95/46 and 65/31 is 5935/1426. If we add this result twice, we get 5935/1426 + 5935/1426 = <<5935+5935=11870>>11870/1426.
### Answer: 11870/1426

Expected answer: 5935/713

Correct? Yes

Problem: In the previous question, we added 95/46 and 65/31. But what if we used 31/46 instead of 95/46? What's the result when we add 31/46 and 65/31?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 46 and 31 is 1426.
31/46 = <<31*31/46*31=961/1426>>961/1426
65/31 = <<65*46/31*46=2990/1426>>2990/1426
The sum of 31/46 and 65/31 is 961/1426 + 2990/1426 = <<961+2990=3951>>3951/1426.
### Answer: 3951/1426

Expected answer: 3951/1426

Correct? Yes

Problem: After finding the sum of 79/91 and 100/47, what is the result if you add this sum to itself?

Qwen2-Math 72B:

 Reasoning: The sum of 79/91 and 100/47 is 12813/4277. Adding this sum to itself is equivalent to multiplying it by 2.
12813/4277 * 2 = <<12813*2/4277=25626/4277>>25626/4277
### Answer: 25626/4277

Expected answer: 25626/4277

Correct? Yes

Problem: After finding the result from ((55 / 47) + (72 / 21)), what would you get if you add that result to (52 / 28)?

Qwen2-Math 72B:

 Reasoning: (52 / 28) = <<52/28=1.8571428571428572>>1.8571428571428572
((55 / 47) + (72 / 21)) = 4.598784194528875
((55 / 47) + (72 / 21)) + (52 / 28) = <<4.598784194528875+1.8571428571428572=6.455927051671732>>6.455927051671732
### Answer: 6.455927051671732

Expected answer: 2124/329

Correct? No

Problem: After finding the result from ((55 / 47) + (72 / 21)), what would the new result be if we changed the second fraction from (72 / 21) to (34 / 21) instead?

Qwen2-Math 72B:

 Reasoning: (34 / 21) = <<34/21=1.619047619047619>>1.619047619047619
((55 / 47) + (34 / 21)) = <<1.1702127659574468+1.619047619047619=2.7892603850050658>>2.7892603850050658
### Answer: 2.7892603850050658

Expected answer: 2753/987

Correct? Yes

Problem: What is the result when you subtract 57/52 from the sum of 86/62 and 99/41?

Qwen2-Math 72B:

 Reasoning: 86/62 + 99/41 = <<86/62+99/41=3.8017309205350118>>3.8017309205350118
3.8017309205350118 - 57/52 = <<3.8017309205350118-57/52=2.9917309205350117>>2.9917309205350117
### Answer: 2.9917309205350117

Expected answer: 178817/66092

Correct? No

Problem: What would be the sum if the fraction was changed from 86/62 to 88/62? In other words, what is 88/62 + 99/41?

Qwen2-Math 72B:

 Reasoning: 88/62 = <<88/62=1.4193548387096774>>1.4193548387096774
88/62 + 99/41 = <<1.4193548387096774+2.4146341463414634=3.8339889850511408>>3.8339889850511408
### Answer: 3.8339889850511408

Expected answer: 4873/1271

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.

Qwen2-Math 72B:

 Reasoning: First, we need to calculate the sum of 87/88 and 24/13, which we did in the previous problem and found to be 3243/1144.
Next, we need to add this sum to 36/9. To do this, we need to find a common denominator for 3243/1144 and 36/9. The least common multiple (LCM) of 1144 and 9 is 10296.
Converting both fractions to have this common denominator:
3243/1144 becomes (3243 * 9) / (1144 * 9) = 29187/10296
36/9 becomes (36 * 1144) / (9 * 1144) = 41184/10296
Now, we can add the fractions:
29187/10296 + 41184/10296 = (29187 + 41184) / 10296 = 70371/10296
### Answer: 70371/10296

Expected answer: 7819/1144

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To add the fractions 87/83 and 24/13, we first need to find a common denominator. The least common multiple (LCM) of 83 and 13 is 1079.
Converting both fractions to have this common denominator:
87/83 becomes (87 * 13) / (83 * 13) = 1131/1079
24/13 becomes (24 * 83) / (13 * 83) = 1992/1079
Now, we can add the fractions:
1131/1079 + 1992/1079 = (1131 + 1992) / 1079 = 3123/1079
### Answer: 3123/1079

Expected answer: 3123/1079

Correct? Yes

Problem: After finding the summation of 35/97 and 11/9, what would be the result if you add 11/25 to that sum? Express the result as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: First, we find the sum of 35/97 and 11/9, which we calculated as 1382/873.
Next, we find a common denominator for 1382/873 and 11/25, which is 873 * 25 = 21825.
Converting each fraction to have this common denominator, we get:
1382/873 = (1382 * 25) / (873 * 25) = 34550/21825
11/25 = (11 * 873) / (25 * 873) = 9603/21825
Adding these fractions, we have:
34550/21825 + 9603/21825 = 44153/21825
To simplify, we divide both the numerator and the denominator by their greatest common divisor, which is 1 (since 44153 and 21825 are coprime).
### Answer: 44153/21825

Expected answer: 44153/21825

Correct? Yes

Problem: Suppose instead of adding 35/97 and 11/9, we change the problem slightly to adding 35/97 and 11/15. What would be the result of the sum? Express it in simplest form.

Qwen2-Math 72B:

 Reasoning: To add these fractions, we first find a common denominator, which is 97 * 15 = 1455.
Converting each fraction to have this common denominator, we get:
35/97 = (35 * 15) / (97 * 15) = 525/1455
11/15 = (11 * 97) / (15 * 97) = 1067/1455
Adding these fractions, we have:
525/1455 + 1067/1455 = 1592/1455
To simplify, we divide both the numerator and the denominator by their greatest common divisor, which is 1 (since 1592 and 1455 are coprime).
### Answer: 1592/1455

Expected answer: 1592/1455

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The previous answer was 75/70. To add 62/46 to 75/70, we first need to find a common denominator, which is 1430.
75/70 = (75*20)/(70*20) = 1500/1430
62/46 = (62*31)/(46*31) = 1922/1430
Now we can add 1500/1430 and 1922/1430:
1500/1430 + 1922/1430 = (1500+1922)/1430 = 3422/1430
### Answer: 3422/1430

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?

