Problem: John has been learning to add and subtract fractions at school. He was given a problem during his homework that puzzled him. He had to take the sum of 48/56 and 95/23 and then subtract 34/26 from the result. What was the value that John found for this operation? Answer in simplest form.

Gemini-1.5 Pro:

Reasoning: 
* First, we need to find the least common denominator (LCD) of 56, 23 and 26 to perform these operations. The least common denominator is 1624.
* We can then rewrite the problem as (48*29)/(56*29) + (95*70)/(23*70) - (34*62)/(26*62).
* This becomes 1392/1624 + 6650/1624 - 2108/1624.
* Adding the first two fractions gives us 8042/1624
* Subtracting the third fraction from the sum gives us 5934/1624
* Finally, we simplify the fraction 5934/1624 to its simplest form which is 2967/812

### Answer: 2967/812

Expected answer: 7702/2093

Correct? No

Problem: First, add the fractions 88/9 and 28/65. Then subtract the fraction 18/37 from the result. What is the result expressed as a simple fraction?

Gemini-1.5 Pro:

Reasoning: To add or subtract fractions, they must have a common denominator. The least common denominator of 9, 65, and 37 is 21935. Therefore, we have:

88/9 + 28/65 - 18/37 = (88*2435)/(9*2435) + (28*337)/(65*337) - (18*595)/(37*595)
= 214280/21935 + 9436/21935 - 10710/21935
= (214280 + 9436 - 10710)/21935
= 213006/21935

The greatest common divisor of 213006 and 21935 is 29, so we can simplify the fraction by dividing the numerator and denominator by 29:

213006/21935 = (213006/29)/(21935/29) = 7345/755

### Answer: 7345/755

Expected answer: 210434/21645

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, simplify each fraction: 63/41 is already in its simplest form. 44/50 can be simplified to 22/25 by dividing the numerator and denominator by their greatest common factor, 2.
Next, find a common denominator for the two fractions: The least common multiple of 41 and 25 is 1025. Convert 63/41 to 15375/1025 and 22/25 to 902/1025.
Finally, add the two fractions: (15375/1025) + (902/1025) = 16277/1025.

### Answer: 16277/1025 

Expected answer: 2477/1025

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To solve this we need to find a common denominator for the fractions. The least common denominator for 41 and 77 is their product, 3157.
We can rewrite 71/41 as (71 * 77) / (41 * 77) = 5467 / 3157
We can rewrite 41/77 as (41 * 41) / (77 * 41) = 1681 / 3157
Adding the two fractions we get (5467 + 1681) / 3157 = 7148/ 3157.

### Answer: 7148/3157

Expected answer: 7148/3157

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
 First we need to find a common denominator for the two fractions. The least common multiple of 65 (5*13) and 35 (5*7) is 5*7*13 = 455.
 
 To get a denominator of 455 for 10/65, we multiply both numerator and denominator by 7: (10*7)/(65*7) = 70/455.
 
 To get a denominator of 455 for 56/35, we multiply both numerator and denominator by 13: (56*13)/(35*13) = 728/455.
 
 Now we can add the two fractions:  70/455 + 728/455 = 798/455
 
 
 ### Answer: 798/455

Expected answer: 114/65

Correct? Yes

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

Gemini-1.5 Pro:

To add fractions, they must have a common denominator.  We can find this by multiplying the denominators of the two fractions: 81 * 47.

Then we adjust the numerators accordingly:

(75/81) + (97/47) = (75 * 47)/(81 * 47) + (97 * 81)/(47 * 81) 

This gives us:

(3525)/(3807) + (7857)/(3807)

Now, we can add the numerators:

(3525 + 7857)/(3807)

### Answer: 11382/3807 

Expected answer: 3794/1269

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To subtract fractions, they must have a common denominator.  The least common denominator of 1 and 53 is 53. We can rewrite 88/1 as a fraction over 53: (88/1)*(53/53) = 4664/53.
Therefore the problem becomes 4664/53 - 38/53.
This simplifies to (4664-38)/53 = 4626/53.
### Answer: 4626/53

Expected answer: 4626/53

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, we must simplify the fractions, 80/94 can be simplified to 40/47, and 78/59 cannot be simplified.
Next, we must find a common denominator; the least common denominator is 2773 (47 * 59), so we get (2280 / 2773) + (3654 / 2773).
Then we perform the addition: (2280 + 3654) / 2773 = 5934/2773.
This fraction can be simplified to 2/1.
### Answer: 2 

Expected answer: 6026/2773

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the least common denominator: 1400. Then convert the fractions: (89/56)*(25/25)=2225/1400 and (48/50)*(28/28)=1344/1400. Finally, add the fractions: 2225/1400 + 1344/1400 = 3569/1400.
### Answer: 3569/1400 

Expected answer: 3569/1400

Correct? Yes

Problem: What is the result when you subtract 38/87 from the sum of 96/11 and 12/5? Please leave your answer as a fraction.

Gemini-1.5 Pro:

Reasoning: 
First, we need to find the sum of 96/11 and 12/5. To add fractions, they must have a common denominator. The least common denominator of 11 and 5 is 55. 
Therefore:
96/11 + 12/5 = (96/11)*(5/5) + (12/5)*(11/11) = 480/55 + 132/55 = 612/55

Now, we need to subtract 38/87 from the result. Again, we need a common denominator. The least common denominator of 55 and 87 is their product, 4785.
Therefore:
612/55 - 38/87 = (612/55)*(87/87) - (38/87)*(55/55) = 53244/4785 - 2090/4785 = 51154/4785

### Answer: 51154/4785 

Expected answer: 51154/4785

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 82 divided by 9 is 82/9, and 82 divided by 63 is 82/63.
Therefore, the required value is 82/9 - 82/63 = (82*7 - 82)/63 = (574 - 82)/63 = 492/63 = 164/21
### Answer: 164/21 

Expected answer: 164/21

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First find the sum of 80/91 and 26/24.  A common denominator for these fractions is their least common multiple, but since we're aiming for a simple answer, let's just multiply 91 by 24 to get a denominator of 2184.  Converting to this denominator we get (80*24)/(91*24) + (26*91)/(24*91) = 1920/2184 + 2366/2184 = 4286/2184. 
Next, convert 23/3 to a fraction with a denominator of 2184. That's (23*728)/(3*728) = 16744/2184.
Finally, 16744/2184 - 4286/2184 = 12458/2184. This simplifies to 6229/1092.
### Answer: 6229/1092 

Expected answer: 6229/1092

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, we need to simplify 24/60 to its lowest terms, which is 2/5. Then, we find a common denominator for 37/18 and 2/5, which is 90.
37/18 is equivalent to 185/90, and 2/5 is equivalent to 36/90.
Therefore, 185/90 + 36/90 = 221/90.
### Answer: 221/90

Expected answer: 221/90

Correct? Yes

Problem: Determine the sum of 33/41 and 95/62. Write your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator. The least common denominator for 41 and 62 is their product, 2542.  We can rewrite each fraction as:

* 33/41 = (33 * 62) / (41 * 62) = 2046/2542
* 95/62 = (95 * 41) / (62 * 41) = 3895/2542

Now, we can add the fractions: 2046/2542 + 3895/2542 = 5941/2542

### Answer: 5941/2542 

Expected answer: 5941/2542

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, we simplify (30/11) + (72/38). Both 30 and 11 are prime numbers so (30/11) remains as it is. We can simplify (72/38) to (36/19). Our expression now becomes (30/11) + (36/19). To add the two fractions, we need to find a common denominator. The least common denominator for 11 and 19 is their product, which is 209. We can rewrite (30/11) as (570/209) and (36/19) as (396/209). Our expression now becomes (570/209)+(396/209), which simplifies to 966/209.

