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 Flash:

Here's how to solve the problem step-by-step:

**1. Find the Least Common Multiple (LCM) of the denominators:**

* The denominators are 56, 23, and 26.
* The LCM of these numbers is 8008.

**2. Convert each fraction to an equivalent fraction with the LCM as the denominator:**

* 48/56 = (48 * 143) / (56 * 143) = 6864/8008
* 95/23 = (95 * 348) / (23 * 348) = 33060/8008
* 34/26 = (34 * 308) / (26 * 308) = 10472/8008

**3. Add the first two fractions:**

* 6864/8008 + 33060/8008 = 39924/8008

**4. Subtract the third fraction:**

* 39924/8008 - 10472/8008 = 29452/8008

**5. Simplify the result:**

* Both the numerator and denominator can be divided by 8.
* 29452/8008 = (29452/8) / (8008/8) = 3681/1001

**Therefore, the value John found for the operation is 3681/1001.**
### Answer: 3681/1001 

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 Flash:

Here's how to solve the problem step-by-step:

1. **Find a common denominator for 88/9 and 28/65:**
   - The least common multiple of 9 and 65 is 585.
   - Convert 88/9 to an equivalent fraction with a denominator of 585: (88/9) * (65/65) = 5720/585
   - Convert 28/65 to an equivalent fraction with a denominator of 585: (28/65) * (9/9) = 252/585

2. **Add the fractions:**
   - (5720/585) + (252/585) = 5972/585

3. **Find a common denominator for 5972/585 and 18/37:**
   - The least common multiple of 585 and 37 is 21645.
   - Convert 5972/585 to an equivalent fraction with a denominator of 21645: (5972/585) * (37/37) = 221044/21645
   - Convert 18/37 to an equivalent fraction with a denominator of 21645: (18/37) * (585/585) = 10530/21645

4. **Subtract the fractions:**
   - (221044/21645) - (10530/21645) = 210514/21645

5. **Simplify the fraction:**
   - Both the numerator and denominator are divisible by 2, so we can simplify to 105257/10823.

### Answer: 105257/10823 

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 Flash:

Here's how to simplify the expression:

1. **Calculate the fractions:**
   * 63 / 41 = 1.5366 (approximately)
   * 44 / 50 = 0.88

2. **Add the results:**
   * 1.5366 + 0.88 = 2.4166 (approximately)

3. **Convert to a fraction:** 
   * We can approximate 2.4166 as 24166/10000

4. **Simplify the fraction:**
   * Both the numerator and denominator are divisible by 2: 24166/10000 = 12083/5000

**Therefore, the simplified result of (63 / 41) + (44 / 50) is 12083/5000.**

### Answer: 12083/5000 

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 Flash:

Reasoning: To add fractions, they need to have the same denominator.  The least common multiple of 41 and 77 is 3167. We can rewrite the fractions as:

* 71/41 = (71 * 77) / (41 * 77) = 5487 / 3167
* 41/77 = (41 * 41) / (77 * 41) = 1681 / 3167

Now we can add the fractions:

* 5487/3167 + 1681/3167 = (5487 + 1681)/3167 = 7168/3167

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

* 7168/3167 = (7168 / 1) / (3167 / 1) = 7168/3167

### Answer: 7168/3167 

Expected answer: 7148/3157

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator.  The least common multiple of 65 and 35 is 910.

* **10/65:**  Multiply numerator and denominator by 14: (10 * 14) / (65 * 14) = 140/910
* **56/35:** Multiply numerator and denominator by 26: (56 * 26) / (35 * 26) = 1456/910

Now we can add the fractions:
140/910 + 1456/910 = (140 + 1456)/910 = 1596/910

We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 2: 
(1596 / 2) / (910 / 2) = 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 Flash:

To add fractions, they need to have the same denominator.  We find the least common multiple (LCM) of 81 and 47, which is 3807.

*  We multiply 75/81 by 47/47: (75/81) * (47/47) = 3525/3807
*  We multiply 97/47 by 81/81: (97/47) * (81/81) = 7857/3807

Now we can add the fractions: 3525/3807 + 7857/3807 = (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 Flash:

Reasoning:
1.  First, we need to find a common denominator for the fractions. The least common multiple of 1 and 53 is 53. 
2.  We can rewrite 88/1 as (88 * 53) / (1 * 53) = 4664/53. 
3.  Now we have: (4664/53) - (38/53) 
4.  Since they have the same denominator, we can simply subtract the numerators: (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 Flash:

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

1. **Parentheses/Brackets:**  We have two sets of parentheses, so we need to evaluate the fractions inside them first.
   * 80 / 94 = 0.851 (approximately)
   * 78 / 59 = 1.322 (approximately)

2. **Addition:** Now we add the results of the two fractions.
   * 0.851 + 1.322 = 2.173 (approximately)

Therefore, the simplified form of the expression is approximately **2.173**. 

### Answer: 2.173 (approximately) 

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 Flash:

Reasoning: To add fractions, they need to have the same denominator.  The least common multiple of 56 and 50 is 1400. 
* 89/56 = (89*25)/(56*25) = 2225/1400
* 48/50 = (48*28)/(50*28) = 1344/1400

Now we can add: 2225/1400 + 1344/1400 = (2225+1344)/1400 = 3569/1400

We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 11.

3569/1400 = (3569/11) / (1400/11) = 324.45/127.27

Since 324.45/127.27 is not a simplified fraction, we will leave the answer as it is.

### 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 Flash:

First, we need to find the sum of 96/11 and 12/5. To do this, we need a common denominator:

* The least common multiple of 11 and 5 is 55.
* 96/11 * (5/5) = 480/55
* 12/5 * (11/11) = 132/55

Now we add the two fractions:

* 480/55 + 132/55 = 612/55

Finally, we subtract 38/87 from the sum:

* To subtract fractions, we need a common denominator. The least common multiple of 55 and 87 is 4785.
* 612/55 * (87/87) = 53244/4785
* 38/87 * (55/55) = 2090/4785

Now we can subtract:

* 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 Flash:

Here's how to solve this problem:

1. **Calculate the first division:** 82 divided by 9 is 82/9.

2. **Calculate the second division:** 82 divided by 63 is 82/63.

3. **Subtract the second division from the first:** (82/9) - (82/63)

4. **Find a common denominator:** The least common denominator of 9 and 63 is 63.  To get a denominator of 63 for the first fraction, multiply both numerator and denominator by 7: (82/9) * (7/7) = 574/63.

5. **Subtract the fractions:** (574/63) - (82/63) = (574-82)/63 = 492/63.

6. **Simplify the fraction:** Both 492 and 63 are divisible by 9.  (492/9) / (63/9) = 54/7

### Answer: 54/7 

Expected answer: 164/21

Correct? No

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

Gemini-1.5 Flash:

First, we need to find a common denominator for 80/91 and 26/24. The least common multiple of 91 and 24 is 2184.

* 80/91 * (24/24) = 1920/2184
* 26/24 * (91/91) = 2366/2184

Now we can add these fractions: 1920/2184 + 2366/2184 = 4286/2184

Next, we simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 2: 4286/2184 = 2143/1092

Now we can subtract this simplified fraction from 23/3: 23/3 - 2143/1092

To subtract these fractions, we need a common denominator:

* 23/3 * (364/364) = 8382/1092
* 2143/1092 stays the same

Now we can subtract: 8382/1092 - 2143/1092 = 6239/1092

Finally, we simplify this fraction: 6239/1092 = 2079/364

### Answer: 2079/364 

Expected answer: 6229/1092

Correct? No

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

Gemini-1.5 Flash:

Reasoning:
1. Find a common denominator for 18 and 60. The least common multiple of 18 and 60 is 180.
2. Convert 37/18 to an equivalent fraction with a denominator of 180: (37/18) * (10/10) = 370/180.
3. Convert 24/60 to an equivalent fraction with a denominator of 180: (24/60) * (3/3) = 72/180.
4. Add the fractions: 370/180 + 72/180 = 442/180.
5. Simplify the fraction to its lowest terms by dividing both numerator and denominator by their greatest common factor, which is 2: (442/180) / (2/2) = 221/90.