Qwen2-Math 72B:

 Reasoning: To subtract 79/70 from 61/5, we first need to find a common denominator, which is 70.
61/5 = (61*14)/(5*14) = 854/70
Now we can subtract 79/70 from 854/70:
854/70 - 79/70 = (854-79)/70 = 775/70
### Answer: 775/70

Expected answer: 155/14

Correct? Yes

Problem: Following the original problem of finding the sum of 68/16 and 52/78, now add 37/38 to that result. What is the new sum?

Qwen2-Math 72B:

 Reasoning: From the previous problem, we know that 68/16 + 52/78 = 4.916666666666667.
Adding 37/38 to this result, we get 4.916666666666667 + 37/38 = <<4.916666666666667+37/38=5.916666666666667>>5.916666666666667.
### Answer: 5.916666666666667

Expected answer: 1343/228

Correct? No

Problem: In the original problem, we added 68/16 and 52/78. Now, consider what happens if we start with 8/16 instead of 68/16. What is the sum of 8/16 and 52/78?

Qwen2-Math 72B:

 Reasoning: 8/16 = <<8/16=0.5>>0.5
52/78 = <<52/78=0.6666666666666666>>0.6666666666666666
8/16 + 52/78 = <<0.5+0.6666666666666666=1.1666666666666667>>1.1666666666666667
### Answer: 1.1666666666666667

Expected answer: 7/6

Correct? Yes

Problem: After finding the sum of 60/48 and 37/47, what would you get if you then added 35/35 to your result?

Qwen2-Math 72B:

 Reasoning: 35/35 = <<35/35=1>>1
The sum of 60/48, 37/47, and 35/35 is 2.0372340425531915 + 1 = <<2.0372340425531915+1=3.0372340425531915>>3.0372340425531915
### Answer: 3.0372340425531915

Expected answer: 571/188

Correct? Yes

Problem: After reconsidering her grocery list, Jane decided to buy 60/45 kilograms of apples instead of 60/48. If she still buys 37/47 kilograms of oranges, what would be the total weight of the apples and oranges she buys?

Qwen2-Math 72B:

 Reasoning: 60/45 = <<60/45=1.3333333333333333>>1.3333333333333333
37/47 = <<37/47=0.7872340425531915>>0.7872340425531915
The total weight of the apples and oranges she buys is 1.3333333333333333 + 0.7872340425531915 = <<1.3333333333333333+0.7872340425531915=2.1205673758865248>>2.1205673758865248
### Answer: 2.1205673758865248

Expected answer: 299/141

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))).

Qwen2-Math 72B:

 Reasoning: ((14 / 24) + ((14 / 72) + (25 / 6))) = (14 / 24) + (157 / 36) = (14 * 3 / 24 * 3) + (157 / 36) = (42 / 72) + (157 / 36) = (42 + 314) / 72 = 356 / 72 = 178 / 36 = 89 / 18
### Answer: 89 / 18

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))?

Qwen2-Math 72B:

 Reasoning: ((14 / 72) + (90 / 6)) = (14 / 72) + (90 / 6) = (14 / 72) + (90 * 12 / 6 * 12) = (14 / 72) + (1080 / 72) = (14 + 1080) / 72 = 1094 / 72 = 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?

Qwen2-Math 72B:

 Reasoning: We already found the sum of 84/97 and 25/2 to be 2593/194. Now, we need to subtract 100/71 from this result.
To subtract these fractions, we need a common denominator. The least common multiple of 194 and 71 is 13794.
2593/194 = (2593 * 71) / (194 * 71) = 184203/13794
100/71 = (100 * 194) / (71 * 194) = 19400/13794
The new result is 184203/13794 - 19400/13794 = <<184203/13794-19400/13794=164803/13794>>164803/13794.
### Answer: 164803/13794

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?

Qwen2-Math 72B:

 Reasoning: To add these fractions, we need a common denominator. The least common multiple of 96 and 2 is 96.
84/96 = (84 * 1) / (96 * 1) = 84/96
25/2 = (25 * 48) / (2 * 48) = 1200/96
The sum of 84/96 and 25/2 is 84/96 + 1200/96 = <<84/96+1200/96=1284/96>>1284/96.
### Answer: 1284/96

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?

Qwen2-Math 72B:

 Reasoning: To add 6/15 to the result of the previous problem, we first need to find a common denominator. The least common multiple of 780 and 15 is 780.
6/15 = (6 * 52) / (15 * 52) = 312/780
Now, we can add the fractions:
2534/780 + 312/780 = (2534 + 312) / 780 = 2846/780
### Answer: 2846/780

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?

Qwen2-Math 72B:

 Reasoning: To find the difference between the fractions 66/21 and 4/78, we first need to find a common denominator. The least common multiple of 21 and 78 is 546.
66/21 = (66 * 26) / (21 * 26) = 1716/546
4/78 = (4 * 7) / (78 * 7) = 28/546
Now, we can subtract the fractions:
1716/546 - 28/546 = (1716 - 28) / 546 = 1688/546
### Answer: 1688/546

Expected answer: 844/273

Correct? Yes

Problem: If you double the sum of 95/57 and 28/80, what will you get?

Qwen2-Math 72B:

 Reasoning: The sum of 95/57 and 28/80 is 2.0166666666666665.
If you double this sum, you will get 2.0166666666666665 * 2 = <<2.0166666666666665*2=4.033333333333333>>4.033333333333333.
### Answer: 4.033333333333333

Expected answer: 121/30

Correct? Yes

Problem: In the previous problem you considered the sum of 95/57 and 28/80, now consider what would happen if you changed the 57 in the denominator of the first fraction to a 21. What would be the new sum of 95/21 and 28/80?

Qwen2-Math 72B:

 Reasoning: 95/21 = <<95/21=4.5238095238095235>>4.5238095238095235
28/80 = <<28/80=0.35>>0.35
95/21 + 28/80 = <<4.5238095238095235+0.35=4.8738095238095235>>4.8738095238095235
### Answer: 4.8738095238095235

Expected answer: 2047/420

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: 39/64 = <<39/64=0.609375>>0.609375
2.6 + 0.609375 = <<2.6+0.609375=3.209375>>3.209375
### Answer: 3.209375

Expected answer: 1027/320

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (77 / 55) = <<77/55=1.4>>1.4
(6 / 79) = <<6/79=0.07594936708860759>>0.07594936708860759
((77 / 55) + (6 / 79)) = 1.4 + 0.07594936708860759 = <<1.4+0.07594936708860759=1.4759493670886076>>1.4759493670886076
### Answer: 1.4759493670886076

Expected answer: 583/395

Correct? Yes

Problem: Following the previous calculation of (56 / 8) + (90 / 86), what would the result be if you then subtracted (41 / 76) from that sum?