Next, we need to add the result to (81/34). Again, we need a common denominator. The least common denominator for 209 and 34 is 7106. We can rewrite (966/209) as (32844/7106) and (81/34) as (17091/7106). Our expression now becomes (32844/7106) + (17091/7106), which we can add directly to get 49935/7106. 

Therefore, the simplified answer is 49935/7106.

### Answer: 49935/7106

Expected answer: 49773/7106

Correct? No

Problem: What is the result of adding (64 / 34) + (3 / 24) and then adding the result to (41 / 96)? Answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: 
* First, we need to find a common denominator for the first two fractions. The least common multiple of 34 and 24 is 408. 
* We convert the fractions: (64/34) = (768/408) and (3/24) = (51/408)
* Adding these fractions gives us: (768/408) + (51/408) = 819/408
* Now we simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 3: (819/3) / (408/3) = 273/136
* Next, we need to add this simplified fraction to 41/96. The least common multiple of 136 and 96 is 1632.
* We convert the fractions: (273/136) = (3159/1632) and (41/96) = (703/1632)
* Finally, we add these two fractions: (3159/1632) + (703/1632) = 3862/1632 = 1931/816
### Answer: 1931/816 

Expected answer: 3973/1632

Correct? No

Problem: Daniel has to solve a math problem for his homework that includes fractions. Initially, he has been asked to add 83/73 and 53/77. The result of this step he saved as 'w'. Then, he needs to add 80/76 to the result 'w'. How would he calculate the final answer in simplified fraction form?

Gemini-1.5 Pro:

Reasoning: 
First find the least common multiple of the denominators for the first addition: LCM(73,77)=5621.
Then adjust the fractions: (83*77)/(73*77)=6391/5621 and (53*73)/(77*73)=3869/5621.
We obtain w=(6391+3869)/5621=10260/5621.
Next, calculate w+80/76, for which LCM(5621,76)=426996.
Adjust the fractions: (10260*76)/(5621*76)=779760/426996 and (80*5621)/(76*5621)=449680/426996.
Finally, add the adjusted fractions: (779760+449680)/426996=1229440/426996.
Simplifying the fraction, we get 880/307.

### Answer: 880/307

Expected answer: 307360/106799

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the least common multiple of the denominators 20 and 66.
The least common multiple is 660.
To get 660 in the denominator of 27/20, multiply the numerator and denominator by 33 to get the fraction 891/660.
To get 660 in the denominator of 14/66, multiply the numerator and denominator by 10 to get the fraction 140/660.
Now add the numerators: 891/660 + 140/660 = 1031/660.
Simplify the fraction by dividing both numerator and denominator by 3: 343/220
### Answer: 343/220

Expected answer: 1031/660

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, simplify the divisions: (32/14) = 16/7 and (22/47) can't be simplified further.
Next, find a common denominator for the subtraction: 16/7 - 22/47 = (16*47)/(7*47) - (22*7)/(47*7) = 752/329 - 154/329
Finally, subtract the fractions: 752/329 - 154/329 = 598/329
### Answer: 598/329

Expected answer: 598/329

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To get the sum of the two fractions, we first need to find their least common denominator (LCD).
The LCD is the least common multiple (LCM) of 61 and 53, which is 3233.
Next, we express the fractions using the LCD:
74/61 = (74 x 53)/(61 x 53) = 3922/3233
41/53 = (41 x 61)/(53 x 61) = 2501/3233
Finally, we add the two fractions: 3922/3233 + 2501/3233 = (3922+2501)/3233 = 6423/3233
### Answer: 6423/3233

Expected answer: 6423/3233

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, we perform the divisions: 94 / 2 = 47 and 74 / 57 = 1.298 (approximately). 
Then, we subtract: 47 - 1.298 = 45.702 (approximately).
Finally, we add 56/97:  45.702 + 56/97 = 45.702 + 0.577 = 46.279 (approximately).

### Answer: 46.279 (approximately) 

Expected answer: 255877/5529

Correct? No

Problem: What is the sum of 14/89 and the sum of 24/34 and 44/87? Give your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: First find the sum of 24/34 and 44/87.  Both 24/34 and 44/87 can be simplified to 12/17, so their sum is 12/17+12/17 = 24/17
Then add 14/89 and 24/17. Since these fractions have different denominators, find a common denominator: 89*17 = 1513
Rewrite the fractions with the common denominator: 14/89 = 238/1513 and 24/17 = 2124/1513.
Finally, 238/1513 + 2124/1513 = 2362/1513
### Answer: 2362/1513 

Expected answer: 180194/131631

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, find the least common denominator of 30 and 60, which is 60.
Then, convert each fraction to have a denominator of 60:
- 73/30 is equivalent to (73 * 2) / (30 * 2) = 146/60
- 8/60 remains the same.
Finally, add the two fractions: 146/60 + 8/60 = 154/60

### Answer: 154/60 

Expected answer: 77/30

Correct? Yes

Problem: Suppose you have the following three fractions: 82/49, 45/60, and 99/59. If you add the first fraction (82/49) with the second one (45/60), call this result 'd'. Then, add 'd' to the third fraction (99/59). What would be the resulting sum? Please provide your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: Let's solve this step-by-step.

First, we need to find a common denominator for 82/49 and 45/60. The least common denominator is 2940.
- Converting 82/49 to a fraction with denominator 2940: (82 * 60) / (49 * 60) = 4920 / 2940
- Converting 45/60 to a fraction with denominator 2940: (45 * 49) / (60 * 49) = 2205 / 2940

Now we can add the two fractions: 4920/2940 + 2205/2940 = 7125/2940. This is 'd'.

Finally, we add 'd' (7125/2940) to 99/59. Again, we need a common denominator, which is 2940.
- Converting 99/59 to a fraction with denominator 2940: (99 * 50) / (59 * 50) = 4950 / 2940

Adding the two fractions: 7125/2940 + 4950/2940 = 12075/2940

Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (1470), we get 2415/588, which can be further simplified to 805/196.

