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

Gemini-1.5 Pro:

Reasoning: We need to add 471/25 and 73/89. First, we need to find a common denominator: The least common multiple of 25 and 89 is 2225. 
Then we convert our two fractions to equivalent fractions with a denominator of 2225: 471/25 is equivalent to 42019/2225, and 73/89 is equivalent to 1825/2225
Finally, we add our two fractions: 42019/2225 + 1825/2225 = 43844/2225 
### Answer: 43844/2225 

Expected answer: 43744/2225

Correct? No

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?

Gemini-1.5 Pro:

Reasoning:  To add fractions, they must have the same denominator. The least common denominator for 89 and 25 (which are prime to each other) is 89*25. So, we convert the fractions: 
94/89 = (94*25)/(89*25) = 2350/2225
1/25 = (1*89)/(25*89) = 89/2225

Finally, we add the two fractions: 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.

Gemini-1.5 Pro:

Reasoning:
Let's find a common denominator for 14 and 8.  The least common multiple is 56.
- $\frac{48}{14}=\frac{48\times 4}{14 \times 4} = \frac{192}{56}$
- $\frac{49}{8} = \frac{49 \times 7}{8 \times 7} = \frac{343}{56}$

Now, subtract the two fractions:
- $\frac{343}{56}-\frac{192}{56} = \frac{151}{56}$

### Answer: $\frac{151}{56}$ 

Expected answer: 151/56

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 79/91 and 100/47 is 12813/4277.  Adding a number to itself is the same as multiplying it by 2.
So, (12813/4277) * 2 = 25626/4277
### Answer: 25626/4277

Expected answer: 25626/4277

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.

Gemini-1.5 Pro:

Reasoning: In the previous problem we calculated that the sum of 87/88 and 24/13 is 3243/1144.  We need to add this to 36/9.  First, we simplify 36/9, which is equal to 4.  To add 3243/1144 and 4, we need to write 4 as a fraction with a denominator of 1144.  This is equivalent to (4 * 1144) / 1144 = 4576/1144.  Therefore, 3243/1144 + 4 = 3243/1144 + 4576/1144 = 7819/1144. 
### Answer: 7819/1144

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?

Gemini-1.5 Pro:

Reasoning: We need to find the sum of 87/83 and 24/13. First, find a common denominator for the two fractions. The least common multiple of 83 and 13 is 1079. To get a denominator of 1079 for 87/83, we multiply both the numerator and denominator by 13: (87 * 13) / (83 * 13) = 1131/1079. To get a denominator of 1079 for 24/13, we multiply both the numerator and denominator by 83: (24 * 83) / (13 * 83) = 1992/1079. We can now add the two fractions: 1131/1079 + 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?

Gemini-1.5 Pro:

Reasoning: Our previous answer was 15/14. To add 62/46 to 15/14, we need to find a common denominator. The least common denominator for 14 and 46 is 322.
 To get a denominator of 322 in the first fraction, we multiply both numerator and denominator by 23: (15/14)*(23/23) = 345/322
 To get a denominator of 322 in the second fraction, we multiply both numerator and denominator by 7: (62/46)*(7/7) = 434/322
 Our problem is now 345/322 + 434/322
 345/322 + 434/322 = 779/322
 ### Answer: 779/322

Expected answer: 779/322

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning:  First we need to find a common denominator for our two fractions. The least common denominator for 5 and 70 is 70.
 To give 61/5 a denominator of 70, we multiply numerator and denominator by 14: (61/5)*(14/14) = 854/70.
 Our problem is now 854/70 - 79/70.
 854/70-79/70 = 775/70.
 This can be simplified to 155/14.
 ### Answer: 155/14

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?

Gemini-1.5 Pro:

Reasoning: From the previous problem, the sum of 68/16 and 52/78 is 59/12.
To add 37/38, we need a common denominator. The least common multiple of 12 and 38 is 228.
59/12 is equivalent to 1121/228, and 37/38 is equivalent to 222/228.
Finally, 1121/228 + 222/228 = 1343/228.
### Answer: 1343/228 

Expected answer: 1343/228

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: 8/16 simplifies to 1/2, and 52/78 simplifies to 2/3.
To add these fractions, we need a common denominator, which is 6. 
1/2 is equivalent to 3/6, and 2/3 is equivalent to 4/6.
Therefore, 3/6 + 4/6 = 7/6.
### Answer: 7/6 

Expected answer: 7/6

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: We know from the previous calculation that the sum of 21/75 and 44/47 is 4287/3525.
Adding two of these sums is the same as multiplying the sum by 2: 2 * (4287/3525) = 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?

Gemini-1.5 Pro:

Reasoning: To add the fractions, we need to find a common denominator. The least common denominator for 63 and 47 is their product, which is 2961. 
We can rewrite 21/63 as (21*47)/(63*47) = 987/2961
Similarly, we can rewrite 44/47 as (44*63)/(47*63) = 2772/2961.
Therefore, 21/63 + 44/47 = 987/2961 + 2772/2961 = (987+2772)/2961 = 3759/2961.

### Answer: 3759/2961 

Expected answer: 179/141

Correct? Yes

Problem: After finding the result of (77/5 + 4/11), add that result to 94/60. What is the final answer?

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know (77/5 + 4/11) = 867/55.  Now we need to add that to 94/60.  First, we need to find a common denominator. The least common multiple of 55 and 60 is 660. 

Therefore:

(867/55 + 94/60) = (867 * 12) / (55 * 12) + (94 * 11) / (60 * 11) = 10404/660 + 1034/660 = 11438/660

This fraction can be simplified by dividing the numerator and denominator by 2: 11438/660 = 5719/330

### Answer: 5719/330

Expected answer: 5719/330

Correct? Yes

Problem: Instead of the original problem (77/5 + 4/11), consider a change such that now we are adding 77/5 and 4/79 instead. In the context of the previous word problem, if we were originally adding parts of a recipe, we could consider the change as modifying one part of the recipe. What happens if we modify the recipe in this way, by replacing the quantity we originally added with 4/79?

Gemini-1.5 Pro:

Reasoning: Replacing 4/11 with 4/79 means we are adding a much smaller quantity to 77/5.  

Think of it like this: if you were originally adding 4/11 of a cup of sugar to a recipe, and then changed it to 4/79 of a cup, you're now using a much smaller amount of sugar.  

This modification would make the overall sum smaller because the fraction 4/79 represents a smaller portion than 4/11. 
### Answer: The overall sum will be smaller. 