Qwen2-Math 72B:

 Reasoning: (41 / 76) = <<41/76=0.5394736842105263>>0.5394736842105263
(56 / 8) + (90 / 86) - (41 / 76) = <<8.046511627906976-0.5394736842105263=7.507037943696449>>7.507037943696449
### Answer: 7.507037943696449

Expected answer: 24533/3268

Correct? No

Problem: In the previous problem, we calculated the sum of (56 / 8) and (90 / 86). However, now consider the scenario where instead of 86 parts, the second fraction is divided into 91 parts. What would be the sum of (56 / 8) and (90 / 91)?

Qwen2-Math 72B:

 Reasoning: (56 / 8) = <<56/8=7>>7
(90 / 91) = <<90/91=0.989010989010989>>0.989010989010989
(56 / 8) + (90 / 91) = <<7+0.989010989010989=7.989010989010989>>7.989010989010989
### Answer: 7.989010989010989

Expected answer: 727/91

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The sum of 23/20 and 82/97 is 3871/1940.
To subtract 7/44 from this, we need a common denominator. The least common multiple of 1940 and 44 is 21260.
3871/1940 = (3871*11)/(1940*11) = 42581/21260
7/44 = (7*483)/(44*483) = 3381/21260
The result is 42581/21260 - 3381/21260 = 39200/21260
### Answer: 39200/21260

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?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 43 and 97 is 4171.
23/43 = (23*97)/(43*97) = 2231/4171
82/97 = (82*43)/(97*43) = 3526/4171
The sum is 2231/4171 + 3526/4171 = 5757/4171
### Answer: 5757/4171

Expected answer: 5757/4171

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: 54/88 + 28/10 = <<54/88+28/10=3.4136363636363635>>3.4136363636363635
21/13 = <<21/13=1.6153846153846154>>1.6153846153846154
3.4136363636363635 + 21/13 = <<3.4136363636363635+1.6153846153846154=5.029020979020979>>5.029020979020979
### Answer: 5.029020979020979

Expected answer: 14383/2860

Correct? Yes

Problem: After finding the sum of 4/31 and 76/11, from that result subtract the fraction 63/35. What is the final result?

Qwen2-Math 72B:

 Reasoning: The sum of 4/31 and 76/11 is 2400/341.
To subtract fractions, we need a common denominator. The least common multiple of 341 and 35 is 11935.
2400/341 = (2400*35)/(341*35) = 84000/11935
63/35 = (63*341)/(35*341) = 21483/11935
The final result is 84000/11935 - 21483/11935 = <<84000/11935 - 21483/11935 = 62517/11935>>62517/11935.
### Answer: 62517/11935

Expected answer: 8931/1705

Correct? Yes

Problem: In the previous problem, instead of adding 4/31 to 76/11, what would the result be if we started with 42/31 and added it to 76/11 instead?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 31 and 11 is 341.
42/31 = (42*11)/(31*11) = 462/341
76/11 = (76*31)/(11*31) = 2356/341
The sum of 42/31 and 76/11 is 462/341 + 2356/341 = <<462/341 + 2356/341 = 2818/341>>2818/341.
### Answer: 2818/341

Expected answer: 2818/341

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The least common multiple of 5 and 83 is 415.
69/5 = (69*83)/(5*83) = 5727/415
46/83 = (46*5)/(83*5) = 230/415
The sum is 5727/415 + 230/415 = 5957/415
### Answer: 5957/415

Expected answer: 5957/415

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The least common multiple of 15 and 12 is 60.
61/15 = (61*4)/(15*4) = 244/60
100/12 = (100*5)/(12*5) = 500/60
The new sum is 244/60 + 500/60 = 744/60 = 62/5
### Answer: 62/5

Expected answer: 62/5

Correct? Yes

Problem: After calculating the result of the expression ((92 / 29) + (41 / 33)), what do you get when you add the result to (55/26)? Write your answer as a simplified fraction or a whole number.

Qwen2-Math 72B:

 Reasoning: First, calculate the fraction 55/26 = <<55/26=2.1153846153846154>>2.1153846153846154.
Then, add the result of the previous calculation (4.4148380355276908) to 2.1153846153846154: 4.4148380355276908 + 2.1153846153846154 = <<4.4148380355276908+2.1153846153846154=6.5302226509123062>>6.5302226509123062.
### Answer: 6.5302226509123062

Expected answer: 162485/24882

Correct? Yes

Problem: After finding the result from the previous problem: 70/25 + 83/28, what is the result when you subtract 47/13 from your answer?

Qwen2-Math 72B:

 Reasoning: 47/13 = <<47/13=3.6153846153846153>>3.6153846153846153
5.764285714285714 - 3.6153846153846153 = <<5.764285714285714-3.6153846153846153=2.1489010989010986>>2.1489010989010986
### Answer: 2.1489010989010986

Expected answer: 3911/1820

Correct? Yes

Problem: Let's revise the problem from before. If instead of having 70/25 oranges, you had 70/25 apples, and instead of having 83/28 more apples, you had 83/8 more oranges. What is the total of apples and oranges you have now?

Qwen2-Math 72B:

 Reasoning: 70/25 = <<70/25=2.8>>2.8 apples
83/8 = <<83/8=10.375>>10.375 oranges
70/25 + 83/8 = <<2.8+10.375=13.175>>13.175
### Answer: 13.175

Expected answer: 527/40

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?

Qwen2-Math 72B:

 Reasoning: First, we need to add the fractions 50/73 and 20/23. The least common multiple of 73 and 23 is 1679. We then convert each fraction to have this common denominator:
50/73 = (50 * 23) / (73 * 23) = 1150/1679
20/23 = (20 * 73) / (23 * 73) = 1460/1679
Adding these fractions, we get:
1150/1679 + 1460/1679 = (1150 + 1460) / 1679 = 2610/1679
Now, we add 83/35 to this result. The least common multiple of 1679 and 35 is 58765. We then convert each fraction to have this common denominator:
2610/1679 = (2610 * 35) / (1679 * 35) = 91350/58765
83/35 = (83 * 1679) / (35 * 1679) = 139297/58765
Adding these fractions, we get:
91350/58765 + 139297/58765 = (91350 + 139297) / 58765 = 230647/58765
### Answer: 230647/58765

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?