### Answer: 805/196 

Expected answer: 47429/11564

Correct? No

Problem: Solve the following two steps: first, subtract 76/30 from 91/16 and second, add the answer to 18/44. Round the final answer to the nearest hundredth.

Gemini-1.5 Pro:

Reasoning: 
First, 91/16 - 76/30 = 229/120.
Then, 229/120 + 18/44 = 1321/660 = 1.99 rounded to the nearest hundredth. 
### Answer: 1.99 

Expected answer: 9407/2640

Correct? No

Problem: Calculate the result of ((8 / 91) + (49 / 5)) and subtract (32 / 76) from the result. Provide your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: 
First, we need to simplify the expressions inside the parentheses:
  * 8/91 cannot be simplified further.
  * 49/5 is already in its simplest form.

Next, we need to find a common denominator for 8/91 and 49/5 to add them. The least common multiple of 91 and 5 is 455:
 * (8/91) + (49/5) = (8 * 5)/(91 * 5) + (49 * 91)/(5 * 91) = 40/455 + 4459/455 = 4499/455

Now we need to subtract 32/76 from 4499/455. First, we simplify 32/76 to 8/19. Then, we find a common denominator for 4499/455 and 8/19. The least common multiple of 455 and 19 is 8645:

* (4499/455) - (8/19) = (4499 * 19)/(455 * 19) - (8 * 455)/(19 * 455) = 85481/8645 - 3640/8645 = 81841/8645

### Answer: 81841/8645 

Expected answer: 81841/8645

Correct? Yes

Problem: Calculate the value of ((75 / 45) + (5 / 49)) first. Then add this value with 3 / 58. Provide the answer as a simple fraction.

Gemini-1.5 Pro:

Reasoning:
First, simplify (75 / 45) to 5/3 and (5 / 49) remains as 5/49.
Next, add the simplified fractions 5/3 and 5/49 which is (5/3) + (5/49) = 260/147.
Finally, add 3/58 to the result: (260/147) + (3/58) = 15619/8526
### Answer: 15619/8526

Expected answer: 15521/8526

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, find the least common denominator of 15 and 95, which is 285.
Then, rewrite both fractions with the common denominator: (43/15)*(19/19) - (33/95)*(3/3) = 817/285 - 99/285.
Finally, subtract the numerators and simplify: (817-99)/285 = 718/285 = 2 138/285.
### Answer: 2 138/285

Expected answer: 718/285

Correct? No

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

Gemini-1.5 Pro:

Reasoning:  First, find the sum of (78/45) + (89/36). The least common multiple of 45 and 36 is 180. Therefore: 
 (78/45) + (89/36) = (78 * 4 / 180) + (89 * 5 / 180) = (312 / 180) + (445 / 180) = 757/180
 
 Next, add the fraction to itself:
 (757 / 180) + (757 / 180) = 1514 / 180
 
 Finally, simplify the resulting fraction by dividing both numerator and denominator by their greatest common divisor, which is 18:
 (1514 / 18) / (180 / 18) = 841/100

### Answer: 841/100

Expected answer: 757/90

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
* First, we perform the division: 93 divided by 34 is represented as 93/34.
* Next, we need to subtract 77/74 from 93/34. To subtract fractions, they need a common denominator. The least common denominator for 34 and 74 is 1258.
* We convert 93/34 to an equivalent fraction with a denominator of 1258: (93 * 37) / (34 * 37) = 3441/1258.
* We convert 77/74 to an equivalent fraction with a denominator of 1258: (77 * 17) / (74 * 17) = 1309/1258.
* Now, we can perform the subtraction: 3441/1258 - 1309/1258 = 2132/1258.
* Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2: 2132/2 = 1066 and 1258/2 = 629.

### Answer: 1066/629 

Expected answer: 1066/629

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator.  The least common denominator of 35 and 85 is 595.

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

Therefore, the sum is (1462 + 476)/595 = 1938/595

This fraction can be simplified by dividing numerator and denominator by their greatest common factor, 1938:

1938/595 = (1938 / 1938) / (595 / 1938) = 1/ (5/17) = 17/5

### Answer: 17/5

Expected answer: 114/35

Correct? No

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

Gemini-1.5 Pro:

Reasoning: We cannot add fractions unless they share a common denominator. The least common denominator for 53 and 94 is their product, which is 4982. 
Rewriting our fractions, we get (99/53)*(94/94) = 9306/4982 and (67/94)*(53/53) = 3551/4982.
The sum of these two fractions is 12857/4982. Since the numerator is larger than the denominator, we know this fraction is greater than 1 and can be simplified. 
12857/4982 = 2 + 2893/4982
This fraction can be simplified by dividing the numerator and denominator by 37 to get 78/134, which cannot be simplified further. 
Therefore, the final answer is 2 + 78/134. 
### Answer: 2 78/134

Expected answer: 12857/4982

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To subtract fractions, they must have a common denominator. The least common denominator of 27 and 33 is 297. We can rewrite 74/27 as 814/297 and 56/33 as 496/297.
814/297-496/297=318/297
318/297 can be simplified to 38/33
### Answer: 38/33

Expected answer: 310/297

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the sum of the first two fractions:  96/40 + 11/99 = (96*99)/(40*99) + (11*40)/(99*40) = 9504/3960 + 440/3960 = 9944/3960.
Then, subtract 91/65 from the result: 9944/3960 - 91/65 = 9944/3960 - (91*61)/(65*61) = 9944/3960 - 5551/3960 = 4393/3960.
Finally, simplify the fraction by dividing both numerator and denominator by their greatest common factor, 13:  (4393/13)/(3960/13) = 338/305.
### Answer: 338/305 

Expected answer: 10/9

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
1) 10 divided by 5 is 2. 35 divided by 27 is 1.296. Adding these together, we get h = 2 + 1.296 = 3.296
2) 47 divided by 99 is 0.475. Adding this to h, we get p = 3.296 + 0.475 = 3.771 
### Answer: p = 3.771

Expected answer: 1120/297

Correct? No

Problem: Consider the fraction 90/81. Add it to 2/66 and simplify your answer to the simplest form. What is the result?

Gemini-1.5 Pro:

Reasoning: First, simplify the fractions: 90/81 = 10/9 and 2/66 = 1/33.
Then, find a common denominator: 10/9 + 1/33 = 110/99 + 3/99 = 113/99.
The fraction cannot be simplified any further. 
### Answer: 113/99

Expected answer: 113/99

Correct? Yes

Problem: If Oliver has a piece of ribbon that is 56/41 yards long and he gets another piece of the same length, how long would both pieces of ribbon be together?