Expected answer: 6103/395

Correct? No

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

Gemini-1.5 Pro:

Reasoning: From the previous problem, the sum of 60/48 and 37/47 is 383/188.  35/35 simplifies to 1.  Any number added to 1 is itself plus 1.  Therefore, we have (383/188) + 1 = 571/188.
### Answer: 571/188 

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?

Gemini-1.5 Pro:

Reasoning: First, simplify the weight of the apples, 60/45, which simplifies to 4/3 kilograms.  Then, since 4/3 and 37/47 cannot be simplified further,  find a common denominator of 141 resulting in 188/141 and 111/141. Adding those fractions, we get (188+111)/141 = 299/141 kilograms.
### Answer: 299/141 kilograms 

Expected answer: 299/141

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We previously found that 84/97 + 25/2 = 2593/194.  We can write 2593/194 - 100/71 = 184103/13774 - 19400/13774 = 164703/13774. 
### Answer: 164703/13774 

Expected answer: 164703/13774

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: We can simplify 84/96 to 7/8. Then 7/8 + 25/2 = 7/8 + 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?

Gemini-1.5 Pro:

Reasoning:
* From the previous problem, the difference between 66/20 and 4/78 is 1267/390.
* We need to add 6/15 to 1267/390. First, find the LCM of 390 and 15, which is 780.
* Rewrite both fractions with a denominator of 780:
    * (1267/390) * (2/2) = 2534/780
    * (6/15) * (52/52) = 312/780
* Add the fractions: 2534/780 + 312/780 = 2846/780
* Simplify the fraction: 2846/780 = 1423/390

### Answer: 1423/390 

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?

Gemini-1.5 Pro:

Reasoning: 
* First, find the least common multiple (LCM) of 21 and 78. The LCM of 21 and 78 is 546.
* Rewrite both fractions as equivalent fractions with a denominator of 546:
    * (66/21) * (26/26) = 1716/546
    * (4/78) * (7/7) = 28/546
* Subtract the fractions: 1716/546 - 28/546 = 1688/546
* Simplify the resulting fraction: 1688/546 = 844/273

### Answer: 844/273

Expected answer: 844/273

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know the sum of 95/57 and 28/80 is 2299/1140. To double this sum, we multiply it by 2:  (2299/1140) * 2 = 4598/1140.
This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 2: (4598/2) / (1140/2) = 2299/570
### Answer: 2299/570

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?

Gemini-1.5 Pro:

Reasoning:  First, we need to find a common denominator for 95/21 and 28/80. The least common multiple of 21 (3 x 7) and 80 (2 x 2 x 2 x 2 x 5) is 1680.
To get a denominator of 1680 for 95/21, we multiply both numerator and denominator by 80: (95 * 80) / (21 * 80) = 7600 / 1680
To get a denominator of 1680 for 28/80, we multiply both the numerator and denominator by 21: (28 * 21) / (80 * 21) = 588 / 1680
Now we can add the two fractions: 7600/1680 + 588/1680 = 8188/1680
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4: (8188/4) / (1680/4) = 2047/420
### Answer: 2047/420 

Expected answer: 2047/420

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?

Gemini-1.5 Pro:

Reasoning: You're asking to calculate (23/20 + 82/97) - 7/44. We already know from the previous problem that 23/20 + 82/97 = 3871/1940. 

To subtract fractions, they must also have a common denominator. The least common denominator of 1940 and 44 is 42680. Let's rewrite both fractions with that denominator:

3871/1940 = (3871 * 22)/(1940 * 22) = 85162/42680
7/44 = (7 * 970)/(44 * 970) = 6790/42680

Now we can perform the subtraction: 85162/42680 - 6790/42680 = (85162 - 6790)/42680 = 78372/42680

Finally, let's simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 872: (78372/872) / (42680/872) = 90/49

### Answer: 90/49 

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?

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator. The least common denominator of 43 and 97 is 4171. Therefore, we should rewrite both fractions with a denominator of 4171:
23/43 = (23*97)/(43*97) = 2231/4171
82/97 = (82*43)/(97*43) = 3526/4171

We can now add the fractions: 2231/4171 + 3526/4171 = (2231+3526)/4171 = 5757/4171.
### Answer: 5757/4171

Expected answer: 5757/4171

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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that the sum of 4/31 and 76/11 is 2400/341. Now we need to subtract 63/35 from that result. The least common denominator for 341 and 35 is 11935. To get a denominator of 11935 for 2400/341 we multiply by 35/35: (2400/341)*(35/35) = 84000/11935. To get a denominator of 11935 for 63/35 we multiply by 341/341: (63/35)*(341/341) = 21483/11935. Finally, we subtract the two fractions: 84000/11935 - 21483/11935 = 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?

Gemini-1.5 Pro:

Reasoning: Similar to the previous problem, we need to find a common denominator. The least common denominator for 31 and 11 is 341. To get a denominator of 341 for 42/31 we multiply by 11/11: (42/31)*(11/11) = 462/341. To get a denominator of 341 for 76/11 we multiply by 31/31: (76/11)*(31/31) = 2356/341. Finally, we add the two fractions: 462/341 + 2356/341 = 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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous question that 82/15 + 100/12 = 13 4/5, which can be written as the improper fraction 69/5.

To add 46/83 to 69/5, we need a common denominator. The least common denominator for 83 and 5 is 415.

Converting both fractions:
- 69/5 is equivalent to (69 * 83) / (5 * 83) = 5727/415
- 46/83 is equivalent to (46 * 5) / (83 * 5) = 230/415

Finally, we add the two fractions: 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?

Gemini-1.5 Pro:

Reasoning: Similar to the previous problem, we need a common denominator to add these fractions. The least common denominator of 15 and 12 is 60.
61/15 is equivalent to (61 * 4) / (15 * 4) = 244/60
100/12 is equivalent to (100 * 5) / (12 * 5) = 500/60
Adding these two fractions: 244/60 + 500/60 = 744/60
This simplifies to 12 2/5. 
### Answer: 12 2/5

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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that 50/73 + 20/23 = 2610/1679
To add 83/35 to this result, we need to find a common denominator for 1679 and 35, which is their product: 1679 * 35 = 58765
We can rewrite 2610/1679 as (2610*35)/(1679*35) = 91350/58765
We can rewrite 83/35 as (83*1679)/(35*1679) = 139057/58765
Finally, 91350/58765 + 139057/58765 = (91350 + 139057)/58765 = 230407/58765
### Answer: 230407/58765

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?

Gemini-1.5 Pro:

Reasoning: To find the total time, we need to add the two fractions: 50/57 and 20/23.

First, we need to find a common denominator. The least common multiple of 57 and 23 is 1311.