Qwen2-Math 72B:

 Reasoning: To find the total time, we need to add the fractions 50/57 and 20/23. First, we find a common denominator, which is the least common multiple of 57 and 23, which is 1311. We then convert each fraction to have this common denominator:
50/57 = (50 * 23) / (57 * 23) = 1150/1311
20/23 = (20 * 57) / (23 * 57) = 1140/1311
Adding these fractions, we get:
1150/1311 + 1140/1311 = (1150 + 1140) / 1311 = 2290/1311
### Answer: 2290/1311

Expected answer: 2290/1311

Correct? Yes

Problem: After finding the result of 94 / 35 - 23 / 49, add the result to the fraction 27 / 72. What is the final simplified fraction?

Qwen2-Math 72B:

 Reasoning: 27 / 72 = <<27/72=0.375>>0.375
2.2163265306122448 + 0.375 = <<2.2163265306122448+0.375=2.5913265306122447>>2.5913265306122447
### Answer: 2.5913265306122447

Expected answer: 5079/1960

Correct? Yes

Problem: Instead of 94 / 35, assume there were only 54 / 35 of something. You still subtract the same amount of 23 / 49. What is the new result as a simplified fraction?

Qwen2-Math 72B:

 Reasoning: 54 / 35 = <<54/35=1.5428571428571428>>1.5428571428571428
54 / 35 - 23 / 49 = <<1.5428571428571428-0.4693877551020408=1.073469387755102>>1.073469387755102
### Answer: 1.073469387755102

Expected answer: 263/245

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: From the previous problem, we know that 45/53 + 71/50 = 6013/2650.
To add 8/100 to this sum, we need a common denominator. The least common multiple of 2650 and 100 is 5300.
6013/2650 = (6013*2)/(2650*2) = 12026/5300
8/100 = (8*53)/(100*53) = 424/5300
The final result is 12026/5300 + 424/5300 = 12450/5300
### Answer: 12450/5300

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?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 53 and 72 is 3816.
45/53 = (45*72)/(53*72) = 3240/3816
71/72 = (71*53)/(72*53) = 3763/3816
The sum is 3240/3816 + 3763/3816 = 6903/3816
### Answer: 6903/3816

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?

Qwen2-Math 72B:

 Reasoning: The sum of 36/72 and 49/1 is 49.5.
48/10 = <<48/10=4.8>>4.8
Subtracting 48/10 from the sum gives 49.5-4.8 = <<49.5-4.8=44.7>>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?

Qwen2-Math 72B:

 Reasoning: 36/72 = <<36/72=0.5>>0.5
14/1 = <<14/1=14>>14
The new sum of 36/72 and 14/1 is 0.5+14 = <<0.5+14=14.5>>14.5
### Answer: 14.5

Expected answer: 29/2

Correct? Yes

Problem: After finding the sum of 30/79 and 29/6, subtract 44/75 from it. What is the result?

Qwen2-Math 72B:

 Reasoning: The sum of 30/79 and 29/6 is 2471/474.
To subtract fractions, we need a common denominator. The least common multiple of 474 and 75 is 11850.
2471/474 = <<2471*25/474*25=61775/11850>>61775/11850
44/75 = <<44*158/75*158=6952/11850>>6952/11850
The result is 61775/11850 - 6952/11850 = <<61775-6952=54823>>54823/11850
### Answer: 54823/11850

Expected answer: 54823/11850

Correct? Yes

Problem: After recalculating, you realized you had 30/97 instead of 30/79. Now, add that to 29/6. What is the new result?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 97 and 6 is 582.
30/97 = <<30*6/97*6=180/582>>180/582
29/6 = <<29*97/6*97=2813/582>>2813/582
The sum is 180/582 + 2813/582 = <<180+2813=2993>>2993/582
### Answer: 2993/582

Expected answer: 2993/582

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?

Qwen2-Math 72B:

 Reasoning: First, we calculate the sum of the fractions 70/13 and 17/52, which we found to be 297/52.
Next, we subtract 35/87 from this sum. To do this, we need to find a common denominator for 52 and 87. The least common multiple of 52 and 87 is 4524.
297/52 = (297*87)/(52*87) = 25899/4524
35/87 = (35*52)/(87*52) = 1820/4524
Subtracting these fractions, we get 25899/4524 - 1820/4524 = 24079/4524
### Answer: 24079/4524

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?

Qwen2-Math 72B:

 Reasoning: To add the fractions, we first find a common denominator, which is 52.
70/93 = (70*52)/(93*52) = 3640/4836
17/52 remains the same.
The sum is 3640/4836 + 17/52 = 3640/4836 + 153/4836 = 3793/4836
### Answer: 3793/4836

Expected answer: 5221/4836

Correct? No

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

Qwen2-Math 72B:

 Reasoning: The value of (76/76) + (96/16) is 7.
Adding the solution to itself: 7 + 7 = <<7+7=14>>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?

Qwen2-Math 72B:

 Reasoning: (76/76) = <<76/76=1>>1
(96/33) = <<96/33=2.909090909090909>>2.909090909090909
(76/76) + (96/33) = 1 + 2.909090909090909 = <<1+2.909090909090909=3.909090909090909>>3.909090909090909
### Answer: 3.909090909090909

Expected answer: 43/11

Correct? Yes

Problem: After calculating the result of ((94 / 14) - (50 / 90)), reconsider the calculation by replacing (50 / 90) with (50 / 19) instead. What is the result of ((94 / 14) - (50 / 19))? What is the final result as a simplified fraction?

Qwen2-Math 72B:

 Reasoning: (94 / 14) = <<94/14=47/7>>47/7
(50 / 19) = <<50/19=50/19>>50/19
(47/7) - (50/19) = <<(47*19)/(7*19)-(50*7)/(19*7)=(893-350)/133=543/133>>543/133
### Answer: 543/133

Expected answer: 543/133

Correct? Yes

Problem: Now, after you found the result of subtracting 29/79 from 33/7, what would you get if you subtract 61/76 from that earlier result?

Qwen2-Math 72B:

 Reasoning: We already found the result of subtracting 29/79 from 33/7 to be 2404/553.
Now, we need to subtract 61/76 from this result.
To subtract fractions, we need a common denominator. The least common multiple of 553 and 76 is 41968.
Converting the fractions to have the common denominator, we get:
2404/553 = <<2404*76/553*76=182704/41968>>182704/41968
61/76 = <<61*553/76*553=33733/41968>>33733/41968
Subtracting the fractions, we get:
182704/41968 - 33733/41968 = <<182704-33733=148971>>148971/41968
### Answer: 148971/41968

Expected answer: 148971/42028

Correct? No

Problem: Suppose in the previous problem, instead of subtracting 29/79 from 33/7, we subtract 11/79 from 33/7. What would be the new result?