Gemini-1.5 Pro:

Reasoning: We need to add the length of the first ribbon to the length of the second ribbon to find the total length. Since they are the same length, the total length will be (56/41)+(56/41) = 112/41 yards long.
### Answer: 112/41 yards 

Expected answer: 112/41

Correct? Yes

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

Gemini-1.5 Pro:

To add fractions, they must have a common denominator. The least common denominator for 75 and 92 is their least common multiple.  However, finding the least common multiple of 75 and 92 will result in rather large numbers.  Since we only need to simplify the expression, let's simply multiply the denominators together and convert the fractions:

92/75 + 66/92 = (92*92)/(75*92) + (66*75)/(92*75) 
                   = 8464/6900 + 4950/6900
                   = 13414/6900

Now we simplify by finding the greatest common factor of 13414 and 6900, which is 2:

13414/6900 = (2*6707)/(2*3450)
                 = 6707/3450

### Answer: 6707/3450

Expected answer: 6707/3450

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator.  The least common denominator of 65 and 22 is their product because their greatest common factor is 1.
So, 32/65 is equivalent to (32*22)/(65*22) = 704/1430.
And, 73/22 is equivalent to (73*65)/(22*65) = 4745/1430
The sum of 704/1430 and 4745/1430 is (704+4745)/1430 = 5449/1430.
### Answer: 5449/1430

Expected answer: 5449/1430

Correct? Yes

Problem: What is the difference between 51/34 and 12/86? Express your answer in its simplest form.

Gemini-1.5 Pro:

Reasoning: First find the least common multiple (LCM) of 34 and 86, which is 17*2= <<17*2=34>>34.
To get a denominator of 34 for 51/34, multiply both the numerator and denominator by 1: 51/34 = (51*1)/(34*1) = 51/34
To get a denominator of 34 for 12/86, multiply both the numerator and denominator by 2/3: 12/86 = (12*(2/3))/(86*(2/3))= 8/34.
Therefore, the difference between 51/34 and 12/86 is 51/34-12/86 = 51/34-8/34 = 43/34.
### Answer: 43/34

Expected answer: 117/86

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, we convert the whole number to a fraction: 51 = 51/1.
Then we get a common denominator for 51/1 and 93/8 by multiplying 51/1 by 8/8: (51/1)*(8/8)=408/8.
Now we can add 51 and 93/8:  408/8 + 93/8 = 501/8.
Next, we simplify 58/44 by dividing numerator and denominator by their greatest common factor, 2: 58/44 = 29/22
Then we get a common denominator for 501/8 and 29/22 by multiplying the numerator and denominator of the first fraction by 11 and the numerator and denominator of the second fraction by 4: (501/8)*(11/11)=5511/88 and (29/22)*(4/4)=116/88
Now we can add 501/8 and 58/44:  5511/88 + 116/88 = 5627/88. 
The fraction 5627/88 cannot be simplified as it doesn’t have any common factors. 
### Answer: 5627/88

Expected answer: 5627/88

Correct? Yes

Problem: Calculate the result of the following fraction subtraction: 82/5 - 98/25. Write the answer in the simplest form.

Gemini-1.5 Pro:

Reasoning:  First, find a common denominator for the two fractions. The least common denominator for 5 and 25 is 25. To get 25 in the denominator of 82/5, we multiply both the numerator and denominator by 5: (82 * 5) / (5 * 5) = 410/25.

Now, the subtraction becomes: 410/25 - 98/25

Since we have the same denominator, we can directly subtract the numerators: (410 - 98) / 25 = 312/25

Therefore, the result of the fraction subtraction is 312/25. 

### Answer: 312/25 

Expected answer: 312/25

Correct? Yes

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

Gemini-1.5 Pro:

We begin by individually simplifying the fractions:
 
 $64/50 = (8*8)/(2*25) = (2*4*2*4)/(2*25) = (4*4*2)/25 = 32/25$
 
 $70/22 = (2*5*7)/(2*11) = (5*7)/11 = 35/11$
 
 Next, we find a common denominator for the two fractions. The least common denominator is $25\times11=275$. We can re-express our fractions as:
 
 $32/25 = (32\times11)/(25\times11) = 352/275$
 
 $35/11 = (35\times25)/(11\times25)=875/275$
 
 Now we can add the fractions:
 
 $(352/275) + (875/275) = 1227/275$
 
 ### Answer: 1227/275

Expected answer: 1227/275

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 24 divided by 6 is 24/6 = <<24/6=4>>4.
40 divided by 5 is 40/5 = <<40/5=8>>8.
Adding those two numbers we get s = 4 + 8 = <<4+8=12>>12.
Then we add s to itself to get b = 12 + 12 = <<12+12=24>>24.
### Answer: 24

Expected answer: 504/53

Correct? No

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

Gemini-1.5 Pro:

Reasoning:  
 
 First, simplify 80/90: 80/90 = 8/9.  
 
 Then simplify 52/11: 52/11 = 4 8/11.
 
 Now add the two simplified fractions: 8/9 + 4 8/11
 
 To add these fractions, we need a common denominator. The least common denominator for 9 and 11 is 99. 
 
 Convert 8/9 to a fraction with a denominator of 99: (8/9) * (11/11) = 88/99.
 
 Convert 4 8/11 to a fraction with a denominator of 99: (4 8/11) * (9/9) = 44/99 + 72/99 = 116/99.
 
 Now, add the fractions with the common denominator: 88/99 + 116/99 = 204/99.
 
 Simplify the fraction 204/99: 204/99 = 2 6/99 = 2 2/33.
 ### Answer: 2 2/33 
 
 
 
 
 
 

Expected answer: 556/99

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find the least common multiple of 18 and 74, which is 666. 
To get 666 in the denominator of 12/18, we need to multiply it by 37/37, so 12/18 is equivalent to (12/18)*(37/37)=444/666. 
To get 666 in the denominator of 91/74, we need to multiply by 9/9, so 91/74 is equivalent to (91/74)*(9/9)=819/666
The sum of 12/18 and 91/74 is equivalent to 444/666+819/666=1263/666
1263/666 can be simplified to 421/222.
### Answer: 421/222

Expected answer: 421/222

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add the fractions, we need a common denominator. The least common denominator for 2 and 25 is 50.

*  7/2 is equivalent to (7 * 25) / (2 * 25) = 175/50 
* 51/25 is equivalent to (51 * 2) / (25 * 2) = 102/50

Now we can add the fractions: 175/50 + 102/50 = 277/50

### Answer: 277/50 

Expected answer: 277/50

Correct? Yes

Problem: Calculate the following expression: ((68 / 69) + (93 / 7)) is a monomial. Add this to (3 / 46). Provide the resulting value as a simple fraction.

Gemini-1.5 Pro:

Reasoning: Let's first simplify (68/69) + (93/7).  Note that these fractions can't be simplified as they share no common factors in their numerator and denominator. We get a common denominator through multiplication: 
(68/69)*(7/7) + (93/7)*(69/69) = 476/483 + 6417/483 = 6893/483.
 