### Answer: 221/90 

Expected answer: 221/90

Correct? Yes

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

Gemini-1.5 Flash:

To add fractions, they need to have a common denominator.  The least common multiple of 41 and 62 is 2542.

* Convert 33/41 to have a denominator of 2542: (33/41) * (62/62) = 2046/2542
* Convert 95/62 to have a denominator of 2542: (95/62) * (41/41) = 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 Flash:

Here's how to solve the problem:

**1. Simplify the fractions inside the parentheses:**

* (30 / 11)  is already in its simplest form.
* (72 / 38) can be simplified by dividing both numerator and denominator by their greatest common factor, 2: (72/38) = (36/19)

**2. Add the simplified fractions inside the parentheses:**

* To add fractions, they need a common denominator. The least common denominator of 11 and 19 is 209.
* (30/11) + (36/19) = (30 * 19 / 11 * 19) + (36 * 11 / 19 * 11) = (570 / 209) + (396 / 209) = (966 / 209)

**3. Add the result to (81/34):**

* Find a common denominator for 209 and 34. The least common denominator is 7086.
* (966 / 209) + (81 / 34) = (966 * 34 / 209 * 34) + (81 * 209 / 34 * 209) = (32844 / 7086) + (16929 / 7086) = (49773 / 7086)

**4. Simplify the final fraction:**

* The greatest common factor of 49773 and 7086 is 1. Therefore, the fraction is already in its simplest form.

### Answer: 49773/7086 

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 Flash:

Here's how to solve the problem step-by-step:

1. **Simplify the fractions:**
   - (64 / 34) can be simplified to (32 / 17) by dividing both numerator and denominator by 2.
   - (3 / 24) can be simplified to (1 / 8) by dividing both numerator and denominator by 3.

2. **Find a common denominator for (32 / 17) and (1 / 8):**
   - The least common multiple of 17 and 8 is 136.
   - Convert (32 / 17) to (256 / 136) by multiplying both numerator and denominator by 8.
   - Convert (1 / 8) to (17 / 136) by multiplying both numerator and denominator by 17.

3. **Add the fractions:**
   - (256 / 136) + (17 / 136) = (273 / 136)

4. **Find a common denominator for (273 / 136) and (41 / 96):**
   - The least common multiple of 136 and 96 is 1088.
   - Convert (273 / 136) to (849 / 1088) by multiplying both numerator and denominator by 8.
   - Convert (41 / 96) to (461 / 1088) by multiplying both numerator and denominator by 11.

5. **Add the fractions:**
   - (849 / 1088) + (461 / 1088) = (1310 / 1088)

6. **Simplify the fraction:**
   - Both 1310 and 1088 are divisible by 2, so we get (655 / 544).

### Answer: 655/544 

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 Flash:

Here's how Daniel can calculate the final answer in simplified fraction form:

**Step 1: Add the first two fractions**

* Find a common denominator for 73 and 77. The least common multiple is 5621.
* Convert the fractions:
    * 83/73 * (77/77) = 6391/5621
    * 53/77 * (73/73) = 3869/5621
* Add the fractions: 6391/5621 + 3869/5621 = 10260/5621 
* This is the value of 'w'.

**Step 2: Add 80/76 to 'w'**

* Find a common denominator for 5621 and 76. The least common multiple is 426876.
* Convert the fractions:
    * 10260/5621 * (76/76) = 779760/426876
    * 80/76 * (5621/5621) = 449680/426876
* Add the fractions: 779760/426876 + 449680/426876 = 1229440/426876

**Step 3: Simplify the result**

* Find the greatest common factor (GCD) of 1229440 and 426876.  The GCD is 15368.
* Divide both numerator and denominator by 15368:
    * (1229440 / 15368) / (426876 / 15368) = 80/28

**Step 4: Further simplification**

* The fraction 80/28 can be further simplified by dividing both numerator and denominator by 4:
    * (80 / 4) / (28 / 4) = 20/7

### Answer: 20/7 

Expected answer: 307360/106799

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator.  We find the least common multiple (LCM) of 20 and 66:

* Factors of 20: 1, 2, 4, 5, 10, 20
* Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

The LCM of 20 and 66 is 660.

Now, we rewrite each fraction with a denominator of 660:

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

Finally, we add the fractions:

* 891/660 + 140/660 = (891 + 140)/660 = 1031/660

This fraction can be simplified by finding the greatest common factor (GCF) of 1031 and 660.  The GCF is 1, so the fraction is already in its simplest form.

### Answer: 1031/660 

Expected answer: 1031/660

Correct? Yes

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

Gemini-1.5 Flash:

Reasoning: 
First, we need to simplify the fractions:
32/14 = 16/7 
22/47 cannot be simplified further

Now, we need to find a common denominator for the two fractions. The least common multiple of 7 and 47 is 329.

(16/7) * (47/47) = 752/329
(22/47) * (7/7) = 154/329

Finally, we subtract the fractions:
(752/329) - (154/329) = (752-154)/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 Flash:

To add fractions, they must have a common denominator.  We find the least common multiple (LCM) of 61 and 53.  Since 61 and 53 are both prime numbers, their LCM is their product: 61 * 53 = 3233.

Now we rewrite each fraction with a denominator of 3233:

* (74/61) * (53/53) = 3922/3233
* (41/53) * (61/61) = 2501/3233

Finally, we add the numerators:

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 Flash:

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

1. **Calculate 94 / 2:** 94 divided by 2 equals 47.

2. **Calculate 74 / 57:** This fraction cannot be simplified further.

3. **Subtract the results:** 47 - (74/57) = (2679 - 74) / 57 = 2605 / 57

4. **Add 56/97:** (2605/57) + (56/97) = (252465 + 3092) / 5529 = 255557 / 5529

### Answer: 255557/5529 

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 Flash:

First, we need to find the sum of 24/34 and 44/87. To do this, we need a common denominator. The least common multiple of 34 and 87 is 2958.

* 24/34 * 87/87 = 2088/2958
* 44/87 * 34/34 = 1496/2958

Now we can add the two fractions: 2088/2958 + 1496/2958 = 3584/2958

Next, we need to add 14/89 to this sum. Again, we need a common denominator. The least common multiple of 2958 and 89 is 263462.

* 3584/2958 * 89/89 = 318976/263462
* 14/89 * 2958/2958 = 41412/263462

Now we can add the two fractions: 318976/263462 + 41412/263462 = 360388/263462

Finally, we can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 2:

360388/263462 = 180194/131731

### Answer: 180194/131731 

Expected answer: 180194/131631

Correct? No

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

Gemini-1.5 Flash:

First, we need to find a common denominator for the two fractions. The least common multiple of 30 and 60 is 60. 

* We can rewrite 73/30 as (73 * 2) / (30 * 2) = 146/60

Now we can add the fractions:

* 146/60 + 8/60 = (146 + 8) / 60 = 154/60

Finally, we can simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2:

* 154/60 = (154 / 2) / (60 / 2) = 77/30

### Answer: 77/30 

Expected answer: 77/30

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Simplify the second fraction:** 45/60 simplifies to 3/4 by dividing both numerator and denominator by 15.