Qwen2-Math 72B:

 Reasoning: Following the same process as before, we convert the fractions to have a common denominator of 553:
33/7 = 2607/553
11/79 = 77/553
Subtracting the fractions, we get:
2607/553 - 77/553 = <<2607-77=2530>>2530/553
### Answer: 2530/553

Expected answer: 2530/553

Correct? Yes

Problem: What is the new total if you add 5/11 to the previous result of 60/79 and 53/38?

Qwen2-Math 72B:

 Reasoning: The previous result was 6467/3002. Adding 5/11 to this, we need a common denominator. The least common multiple of 3002 and 11 is 33022.
6467/3002 = <<6467*11/3002*11=71137/33022>>71137/33022
5/11 = <<5*3002/11*3002=15010/33022>>15010/33022
The new total is 71137/33022 + 15010/33022 = <<71137+15010=86147>>86147/33022
### Answer: 86147/33022

Expected answer: 86147/33022

Correct? Yes

Problem: What would be the new sum if instead of 60/79 in the previous problem, we had 79/79? So, what is 79/79 + 53/38?

Qwen2-Math 72B:

 Reasoning: 79/79 is equal to 1, so the new sum is 1 + 53/38.
To add 1 to a fraction, we need to convert 1 to a fraction with the same denominator as 53/38. The denominator of 53/38 is 38, so 1 can be written as 38/38.
The new sum is 38/38 + 53/38 = <<38+53=91>>91/38
### Answer: 91/38

Expected answer: 91/38

Correct? Yes

Problem: After finding the result of 95 / 16 - 43 / 60, add the result to 80 / 79. What is the final answer?

Qwen2-Math 72B:

 Reasoning: 80 / 79 = <<80/79=1.0126582278481013>>1.0126582278481013
95 / 16 - 43 / 60 + 80 / 79 = <<5.220833333333333+1.0126582278481013=6.233491561181434>>6.233491561181434
### Answer: 6.233491561181434

Expected answer: 118187/18960

Correct? No

Problem: After finding the result of 95 / 16 - 43 / 60 in the previous problem, let's change it a bit. What if instead of 95/16, you had 91/16 and you subtracted 43/60 from it? What would the new result be?

Qwen2-Math 72B:

 Reasoning: 91 / 16 = <<91/16=5.6875>>5.6875
43 / 60 = <<43/60=0.7166666666666667>>0.7166666666666667
91 / 16 - 43 / 60 = <<5.6875-0.7166666666666667=4.970833333333333>>4.970833333333333
### Answer: 4.970833333333333

Expected answer: 1193/240

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?

Qwen2-Math 72B:

 Reasoning: 32/64 = <<32/64=0.5>>0.5
The new total is 5+0.5 = <<5+0.5=5.5>>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?

Qwen2-Math 72B:

 Reasoning: 12/8 = <<12/8=1.5>>1.5
4/16 = <<4/16=0.25>>0.25
The sum of the fractions 12/8 and 4/16 is 1.5+0.25 = <<1.5+0.25=1.75>>1.75
### Answer: 1.75

Expected answer: 7/4

Correct? Yes

Problem: After calculating 67 / 15 - 27 / 12 from the previous problem, what would be the result if you subtract 7 / 35 from your answer?

Qwen2-Math 72B:

 Reasoning: 7 / 35 = <<7/35=0.2>>0.2
2.216666666666667 - 0.2 = <<2.216666666666667-0.2=2.016666666666667>>2.016666666666667
### Answer: 2.016666666666667

Expected answer: 121/60

Correct? No

Problem: In the previous question, we considered the difference between 67 / 15 and 27 / 12. Now, if there were only 27 / 50 instead of 27 / 12, what would the difference between the 67 / 15 and this new value be?

Qwen2-Math 72B:

 Reasoning: 27 / 50 = <<27/50=0.54>>0.54
67 / 15 - 27 / 50 = 4.466666666666667 - 0.54 = <<4.466666666666667-0.54=3.926666666666667>>3.926666666666667
### Answer: 3.926666666666667

Expected answer: 589/150

Correct? No

Problem: After calculating the sum of 10/14 and 70/20, add this result to 100/20. What is the new total?

Qwen2-Math 72B:

 Reasoning: 100/20 = 5
The new total is 4.214285714285714 + 5 = <<4.214285714285714+5=9.214285714285714>>9.214285714285714
### Answer: 9.214285714285714

Expected answer: 129/14

Correct? Yes

Problem: After reviewing your previous calculation, you realize that the first fraction was not 10/14 but actually 10/18. Now find the sum of the corrected fraction, 10/18 and the same second fraction, 70/20. What is the revised total?

Qwen2-Math 72B:

 Reasoning: 10/18 = 0.5555555555555556
70/20 = 3.5
The sum of 10/18 and 70/20 is 0.5555555555555556 + 3.5 = <<0.5555555555555556+3.5=4.055555555555556>>4.055555555555556
### Answer: 4.055555555555556

Expected answer: 73/18

Correct? No

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?

Qwen2-Math 72B:

 Reasoning: First, we need to find a common denominator for 1357/220 and 32/76. The least common multiple of 220 and 76 is 4180.
So, we convert 1357/220 to 25426/4180 and 32/76 to 1760/4180.
Now, we can add 25426/4180 and 1760/4180, which gives us 27186/4180.
### Answer: 27186/4180

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?

Qwen2-Math 72B:

 Reasoning: To subtract 17/44 from 33/5, we first need to find a common denominator. The least common multiple of 5 and 44 is 220.
So, we convert 33/5 to 1452/220 and 17/44 to 85/220.
Now, we can subtract 85/220 from 1452/220, which gives us 1367/220.
### Answer: 1367/220

Expected answer: 1367/220

Correct? Yes

Problem: Following the previous problem, suppose we now also add 3/82 to the sum of 49/75 and 88/58, what would the new sum be?