 Now let's add 3/46 to our previous result. Again, we need a common denominator:
(6893/483)*(46/46) + (3/46)*(483/483) = 317078/22218 + 1449/22218 = 318527/22218. This fraction can't be simplified further.
 
 While 318527/22218 is technically a monomial (a monomial can be a constant, a variable or a product of a constant and variables) the problem statement is technically incorrect. (68 / 69) + (93 / 7) is not a monomial, it is a binomial.  It is only after the addition operation is performed that it becomes a monomial. 

### Answer: 318527/22218 

Expected answer: 13849/966

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, simplify 60/4 to 15. Then, to add the fractions, find a common denominator: 
31/98 + 15 = 31/98 + 1470/98 = 1501/98
### Answer: 1501/98

Expected answer: 1501/98

Correct? Yes

Problem: Calculate ((3 / 2) + (24 / 36)) and state your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: First, simplify (24/36) by dividing both numerator and denominator by their greatest common factor, 12. This gives us (24/12)/(36/12) = 2/3.
Now we have (3/2) + (2/3). To add these fractions, we need a common denominator. The least common denominator for 2 and 3 is 6.
Convert (3/2) to a fraction with denominator 6: (3/2)*(3/3) = 9/6.
Convert (2/3) to a fraction with denominator 6: (2/3)*(2/2) = 4/6.
Now we can add the fractions: (9/6) + (4/6) = 13/6.

### Answer: 13/6 

Expected answer: 13/6

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First, we simplify the fractions: 92/54 = 46/27 and 90/13 = 30/13
Adding the first two fractions: 46/27 + 30/13 = (46*13)/(27*13) + (30*27)/(13*27) = 1398/351
Now, subtract the third fraction from the sum: 1398/351 - 46/41 = (1398*41)/(351*41) - (46*351)/(41*351) = (57318-16146)/14491 = 41172/14491
The simplified form of 41172/14491 is 1144/403
### Answer: 1144/403

Expected answer: 108002/14391

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Twice the value of 29/23 is the same as 29/23 * 2 = 58/23.
### Answer: 58/23

Expected answer: 58/23

Correct? Yes

Problem: What is the sum of 29/20 and 17/72? Answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator.  The least common denominator of 20 and 72 is 360.  Therefore, 29/20 is equivalent to 29*18 / 20*18 = 522/360, and 17/72 is equivalent to 17*5 / 72*5 = 85/360. So, 29/20 + 17/72 = 522/360 + 85/360 = 607/360.
### Answer: 607/360

Expected answer: 607/360

Correct? Yes

Problem: Calculate the value of this expression: ((36 / 27) + (80 / 10)) - (73 / 79). Simplify your answer as much as possible.

Gemini-1.5 Pro:

Reasoning: Let's break down the expression step by step:

* **36 / 27 = 4 / 3** (Both numerator and denominator are divisible by 9)
* **80 / 10 = 8** 
* **73/79** cannot be simplified further

Therefore, the expression becomes: 
(4/3) + 8 - (73/79)

To add and subtract fractions, we need a common denominator. 
The least common denominator for 3, 1 (implied denominator of 8) and 79 is 3 * 79 = 237

Let's convert each term to have the denominator 237:

* (4/3) = (4 * 79)/(3 * 79) = 316/237
* 8 = (8 * 237)/237 = 1896/237
* (73/79) = (73 * 3)/(79 * 3) = 219/237

Now, the expression becomes:
316/237 + 1896/237 - 219/237 = 1993/237

### Answer: 1993/237

Expected answer: 1993/237

Correct? Yes

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

Gemini-1.5 Pro:

First, we perform the divisions: 86 / 71 = 1.21 and 91 / 75 = 1.21.
Then, we add the results: 1.21 + 1.21 = 2.42
### Answer: 2.42

Expected answer: 12911/5325

Correct? No

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

Gemini-1.5 Pro:

Reasoning:  Let's calculate step-by-step:
1. Find a common denominator for the first two fractions: ((21/75)*(43/43)) + ((74/43)*(75/75)) = (903/3225) + (5550/3225)
2. Add the first two fractions: (903 + 5550)/3225 = 6453/3225
3. Find a common denominator for the resulting fraction and the third fraction: (6453/3225)*(62/62) + (10/62)*(3225/3225) = 399986/199950 + 32250/199950
4. Add the two fractions: (399986 + 32250)/199950 = 432236/199950
5. Simplify the fraction: 432236/199950 = 216118/99975 = 72039/33325

### Answer: 72039/33325

Expected answer: 72056/33325

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, we need to find a common denominator for the two fractions:
* The least common multiple of 66 and 61 is 4026.
* To get 4026 as the denominator of the first fraction, we multiply both its numerator and denominator by 61: (75/66) = (75*61)/(66*61) = 4575/4026
* To get 4026 as the denominator of the second fraction, we multiply both its numerator and denominator by 66: (81/61) = (81*66)/(61*66) = 5346/4026
* Now, we can add the two fractions: (4575/4026) + (5346/4026) = (4575+5346)/4026 = 9921/4026
This fraction can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 3: 9921/4026 = (9921/3) / (4026/3) = 3307/1342
### Answer: 3307/1342 

Expected answer: 3307/1342

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
First, we need to find the sum of 53/18 and 21/99: 
53/18 + 21/99 = (53*11)/(18*11) + (21*2)/(99*2) = 583/198 + 42/198 = 625/198
Then we double 625/198 to find the sum of the two identical fractions:
2*(625/198) = 1250/198

### Answer: 1250/198 

Expected answer: 625/99

Correct? Yes

Problem: First, calculate the result of 58/49 + 31/34. Then, add that result to the fraction 74/38. What is the final result as a simple fraction?

Gemini-1.5 Pro:

Reasoning: 
First find a common denominator for 58/49 and 31/34. The least common denominator is 1666. 
We get: (58 * 34)/(49 * 34) + (31 * 49)/(34 * 49) = 1972/1666 + 1519/1666 = 3491/1666
Now we need to add 74/38 to that result. Let's find the least common denominator for these two fractions, which is 3193:
(3491 * 19)/(1666 * 19) + (74 * 84)/(38 * 84) = 66329/31934 + 6216/31934
The result of this addition is (66329 + 6216)/31934 = 72545/31934
Finally, we can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 17: 
(72545/17) / (31934/17) = 4267/1879
### Answer: 4267/1879

Expected answer: 127971/31654

Correct? No

Problem: Calculate the sum of 100 divided by 76 and 29 divided by 14. Please provide your answer as a simplified fraction or decimal.