2. **Find a common denominator for the first two fractions:** The least common denominator for 49 and 4 is 196.
   * 82/49 becomes (82 * 4) / (49 * 4) = 328/196
   * 3/4 becomes (3 * 49) / (4 * 49) = 147/196

3. **Add the first two fractions:** 328/196 + 147/196 = 475/196

4. **Find a common denominator for 'd' and the third fraction:** The least common denominator for 196 and 59 is 11524.
   * 475/196 becomes (475 * 59) / (196 * 59) = 28075/11524
   * 99/59 becomes (99 * 196) / (59 * 196) = 19404/11524

5. **Add 'd' and the third fraction:** 28075/11524 + 19404/11524 = 47479/11524

6. **Simplify the resulting fraction:** The greatest common factor of 47479 and 11524 is 1. Therefore, the simplified fraction is **47479/11524**. 

### Answer: 47479/11524 

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 Flash:

First, we need to find a common denominator for 76/30 and 91/16. The least common multiple of 30 and 16 is 240. 
 
 76/30 = (76 * 8)/(30 * 8) = 608/240
 91/16 = (91 * 15)/(16 * 15) = 1365/240
 
 Now, we can subtract:
 
 1365/240 - 608/240 = (1365 - 608)/240 = 757/240
 
 Next, we need to add this result to 18/44. We can simplify 18/44 to 9/22. The least common multiple of 240 and 22 is 2640.
 
 757/240 = (757 * 11)/(240 * 11) = 8327/2640
 9/22 = (9 * 120)/(22 * 120) = 1080/2640
 
 Now, we can add:
 
 8327/2640 + 1080/2640 = (8327 + 1080)/2640 = 9407/2640
 
 Finally, we round 9407/2640 to the nearest hundredth:
 
 9407/2640 ≈ 3.56
 
 ### Answer: 3.56 

Expected answer: 9407/2640

Correct? No

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Calculate (8 / 91) + (49 / 5):**
   - Find a common denominator for the fractions: 91 * 5 = 455
   - Convert the fractions: (8 * 5) / 455 + (49 * 91) / 455
   - Add the numerators: (40 + 4459) / 455 
   - Simplify: 4509 / 455

2. **Calculate (32 / 76):**
   - Simplify the fraction by dividing both numerator and denominator by their greatest common factor (4): 8/19

3. **Subtract (8/19) from (4509/455):**
   - Find a common denominator: 455 * 19 = 8645
   - Convert the fractions: (4509 * 19) / 8645 - (8 * 455) / 8645
   - Subtract the numerators: (85671 - 3640) / 8645
   - Simplify: 82031 / 8645

### Answer: 82031/8645 

Expected answer: 81841/8645

Correct? No

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

Gemini-1.5 Flash:

Here's how we can solve this step-by-step:

1. **Simplify the first fraction:** 75 / 45 can be simplified by dividing both numerator and denominator by 15, resulting in 5/3.

2. **Simplify the second fraction:** 5/49 is already in its simplest form.

3. **Add the first two fractions:**  (5/3) + (5/49) requires a common denominator. The least common multiple of 3 and 49 is 147.  
    * (5/3) * (49/49) = 245/147
    * (5/49) * (3/3) = 15/147
    * Adding these: (245/147) + (15/147) = 260/147

4. **Add the third fraction:** (260/147) + (3/58) requires another common denominator. The least common multiple of 147 and 58 is 8526.
    * (260/147) * (58/58) = 15080/8526
    * (3/58) * (147/147) = 441/8526
    * Adding these: (15080/8526) + (441/8526) = 15521/8526

5. **Simplify the final fraction:**  Both 15521 and 8526 are divisible by 3, giving us 5173/2842.

### Answer: 5173/2842 

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 Flash:

First, we need to find a common denominator for the two fractions.  The least common multiple of 15 and 95 is 285.

*  (43/15) * (19/19) = 817/285
*  (33/95) * (3/3) = 99/285

Now we can subtract the fractions:

* (817/285) - (99/285) = (817 - 99) / 285 = 718 / 285

Finally, we can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 19:

* (718 / 19) / (285 / 19) = 38/15

### Answer: 38/15 

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 Flash:

Here's how to solve the problem:

1. **Find a common denominator for the fractions:**  The least common multiple of 45 and 36 is 180.
   * (78/45) * (4/4) = 312/180
   * (89/36) * (5/5) = 445/180

2. **Add the fractions:** 312/180 + 445/180 = 757/180

3. **Double the sum:** (757/180) * 2 = 1514/180

4. **Simplify the fraction:** Both the numerator and denominator are divisible by 2.  
   * 1514/180 = 757/90 

### Answer: 757/90 

Expected answer: 757/90

Correct? Yes

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 Flash:

Here's how to solve this problem step-by-step:

1. **Divide 93 by 34:**  93 / 34 = 2.735 (approximately)

2. **Convert the decimal to a fraction:**  2.735 can be written as 2735/1000.  We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 5: (2735/5) / (1000/5) = 547/200.

3. **Subtract the second fraction:** (547/200) - (77/74)

4. **Find a common denominator:** The least common denominator for 200 and 74 is 3700.  We get:
   * (547/200) * (18.5/18.5) = 10106.5 / 3700 
   * (77/74) * (50/50) = 3850 / 3700

5. **Subtract the fractions:** (10106.5 / 3700) - (3850 / 3700) = 6256.5 / 3700

6. **Simplify the fraction:** Both the numerator and denominator are divisible by 0.5. 
  * (6256.5 / 0.5) / (3700 / 0.5) = 12513 / 7400

7. **Further simplification:** The numerator and denominator have a common factor of 13.
   * (12513 / 13) / (7400 / 13) = **963/569**

### Answer: 963/569 

Expected answer: 1066/629

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have a common denominator.  The least common multiple of 35 and 85 is 595.

*  We multiply the numerator and denominator of 86/35 by 17 to get (86 * 17)/(35 * 17) = 1462/595
* We multiply the numerator and denominator of 68/85 by 7 to get (68 * 7)/(85 * 7) = 476/595

Now we can add the fractions: 1462/595 + 476/595 = (1462 + 476)/595 = 1938/595

Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 19: 1938/595 = (1938/19)/(595/19) = 102/31

### Answer: 102/31 

Expected answer: 114/35

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator.  We find the least common multiple (LCM) of 53 and 94.  Since 53 is prime, the LCM is simply 53 * 94 = 4982.

* We multiply 99/53 by 94/94: (99/53)*(94/94) = 9306/4982
* We multiply 67/94 by 53/53: (67/94)*(53/53) = 3551/4982

Now we can add the fractions: 9306/4982 + 3551/4982 = 12857/4982

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 1.  So the answer is:

### Answer: 12857/4982 

Expected answer: 12857/4982

Correct? Yes

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

Gemini-1.5 Flash:

To subtract fractions, they must have a common denominator.  The least common multiple of 27 and 33 is 297.

*  We multiply 74/27 by 11/11 to get (74 * 11) / (27 * 11) = 814/297.
*  We multiply 56/33 by 9/9 to get (56 * 9) / (33 * 9) = 504/297.

Now we can subtract: 814/297 - 504/297 = (814 - 504) / 297 = 310/297.