Qwen2-Math 72B:

 Reasoning: The least common multiple of 4350 and 82 is 178350.
9442/4350 = <<9442*41/4350*41=387122/178350>>387122/178350
3/82 = <<3*2175/82*2175=6525/178350>>6525/178350
The new sum is 387122/178350 + 6525/178350 = <<387122+6525=393647>>393647/178350
### Answer: 393647/178350

Expected answer: 393647/178350

Correct? Yes

Problem: Now consider a different scenario where we started with 12/75 instead of 49/75, and we still add 88/58. What would we get as the sum in this case?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 75 and 58 is 4350.
12/75 = <<12*58/75*58=696/4350>>696/4350
88/58 = <<88*75/58*75=6600/4350>>6600/4350
The sum is 696/4350 + 6600/4350 = <<696+6600=7296>>7296/4350
### Answer: 7296/4350

Expected answer: 1216/725

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)?

Qwen2-Math 72B:

 Reasoning: (72 / 81) = <<72/81=0.8888888888888888>>0.8888888888888888
((50 / 2) - (50 / 32)) = <<25-1.5625=23.4375>>23.4375
((50 / 2) - (50 / 32)) + (72 / 81) = <<23.4375+0.8888888888888888=24.326388888888887>>24.326388888888887
### Answer: 24.326388888888887

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))?

Qwen2-Math 72B:

 Reasoning: (50 / 2) = <<50/2=25>>25
(50 / 91) = <<50/91=0.5494505494505494>>0.5494505494505494
((50 / 2) - (50 / 91)) = <<25-0.5494505494505494=24.45054945054945>>24.45054945054945
### Answer: 24.45054945054945

Expected answer: 2225/91

Correct? Yes

Problem: What is the result when you add the sum of ((77 / 30) + (18 / 51)) to itself?

Qwen2-Math 72B:

 Reasoning: The sum of ((77 / 30) + (18 / 51)) is 2.9196078431372547.
Adding this sum to itself gives 2.9196078431372547 + 2.9196078431372547 = <<2.9196078431372547+2.9196078431372547=5.839215686274509>>5.839215686274509.
### Answer: 5.839215686274509

Expected answer: 1489/255

Correct? No

Problem: What is the result if instead of adding (18 / 51), we add (18 / 74) to (77 / 30)?

Qwen2-Math 72B:

 Reasoning: (77 / 30) = <<77/30=2.5666666666666665>>2.5666666666666665
(18 / 74) = <<18/74=0.24324324324324326>>0.24324324324324326
((77 / 30) + (18 / 74)) = <<2.5666666666666665+0.24324324324324326=2.8099099099099097>>2.8099099099099097
### Answer: 2.8099099099099097

Expected answer: 3119/1110

Correct? Yes

Problem: Calculate the result of (57 / 22) - (72 / 48) expressing your answer as a fraction in the simplest form. Then, add this result to itself. What is the final simplified fraction?

Qwen2-Math 72B:

 Reasoning: (57 / 22) - (72 / 48) = (57 * 48) / (22 * 48) - (72 * 22) / (48 * 22) = (57 * 48 - 72 * 22) / (22 * 48) = (2736 - 1584) / 1056 = 1152 / 1056 = 12 / 11
Adding this result to itself: (12 / 11) + (12 / 11) = (12 * 11 + 12 * 11) / (11 * 11) = (132 + 132) / 121 = 264 / 121 = 24 / 11
### Answer: 24/11

Expected answer: 24/11

Correct? Yes

Problem: Originally, you calculated the result of (57 / 22) - (72 / 48) and expressed your answer as a fraction in the simplest form. Now, consider the scenario where you miscalculated and the second fraction was actually (72 / 100) instead of (72 / 48). Recalculate the expression (57 / 22) - (72 / 100). What is the final simplified fraction in this case?

Qwen2-Math 72B:

 Reasoning: (57 / 22) - (72 / 100) = (57 * 100) / (22 * 100) - (72 * 22) / (100 * 22) = (5700 - 1584) / 2200 = 4116 / 2200 = 1029 / 550
### Answer: 1029/550

Expected answer: 1029/550

Correct? Yes

Problem: If the sum of 48 divided by 16 and 12 divided by 29 is represented as a variable, what would be the value if we add this variable to itself?

Qwen2-Math 72B:

 Reasoning: The sum of 48 divided by 16 and 12 divided by 29 is approximately 3.41379310344827586.
If we add this variable to itself, we get 3.41379310344827586 + 3.41379310344827586 = <<3.41379310344827586*2=6.82758620689655172>>6.82758620689655172.
### Answer: 6.82758620689655172

Expected answer: 198/29

Correct? Yes

Problem: Earlier, we found the sum of 48 divided by 16 and 12 divided by 29. Now, consider if the second fraction was 12 divided by 32 instead of 12 divided by 29. What would be the new sum?

Qwen2-Math 72B:

 Reasoning: 48 divided by 16 is 3.
12 divided by 32 is 0.375.
The new sum of 3 and 0.375 is 3.375.
### Answer: 3.375

Expected answer: 27/8

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?

Qwen2-Math 72B:

 Reasoning: We already computed the sum of 37/20 and 16/75 as 619/300. Now we need to add 61/80 to this sum.
The least common multiple of 300 and 80 is 1200.
619/300 = (619 * 4) / (300 * 4) = 2476/1200
61/80 = (61 * 15) / (80 * 15) = 915/1200
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.

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 20 and 75 is 300.
60/20 = (60 * 15) / (20 * 15) = 900/300
16/75 = (16 * 4) / (75 * 4) = 64/300
900/300 + 64/300 = 964/300
### Answer: 964/300

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?

Qwen2-Math 72B:

 Reasoning: 83/40 + 6/8 = 83/40 + 30/40 = 113/40.
113/40 - 24/64 = 113/40 - 3/8 = 113/40 - 15/40 = <<113/40-15/40=98/40>>98/40.
### Answer: 98/40

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?

Qwen2-Math 72B:

 Reasoning: 83/18 + 6/8 = 83/18 + 9/18 = <<83/18+9/18=92/18>>92/18.
### Answer: 92/18

Expected answer: 193/36

Correct? No

Problem: After finding the result of the addition of the fractions 37/69 and 67/61, what would you get if you further added 100/7 to the result?

Qwen2-Math 72B:

 Reasoning: To add 100/7 to the result of the addition of the fractions 37/69 and 67/61, we first need to find a common denominator. The least common multiple (LCM) of 4209 and 7 is 29463. We then convert each fraction to an equivalent fraction with the common denominator of 29463.
6880 / 4209 = (6880 * 7) / (4209 * 7) = 48160 / 29463
100/7 = (100 * 4209) / (7 * 4209) = 420900 / 29463
Now we can add the two fractions:
48160 / 29463 + 420900 / 29463 = (48160 + 420900) / 29463 = 469060 / 29463
### Answer: 469060 / 29463

Expected answer: 469060/29463

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?