Gemini-1.5 Pro:

Reasoning: 100 divided by 76 is 1.31578947... . 29 divided by 14 is 2.07142857... . 1.31578947... plus 2.07142857... is 3.38721804... .
### Answer: 3.39 

Expected answer: 901/266

Correct? No

Problem: Given that Evan has read 51/18 of his novel, and Olivia has read (8/42) after reading the same amount of novel as Evan, how much of the novel has Olivia read in total? Answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: We can simplify (8/42) by dividing both numerator and denominator by their greatest common divisor, 2: (8/42) = (8/2)/(42/2) = 4/21
Since Olivia read 4/21 of the novel after reading the same amount as Evan (51/18), in total she has read (4/21) + (51/18).
Before adding these fractions together, we must find a common denominator. The least common multiple of 21 and 18 is 126.
We can rewrite 4/21 as 24/126: (4 * 6)/(21 * 6) = 24/126
We can rewrite 51/18 as 357/126: (51 * 7)/(18 * 7) = 357/126
Adding these two fractions, we get (24/126) + (357/126) = 381/126
Finally, we can simplify 381/126 by dividing both numerator and denominator by their greatest common divisor, 9: (381/9)/(126/9) = 42/14
We can further simplify 42/14 by dividing both numerator and denominator by their greatest common divisor, 14: (42/14)/(14/14) = 3/1 = 3

### Answer: 3/1 

Expected answer: 127/42

Correct? No

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

Gemini-1.5 Pro:

We perform the divisions first: 
* 48 divided by 13 is approximately 3.69
* 31 divided by 22 is approximately 1.41

Then we add the results: 3.69 + 1.41 = 5.1

### Answer: 5.1 

Expected answer: 1459/286

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
24/86 + 76/77 is about 0.28 + 0.99 = 1.27.
27/6 is equal to 4.5
4.5 - 1.27 = 3.23
### Answer: 3.23

Expected answer: 21415/6622

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator. The least common multiple of 39 and 14 is 546.
73/39 is equivalent to (73 * 14) / (39 * 14) = 1022 / 546.
49/14 is equivalent to (49 * 39) / (14 * 39) = 1911 / 546.
Adding the two fractions, we get (1022 + 1911) / 546 = 2933 / 546.
This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 13. This gives us (2933 / 13) / (546 / 13) = 225/42.
### Answer: 225/42

Expected answer: 419/78

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator. The least common denominator of 65 and 39 is 195. 
We can rewrite 75/65 as 225/195, since  (75 x 3)/(65 x 3) = 225/195.
We can rewrite 7/39 as 35/195, since (7 x 5)/(39 x 5) = 35/195.
Therefore, 75/65 + 7/39 = 225/195 + 35/195 = 260/195.
This can be simplified to 52/39, since (260/5)/(195/5) = 52/39.
### Answer: 52/39

Expected answer: 4/3

Correct? Yes

Problem: First, calculate 79/1 - 30/92. Then, subtract 61/63 from the result. What value do you get?

Gemini-1.5 Pro:

Reasoning:
Let's break down the calculation step by step.

**Step 1: Calculate 79/1 - 30/92**

*  79/1 simplifies to 79.
*  30/92 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 2. This gives us 15/46.
*  Therefore, 79/1 - 30/92 = 79 - 15/46 

To subtract fractions, we need a common denominator. The least common multiple of 1 and 46 is 46.

*  Rewriting 79 as a fraction with a denominator of 46, we get (79 * 46) / 46 = 3634/46
*  Now we can subtract: 3634/46 - 15/46 = 3619/46

**Step 2: Subtract 61/63 from the result**

*  We need to subtract 61/63 from 3619/46. 
*  Again, we need a common denominator. The least common multiple of 46 and 63 is 2898.
*  Rewriting both fractions with a denominator of 2898:
    * (3619/46) * (63/63) = 228157/2898
    * (61/63) * (46/46) = 2806/2898
*  Finally, subtract: 228157/2898 - 2806/2898 = 225351/2898

### Answer: 225351/2898 

Expected answer: 225191/2898

Correct? No

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

Gemini-1.5 Pro:

Reasoning: (58/26) + (58/26) is the same as 2 * (58 / 26).
58 / 26 can be simplified, as both numerator and denominator share a common divisor of 2. 
Dividing both by 2, we get 29/13. So, our problem becomes 2 * (29 / 13).
This results in 58/13. 

### Answer: 58/13 

Expected answer: 58/13

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
First find the total Alex has after buying more juice: 69/63 + 77/5 = 986/63 gallons
Then add the amount he received from Sally to find the final total: 986/63 + 47/71 =  7655/4473 gallons
### Answer: 7655/4473 gallons 

Expected answer: 127907/7455

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
 First, let's simplify (39/6): (39/6) = 13/2
 Next, let's find a common denominator for 2 and 49, which is 98.
 (13/2) = (637/98) 
 (67/49) = (134/98)
 Now, let's add the simplified fractions: (637/98) + (134/98) = 771/98
 Next, let's find a common denominator for 61 and 98, which is 5978.
 (100/61) = (9800/5978)
 (771/98) = (4626/5978)
 Finally, let's add those fractions: (9800/5978) + (4626/5978) = 14426/5978
 This simplifies to 7213/2989
 
### Answer: 7213/2989

Expected answer: 56831/5978

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 83/69 simplified is 1 and 14/69
85/1 is equivalent to 85
85 + 1 and 14/69 = 86 and 14/69
### Answer: 86 and 14/69

Expected answer: 5948/69

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator. The least common multiple of 13 and 86 is 1118.

To get a denominator of 1118 for 92/13, we multiply the numerator and denominator by 86: (92/13) * (86/86) = 7912/1118.

To get a denominator of 1118 for 43/86, we multiply the numerator and denominator by 13: (43/86) * (13/13) = 559/1118.

Now we can add the two fractions: 7912/1118 + 559/1118 = 8471/1118

### Answer: 8471/1118 

Expected answer: 197/26

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First find a common denominator for the two fractions: the least common multiple of 32 and 98 is 1568.
Then convert each fraction to an equivalent fraction that has 1568 as the denominator. Since 1568 / 32 = 49, the fraction 67/32 is equivalent to (67 * 49) / (32 * 49) = 3283 / 1568.  Since 1568 / 98 = 16, the fraction 10/98 is equivalent to (10 * 16) / (98 * 16) = 160/1568.
The sum of 67/32 and 10/98 is therefore (3283 + 160)/1568 = 3443/1568.
### Answer: 3443/1568

Expected answer: 3443/1568

Correct? Yes

Problem: What is the sum of 59/52 and 70/32? Please provide your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: 
* First, find the least common multiple (LCM) of the denominators, 52 and 32. The LCM of 52 and 32 is 416.
* To get a denominator of 416 in the first fraction, we multiply by 8/8: (59/52)*(8/8) = 472/416.
* To get a denominator of 416 in the second fraction, we multiply by 13/13: (70/32)*(13/13) = 910/416.
* Now we can add the fractions: 472/416 + 910/416 = 1382/416
* This simplifies to 691/208. 