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

310/297 = (310/2) / (297/2) = 155/148.5

### Answer: 155/148.5 

Expected answer: 310/297

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to solve the problem step-by-step:

1. **Find the sum of 96/40 and 11/99:**
   * Simplify 96/40:  96/40 = 24/10 = 12/5
   * Find a common denominator for 12/5 and 11/99. The least common multiple of 5 and 99 is 495.
   * Convert 12/5: (12/5) * (99/99) = 1188/495
   * Convert 11/99: (11/99) * (5/5) = 55/495
   * Add the fractions: 1188/495 + 55/495 = 1243/495

2. **Subtract 91/65 from the sum:**
   * Simplify 91/65: 91/65 = 13/5
   * Find a common denominator for 1243/495 and 13/5. The least common multiple of 495 and 5 is 495.
   * Convert 13/5: (13/5) * (99/99) = 1287/495
   * Subtract the fractions: 1243/495 - 1287/495 = -44/495

3. **Simplify the result:**
   * The fraction -44/495 can be simplified by dividing both numerator and denominator by their greatest common factor, which is 11: 
   * -44/495 = (-4*11)/(45*11) = -4/45

### Answer: -4/45 

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 Flash:

Let's break down the calculation step by step:

1. **Calculate h:**
   - Divide 10 by 5: 10 / 5 = 2
   - Divide 35 by 27: 35 / 27 ≈ 1.296
   - Add the results: 2 + 1.296 = 3.296 
   - Therefore, h = 3.296

2. **Calculate p:**
   - Divide 47 by 99: 47 / 99 ≈ 0.475
   - Add this result to h: 3.296 + 0.475 = 3.771

### Answer: 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 Flash:

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

1. **Simplify the fractions:**
    - 90/81 can be simplified by dividing both numerator and denominator by 9, giving us 10/9.
    - 2/66 can be simplified by dividing both numerator and denominator by 2, giving us 1/33.

2. **Find a common denominator:**
    - The least common multiple of 9 and 33 is 99. 
    - To get a denominator of 99 for 10/9, we multiply both numerator and denominator by 11: (10*11)/(9*11) = 110/99
    - To get a denominator of 99 for 1/33, we multiply both numerator and denominator by 3: (1*3)/(33*3) = 3/99

3. **Add the fractions:**
    - 110/99 + 3/99 = (110+3)/99 = 113/99

Therefore, the simplified answer is 113/99.

### 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 Flash:

Reasoning: Oliver would have two pieces of ribbon, each 56/41 yards long. To find the total length, we need to add the length of both pieces. So, we add 56/41 yards + 56/41 yards. Since the denominators are the same, we can directly add the numerators. 
Total length = (56 + 56)/41 = 112/41 yards.
### 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 Flash:

To add fractions, they need to have the same denominator.  Here's how to find the solution:

1. **Find the Least Common Multiple (LCM) of the denominators:**
   * The LCM of 75 and 92 is 6900.

2. **Convert each fraction to have the denominator of 6900:**
   * 92/75 = (92 * 92) / (75 * 92) = 8464 / 6900
   * 66/92 = (66 * 75) / (92 * 75) = 4950 / 6900

3. **Add the fractions:**
   * 8464/6900 + 4950/6900 = (8464 + 4950) / 6900 = 13414 / 6900

4. **Simplify the fraction:**
   * Both the numerator and denominator are divisible by 2: 13414 / 6900 = 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 Flash:

Reasoning: To add fractions, they must have the same denominator. The least common multiple of 65 and 22 is 65 * 22 = 1430. 

* We need to multiply 32/65 by 22/22 to get (32 * 22)/(65 * 22) = 704/1430.
* We need to multiply 73/22 by 65/65 to get (73 * 65)/(22 * 65) = 4745/1430.

Now we can add the fractions: 704/1430 + 4745/1430 = (704 + 4745)/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 Flash:

Reasoning: To find the difference, we need to subtract the smaller fraction from the larger fraction. However, to do that, they need to have the same denominator. The least common multiple of 34 and 86 is 172.

To get a denominator of 172 for the first fraction, we multiply both the numerator and denominator by 5: 
(51/34) * (5/5) = 255/172

To get a denominator of 172 for the second fraction, we multiply both the numerator and denominator by 2:
(12/86) * (2/2) = 24/172

Now we can subtract the fractions: 
255/172 - 24/172 = 231/172

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 3:
231/172 = (231/3) / (172/3) = 77/57 

### Answer: 77/57

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 Flash:

Here's how to solve this step-by-step:

1. **Convert the whole number to a fraction:** 51 can be written as 51/1.

2. **Find a common denominator for 51/1 and 93/8:** The least common denominator is 8.  
   * 51/1 * 8/8 = 408/8

3. **Add the fractions:** 408/8 + 93/8 = 501/8

4. **Find a common denominator for 501/8 and 58/44:** The least common denominator is 88.
   * 501/8 * 11/11 = 5511/88
   * 58/44 * 2/2 = 116/88

5. **Add the fractions:** 5511/88 + 116/88 = 5627/88

**Therefore, the final result as a simplified fraction is 5627/88.** 
### 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 Flash:

To subtract fractions, they must have a common denominator. The least common multiple of 5 and 25 is 25.  

We can rewrite 82/5 as (82 * 5) / (5 * 5) = 410/25.

Now we can perform the subtraction:

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

The fraction 312/25 can be simplified as a mixed number:

312/25 = 12 12/25

### Answer: 12 12/25 

Expected answer: 312/25

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to calculate the expression:

1. **Find a common denominator:** The least common denominator for 50 and 22 is 550.
2. **Convert the fractions:**
   * (64/50) * (11/11) = 704/550
   * (70/22) * (25/25) = 1750/550
3. **Add the fractions:** 704/550 + 1750/550 = 2454/550

### Answer: 2454/550 

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 Flash:

Reasoning: 
1. First, we need to calculate 24 divided by 6: 24 / 6 = 4.
2. Then, we calculate 40 divided by 53: 40 / 53 ≈ 0.75 (rounded to two decimal places).
3. Now we add these two results to find s: 4 + 0.75 = 4.75.
4. Finally, we add s to itself to find b: 4.75 + 4.75 = 9.5.

### Answer: 9.5 

Expected answer: 504/53

Correct? No

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

Gemini-1.5 Flash:

Here's how to calculate the expression and express the answer as a mixed number:

1. **Simplify the fractions:** 
   * 80/90 simplifies to 8/9
   * 52/11 remains as is (it's already in simplest form)

2. **Find a common denominator:**
   * The least common multiple of 9 and 11 is 99.
   * (8/9) * (11/11) = 88/99
   * (52/11) * (9/9) = 468/99

3. **Add the fractions:**
   * 88/99 + 468/99 = 556/99

4. **Convert to a mixed number:**
   * 556 divided by 99 is 5 with a remainder of 51.
   * Therefore, 556/99 is equal to 5 51/99.

### Answer: 5 51/99 

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 Flash:

To add fractions, they must have a common denominator.  The least common multiple of 18 and 74 is 666.

* We multiply the numerator and denominator of $\frac{12}{18}$ by $\frac{37}{37}$ to get $\frac{444}{666}$.
* We multiply the numerator and denominator of $\frac{91}{74}$ by $\frac{9}{9}$ to get $\frac{819}{666}$.

Now we can add the fractions:

$$\frac{444}{666} + \frac{819}{666} = \frac{444+819}{666} = \frac{1263}{666}$$

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

$$\frac{1263}{666} = \frac{1263 \div 3}{666 \div 3} = \boxed{\frac{421}{222}}$$ 

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 Flash:

To add fractions, they need to have the same denominator. The least common multiple of 2 and 25 is 50.

* Convert 7/2 to an equivalent fraction with a denominator of 50: (7/2) * (25/25) = 175/50
* Convert 51/25 to an equivalent fraction with a denominator of 50: (51/25) * (2/2) = 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 Flash:

Let's break down the calculation step-by-step:

1. **Calculate the fractions inside the parentheses:**
   - (68 / 69) ≈ 0.9855
   - (93 / 7) ≈ 13.2857

2. **Add the two results:**
   - 0.9855 + 13.2857 ≈ 14.2712

3. **Add the result to (3 / 46):**
   - 14.2712 + (3 / 46) ≈ 14.3372

4. **Convert the decimal result to a fraction:**
   - Since the decimal is recurring, it's impossible to express it as a simple fraction. Therefore, we leave the result as it is.