Next, we need to rewrite each fraction with the common denominator:

(50/57) * (23/23) = 1150/1311

(20/23) * (57/57) = 1140/1311

Now we can add the fractions: 1150/1311 + 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?

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know 94/35 - 23/49 = 543/245.  We need to add this result to 27/72.
 
 The least common denominator of 245 (5 * 7 * 7) and 72 (2 * 2 * 2 * 3 * 3) is 2 * 2 * 2 * 3 * 3 * 5 * 7 * 7 = 17640.
 
 Rewriting our fractions, we get (543 * 72)/(245 * 72) + (27 * 245)/(72 * 245) = 39096/17640 + 6615/17640
 
 Performing the addition, we find (39096 + 6615)/17640 = 45711/17640.  This fraction does not simplify any further.

### Answer: 45711/17640 

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?

Gemini-1.5 Pro:

Reasoning:  We follow the same process as before, needing a common denominator to subtract fractions. The least common denominator for 35 and 49 is still 245.

The problem becomes (54 * 7)/(35 * 7) - (23 * 5)/(49 * 5). After multiplication: 378/245 - 115/245

Finally, subtracting the numerators: (378 - 115)/245 = 263/245

### Answer: 263/245 

Expected answer: 263/245

Correct? Yes

Problem: If the sum of 58/30 and 49/37 is represented by the variable 't', what would be the value of 't' added to 't'?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that the sum of 58/30 and 49/37 is 1808/555. So, 't' equals 1808/555. 
Adding 't' to 't' means (1808/555) + (1808/555) = 3616/555.
### Answer: 3616/555 

Expected answer: 3616/555

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We know from our previous calculation that the sum of 45/53 and 71/50 is 6013/2650.  We need to add this to 8/100.
First we simplify 8/100 to 2/25.
Then we find the least common denominator of 2650 and 25, which is 13250.
Finally, we have 6013/2650 + 2/25 = (6013*5)/(2650*5) + (2*530)/(25*530) = 30065/13250 + 1060/13250 = 31125/13250.
This simplifies to 25/106.
### Answer: 25/106 

Expected answer: 249/106

Correct? No

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?

Gemini-1.5 Pro:

Reasoning: To get the sum of two fractions with unlike denominators, we first find their least common denominator. The LCD of 53 and 72 is 3816. 
Then we have 45/53 + 71/72 = (45*72)/(53*72) + (71*53)/(72*53).
Which is equal to 3240/3816 + 3763/3816 = <<3240/3816 + 3763/3816=7003/3816>>7003/3816.
### Answer: 7003/3816 

Expected answer: 7003/3816

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that the sum of 61/20 and 29/15 is 299/60. Now we need to add that to 58/31.
First, find a common denominator for 60 and 31: the least common denominator is 1860.
Convert our fractions to have a denominator of 1860: (299/60)*(31/31) = 9269/1860, and (58/31)*(60/60) = 3480/1860.
Finally, add the two fractions: 9269/1860 + 3480/1860 = 12749/1860
### Answer: 12749/1860 

Expected answer: 12749/1860

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: First find a common denominator: 20 and 67 share no common factors, so their least common multiple is simply 20*67 = 1340.
Converting both fractions to have a denominator of 1340, we get: (61/20)*(67/67) = 4087/1340, and (29/67)*(20/20) = 580/1340.
Finally, we add the two fractions: 4087/1340 + 580/1340 = 4667/1340.
### Answer: 4667/1340

Expected answer: 4667/1340

Correct? Yes

Problem: In continuation of the previous question, what would you get if you subtract 7/89 from the result of ((33 / 90) + (77 / 79))? Please give your answer as an unsimplified fraction.

Gemini-1.5 Pro:

Reasoning: 
We know from the previous question that ((33/90) + (77/79)) is 9537/7110. 

To subtract 7/89 from 9537/7110, we need to find a common denominator. The least common denominator for 7110 and 89 is 632790.

Converting to fractions with a denominator of 632790, we get (9537/7110)*(89/89) = 848793/632790 and (7/89)*(7110/7110) = 49770/632790.

Subtracting these fractions, we get (848793 - 49770)/632790.

### Answer: 799023/632790

Expected answer: 266341/210930

Correct? Yes

Problem: Taking the previous problem into consideration, what if the fraction you were initially adding to 33/90 was 98/79 instead of 77/79? Solve the expression ((33 / 90) + (98 / 79)) and give your answer as an unsimplified fraction.

Gemini-1.5 Pro:

Reasoning: 
To add fractions, they must have a common denominator. The least common denominator for 90 and 79 is their product, 7110.

Converting to fractions with a denominator of 7110, we get (33/90)*(79/79) = 2607/7110 and (98/79)*(90/90) = 8820/7110.

Adding these fractions, we get (2607 + 8820)/7110.

### Answer: 11427/7110

Expected answer: 3809/2370

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: In the previous problem we calculated the sum of 30/79 and 29/6 to be 2471/474.  We need to find a common denominator for 2471/474 and 44/75: 474 * 75 = <<474*75=35550>>35550.
Convert the fractions: (2471*75)/35550 = 185325/35550, and (44 * 474)/35550 = 20856/35550.
Finally, subtract the two fractions: 185325/35550 - 20856/35550 = 164469/35550
### Answer: 164469/35550 

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?

Gemini-1.5 Pro:

Reasoning: First find a common denominator: 97 * 6 = <<97*6=582>>582
Then convert each fraction: (30*6)/582 = 180/582, and (29*97)/582 = 2813/582
Finally, add the two fractions: 180/582 + 2813/582 = 2993/582
### Answer: 2993/582 

Expected answer: 2993/582

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We already found out from the previous problem that subtracting 11/66 from 59/2 results in 88/3. So, the problem becomes 63/51 + 88/3. To add these fractions, we need a common denominator. The least common denominator for 51 and 3 is 153.  We can rewrite 63/51 as (63/51)*(3/3) = 189/153. We can rewrite 88/3 as (88/3)*(51/51) = 4488/153.  Now, the problem becomes 189/153 + 4488/153 = (189+4488)/153 = 4677/153. This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 3. This gives us (4677/3)/(153/3) = 1559/51.

### Answer: 1559/51

Expected answer: 1559/51

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: As before, we need a common denominator. The least common denominator for 31 and 2 is 62.  We already know 59/2 is equivalent to 1947/66, so we can divide both numerator and denominator by 3 to get the equivalent fraction with a denominator of 62:  (1947/3)/(66/3) = 649/22. We also need to rewrite 11/31 with a denominator of 62: (11/31)*(2/2) = 22/62. Our problem now becomes 649/62 - 22/62. Subtracting the numerators gives us (649-22)/62 = 627/62. 