### Answer: 691/208

Expected answer: 691/208

Correct? Yes

Problem: Let's first perform this operation: 48 divided by 5 subtracted from 11 divided by 65. Then, add the result to 28 divided by 2. What is the answer?

Gemini-1.5 Pro:

Let's break this problem down step-by-step:

1. **48 divided by 5:** 48 / 5 = 9.6

2. **11 divided by 65:** 11 / 65 = 0.169 (rounded to three decimal places)

3. **Subtract the result of step 2 from step 1:** 9.6 - 0.169 = 9.431

4. **28 divided by 2:** 28 / 2 = 14

5. **Add the result of step 3 to step 4:**  9.431 + 14 = 23.431

### Answer: 23.431 

Expected answer: 1523/65

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator. The least common denominator for 52 and 82 is 2132. We can rewrite 20/52 as 820/2132 and 75/82 as 1950/2132. Therefore 20/52 + 75/82 = 820/2132 + 1950/2132 = 2770/2132. This fraction can be simplified to 1385/1066.
### Answer: 1385/1066

Expected answer: 1385/1066

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
* First, we simplify 92/84 by dividing both numerator and denominator by their greatest common factor, 4:  92/84 = (92/4)/(84/4) = 23/21
* Next, we need to find a common denominator for 31/5 and 23/21. The least common multiple of 5 and 21 is 105. 
* We convert both fractions to have this denominator: (31/5)*(21/21) = 651/105 and (23/21)*(5/5) = 115/105
* Now we can subtract: 651/105 - 115/105 = 536/105

### Answer: 536/105 

Expected answer: 536/105

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
* First, we need to find the sum of the two fractions: 81/90 + 94/49. To add fractions, they need a common denominator. The least common denominator for 90 and 49 is 4410. We get: (81*49)/(90*49) + (94*90)/(49*90) = 3969/4410 + 8460/4410 = 12429/4410. 
* Next, we simplify the fraction 12429/4410 by dividing both numerator and denominator by their greatest common divisor, which is 49. This gives us: 253/90. 
* Finally, we double the result: 2 * (253/90) = 253/45.

### Answer: 253/45 

Expected answer: 1381/245

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First find a common denominator for the two fractions. The least common denominator is 2736. 
To get a denominator of 2736 for 69/21, we multiply both the numerator and denominator by 132: (69 * 132) / (21 * 132) = 9108/2772
To get a denominator of 2736 for 10/92, we multiply both the numerator and denominator by 29: (10 * 29) / (92 * 29) = 290/2736
Now, we can subtract the two fractions: 9108/2736 - 290/2736 = 8818/2736
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, 62: (8818 / 62) / (2736 / 62) = 142/44
### Answer: 142/44 

Expected answer: 1023/322

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, we need to simplify the fractions:
* 26/87 simplifies to 2/3 (because both numerator and denominator can be divided by 13).
* 92/88 simplifies to 23/22 (because both numerator and denominator can be divided by 4).
Now, let's add the simplified fractions (2/3) + (23/22):
* To add fractions, they need a common denominator, which is 66 in this case.
* (2/3) is equivalent to (44/66) and (23/22) is equivalent to (69/66).
* Therefore (44/66) + (69/66) = 113/66
Finally, we add the result to 26/57:
* (113/66) + (26/57) requires a common denominator, which is 1342
* (113/66) is equivalent to (2299/1342) and (26/57) is equivalent to (602/1342)
* Therefore (2299/1342) + (602/1342) = 2901/1342
### Answer: 2901/1342 

Expected answer: 21825/12122

Correct? No

Problem: What is the result if you add 78/66, 28/6, and 90/34 together? Please provide your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: First, we need to find a common denominator for all three fractions. The least common denominator for 66, 6, and 34 is 6804. 
Then, we convert each fraction to have this denominator:
- 78/66 = 858/6804
- 28/6 = 3172/6804
- 90/34 = 18090/6804
Finally, we add the numerators: 858 + 3172 + 18090 = 22120

Therefore, the sum is 22120/6804, which simplifies to 553/171.

### Answer: 553/171

Expected answer: 4766/561

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To subtract fractions, they need a common denominator. The least common denominator for 7 and 23 is their product, 161. 
Let's convert both fractions to have this denominator:
 (12/7) - (9/23) = (12 * 23)/(7 * 23) - (9 * 7)/(23 * 7) = 276/161 - 63/161
Now, we can subtract the numerators: 
(276 - 63)/161 = 213/161
This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, which is 7:
(213/7)/(161/7) = 39/23
### Answer: 39/23 

Expected answer: 213/161

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have a common denominator. The least common denominator of 18 and 61 is their product, 1188. Therefore, we rewrite the fractions as follows:

95/18 + 51/61 = (95 * 61)/(18 * 61) + (51 * 18)/(61 * 18) = 5795/1188 + 918/1188

Now that the fractions have the same denominator, we can add the numerators:

(5795 + 918)/1188 = 6713/1188

Therefore, the sum of 95/18 and 51/61 is 6713/1188.
### Answer: 6713/1188

Expected answer: 6713/1098

Correct? No

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

Gemini-1.5 Pro:

Reasoning: To subtract fractions, they must have a common denominator. The least common denominator for 46 and 84 is their least common multiple. However, simplifying the first fraction by dividing the numerator and denominator by 46 gives us (93/46) = (3/2). The least common multiple of 2 and 84 is 84. Therefore, we need to rewrite (3/2) with a denominator of 84, which we can do by multiplying the numerator and denominator by 42: (3/2) * (42/42) = (126/84). Finally, we can subtract the fractions: (126/84) - (51/84) = 75/84. Simplifying this fraction by dividing the numerator and denominator by 3 gives us our final answer: 25/28
### Answer: 25/28

Expected answer: 911/644

Correct? No

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

Gemini-1.5 Pro:

Reasoning: First, we need to simplify both fractions: 12/70 (divide both numerator and denominator by 2) = 6/35 and 84/9 (divide both numerator and denominator by 3) = 28/3.
To add fractions, they must have the same denominator. The least common multiple of 35 and 3 is 105.
Thus, we have 6/35 (multiply both numerator and denominator by 3) = 18/105 and 28/3 (multiply both numerator and denominator by 35) = 980/105.
Finally, 18/105 + 980/105 = 998/105.
### Answer: 998/105

Expected answer: 998/105

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 
Let's first simplify the fractions: 40/92 simplifies to 10/23 (by dividing both numerator and denominator by 4), and 32/3 remains the same.