### Answer: 14.3372 

Expected answer: 13849/966

Correct? No

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

Gemini-1.5 Flash:

Reasoning: To add fractions, they need to have the same denominator.  We can find a common denominator by finding the least common multiple (LCM) of 98 and 4. 

The LCM of 98 and 4 is 98. To get a denominator of 98 for 60/4, we multiply both numerator and denominator by 24.5:

(60/4) * (24.5/24.5) = 1470/98

Now we can add the fractions:

31/98 + 1470/98 = (31 + 1470)/98 = 1501/98

This fraction cannot be simplified further.

### 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 Flash:

First, simplify the fractions:
* 24/36 simplifies to 2/3 (dividing both numerator and denominator by 12).

Now we have: 
(3/2) + (2/3)

To add fractions, they need a common denominator.  The least common denominator of 2 and 3 is 6.

* (3/2) * (3/3) = 9/6
* (2/3) * (2/2) = 4/6

Now we can add:
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 Flash:

Here's how to solve this problem step-by-step:

1. **Find a common denominator for 92/54 and 90/13:**
   * The least common multiple of 54 and 13 is 702.
   * Convert 92/54: (92/54) * (13/13) = 1196/702
   * Convert 90/13: (90/13) * (54/54) = 4860/702

2. **Add the fractions:**
   * (1196/702) + (4860/702) = 6056/702

3. **Simplify the fraction:**
   * Both 6056 and 702 are divisible by 4.
   * (6056/4) / (702/4) = 1514/175.5

4. **Subtract 46/41 from the result:**
   * To subtract fractions, we need a common denominator. The least common multiple of 175.5 and 41 is 7200.5.
   * Convert 1514/175.5: (1514/175.5) * (41/41) = 62074/7200.5
   * Convert 46/41: (46/41) * (175.5/175.5) = 8071/7200.5
   * Subtract: (62074/7200.5) - (8071/7200.5) = 54003/7200.5

5. **Simplify the final fraction:**
   * Both 54003 and 7200.5 are divisible by 1.5.
   * (54003/1.5) / (7200.5/1.5) = 36002/4800.33333...

**Therefore, the final result as a simplified fraction is approximately 36002/4800.33333...** 

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 Flash:

Twice the value of 29/23 means multiplying it by 2:

(29/23) * 2 = 58/23

This fraction is already in its simplest form because 58 and 23 share no common factors other than 1.

### 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 Flash:

To add fractions, they must have a common denominator.  The least common multiple of 20 and 72 is 360.

*  Convert 29/20 to an equivalent fraction with a denominator of 360:  (29/20) * (18/18) = 522/360
*  Convert 17/72 to an equivalent fraction with a denominator of 360: (17/72) * (5/5) = 85/360

Now we can add:  522/360 + 85/360 = 607/360

This fraction can be simplified: 607/360 = 1 247/360

### Answer: 1 247/360 

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 Flash:

Here's how to solve the expression step-by-step:

1. **Simplify the fractions inside the parentheses:**
   * (36 / 27) = 4/3 
   * (80 / 10) = 8
   * (73 / 79)  (This fraction cannot be simplified further)

2. **Calculate the expression within the first set of parentheses:**
   * (4/3) + 8 = 28/3 

3. **Subtract the simplified fraction:**
   * (28/3) - (73/79) = (2184/237) - (219/237) = 1965/237

4. **Simplify the final fraction:**
   * 1965/237 = (3 * 655)/(3 * 79) = 655/79

### Answer: 655/79 

Expected answer: 1993/237

Correct? No

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

Gemini-1.5 Flash:

First, we'll calculate the individual divisions:

* 86 / 71 ≈ 1.21
* 91 / 75 ≈ 1.21

Now, we add these 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 Flash:

Let's break this down step by step:

1. **Simplify each fraction:**
   * 21/75 can be simplified by dividing both numerator and denominator by 3: 7/25
   * 74/43 is already in its simplest form.
   * 10/62 can be simplified by dividing both numerator and denominator by 2: 5/31

2. **Find a common denominator for the first two fractions:**
   * The least common multiple of 25 and 43 is 1075.
   * Convert 7/25 to have a denominator of 1075: (7/25) * (43/43) = 301/1075
   * Convert 74/43 to have a denominator of 1075: (74/43) * (25/25) = 1850/1075

3. **Add the first two fractions:**
   * (301/1075) + (1850/1075) = 2151/1075

4. **Find a common denominator for the result and the third fraction:**
   * The least common multiple of 1075 and 31 is 33325
   * Convert 2151/1075 to have a denominator of 33325: (2151/1075) * (31/31) = 66681/33325
   * Convert 5/31 to have a denominator of 33325: (5/31) * (1075/1075) = 5375/33325

5. **Add the final two fractions:**
   * (66681/33325) + (5375/33325) = 72056/33325

6. **Simplify the result:**
   * Both 72056 and 33325 are divisible by 9, giving us 8006/3703.

### Answer: 8006/3703 

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 Flash:

Here's how to compute the expression:

1. **Find a common denominator for the fractions:**
   * The least common multiple of 66 and 61 is 4026.
   *  (75/66) * (61/61) = 4575/4026
   *  (81/61) * (66/66) = 5346/4026

2. **Add the fractions:**
   * (4575/4026) + (5346/4026) = 9921/4026

3. **Simplify the fraction:**
   * Both 9921 and 4026 are divisible by 3.
   * (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 Flash:

First, we need to find a common denominator for 53/18 and 21/99. The least common multiple of 18 and 99 is 594.

* Convert 53/18 to an equivalent fraction with a denominator of 594: (53/18) * (33/33) = 1749/594
* Convert 21/99 to an equivalent fraction with a denominator of 594: (21/99) * (6/6) = 126/594

Now, add the two fractions: 1749/594 + 126/594 = 1875/594

Since each identical fraction, t, is equal to this sum, we have:

t = 1875/594

Finally, the total sum, l, of these two fractions is:

l = t + t = 2 * (1875/594) = 3750/594

We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 18:

l = (3750/18) / (594/18) = 208.333 / 33

### Answer: 208.333/33 

Expected answer: 625/99

Correct? No

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 Flash:

First, we need to find a common denominator for 58/49 and 31/34. The least common multiple of 49 and 34 is 1666.

* (58/49) * (34/34) = 1972/1666
* (31/34) * (49/49) = 1519/1666

Now we can add the two fractions:

* 1972/1666 + 1519/1666 = 3491/1666

Next, we need to add 74/38 to this result. Again, we need a common denominator. The least common multiple of 1666 and 38 is 31674.

* (3491/1666) * (19/19) = 66329/31674
* (74/38) * (834/834) = 61676/31674

Now we can add the two fractions:

* 66329/31674 + 61676/31674 = 128005/31674

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

* 128005/31674 = 128005/31674

### Answer: 128005/31674 

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 Flash:

First, we calculate each division separately:

* 100 divided by 76 = 100/76 = 25/19
* 29 divided by 14 = 29/14

Now we need to add these fractions. To do that, they need to have the same denominator.  The least common multiple of 19 and 14 is 266.

* (25/19) * (14/14) = 350/266
* (29/14) * (19/19) = 551/266

Finally, we add the fractions:

* 350/266 + 551/266 = 901/266

This fraction can't be simplified further. 

### Answer: 901/266 

Expected answer: 901/266

Correct? Yes

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 Flash:

Here's how to solve this problem:

1. **Find a common denominator for the fractions representing Evan's reading:**
   * The least common multiple of 18 and 42 is 126.
   * Convert 51/18 to an equivalent fraction with a denominator of 126: (51/18) * (7/7) = 357/126

2. **Determine the fraction representing the amount Olivia read after Evan:**
   * Olivia read the same amount as Evan, so she also read 357/126 of the novel.