### Answer: 627/62 

Expected answer: 1807/62

Correct? No

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?

Gemini-1.5 Pro:

Reasoning: The difference between the original first fraction (58/23) and the new first fraction (45/23) is 58/23 - 45/23 = 13/23. 
Since we are only changing the first addend and keeping the second addend the same, the new sum will be 13/23 less than the original sum. 
### Answer: The sum of 45/23 and 25/26 will be 13/23 less than the sum of 58/23 and 25/26. 

Expected answer: 1745/598

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 70/13 and 17/52 is 297/52.  To subtract 35/87 from this, we need to find a common denominator.  The least common denominator for 52 and 87 is 4524.
 
 First, we convert 297/52 to a fraction with a denominator of 4524 by multiplying by 87/87: (297/52)*(87/87) = 25839/4524
 
 Next, we convert 35/87 to a fraction with a denominator of 4524 by multiplying by 52/52: (35/87)*(52/52) = 1820/4524
 
 Finally, we subtract the two fractions: 25839/4524 - 1820/4524 = 24019/4524
### Answer: 24019/4524 

Expected answer: 24019/4524

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: Our fractions are now 70/93 and 17/52. To add these fractions, they must share a common denominator. The least common denominator of 93 and 52 is 4836. 

To get a denominator of 4836 in the first fraction, we multiply by 52/52: (70/93)*(52/52) = 3640/4836

To get a denominator of 4836 in the second fraction, we multiply by 93/93: (17/52)*(93/93) = 1581/4836

We can now add the fractions: 3640/4836 + 1581/4836 = 5221/4836

### Answer: 5221/4836

Expected answer: 5221/4836

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, we need to find the sum of the first two fractions. We can add the numerators of the fractions because they share a common denominator: 43/4 + 71/4 = (43+71)/4 = 114/4
We can simplify the fraction by dividing the numerator and denominator by 2: 114/4 = 57/2

Now we need to add 57/2 to 92/79. To do this, we need to find a common denominator. The least common denominator is 2*79 = 158.  
We can rewrite 57/2 as a fraction with a denominator of 158: (57*79)/(2*79) = 4503/158
We can rewrite 92/79 as a fraction with a denominator of 158: (92*2)/(79*2) = 184/158

Finally, we can add the two fractions: 4503/158 + 184/158 = (4503+184)/158 = 4687/158
### Answer: 4687/158

Expected answer: 4687/158

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must share a common denominator. The least common denominator for 4 and 89 is their product, 356. We can rewrite both fractions with this denominator:
- 43/4 is equivalent to (43 * 89) / (4 * 89) = 3827/356
- 71/89 is equivalent to (71 * 4) / (89 * 4) = 284/356

Now we can add the fractions: 3827/356 + 284/356 = (3827 + 284) / 356 = 4111/356
### Answer: 4111/356 

Expected answer: 4111/356

Correct? Yes

Problem: If the result from the previous calculation is subtracted by 23/29, what is the final result?

Gemini-1.5 Pro:

Reasoning: We need to subtract 23/29 from 4381/1998. First, we find a common denominator: the least common multiple of 29 and 1998 is their product, 57942.  Rewriting the fractions with this denominator, we have 4381/1998 = (4381 x 29)/(1998 x 29) = 127249/57942 and 23/29 = (23 x 1998)/(29 x 1998) = 45954/57942.  Therefore, 4381/1998 - 23/29 = 127249/57942 - 45954/57942 = (127249 - 45954)/57942 = 81295/57942.
### Answer: 81295/57942

Expected answer: 81095/57942

Correct? No

Problem: If initially, instead of having 17/74 of the fruit basket filled with oranges, we had 28/74 of it filled with oranges, and we still added the same 53/27 fraction of the basket filled with apples, then what would the total fraction of the fruit basket be when filled with these fruits?

Gemini-1.5 Pro:

Reasoning: We need to add the fractions 28/74 and 53/27.  As before, the least common denominator is 1998.  Rewriting each fraction with a denominator of 1998, we get 28/74 = (28 x 27)/(74 x 27) = 756/1998 and 53/27 = (53 x 74)/(27 x 74) = 3922/1998.  Therefore, 28/74 + 53/27 = 756/1998 + 3922/1998 = (756 + 3922)/1998 = 4678/1998. This fraction can be simplified by dividing the numerator and denominator by their greatest common factor of 2 to get 2339/999.
### Answer: 2339/999 

Expected answer: 2339/999

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
We know from the previous problem that (76/76) + (96/16) = 7.
Adding the solution to itself, we have 7 + 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?

Gemini-1.5 Pro:

Reasoning:
As before, 76/76 = 1.
96/33 = 32/11 when simplified.

Finally, 1 + 32/11 = 43/11
### Answer: 43/11

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?

Gemini-1.5 Pro:

Reasoning:
First, simplify 94/14 to 47/7. 
Then, find a common denominator for 47/7 and 50/19. The least common denominator for 7 and 19 is 133. 
Therefore, 47/7 is equivalent to (47 * 19) / (7 * 19) = 893/133, and 50/19 is equivalent to (50 * 7) / (19 * 7) = 350/133.
Finally, subtract the two fractions: 893/133 - 350/133 = 543/133.
This fraction can be further simplified to 27/22.

### Answer: 27/22

Expected answer: 543/133

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that the sum of 60/79 and 53/38 is 6467/3002. To add 5/11 to this sum, we need to find a common denominator. The least common denominator for 3002 and 11 is 33022. We rewrite the fractions as follows: (6467/3002) = (6467*11)/(3002*11) = 71137/33022 and (5/11) = (5*3002)/(11*3002) = 15010/33022.  Now we can add all three fractions: 71137/33022 + 15010/33022 = 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?

Gemini-1.5 Pro:

Reasoning: 79/79 is equal to 1.  We can rewrite 1 with the denominator of 38: 1 = 38/38. So the problem becomes 38/38 + 53/38.  The sum of the numerators is 38 + 53 = 91.
### Answer: 91/38 

Expected answer: 91/38

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that 39/48 + 19/84 = 349/336. 
Adding a fraction to itself is the same as multiplying by 2:  (349/336) * 2 = 698/336. 
This can be simplified by dividing both numerator and denominator by 2: 698/336 = 349/168
### Answer: 349/168 

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?

Gemini-1.5 Pro:

Reasoning: To add fractions, they need a common denominator. The least common denominator for 48 and 13 is their product, 624.  We can rewrite both fractions: (39/48) * (13/13) = 507/624 and (19/13) * (48/48) = 912/624.
Now we can add the fractions: 507/624 + 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?