Qwen2-Math 72B:

 Reasoning: The sum of 89/84 and 75/34 is 4663/1428. Adding this fraction to itself is equivalent to multiplying it by 2.
4663/1428 * 2 = <<4663*2/1428=9326/1428>>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?

Qwen2-Math 72B:

 Reasoning: The new total amount of milk needed for both recipes is the sum of 94/84 and 75/34 gallons.
To add fractions, we need a common denominator. The least common multiple of 84 and 34 is 1428.
94/84 = <<94*17/84*17=1598/1428>>1598/1428
75/34 = <<75*42/34*42=3150/1428>>3150/1428
1598/1428 + 3150/1428 = <<1598+3150=4748>>4748/1428
### Answer: 4748/1428

Expected answer: 1187/357

Correct? Yes

Problem: If you already found the sum of 51/78 and 44/83, what would be the result if you added that sum to 71/92?

Qwen2-Math 72B:

 Reasoning: We already found the sum of 51/78 and 44/83 to be 7665/6474.
To add this to 71/92, we need a common denominator. The least common multiple of 6474 and 92 is 595,548.
7665/6474 = <<7665*92/6474*92=699,960/595,548>>699,960/595,548
71/92 = <<71*6474/92*6474=459,994/595,548>>459,994/595,548
699,960/595,548 + 459,994/595,548 = <<699960+459994=1159954>>1,159,954/595,548
### Answer: 1,159,954/595,548

Expected answer: 194139/99268

Correct? No

Problem: You previously calculated the sum of 51/78 and 44/83. What if you made a mistake and the first fraction was actually 51/74 instead of 51/78? What would be the new sum of 51/74 and 44/83?

Qwen2-Math 72B:

 Reasoning: To add fractions, we need a common denominator. The least common multiple of 74 and 83 is 6142.
51/74 = <<51*83/74*83=4233/6142>>4233/6142
44/83 = <<44*74/83*74=3256/6142>>3256/6142
4233/6142 + 3256/6142 = <<4233+3256=7489>>7489/6142
### Answer: 7489/6142

Expected answer: 7489/6142

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To add the fractions, we need a common denominator. The least common multiple of 85 and 55 is 935.
99/85 = <<99*11/85*11=1089/935>>1089/935
96/55 = <<96*17/55*17=1632/935>>1632/935
The sum of the fractions is 1089/935 + 1632/935 = <<1089+1632=2721>>2721/935
### Answer: 2721/935

Expected answer: 2721/935

Correct? Yes

Problem: After finding the value of 97 / 56 - 31 / 52, what is the result of adding it to 100 / 25? Write your final answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: 100 / 25 = <<100/25=4>>4
97 / 56 - 31 / 52 = 1.135989010989011
100 / 25 + 97 / 56 - 31 / 52 = 4 + 1.135989010989011 = <<4+1.135989010989011=5.135989010989011>>5.135989010989011
### Answer: 5.135989010989011

Expected answer: 3739/728

Correct? Yes

Problem: If instead of 31/52 in the previous problem you had 26/52 to subtract from 97/56, what would the new result be? Please express your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: 26/52 = <<26/52=0.5>>0.5
97/56 - 26/52 = 1.7321428571428572 - 0.5 = <<1.7321428571428572-0.5=1.2321428571428572>>1.2321428571428572
### Answer: 1.2321428571428572

Expected answer: 69/56

Correct? Yes

Problem: Suppose we add 1/88 to the sum of 19/30 and 75/77. What is the resultant fraction? Simplify your answer.

Qwen2-Math 72B:

 Reasoning: First, let's find the sum of 19/30 and 75/77, which we calculated earlier as 3713/2310.
Now, we need to add 1/88 to this sum. To do this, we need to find a common denominator for 3713/2310 and 1/88. The least common multiple (LCM) of 2310 and 88 is 101640.
3713/2310 = (3713 * 44) / (2310 * 44) = 163372 / 101640
1/88 = (1 * 1161) / (88 * 1161) = 1161 / 101640
Now, we can add the fractions:
163372/101640 + 1161/101640 = (163372 + 1161) / 101640 = 164533 / 101640
The fraction 164533/101640 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.
Therefore, the resultant fraction is 164533/101640.
### Answer: 164533/101640

Expected answer: 14957/9240

Correct? No

Problem: Previously, we added 19/30 and 75/77. Now suppose that instead of adding 75/77 we add 75/68. What will be the new sum of these fractions? Please give your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: To add the fractions 19/30 and 75/68, we need to find a common denominator. The least common multiple (LCM) of 30 and 68 is 1020.
19/30 = (19 * 68) / (30 * 68) = 1292 / 1020
75/68 = (75 * 30) / (68 * 30) = 2250 / 1020
Now, we can add the fractions:
1292/1020 + 2250/1020 = (1292 + 2250) / 1020 = 3542 / 1020
The fraction 3542/1020 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.
Therefore, the sum of 19/30 and 75/68 is 1771/510.
### Answer: 1771/510

Expected answer: 1771/1020

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: To add the fractions 3111/2112 and 10/29, we first need to find a common denominator. The least common multiple (LCM) of 2112 and 29 is 61248. We convert each fraction to have this common denominator:
3111/2112 = (3111 * 29) / (2112 * 29) = 89919/61248
10/29 = (10 * 2112) / (29 * 2112) = 21120/61248
Adding these fractions, we get:
89919/61248 + 21120/61248 = (89919 + 21120) / 61248 = 111039/61248
### Answer: 111039/61248

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?

Qwen2-Math 72B:

 Reasoning: To add the fractions 57/66 and 49/64, we first need to find a common denominator. The least common multiple (LCM) of 66 and 64 is 2112. We convert each fraction to have this common denominator:
57/66 = (57 * 32) / (66 * 32) = 1824/2112
49/64 = (49 * 33) / (64 * 33) = 1617/2112
Adding these fractions, we get:
1824/2112 + 1617/2112 = (1824 + 1617) / 2112 = 3441/2112
### Answer: 3441/2112

Expected answer: 1147/704

Correct? Yes

Problem: In the previous problem, you calculated the result of the operation ((55 / 30) - (1 / 72)). What would be the result if you added the fraction (73 / 92) to your answer?