3. **Add the fractions to find Olivia's total reading:**
   * Olivia's total reading is (357/126) + (8/42)
   * To add these fractions, we need a common denominator (126): (357/126) + (24/126) = 381/126

4. **Simplify the fraction:**
   * Both 381 and 126 are divisible by 9: (381/126) ÷ (9/9) = 42.33/14

### Answer: 42.33/14 

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 Flash:

First, we'll perform the division operations:

* 48 divided by 13 is approximately 3.6923 (rounded to four decimal places).
* 31 divided by 22 is approximately 1.4091 (rounded to four decimal places).

Now, we'll add these results:

3.6923 + 1.4091 = 5.1014

Therefore, the sum of 48 divided by 13 and 31 divided by 22 is approximately **5.1014**. 

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 Flash:

First, we need to find a common denominator for 24/86 and 76/77. The least common multiple of 86 and 77 is 6622. 

*  24/86 = (24 * 77) / (86 * 77) = 1848/6622
*  76/77 = (76 * 86) / (77 * 86) = 6536/6622

Now, we can add the fractions:

* 1848/6622 + 6536/6622 = (1848 + 6536) / 6622 = 8384/6622

Next, we need to simplify the fraction 8384/6622. Both the numerator and denominator are divisible by 4.

* 8384/6622 = (8384/4) / (6622/4) = 2096/1655.5

Finally, we need to subtract this result from 27/6. 

* 27/6 - 2096/1655.5 = (27 * 1655.5 - 2096 * 6) / (6 * 1655.5) = (44749.5 - 12576) / 9933 = 32173.5 / 9933

### Answer: 32173.5 / 9933 

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 Flash:

To add fractions, they need to have the same denominator. The least common multiple of 39 and 14 is 546. 

* We can rewrite 73/39 as (73*14)/(39*14) = 1022/546
* We can rewrite 49/14 as (49*39)/(14*39) = 1911/546

Now we can add the fractions: 1022/546 + 1911/546 = 2933/546

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3: 2933/546 = (2933/3)/(546/3) = 977/182

### Answer: 977/182 

Expected answer: 419/78

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator. The least common multiple of 65 and 39 is 390. 

* We can rewrite 75/65 as (75*6)/(65*6) = 450/390.
* We can rewrite 7/39 as (7*10)/(39*10) = 70/390.

Now we can add the fractions: 450/390 + 70/390 = 520/390.

Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 10: 520/390 = (520/10)/(390/10) = 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 Flash:

Here's how we can solve this problem step-by-step:

1. **Calculate 79/1 - 30/92:**
   * 79/1 = 79
   * 30/92 simplifies to approximately 0.33 (you can use a calculator for this)
   * 79 - 0.33 = 78.67

2. **Subtract 61/63 from the result:**
   * 61/63 is approximately 0.97 (again, using a calculator)
   * 78.67 - 0.97 = 77.7

### Answer: 77.7 

Expected answer: 225191/2898

Correct? No

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

Gemini-1.5 Flash:

We can simplify this problem by recognizing that we are adding the same fraction to itself.  This is equivalent to multiplying the fraction by 2. 

Therefore: (58/26) + (58/26) = 2 * (58/26) 

Now, we can simplify the fraction 58/26 by dividing both the numerator and denominator by their greatest common factor, which is 2. This gives us: 

2 * (58/26) = 2 * (29/13) 

Finally, we multiply the whole number by the numerator: 

2 * (29/13) = 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 Flash:

First, we need to add the initial amount of orange juice Alex had to the amount he bought: 69/63 + 77/5.

To add fractions, they need to have the same denominator. The least common multiple of 63 and 5 is 315.  So, we need to convert each fraction:

* (69/63) * (5/5) = 345/315
* (77/5) * (63/63) = 4851/315

Now we can add: 345/315 + 4851/315 = 5196/315

This is the total amount of orange juice Alex had after buying more.

Next, we need to add the orange juice he received from Sally: 5196/315 + 47/71

Again, we need to find a common denominator. The least common multiple of 315 and 71 is 22485.

* (5196/315) * (71/71) = 368556/22485
* (47/71) * (315/315) = 14805/22485

Now we can add: 368556/22485 + 14805/22485 = 383361/22485

This is the final amount of orange juice Alex has, which we can call 'k'.

### Answer: k = 383361/22485 

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 Flash:

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

1. **Calculate the fractions within the parentheses:**
   - 100 / 61 = 100/61 (this fraction is already simplified)
   - 39 / 6 = 13/2 (simplifying by dividing both numerator and denominator by 3)
   - 67 / 49 = 67/49 (this fraction is already simplified)

2. **Add the fractions inside the second set of parentheses:**
   - (13/2) + (67/49) = (13 * 49) / (2 * 49) + (67 * 2) / (49 * 2) = 637/98 + 134/98 = 771/98

3. **Add the results from steps 1 and 2:**
   - (100/61) + (771/98) = (100 * 98) / (61 * 98) + (771 * 61) / (98 * 61) = 9800/5978 + 47001/5978 = 56801/5978

4. **Simplify the resulting fraction (if possible):**
   - The fraction 56801/5978 doesn't simplify further, as there are no common factors between the numerator and denominator.

### Answer: 56801/5978 

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 Flash:

Reasoning: 
* 85/1 is simply 85.
* To add fractions, they need a common denominator. The least common denominator for 1 and 69 is 69.
* So, we need to rewrite 85/1 as (85*69)/69 = 5865/69.
* Now we can add: 5865/69 + 83/69 = (5865+83)/69 = 5948/69.
* We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 3: (5948/3) / (69/3) = 1982/23

### Answer: 1982/23 

Expected answer: 5948/69

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator.  

1. **Find the Least Common Multiple (LCM) of the denominators:**
   The LCM of 13 and 86 is 1118.

2. **Convert each fraction to have the LCM as the denominator:**
   * (92/13) * (86/86) = 7912/1118
   * (43/86) * (13/13) = 559/1118

3. **Add the numerators:**
   7912/1118 + 559/1118 = 8471/1118

4. **Simplify the fraction (if possible):**
   The fraction 8471/1118 cannot be simplified further.

### 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 Flash:

To add fractions, they must have a common denominator.  

* Find the least common multiple (LCM) of 32 and 98. The LCM of 32 and 98 is 1568.
* Rewrite each fraction with the denominator 1568:
    * (67/32) * (49/49) = 3283/1568
    * (10/98) * (16/16) = 160/1568
* Add the numerators: 3283/1568 + 160/1568 = 3443/1568
* Simplify the fraction (if possible): The greatest common factor of 3443 and 1568 is 1, so the fraction is already simplified. 

### 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 Flash:

To add fractions, they need to have a common denominator.  The least common multiple of 52 and 32 is 416.