Gemini-1.5 Pro:

Reasoning: We need to add 868/43 and 86/82. To do this, we need to find a common denominator. 
* The least common denominator for 43 and 82 is 3526 (43 * 82). 
* Convert 868/43 to a fraction with a denominator of 3526: (868 * 82) / (43 * 82) = 71176/3526.
* Convert 86/82 to a fraction with a denominator of 3526: (86 * 43) / (82 * 43) = 3698/3526.
* Now we can add the fractions: 71176/3526 + 3698/3526 = 74874/3526.
* This fraction can be simplified by dividing both numerator and denominator by 2: 74874/3526 = 37437/1763.

### Answer: 37437/1763 

Expected answer: 37437/1763

Correct? Yes

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?

Gemini-1.5 Pro:

It seems like you're trying to combine parts of a pie with whole slices, which doesn't quite make sense in a real-world context. 

Think of it this way:

* **Fractions of a pie:** When you have a fraction like 75/86, it represents 75 pieces out of a pie that's been cut into 86 slices.
* **Whole slices:**  60/3 simplifies to 20, which represents 20 whole slices of pie.

You can't directly add "pieces of a pie" to "whole slices."  

To figure out the total, you'd need to know:

* **How many pieces are in ONE whole pie**  (Is it still 86 pieces per pie?)

Let me know if you can clarify the problem! 

Expected answer: 1795/86

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
* We already know from the previous calculation that 95/16 - 43/60 = 5 53/240
* Let's convert 5 53/240 to an improper fraction: (5*240 + 53)/240 = 1253/240
* Now we need to add this to 80/79. To do this, we need a common denominator. The least common denominator for 240 and 79 is quite large, so we'll use their product: 240 * 79 = 18960
* Convert both fractions to have this denominator: (1253 * 79)/(240 * 79) = 99087/18960 and (80 * 240)/(79 * 240) = 19200/18960
* Now we can add: 99087/18960 + 19200/18960 = 118287/18960
* This fraction can be simplified to a mixed number: 118287/18960 = 6 4827/18960 

### Answer: 6 4827/18960 

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?

Gemini-1.5 Pro:

Reasoning: 
* We already know from the previous problem that 43/60 is equivalent to 172/240.
* We need to convert 91/16 to a fraction with a denominator of 240:  (91 * 15) / (16 * 15) = 1365/240
* Now we can subtract:  1365/240 - 172/240 = 1193/240
* This can be simplified to a mixed number: 1193/240 = 4 233/240

### Answer: 4 233/240 

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?

Gemini-1.5 Pro:

Reasoning: The sum of 38/8 and 4/16 was 5.  We need to add 32/64 to that.  First, simplify 32/64 by dividing the numerator and denominator by their greatest common factor, 32. This gives us 1/2.  So now we need to add 5 and 1/2.  Since 5 is the same as 5/1, we need a common denominator. The least common denominator for 1 and 2 is 2. We can rewrite 5/1 as 10/2, so the problem becomes 10/2 + 1/2 = 11/2.
### Answer: 11/2 

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?

Gemini-1.5 Pro:

Reasoning: First, find a common denominator for 12/8 and 4/16. The least common denominator for 8 and 16 is 16. To rewrite 12/8 with a denominator of 16, multiply both the numerator and denominator by 2: (12 * 2) / (8 * 2) = 24/16. Now the problem becomes 24/16 + 4/16.  Adding the numerators and keeping the denominator the same gives us 28/16. Finally, simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 4: 28/16 = 7/4.
### Answer: 7/4 

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?

Gemini-1.5 Pro:

Reasoning:
From the previous problem, we know 67/15 - 27/12 = 2 13/60

We need to subtract 7/35 from that result:  2 13/60 - 7/35

First, convert the mixed number to a fraction: 2 13/60 = 133/60
* The least common multiple of 60 and 35 is 420
* 133/60 = 931/420
* 7/35 = 84/420
Therefore, the problem becomes: 931/420 - 84/420 = 847/420
Simplified, this is equal to 2 7/420 

### Answer: 2 7/420 

Expected answer: 121/60

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: 
We need to calculate 67/15 - 27/50.
Let's find a common denominator for the fractions. The least common multiple of 15 and 50 is 150.
* We can rewrite 67/15 as 670/150 (multiply numerator and denominator by 10)
* We can rewrite 27/50 as 81/150 (multiply numerator and denominator by 3)
Now we have: 670/150 - 81/150 = 589/150
This fraction can be written as a mixed number: 3 139/150
### Answer: 3 139/150 

Expected answer: 589/150

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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that 33/5 - 19/44 = 1357/220. Now we need to add 32/76 to this result.  First, simplify 32/76 to 8/19. Then find the least common denominator for 220 and 19, which is 4180. We can rewrite 1357/220 as 26283/4180 and 8/19 as 1760/4180.
Finally, 26283/4180 + 1760/4180 = 28043/4180.
### Answer: 28043/4180 

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?

Gemini-1.5 Pro:

Reasoning:  We already know from our previous calculation that 33/5 is equivalent to 1452/220.  We need to convert 17/44 to have a denominator of 220 as well.  This gives us (17*5)/(44*5) = 85/220.
Subtracting these, we get: 1452/220 - 85/220 = 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?

Gemini-1.5 Pro:

Reasoning: We know from before that the sum of the first two fractions is 9442/4350. To add 3/82 to this, we need to find a common denominator. 
* The least common denominator for 4350 (2*3*5*5*29) and 82 (2*41) is 2*3*5*5*29*41 = 178500
* Rewriting our fractions: 9442/4350 = (9442*41)/(4350*41) = 387122/178500 and 3/82 = (3*2175)/(82*2175) = 6525/178500
* Now we can add: 387122/178500 + 6525/178500 = 393647/178500

### Answer: 393647/178500 

Expected answer: 393647/178350

Correct? No

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?

Gemini-1.5 Pro:

Reasoning: We already know the least common denominator for 75 and 58 is 4350, and that 88/58 is equivalent to 6600/4350.
*  We need to rewrite 12/75 with the denominator 4350: 12/75 = (12*58)/(75*58) = 696/4350
*  Finally, we add: 696/4350 + 6600/4350 = (696+6600)/4350 = 7296/4350

### Answer: 7296/4350

Expected answer: 1216/725

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?

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 48 divided by 16 and 12 divided by 29 is 99/29.  Let's represent 99/29 with the variable *x*.  Adding a number to itself is the same as multiplying it by 2, so we have 2*x = 2*(99/29) = <<2*(99/29)=198/29>>198/29.
### Answer: 198/29 

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?