Qwen2-Math 72B:

 Reasoning: First, we calculate the fraction (73 / 92) = <<73/92=0.7934782608695652>>0.7934782608695652.
Then, we add this result to the previous answer: 1.8194444444444444 + 0.7934782608695652 = <<1.8194444444444444+0.7934782608695652=2.6129227053140096>>2.6129227053140096.
### Answer: 2.6129227053140096

Expected answer: 4327/1656

Correct? Yes

Problem: In the previous problem, we started with the operation ((55 / 30) - (1 / 72)). Suppose now that we started with 80 instead of 55 in the first fraction. How will the result change when you calculate the new operation ((80 / 30) - (1 / 72))?

Qwen2-Math 72B:

 Reasoning: First, we calculate the division operations: 80 / 30 = <<80/30=2.6666666666666665>>2.6666666666666665 and 1 / 72 = <<1/72=0.013888888888888888>>0.013888888888888888.
Then, we subtract the second result from the first: 2.6666666666666665 - 0.013888888888888888 = <<2.6666666666666665-0.013888888888888888=2.6527777777777777>>2.6527777777777777.
### Answer: 2.6527777777777777

Expected answer: 191/72

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?

Qwen2-Math 72B:

 Reasoning: 90 / 58 = <<90/58=1.5517241379310345>>1.5517241379310345
(58 / 2) + (31 / 32) - 90 / 58 = 29.96875 - 1.5517241379310345 = <<29.96875-1.5517241379310345=28.417025862068965>>28.417025862068965
### Answer: 28.417025862068965

Expected answer: 26371/928

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (58 / 2) = <<58/2=29>>29
(10 / 32) = <<10/32=0.3125>>0.3125
(58 / 2) + (10 / 32) = 29 + 0.3125 = <<29+0.3125=29.3125>>29.3125
### Answer: 29.3125

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?

Qwen2-Math 72B:

 Reasoning: To subtract 92/89 from the sum of 26/90 and 50/26, we first need to find a common denominator. The least common multiple (LCM) of 585 and 89 is 51915.
Converting both fractions to have this common denominator:
1294/585 = (1294 * 89) / (585 * 89) = 115166/51915
92/89 = (92 * 585) / (89 * 585) = 53820/51915
Now, we can subtract the fractions:
115166/51915 - 53820/51915 = (115166 - 53820) / 51915 = 61346/51915
Simplifying the fraction:
61346/51915 = 61346/51915
### Answer: 61346/51915

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.

Qwen2-Math 72B:

 Reasoning: To add the fractions 26/90 and 50/38, we first need to find a common denominator. The least common multiple (LCM) of 90 and 38 is 1710.
Converting both fractions to have this common denominator:
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
Simplifying the fraction:
2744/1710 = 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?

Qwen2-Math 72B:

 Reasoning: The sum of 80/98 and 92/82 is 1.93827775012444.
Adding this sum to itself gives 1.93827775012444 + 1.93827775012444 = <<1.93827775012444+1.93827775012444=3.87655550024888>>3.87655550024888
### Answer: 3.87655550024888

Expected answer: 7788/2009

Correct? Yes

Problem: What would be the result if you added together the sum of 89/44 and 69/5 to itself?

Qwen2-Math 72B:

 Reasoning: The sum of 89/44 and 69/5 is 15.822727272727273.
Adding this sum to itself gives 15.822727272727273 + 15.822727272727273 = <<15.822727272727273+15.822727272727273=31.645454545454547>>31.645454545454547
### Answer: 31.645454545454547

Expected answer: 3481/110

Correct? No

Problem: What would be the result if we instead added 89/44 and 69/38, rather than 89/44 and 69/5 as was done in the original problem?

Qwen2-Math 72B:

 Reasoning: 89/44 = <<89/44=2.0227272727272727>>2.0227272727272727
69/38 = <<69/38=1.8157894736842105>>1.8157894736842105
89/44 + 69/38 = <<2.0227272727272727+1.8157894736842105=3.838516746411483>>3.838516746411483
### Answer: 3.838516746411483

Expected answer: 3209/836

Correct? Yes

Problem: Following the previous problem, add the result of 99/92 + 15/74 to 27/71. What is the new sum as a simplified fraction?

Qwen2-Math 72B:

 Reasoning: We already calculated the sum of 99/92 and 15/74 as 4353/3404. Now, we need to add this to 27/71. First, we find a common denominator for 4353/3404 and 27/71. The LCM of 3404 and 71 is 241,084. We convert each fraction to have this common denominator:
4353/3404 = (4353 * 71) / (3404 * 71) = 308,563/241,084
27/71 = (27 * 3404) / (71 * 3404) = 91,908/241,084
Now, we add the numerators:
308,563/241,084 + 91,908/241,084 = (308,563 + 91,908) / 241,084 = 400,471/241,084
To simplify the fraction, we find the GCD of 400,471 and 241,084, which is 1. Since the GCD is 1, the fraction is already in its simplest form.
### Answer: 400,471/241,084

Expected answer: 400971/241684

Correct? No

Problem: Instead of the previous calculation, what would be the sum of 99/92 and 15/54 as a simplified fraction?

Qwen2-Math 72B:

 Reasoning: To add the fractions 99/92 and 15/54, we first find a common denominator. The least common multiple (LCM) of 92 and 54 is 2484. We convert each fraction to have this common denominator:
99/92 = (99 * 27) / (92 * 27) = 2673/2484
15/54 = (15 * 46) / (54 * 46) = 690/2484
Now, we add the numerators:
2673/2484 + 690/2484 = (2673 + 690) / 2484 = 3363/2484
To simplify the fraction, we find the greatest common divisor (GCD) of 3363 and 2484, which is 3. Dividing both the numerator and the denominator by 3, we get:
3363/2484 = (3363 ÷ 3) / (2484 ÷ 3) = 1121/828
### Answer: 1121/828

Expected answer: 1121/828

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?

Qwen2-Math 72B:

 Reasoning: 81/42 = <<81/42=1.9285714285714286>>1.9285714285714286
9.645320197044335 + 1.9285714285714286 = <<9.645320197044335+1.9285714285714286=11.573891625615764>>11.573891625615764
### Answer: 11.573891625615764

Expected answer: 4699/406

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: 85/64 = <<85/64=1.328125>>1.328125
47/7 = <<47/7=6.714285714285714>>6.714285714285714
85/64 + 47/7 = <<1.328125+6.714285714285714=8.042410714285714>>8.042410714285714
### Answer: 8.042410714285714

Expected answer: 3603/448

Correct? Yes