*  We multiply 59/52 by 8/8 (which equals 1, so we don't change the value):
   (59/52) * (8/8) = 472/416

* We multiply 70/32 by 13/13:
   (70/32) * (13/13) = 910/416

Now we can add the fractions:

472/416 + 910/416 = 1382/416

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

1382/416 = (1382/2) / (416/2) = 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 Flash:

Here's how to solve the problem step-by-step:

1. **48 divided by 5:** 48 / 5 = 9.6
2. **11 divided by 65:** 11 / 65 ≈ 0.169
3. **Subtract the result from step 1 from the result of step 2:** 0.169 - 9.6 = -9.431
4. **28 divided by 2:** 28 / 2 = 14
5. **Add the result from step 3 to the result of step 4:** -9.431 + 14 = 4.569

### Answer: 4.569 

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 Flash:

To add fractions, they need to have the same denominator.  We find the least common multiple (LCM) of 52 and 82:

* Prime factorize 52: 2 x 2 x 13
* Prime factorize 82: 2 x 41

The LCM is the product of the highest powers of all the prime factors: 2² x 13 x 41 = 2132

Now we adjust the fractions:

* (20/52) * (41/41) = 820/2132
* (75/82) * (26/26) = 1950/2132

Now we can add:

* 820/2132 + 1950/2132 = 2770/2132

Finally, simplify by dividing both numerator and denominator by their greatest common factor, which is 2:

* 2770/2132 = (2 x 1385) / (2 x 1066) = 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 Flash:

First, we need to find a common denominator for the two fractions. The least common multiple of 5 and 84 is 420. 

*  31/5  is equivalent to (31 * 84) / (5 * 84) = 2604/420
*  92/84 is equivalent to (92 * 5) / (84 * 5) = 460/420

Now we can subtract the fractions:

2604/420 - 460/420 = (2604 - 460) / 420 = 2144/420

Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 4:

2144/420 = (2144/4) / (420/4) = 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 Flash:

Here's how to solve the problem step-by-step:

1. **Find the sum of the fractions:**
   - 81/90 + 94/49 = (81 * 49) / (90 * 49) + (94 * 90) / (49 * 90) 
   - = 3969 / 4410 + 8460 / 4410
   - = 12429 / 4410

2. **Double the sum:**
   - (12429 / 4410) * 2 = 24858 / 4410

3. **Simplify (optional):**
   - The fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 2. 
   - 24858 / 4410 = 12429 / 2205

### Answer: 12429 / 2205 

Expected answer: 1381/245

Correct? Yes

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

Gemini-1.5 Flash:

To find the difference, we need to subtract the second fraction from the first:

69/21 - 10/92

Before we can subtract fractions, they need to have a common denominator. The least common multiple of 21 and 92 is 1932.

*  69/21 * 92/92 = 6348/1932
*  10/92 * 21/21 = 210/1932

Now we can subtract:

6348/1932 - 210/1932 = 6138/1932

Finally, we can simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2:

6138/1932 = 3069/966

### Answer: 3069/966 

Expected answer: 1023/322

Correct? Yes

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

Gemini-1.5 Flash:

First, let's calculate (26 / 87) + (92 / 88):

* 26 / 87 ≈ 0.299
* 92 / 88 ≈ 1.045 
* 0.299 + 1.045 ≈ 1.344

Now, let's add this result to (26 / 57):

* 26 / 57 ≈ 0.456
* 1.344 + 0.456 ≈ 1.8

### Answer: 1.8 

Expected answer: 21825/12122

Correct? No

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

Gemini-1.5 Flash:

To add fractions, they must have a common denominator.  Let's find the least common multiple (LCM) of 66, 6, and 34:

* 66 = 2 x 3 x 11
* 6 = 2 x 3
* 34 = 2 x 17

The LCM is 2 x 3 x 11 x 17 = 1122

Now, let's convert each fraction:

* 78/66 = (78 x 17) / (66 x 17) = 1326 / 1122
* 28/6 = (28 x 187) / (6 x 187) = 5236 / 1122
* 90/34 = (90 x 33) / (34 x 33) = 2970 / 1122

Now, we can add the fractions:

(1326 + 5236 + 2970) / 1122 = 9532 / 1122

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

9532 / 1122 = (9532 / 2) / (1122 / 2) = 4766 / 561

### Answer: 4766/561 

Expected answer: 4766/561

Correct? Yes

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

Gemini-1.5 Flash:

To subtract fractions, they need to have the same denominator.  We find the least common multiple (LCM) of 7 and 23, which is 161.

* (12/7) * (23/23) = 276/161
* (9/23) * (7/7) = 63/161

Now we can subtract:

* (276/161) - (63/161) = (276-63)/161 = 213/161

### Answer: 213/161 

Expected answer: 213/161

Correct? Yes

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

Gemini-1.5 Flash:

To add fractions, they must have a common denominator. The least common multiple of 18 and 61 is 1098.

* Convert 95/18: (95/18) * (61/61) = 5795/1098
* Convert 51/61: (51/61) * (18/18) = 918/1098

Now we can add the fractions: 5795/1098 + 918/1098 = 6713/1098

This fraction can be simplified by finding the greatest common divisor (GCD) of 6713 and 1098, which is 3.

Simplifying the fraction: (6713/3) / (1098/3) = 2237/366

### Answer: 2237/366 

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 Flash:

To subtract fractions, they need to have the same denominator. We'll find the least common multiple (LCM) of 46 and 84.

* Prime factorization of 46: 2 x 23
* Prime factorization of 84: 2 x 2 x 3 x 7
* LCM of 46 and 84: 2 x 2 x 3 x 7 x 23 = 1932

Now we'll adjust the fractions:

* (93 / 46) * (42/42) = 3906/1932
* (51 / 84) * (23/23) = 1173/1932

Now we can subtract:

* (3906 / 1932) - (1173 / 1932) = (3906 - 1173) / 1932 = 2733 / 1932

Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 3:

* (2733 / 3) / (1932 / 3) = 911/644

### Answer: 911/644 

Expected answer: 911/644

Correct? Yes

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

Gemini-1.5 Flash:

To add fractions, they need to have the same denominator. We need to find the least common multiple (LCM) of 70 and 9. 

The LCM of 70 and 9 is 630.

Now, let's convert each fraction to have a denominator of 630:

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

Now, we can add the fractions:

108/630 + 5880/630 = (108 + 5880)/630 = 5988/630

Finally, we simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 6:

5988/630 = (5988/6)/(630/6) = **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 Flash:

Here's how to solve the problem step-by-step:

1. **Find a common denominator for 32/3 and 40/92:**
   - The least common multiple of 3 and 92 is 276.
   - Convert 32/3 to 276ths: (32/3) * (92/92) = 2944/276
   - Convert 40/92 to 276ths: (40/92) * (3/3) = 120/276

2. **Subtract the fractions:**
   - (2944/276) - (120/276) = 2824/276

3. **Double the result:**
   - (2824/276) * 2 = 5648/276

4. **Simplify (if possible):**
   - Both numerator and denominator are divisible by 4.
   - (5648/276) / (4/4) = 1412/69

5. **The final answer:**
   - We can simplify further by dividing both numerator and denominator by 3.
   - (1412/69) / (3/3) = **470.67** (rounded to two decimal places).

### Answer: 470.67 

Expected answer: 1412/69

Correct? No

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

Gemini-1.5 Flash:

When adding fractions with the same denominator, we simply add the numerators and keep the denominator the same.

So, 79/24 + 79/24 = (79 + 79) / 24 = 158/24

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

158/24 = (158/2)/(24/2) = 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 Flash:

To add fractions, they need to have a common denominator.  Let's find the least common multiple (LCM) of 76 and 22:

* Factors of 76: 1, 2, 4, 19, 38, 76
* Factors of 22: 1, 2, 11, 22

The LCM of 76 and 22 is 836.

Now we'll convert each fraction:

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

Finally, add the fractions:

1001/836 + 456/836 = 1457/836

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 11:

1457/836 = (1457/11) / (836/11) = 132.45 / 76.00

### Answer: 132.45/76.00 

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 Flash:

Here's how to solve this problem step-by-step:

**1. Find a common denominator for 88/93 and 6/47:**

* The least common multiple (LCM) of 93 and 47 is 4371.
* Convert 88/93: (88 * 47) / (93 * 47) = 4136 / 4371
* Convert 6/47: (6 * 93) / (47 * 93) = 558 / 4371

**2. Add the fractions:**

* (4136 / 4371) + (558 / 4371) = 4694 / 4371

**3. Find a common denominator for 4694/4371 and 92/4:**

* The least common multiple (LCM) of 4371 and 4 is 17484.
* Convert 4694/4371: (4694 * 4) / (4371 * 4) = 18776 / 17484
* Convert 92/4: (92 * 4371) / (4 * 4371) = 402212 / 17484

**4. Add the fractions:**

* (18776 / 17484) + (402212 / 17484) = 420988 / 17484

**5. Simplify the fraction (optional):**

* The fraction can be simplified by dividing both numerator and denominator by their greatest common factor (GCF), which is 4.
* 420988 / 4 = 105247
* 17484 / 4 = 4371
* Simplified fraction: 105247/4371

### Answer: 105247/4371 

Expected answer: 105227/4371

Correct? No

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

Gemini-1.5 Flash:

First, we need to find a common denominator for 52/21 and 75/67. The least common multiple of 21 and 67 is 1407.  

* 52/21 * (67/67) = 3484/1407
* 75/67 * (21/21) = 1575/1407

Now we can add the two fractions:

3484/1407 + 1575/1407 = 5059/1407

Next, we add 95/83 to this result.  We again need to find a common denominator, which is 116511.

* 5059/1407 * (83/83) = 420247/116511
* 95/83 * (1407/1407) = 133665/116511

Finally, we add the two fractions:

420247/116511 + 133665/116511 = 553912/116511

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 8.

553912/116511 = (553912/8) / (116511/8) = **69239/14564**

### Answer: 69239/14564 

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 Flash:

To subtract fractions, they need to have a common denominator. 

1. **Find the Least Common Multiple (LCM) of the denominators:**
   - The LCM of 27 and 48 is 432.

2. **Convert the fractions to equivalent fractions with the LCM as the denominator:**
   - (73/27) * (16/16) = 1168/432
   - (23/48) * (9/9) = 207/432

3. **Subtract the fractions:**
   - (1168/432) - (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 Flash:

Here's how to solve the expression:

1. **Divide 78 by 2:**  78 / 2 = 39
2. **Divide 70 by 23:** This results in a decimal, approximately 3.04.
3. **Subtract:** 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 Flash:

Reasoning: 34/1 is equal to 34.  To add fractions, they must have the same denominator.  We can rewrite 34 as 34/1 and then multiply both the numerator and denominator by 4 to get 136/4.  Now we can add the fractions:

136/4 + 53/4 = (136+53)/4 = 189/4

To express this as a mixed number, we divide 189 by 4:

189 ÷ 4 = 47 with a remainder of 1

So, 189/4 is equal to 47 1/4.

### Answer: 47 1/4 

Expected answer: 189/4

Correct? Yes

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

Gemini-1.5 Flash:

To add fractions, they must have a common denominator.  The least common multiple of 36 and 96 is 288.

* **Convert 3/36:**  Multiply numerator and denominator by 8: (3 * 8) / (36 * 8) = 24/288

* **Convert 97/96:** Multiply numerator and denominator by 3: (97 * 3) / (96 * 3) = 291/288

Now we can add: 24/288 + 291/288 = 315/288

Finally, simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 3: 315/288 = (315/3) / (288/3) = 105/96

This fraction can be further simplified by dividing both numerator and denominator by 3:  105/96 = (105/3) / (96/3) = **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 Flash:

Here's how to calculate the expression and simplify the answer:

1. **Calculate the first fraction:** 92 / 95. This fraction is already in its simplest form.

2. **Calculate the second fraction:** 4 / 74. We can simplify this by dividing both numerator and denominator by their greatest common factor, which is 2: (4/2) / (74/2) = 2/37

3. **Add the two fractions:**  (92/95) + (2/37). To add fractions, they must have a common denominator.  The least common multiple of 95 and 37 is 3515.

   *  (92/95) * (37/37) = 3404/3515
   *  (2/37) * (95/95) = 190/3515

4. **Add the numerators:** (3404/3515) + (190/3515) = 3594/3515

5. **Simplify the fraction:**  We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 2: (3594/2) / (3515/2) = 1797/1757.5

### Answer: 1797/1757.5 

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 Flash:

First, we need to simplify 88/72. Both the numerator and denominator are divisible by 8, giving us 11/9.

Now, we can substitute the value of 'v' into the equation for 'd':

d = 11/9 + 69/47

To add these fractions, we need a common denominator. The least common multiple of 9 and 47 is 423.  

* Multiply 11/9 by 47/47: (11/9) * (47/47) = 517/423
* Multiply 69/47 by 9/9: (69/47) * (9/9) = 621/423

Now we can add the fractions:

d = 517/423 + 621/423 = 1138/423

### Answer: 1138/423 

Expected answer: 1138/423

Correct? Yes

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 Flash:

Here's how to solve the problem:

1. **Find the difference:** To determine how much oil is left, subtract the amount sold from the initial amount: (41/26) - (41/72)

2. **Find a common denominator:** The least common multiple of 26 and 72 is 936.  Rewrite the fractions with this denominator:
   * (41/26) = (41 * 36) / (26 * 36) = 1476/936
   * (41/72) = (41 * 13) / (72 * 13) = 533/936

3. **Subtract the fractions:** Now that they have the same denominator, we can subtract: 
   (1476/936) - (533/936) = (1476 - 533) / 936 = 943/936

**Therefore, the wholesaler has 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 Flash:

To find the sum, we first need to find a common denominator for the fractions. The least common multiple of 75 and 56 is 2100.

*  85/75 is equivalent to (85 * 28) / (75 * 28) = 2380/2100
*  88/56 is equivalent to (88 * 37.5) / (56 * 37.5) = 3300/2100

Now we can add the fractions:

2380/2100 + 3300/2100 = 5680/2100

Finally, we convert this fraction to decimal form:

5680/2100 = 2.70476190476

### Answer: 2.70476190476 

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 Flash:

Reasoning: To add fractions, they must have a common denominator. The least common multiple of 33 and 2 is 66. We can rewrite the fractions with this denominator:
* 12/33 = (12/33)*(2/2) = 24/66
* 49/2 = (49/2)*(33/33) = 1617/66

Now we can add the fractions: 24/66 + 1617/66 = (24+1617)/66 = 1641/66.

We can convert this improper fraction to a mixed number by dividing 1641 by 66. 1641/66 = 24 with a remainder of 57.  

Therefore, the result is 24 57/66.

### Answer: 24 57/66 

Expected answer: 547/22

Correct? Yes

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

Gemini-1.5 Flash:

Here's how to add two fractions that are both 78/65:

* **Understanding the Problem:** We're essentially multiplying the fraction 78/65 by 2.
* **Adding Fractions:** Since the fractions have the same denominator (65), we can simply add the numerators: 78 + 78 = 156
* **Simplifying:** The resulting fraction is 156/65. This can be simplified by dividing both numerator and denominator by their greatest common factor (13): 156/13 = 12, and 65/13 = 5. 

Therefore, the result is 12/5.

### Answer: 12/5 

Expected answer: 12/5

Correct? Yes

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

Gemini-1.5 Flash:

To add fractions, they must have a common denominator.  The least common multiple of 7 and 90 is 630.

* Convert 16/7 to an equivalent fraction with a denominator of 630: (16/7) * (90/90) = 1440/630

* Convert 11/90 to an equivalent fraction with a denominator of 630: (11/90) * (7/7) = 77/630

Now we can add the fractions:

1440/630 + 77/630 = 1517/630

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 7:

1517/630 = (1517/7) / (630/7) = 217/90

### Answer: 217/90 

Expected answer: 1517/630

Correct? No