Gemini-1.5 Pro:

Reasoning: We already know 48 divided by 16 is 3.  12 divided by 32 can be simplified to 3/8, since both the numerator and denominator are divisible by 4:  <<12/4=3>> and <<32/4=8>>, so <<12/32=3/8>>. The sum of 3 and 3/8 is 3+3/8 = <<3+3/8=27/8>>27/8
### Answer: 27/8 

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?

Gemini-1.5 Pro:

Reasoning: We know from before that the sum of the first two fractions is 619/300. To add 61/80 to this sum, we need to find a common denominator. The least common denominator of 300 and 80 is 1200.
We can rewrite 619/300 as 2476/1200 and 61/80 as 915/1200.
Adding all three fractions, we get 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.

Gemini-1.5 Pro:

Reasoning: First, we simplify 60/20, which simplifies to 3.  This means we have 3 cakes.
Next, we need to add the cake portions together.  To do this, we need a common denominator.  The least common denominator of 1 (because 3 can be written as 3/1) and 75 is 75.
We can rewrite 3/1 as 225/75.
Adding the two fractions gives us 225/75 + 16/75 = 241/75. 
### 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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that 83/40 + 6/8 = 113/40. 
First, simplify 24/64 by dividing the numerator and denominator by their greatest common factor, 8: 24/64 = (24/8)/(64/8) = 3/8
Next, find a common denominator for 113/40 and 3/8. The least common denominator is 40. Rewrite 3/8 as a fraction with a denominator of 40: 3/8 = (3*5)/(8*5) = 15/40
Now the problem becomes 113/40 - 15/40
Since the fractions have the same denominator, we can simply subtract the numerators: (113-15)/40 = 98/40
Finally, simplify the result by dividing the numerator and denominator by their greatest common factor, 2: 98/40 = (98/2)/(40/2) = 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?

Gemini-1.5 Pro:

Reasoning: First find a common denominator for the two fractions. The least common denominator for 18 and 8 is 72. To get a denominator of 72 in the first fraction, multiply both numerator and denominator by 4: (83*4)/(18*4) = 332/72. 
To get a denominator of 72 in the second fraction, multiply both numerator and denominator by 9: (6*9)/(8*9) = 54/72.
Now the summation can be written as 332/72 + 54/72.
Since the fractions have the same denominator, we can simply add the numerators: (332 + 54)/72 = 386/72
This fraction can be simplified by dividing both numerator and denominator by 2: 386/72 = 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?

Gemini-1.5 Pro:

Reasoning: Adding a fraction to itself is the same as multiplying it by 2. Therefore, we need to calculate (4663/1428) * 2. This equals (4663 * 2) / 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?

Gemini-1.5 Pro:

Reasoning: We keep the sum from the previous problem, 4663/1428, and recognize that the only difference is an additional 5/84 gallons of milk.
First we rewrite 5/84 with the common denominator of 1428: 5/84 = 85/1428
Then we add this amount to the previous sum to find the new total: 85/1428 + 4663/1428 = 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?

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 51/78 and 44/83 is 7665/6474. We need to add this to 71/92.

First, find a common denominator for 6474 and 92.  Both numbers are divisible by 2, so let's simplify: 6474/2 = 3237 and 92/2 = 46.  The least common denominator for 3237 and 46 is their product: 3237 * 46 = 148902.  

Now, rewrite each fraction with the common denominator:

- (7665/6474) * (46/46) = 352590/148902
- (71/92) * (1614/1614) = 114594/148902 

Finally, add the fractions: 352590/148902 + 114594/148902 = 467184/148902

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 2:  467184/2 = 233592 and 148902/2 = 74451

### Answer: 233592/74451 

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?

Gemini-1.5 Pro:

Reasoning: We need to find a common denominator for 74 and 83. Since these numbers don't share any common factors, the least common denominator is their product: 74 * 83 = 6142

Next, we rewrite each fraction with the common denominator:
- (51/74) * (83/83) = 4233/6142
- (44/83) * (74/74) = 3256/6142

Now we can add the fractions: 4233/6142 + 3256/6142 = 7489/6142

### Answer: 7489/6142 

Expected answer: 7489/6142

Correct? Yes

Problem: After you have calculated the result of the previous operation (78 / 74) + (72 / 51), find the sum if you add the result of the operation to itself. What is the final answer?

Gemini-1.5 Pro:

Reasoning: 
From the previous calculation, we know (78 / 74) + (72 / 51) = 1551/629. 

Adding the result to itself is the same as multiplying by 2: (1551/629) + (1551/629) = 2 * (1551/629) 

Performing the multiplication: 2 * (1551/629) = 3102/629 

### Answer: 3102/629 

Expected answer: 3102/629

Correct? Yes

Problem: Suppose in our previous operation, instead of adding (72 / 51), we were to add (56 / 51) to (78 / 74). What would be the new result of the operation (78 / 74) + (56 / 51)?

Gemini-1.5 Pro:

Reasoning: 
We already know from the previous problem that 78/74 simplifies to 39/37.

Now we need to find a common denominator for 39/37 and 56/51. The least common denominator is 1887 (37 * 51):
* 39/37 is equivalent to (39 * 51) / (37 * 51) = 2089/1887
* 56/51 is equivalent to (56 * 37) / (51 * 37) = 2072/1887

Finally, we can add the two fractions: 2089/1887 + 2072/1887 = 4161/1887

### Answer: 4161/1887

Expected answer: 4061/1887

Correct? No

Problem: After calculating the result of (33 / 23) - (12 / 75), now find the sum when you add this result to 24 / 81. Express your answer as a fraction.

Gemini-1.5 Pro:

Reasoning: From the previous calculation, we know that (33/23) - (12/75) = 2199/1725. Now we need to add this to 24/81.

First, find a common denominator for 1725 and 81:
* The least common multiple of 1725 and 81 is 139725
* We can rewrite 2199/1725 as (2199 * 81) / (1725 * 81) = 178119 / 139725
* We can rewrite 24/81 as (24 * 1725) / (81 * 1725) = 41400 / 139725

Now, the operation becomes: (178119 / 139725) + (41400 / 139725)

Performing the addition: (178119 + 41400) / 139725 = 219519 / 139725
### Answer: 219519/139725 

Expected answer: 24391/15525

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.

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 19/30 and 75/77 is 3713/2310.  To add 1/88 to this, we need a common denominator. 

The least common denominator for 2310 and 88 is their least common multiple.  Notice that 2310 is divisible by 11 (2310/11 = 210) and 88 is divisible by 11 (88/11 = 8). So, the least common multiple is (210 * 88) = 18480

Now we can add the fractions:

3713/2310 + 1/88 = (3713 * 8)/ (2310 * 8) + (1 * 210)/(88 * 210) = 29704/18480 + 210/18480 = 29914/18480

This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 2:

29914/18480 = (29914/2)/(18480/2) = 14957/9240

### Answer: 14957/9240 

Expected answer: 14957/9240

Correct? Yes

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.

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator.  The least common denominator for 30 and 68 is 1020.  We can see this because the prime factorizations are 30 = 2*3*5 and 68=2*2*17, so the least common denominator is 2*2*3*5*17 = 1020.

We get:

19/30 + 75/68 = (19 * 34)/(30 * 34) + (75 * 15)/(68 * 15) = 646/1020 + 1125/1020 = 1771/1020

### Answer: 1771/1020 

Expected answer: 1771/1020

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.

Gemini-1.5 Pro:

Reasoning:  We already know the sum of 57/66 and 39/64 is 3111/2112. To add 10/29 to this, we need a common denominator. The least common multiple of 2112 and 29 is 61248.
3111/2112 is equivalent to (3111*29)/(2112*29) = 89219/61248
10/29 is equivalent to (10*2112)/(29*2112) = 21120/61248
The sum of 89219/61248 and 21120/61248 is (89219+21120)/61248 = 110339/61248. 
### Answer: 110339/61248

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?

Gemini-1.5 Pro:

Reasoning:  To add fractions, they must have the same denominator. The least common multiple of 66 and 64 is 2112.
57/66 is equivalent to (57*32)/(66*32) = 1824/2112
49/64 is equivalent to (49*33)/(64*33) = 1617/2112
The sum of 1824/2112 and 1617/2112 is (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?

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know (55/30) - (1/72) = 131/72. Now we need to add 73/92 to this result.

First, find the least common multiple (LCM) of 72 and 92. The LCM of 72 and 92 is 1656.

Convert the fractions to have a denominator of 1656:

(131/72) = (131 * 23) / (72 * 23) = 3013/1656
(73/92) = (73 * 18) / (92 * 18) = 1314/1656

Now the operation becomes: (3013/1656) + (1314/1656)

Adding the numerators: (3013 + 1314) / 1656 = 4327/1656

### Answer: 4327/1656

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))?

Gemini-1.5 Pro:

Reasoning: Let's call the original result 'A', where A = (55/30) - (1/72) = 131/72
 
 Now we want to calculate: B = (80/30) - (1/72) 
 
 Notice that the only difference between A and B is in the first fraction: (80/30) instead of (55/30). 
 
 The difference between these two fractions is (80/30) - (55/30) = 25/30
 
 Therefore, the new result B will be greater than the original result A by 25/30. 
 
 To find the exact value of B, we can simplify 25/30 to 5/6 and add it to A:
 
 B = A + (5/6) = (131/72) + (5/6) = (131/72) + (60/72) = 191/72
 
 ### Answer: The result will increase by 5/6, and the new result will be 191/72. 

Expected answer: 191/72

Correct? Yes

Problem: After finding the sum of the fractions 69/21 and 71/86, add the result to 86/62. What is the result?

Gemini-1.5 Pro:

Reasoning:  From the previous problem, we know the sum of 69/21 and 71/86 is 2475/602. Now we need to add this to 86/62.

First, simplify 86/62 by dividing numerator and denominator by their greatest common factor, which is 2: 86/62 = 43/31.

Next, find the least common denominator for 602 and 31, which is 18662.

* Rewrite 2475/602 as (2475 * 31) / (602 * 31) = 76725/18662
* Rewrite 43/31 as (43 * 602) / (31 * 602) = 25886 / 18662

Finally, add the fractions: 76725/18662 + 25886/18662 = 102611/18662

### Answer: 102611/18662 

Expected answer: 102611/18662

Correct? Yes

Problem: Suppose instead that the fractions in the previous problem were 69/60 and 71/86. What is the sum of these fractions?

Gemini-1.5 Pro:

Reasoning: To add these fractions, we first need to find a common denominator. The least common denominator for 60 and 86 is 2580.

* We can rewrite 69/60 as (69 * 43) / (60 * 43) = 2967 / 2580
* We can rewrite 71/86 as (71 * 30) / (86 * 30) = 2130 / 2580

Now we can add the fractions: 2967/2580 + 2130/2580 = 5097/2580

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3: 5097 / 2580 = 1699/860

### Answer: 1699/860 

Expected answer: 1699/860

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.

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know the sum of 24/60 and 42/45 is 4/3.  We need to add this to 66/12. First, simplify 66/12 to 11/2.  To add 4/3 + 11/2, we need a common denominator. The least common denominator for 3 and 2 is 6.  So 4/3 is equivalent to 8/6, and 11/2 is equivalent to 33/6. Finally, 8/6 + 33/6 = 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.

Gemini-1.5 Pro:

Reasoning:  First, we need to find a common denominator for 24/60 and 42/67. The least common denominator for 60 and 67 is their product, 4020. We convert 24/60 to 1608/4020 by multiplying both numerator and denominator by 67. Similarly, we convert 42/67 to 2520/4020 by multiplying both numerator and denominator by 60. Finally, 1608/4020 + 2520/4020 = 4128/4020, which simplifies to 1032/1005. 
### Answer: 1032/1005

Expected answer: 344/335

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: We already know the sum of 64/76 and 35/33 is 1193/627. 
To add 47/38 to 1193/627, we need to find a common denominator.
The least common denominator for 627 and 38 is 23826.
1193/627 is equivalent to (1193*38)/(627*38) = 45334/23826.
47/38 is equivalent to (47*627)/(38*627) = 29569/23826.
(45334+29569)/23826 = 74903/23826.
This fraction can be simplified to 1193/38.
### Answer: 1193/38 

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?

Gemini-1.5 Pro:

Reasoning: We need to find the sum of 43/76 and 35/33.
The least common denominator for 76 and 33 is 2508.
43/76 is equivalent to (43*33)/(76*33) = 1419/2508.
35/33 is equivalent to (35*76)/(33*76) = 2660/2508.
(1419 + 2660)/2508 = 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?

Gemini-1.5 Pro:

Reasoning: We know from the previous problem that the sum of 47/16 and 96/10 is 1003/80.
To subtract 72/22 from 1003/80, we need to find a common denominator. The least common denominator for 80 and 22 is 880. 
We can rewrite 1003/80 as 11033/880, because (1003 * 11)/(80 * 11) = 11033/880.
We can rewrite 72/22 as 2880/880, because (72 * 40)/(22 * 40) = 2880/880.
Now we can subtract the two fractions: 11033/880 - 2880/880 = 8153/880
Finally, we can express the fraction as a mixed number: 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?

Gemini-1.5 Pro:

Reasoning: Similar to the last problem, we need a common denominator to add these fractions. The least common denominator for 16 and 10 is 80.
We can rewrite 47/16 as 235/80, because (47 * 5) / (16 * 5) = 235/80.
We can rewrite 64/10 as 512/80, because (64 * 8) / (10 * 8) = 512/80.
Finally, 235/80 + 512/80 = 747/80.
### Answer: 747/80

Expected answer: 747/80

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?

Gemini-1.5 Pro:

Reasoning: We already calculated the sum of 26/90 and 50/26 to be 1294/585. To subtract 92/89 from this, we need to find a common denominator for 585 (3 x 3 x 5 x 13) and 89. The least common multiple is 52065 (3 x 3 x 5 x 13 x 89).
We convert our fractions to have this denominator: 1294/585 = 1151710/52065 and 92/89 = 52065/52065.
Finally, we perform the subtraction: 1151710/52065 - 52065/52065 = 1099645/52065.
### Answer: 1099645/52065 

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.

Gemini-1.5 Pro:

Reasoning: Let's compare the second fractions in each sum. Notice that 50/26 is greater than 1 (since the numerator is larger than the denominator), while 50/38 is less than 1. 

Therefore, the sum of 26/90 and 50/26 will be greater than the sum of 26/90 and 50/38.

To find the simplified fraction for the second sum, first find the least common multiple of the denominators 90 and 38, which is 1710. Then convert each fraction: 26/90 = 494/1710 and 50/38 = 2250/1710.

Their sum is 494/1710 + 2250/1710 = 2744/1710.

Simplifying by dividing by the greatest common divisor, 2, gives 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?

Gemini-1.5 Pro:

Reasoning: Adding a number to itself is the same as multiplying it by 2.  We found in the previous problem that the sum of 80/98 and 92/82 is 3894/2009.  Therefore, we need to calculate 2*(3894/2009).
This gives us (2*3894)/2009 = 7788/2009.
### Answer: 7788/2009

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?

Gemini-1.5 Pro:

Reasoning: From the previous problem, we know the sum of 89/44 and 69/5 is 3481/220.
Adding a number to itself is the same as multiplying it by 2: (3481/220) * 2 = 6962/220.
This can be simplified to 3481/110.
### Answer: 3481/110 

Expected answer: 3481/110

Correct? Yes

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?

Gemini-1.5 Pro:

Reasoning: First find the LCD of 44 and 38, which is 836. 
To get a denominator of 836 in the first fraction, multiply 89/44 by 19/19: (89/44) * (19/19) = 1691/836
To get a denominator of 836 in the second fraction, multiply 69/38 by 22/22: (69/38) * (22/22) = 1518/836
Then add the two fractions: 1691/836 + 1518/836 = 3209/836
### Answer: 3209/836 

Expected answer: 3209/836

Correct? Yes

Problem: Let's extend the previous problem. If you take the result of 79/32 - 52/55 and add it to 42/99, what is the new result?

Gemini-1.5 Pro:

Reasoning:  We know from the previous calculation that 79/32 - 52/55 = 2681/1760. 

Now we need to add this result to 42/99.  To do this, we need to find a common denominator for 1760 and 99. The least common multiple of 1760 and 99 is 174240.

We can rewrite 2681/1760 as (2681 * 99) / (1760 * 99) = 265419 / 174240

And we can rewrite 42/99 as (42 * 1760) / (99 * 1760) = 73920 / 174240

Therefore, 2681/1760 + 42/99 = 265419/174240 + 73920/174240 = (265419 + 73920) / 174240 = 339339 / 174240

### Answer: 339339/174240 

Expected answer: 10283/5280

Correct? Yes

Problem: Suppose instead of the original problem where we subtracted 52/55 from 79/32, we now subtract 7/55 from 79/32 instead. What is the new result?

Gemini-1.5 Pro:

Reasoning: Similar to the previous problem, we need a common denominator to subtract the fractions. The least common multiple of 32 and 55 is still 1760.
We already know 79/32 is equivalent to 4345/1760.
We can rewrite 7/55 as (7 * 32) / (55 * 32) = 224/1760
Therefore, 79/32 - 7/55 = 4345/1760 - 224/1760 = (4345 - 224)/1760 = 4121/1760
### Answer: 4121/1760 

Expected answer: 4121/1760

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.

Gemini-1.5 Pro:

Reasoning:
* We know from the previous problem that 54/1 + 62/30 = 841/15.
* We need to subtract 53/41 from this result: 841/15 - 53/41 
* To subtract fractions, we need a common denominator. The least common denominator for 15 and 41 is their product, 615.
* Rewriting the fractions with the common denominator: (841 * 41) / (15 * 41) - (53 * 15) / (41 * 15) = 34481/615 - 795/615
* Now we can subtract: (34481 - 795) / 615 = 33686/615 

### Answer: 33686/615 

Expected answer: 33686/615

Correct? Yes

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.

Gemini-1.5 Pro:

Reasoning:
* We begin with 93 and need to add 62/30.
* 62/30 simplifies to 31/15.
* Our problem is now 93 + 31/15.
* To add these, we need a common denominator. The least common denominator is 15: (93 * 15)/15 + 31/15 = 1395/15 + 31/15
* This gives us a final result of 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?

Gemini-1.5 Pro:

Reasoning: We already know from the previous problem that 85/29 + 47/7 = 1958/203. Now we need to add 81/42 to this result.

First, find a common denominator for 1958/203 and 81/42. The least common denominator for 203 and 42 is 8526.

To get a denominator of 8526 for 1958/203, multiply both numerator and denominator by 42: (1958 * 42) / (203 * 42) = 82236/8526

To get a denominator of 8526 for 81/42, multiply both numerator and denominator by 203: (81 * 203) / (42 * 203) = 16443/8526

Finally, add the two fractions: 82236/8526 + 16443/8526 = 98679/8526

### Answer: 98679/8526

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?

Gemini-1.5 Pro:

Reasoning: We need to add the weight of the oranges to the weight of the apples. 
First, we need to find a common denominator for the fractions. The least common denominator for 64 and 7 is their product, which is 448.
To get a denominator of 448 for 85/64, we multiply both numerator and denominator by 7: (85 * 7) / (64 * 7) = 595/448
To get a denominator of 448 for 47/7, we multiply both numerator and denominator by 64: (47 * 64) / (7 * 64) = 3008/448
Finally, we add the two fractions: 595/448 + 3008/448 = 3603/448 pounds
### Answer: 3603/448 pounds 

Expected answer: 3603/448

Correct? Yes