Now, let's subtract 10/23 from 32/3. To do this, we need a common denominator:
* The least common multiple of 3 and 23 is 69.
* Converting 32/3 to a fraction with a denominator of 69:  (32 * 23) / (3 * 23) = 736/69
* Converting 10/23 to a fraction with a denominator of 69: (10 * 3) / (23 * 3) = 30/69
* Subtracting the two fractions: 736/69 - 30/69 = 706/69

Finally, let's double the result: (706/69) * 2 = 1412/69

### Answer: 1412/69 

Expected answer: 1412/69

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:  79/24 + 79/24 is the same as (79 + 79)/24 = 158/24. This simplifies to 79/12.
### Answer: 79/12 

Expected answer: 79/12

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, find the simplest form of 12/22 by dividing the numerator and denominator by 2: 12/2 = 6,  22/2 = 11, so 12/22 = 6/11
To add fractions, they must have the same denominator. The least common denominator of 76 and 11 is 836.
To get a denominator of 836 in the first fraction, multiply the numerator and denominator by 11: 91/76 * 11/11 = 1001/836
To get a denominator of 836 in the second fraction, multiply the numerator and denominator by 76: 6/11 * 76/76 = 456/836
Now, add the two fractions: 1001/836 + 456/836 = 1457/836
The fraction can be simplified by dividing the numerator and denominator by 11: 1457/11 = 132  836/11 = 76
So, 1457/836 = 132/76
The fraction can be further simplified by dividing the numerator and denominator by 4: 132/4 = 33, 76/4 = 19, so 132/76 = 33/19
### Answer: 33/19 

Expected answer: 1457/836

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
To add fractions, they must have a common denominator. The least common denominator of 93, 47, and 4 is their least common multiple. However, since these numbers share no common factors, their least common multiple is simply their product: 93 * 47 * 4 = 17532.

* **Step 1: Express each fraction with a denominator of 17532.**
   * 88/93 = (88 * 47 * 4) / (93 * 47 * 4) = 16576/17532
   * 6/47 = (6 * 93 * 4) / (47 * 93 * 4) = 2232/17532
   * 92/4 = (92 * 93 * 47) / (4 * 93 * 47) = 40292/17532

* **Step 2: Add the fractions with the common denominator.**
   * (16576/17532) + (2232/17532) + (40292/17532) = 59100/17532

* **Step 3: Simplify the result by finding the greatest common factor (GCF) of the numerator and denominator.**
   * The GCF of 59100 and 17532 is 396. Dividing both numerator and denominator by 396 gives us: (59100/396)/(17532/396) = 149/44

### Answer: 149/44 

Expected answer: 105227/4371

Correct? No

Problem: Calculate the sum of 95/83 and the result of 52/21 + 75/67. Write your answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: First find the sum of 52/21 + 75/67, 52/21 + 75/67 = (52*67)/(21*67) + (75*21)/(67*21) = 5089/1407.
Then add the result to 95/83: 95/83 + 5089/1407 = (95*17)/(83*17) + 5089/1407 = 6704/1407.
### Answer: 6704/1407

Expected answer: 553562/116781

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
First, we need to find a common denominator for the fractions: The least common multiple of 27 and 48 is 432.
We can rewrite (73/27) as (73 * 16) / (27 * 16) = 1168/432
We can rewrite (23/48) as (23 * 9) / (48 * 9) = 207/432
Now the expression becomes: (1168/432) - (207/432)
Subtracting the numerators, we get: (1168 - 207) / 432 = 961/432
### Answer: 961/432

Expected answer: 961/432

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning:
Parenthesis/brackets are the highest priority, so let's solve those first.
78/2 = 39
70/23 = 3.04 (Rounded to the nearest hundredth)
Our expression is now 39 - 3.04
39 - 3.04 = 35.96

### Answer: 35.96 

Expected answer: 827/23

Correct? No

Problem: What is the result when you add 34/1 to 53/4? Express your answer as a mixed number.

Gemini-1.5 Pro:

Reasoning: First, we need to convert both fractions to a common denominator:
- 34/1 is equivalent to (34 * 4) / (1 * 4) = 136/4. 
- 53/4 remains the same.

Now, we can add the two fractions: 136/4 + 53/4 = 189/4

Finally, let's convert the improper fraction 189/4 to a mixed number:
- 189 divided by 4 equals 47 with a remainder of 1.

### Answer: 47 1/4 

Expected answer: 189/4

Correct? Yes

Problem: What is the sum of 3/36 and 97/96? Answer as a simplified fraction.

Gemini-1.5 Pro:

Reasoning: To get the sum of the two fractions, we first need to find their least common denominator. The least common denominator of 36 and 96 is 288.

We can then rewrite the fractions as:
* 3/36 = 24/288
* 97/96 = 291/288
 
Then we can add the fractions: 24/288 + 291/288 = 315/288.
Finally, we can simplify 315/288 to 105/96, and then to 35/32. 
### Answer: 35/32 

Expected answer: 35/32

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 95 and 74 is 7030.
 We can rewrite (92/95) as (92 * 74) / (95 * 74) = 6808 / 7030.
 We can rewrite (4/74) as (4 * 95) / (74 * 95) = 380 / 7030.
 Now, we can add the two fractions: (6808 / 7030) + (380 / 7030) = 7188 / 7030
 This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 2: 7188/2 / 7030/2 = 3594 / 3515.
### Answer: 3594/3515

Expected answer: 3594/3515

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 'd' is equal to 88/72 plus the value of 'v', which is 69/47.
So, 'd' = 88/72 + 69/47 = 1195/1416
### Answer: 1195/1416 

Expected answer: 1138/423

Correct? No

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

Gemini-1.5 Pro:

Reasoning:
First, we need to find a common denominator for 26 and 72.  The least common multiple of 26 and 72 is 936.
We can rewrite 41/26 as (41 * 36) / (26 * 36) = 1476/936
We can rewrite 41/72 as (41 * 13) / (72 * 13) = 533/936
The wholesaler has 1476/936 - 533/936 = 943/936 barrels of olive oil left.
### Answer: 943/936

Expected answer: 943/936

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: 85/75 = 1.13333, and 88/56 = 1.57143.
Adding the two decimals gives 1.13333+1.57143 = 2.70476.
### Answer: 2.70476

Expected answer: 284/105

Correct? No

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

Gemini-1.5 Pro:

Reasoning: 
* First, we need to convert the second fraction to a mixed number: 49/2 = 24 1/2.
* Then, we add the whole numbers: 24 + 12 = 36.
* Finally, we combine the whole and fractional parts: 36 + 12/33 + 1/2 = 36 + 24/66 + 33/66 = 36 57/66.

### Answer: 36 57/66 

Expected answer: 547/22

Correct? No

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

Gemini-1.5 Pro:

Reasoning: Adding a fraction to itself is the same as multiplying that fraction by 2.  Therefore, 78/65 + 78/65 = (78/65)*2 = 156/65
### Answer: 156/65 

Expected answer: 12/5

Correct? Yes

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

Gemini-1.5 Pro:

Reasoning: To add fractions, they must have the same denominator. The least common multiple of 7 and 90 is 630.  We can rewrite 16/7 as 1440/630 and 11/90 as 77/630.
1440/630 + 77/630 = 1517/630
### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes