🔗 Problem

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.

Gemma 2B:

     Reasoning: First, we need to find the sum of 48/56 and 95/23. To do this, we need to find a common denominator for the two fractions. The least common multiple of 56 and 23 is 1244.

    So, we convert the fractions to have the same denominator:

    48/56 = (48 \* 23)/(56 \* 23) = 1104/1244

    95/23 = (95 \* 54)/(23 \* 54) = 5130/1244

    Now, we can add the two fractions:

    1104/1244 + 5130/1244 = (1104 + 5130)/1244 = 6234/1244

    Next, we need to subtract 34/26 from the result. To do this, we need to find a common denominator for the two fractions. The least common multiple of 1244 and 26 is 1244.

    So, we convert the fraction to have the same denominator:

    34/26 = (34 \* 48)/(26 \* 48) = 1632/1244

    Now, we can subtract the two fractions:

    6234/1244 - 1632/1244 = (6234 - 1632)/1244 = 4602/1244

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

    4602/1244 = (4602/2)/(1244/2) = 2301/622

    ### Answer: 2301/622

Expected answer: 7702/2093

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning: To add the fractions 88/9 and 28/65, we need to find a common denominator. The least common multiple of 9 and 65 is 585.

    88/9 = (88 \* 65) / (9 \* 65) = 5720/585
    28/65 = (28 \* 9) / (65 \* 9) = 252/585

    Now we can add the two fractions:

    5720/585 + 252/585 = (5720 + 252) / 585 = 5972/585

    Next, we need to subtract the fraction 18/37 from the result. To do this, we need to find a common denominator for 585 and 37. The least common multiple of 585 and 37 is 21615.

    5972/585 = (5972 \* 37) / (585 \* 37) = 220904/21615
    18/37 = (18 \* 585) / (37 \* 585) = 10530/21615

    Now we can subtract the two fractions:

    220904/21615 - 10530/21615 = (220904 - 10530) / 21615 = 210374/21615

    The result is 210374/21615, which can be simplified by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 210374 and 21615 is 1. Therefore, the result expressed as a simple fraction is 210374/21615.

    ### Answer: 210374/21615

Expected answer: 210434/21645

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: (63 / 41) + (44 / 50) = (63 / 41) + (22 / 25) = (63 \* 25 / 41 \* 25) + (44 \* 41 / 50 \* 41) = (1575 / 1025) + (1804 / 2050) = (1575 / 1025) + (1804 / 2050) = (1575 \* 2 / 1025 \* 2) + (1804 \* 2 / 2050 \* 2) = (3150 / 2050) + (3608 / 4100) = (3150 / 2050) + (3608 / 4100) = (3150 \* 41 / 2050 \* 41) + (3608 \* 2050 / 4100 \* 2050) = (129150 / 84050) + (7391600 / 8405000) = (129150 / 84050) + (7391600 / 8405000) = (129150 \* 100 / 84050 \* 100) + (7391600 \* 10 / 8405000 \* 10) = (12915000 / 8405000) + (73916000 / 84050000) = (12915000 / 8405000) + (73916000 / 84050000) = (12915000 + 73916000) / 8405000 = (86831000 / 8405000) = 10.33
    ### Answer: 10.33

Expected answer: 2477/1025

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 41 and 77 is 307.

    John's cake can be expressed as (71/41) \* (77/77) = 5467/307
    Emily's cake can be expressed as (41/77) \* (41/41) = 1681/307

    Adding the two fractions, we get 5467/307 + 1681/307 = 7148/307

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the total amount of cake is 7148/307.

    ### Answer: 7148/307

Expected answer: 7148/3157

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 65 and 35 is 2275.

    10/65 = (10 * 35)/(65 * 35) = 350/2275
    56/35 = (56 * 65)/(35 * 65) = 3640/2275

    Now we can add the two fractions:

    350/2275 + 3640/2275 = (350 + 3640)/2275 = 3990/2275

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:

    3990/2275 = (3990/5)/(2275/5) = 798/455

    Now we can simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 11:

    798/455 = (798/11)/(455/11) = 72/41

    ### Answer: 72/41

Expected answer: 114/65

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 81 and 47 is 3807.

    75/81 = (75 \* 47)/(81 \* 47) = 3525/3807

    97/47 = (97 \* 81)/(47 \* 81) = 7857/3807

    Adding the two fractions, we get:

    3525/3807 + 7857/3807 = (3525 + 7857)/3807 = 11382/3807

    ### Answer: 11382/3807

Expected answer: 3794/1269

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of adding 75/81 and 97/47, what do you get when you add that result to 52/71? Provide your answer as an unsimplified fraction.

Gemma 2B:

     Reasoning: We have already calculated the result of adding 75/81 and 97/47 as 11382/3807.

    To add this result to 52/71, we need to find a common denominator. The least common multiple of 3807 and 71 is 270477.

    11382/3807 = (11382 \* 71)/(3807 \* 71) = 808182/270477

    52/71 = (52 \* 3807)/(71 \* 3807) = 197964/270477

    Adding the two fractions, we get:

    808182/270477 + 197964/270477 = (808182 + 197964)/270477 = 1006146/270477

    ### Answer: 1006146/270477

Expected answer: 335362/90099

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 88/1 - 38/53 = (88 \* 53)/(1 \* 53) - (38 \* 1)/(53 \* 1) = (88 \* 53 - 38)/53 = (4664 - 38)/53 = 4626/53

    Simplifying the fraction 4626/53, we get 87.

    ### Answer: 87

Expected answer: 4626/53

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to simplify the fractions 80/94 and 78/59.

    80/94 = <<80/94=40/47>>40/47
    78/59 = <<78/59=6/5>>6/5

    Now, we can add the two fractions:

    (40/47) + (6/5) = (40/47) \* (5/5) + (6/5) \* (47/47) = (200/235) + (282/235) = <<200/235+282/235=482/235>>482/235

    The answer is 482/235 in simplified form.
    ### Answer: 482/235

Expected answer: 6026/2773

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 56 and 50 is 140.

    89/56 = (89\*2.5)/(56\*2.5) = 222.5/140

    48/50 = (48\*2.8)/(50\*2.8) = 134.4/140

    Now we can add the two fractions:

    222.5/140 + 134.4/140 = (222.5 + 134.4)/140 = 356.9/140

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 140.

    356.9/140 = 2.549285714285714

    Since the question asks for a simplified fraction, we can round the decimal to the nearest whole number, which is 3.

    ### Answer: 3

    Note: The answer is not a simplified fraction, as the question asks for. The correct answer is 2.549285714285714, which can be rounded to 3 for simplicity. However, the question asks for a simplified fraction, so the answer should be written as 3/1.

Expected answer: 3569/1400

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: First, we need to find the sum of 96/11 and 12/5.
    To do this, we need to find a common denominator for the two fractions. The least common multiple of 11 and 5 is 55.
    So, we convert 96/11 to 480/55 and 12/5 to 132/55.
    Now, we can add the two fractions: 480/55 + 132/55 = 612/55.
    Next, we need to subtract 38/87 from 612/55.
    To do this, we need to find a common denominator for the two fractions. The least common multiple of 55 and 87 is 4785.
    So, we convert 612/55 to 5408/4785 and 38/87 to 190/4785.
    Now, we can subtract the two fractions: 5408/4785 - 190/4785 = 5218/4785.
    ### Answer: 5218/4785

Expected answer: 51154/4785

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: 82 divided by 9 is <<82/9=8.88888888888889>>8.88888888888889 (repeating)
    82 divided by 63 is <<82/63=1.3015873015873016>>1.3015873015873016 (approximately)
    Subtracting the second value from the first gives us 8.88888888888889 - 1.3015873015873016 = <<8.88888888888889-1.3015873015873016=7.587301587301587>>7.587301587301587 (approximately)
    To simplify this as a fraction, we can write it as 7587301587301587/10000000000000000
    This can be simplified to 7587301587301587/10^15
    ### Answer: 7587301587301587/10^15

Expected answer: 164/21

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 23/3 = <<23/3=7.666666666666667>>7 2/3
    80/91 = <<80/91=0.8791208791208791>>80/91
    26/24 = <<26/24=1.0833333333333333>>1 1/3
    80/91 + 26/24 = <<80/91+26/24=1.9624489795918367>>1 19/27
    23/3 - (80/91 + 26/24) = <<23/3-(80/91+26/24)=5.700884955752201>>5 17/27
    ### Answer: 5 17/27

Expected answer: 6229/1092

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 37/18 + 24/60 = 37/18 + 2/5 = (37/18) \* (5/5) + (2/5) \* (18/18) = (185 + 36)/90 = 221/90
    ### Answer: 221/90

Expected answer: 221/90

Correct? Yes

🔗 Follow-up

Problem: If the initial sum of 37/18 and 24/60 is added to the fraction 92/28, what would the new total be? Answer as a simplified fraction.

Gemma 2B:

     Reasoning: 37/18 + 24/60 + 92/28 = 221/90 + 92/28 = (221/90) \* (7/7) + (92/28) \* (15/15) = (1547 + 1380)/630 = 2927/630
    ### Answer: 2927/630

Expected answer: 3617/630

Correct? No

🔗 Follow-up

Problem: If instead of the original sum of 37/18 and 24/60, we now have the sum of 37/18 and 24/72, what would the new total be? Please express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: 37/18 + 24/72 = 37/18 + 1/3 = (37/18) \* (3/3) + (1/3) \* (18/18) = (111 + 18)/54 = 129/54
    ### Answer: 129/54, which simplifies to 14/6 or 7/3

Expected answer: 43/18

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 41 and 62 is 2542.

    33/41 = (33 \* 62)/(41 \* 62) = 2046/2542

    95/62 = (95 \* 41)/(62 \* 41) = 3895/2542

    Now we can add the two fractions:

    2046/2542 + 3895/2542 = (2046 + 3895)/2542 = 5941/2542

    The fraction 5941/2542 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the sum of 33/41 and 95/62 is 5941/2542.

    ### Answer: 5941/2542

Expected answer: 5941/2542

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 33/41 and 95/62, add that sum to 95/62 once again. What is the final simplified fraction?

Gemma 2B:

     Reasoning: We have already found that the sum of 33/41 and 95/62 is 5941/2542.

    Now we need to add that sum to 95/62 once again.

    5941/2542 + 95/62 = (5941 \* 62)/(2542 \* 62) + (95 \* 2542)/(62 \* 2542)

    = 368342/157804 + 241490/157804

    = (368342 + 241490)/157804

    = 609832/157804

    The fraction 609832/157804 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

    Therefore, the final simplified fraction is 152458/39451.

    ### Answer: 152458/39451

Expected answer: 4918/1271

Correct? No

🔗 Follow-up

Problem: After reconsidering the previous problem, suppose instead of 95/62, we now have 83/62. What would the sum of 33/41 and 83/62 be? Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 41 and 62 is 2542.

    33/41 = (33 \* 62)/(41 \* 62) = 2046/2542

    83/62 = (83 \* 41)/(62 \* 41) = 3403/2542

    Now we can add the two fractions:

    2046/2542 + 3403/2542 = (2046 + 3403)/2542 = 5449/2542

    The fraction 5449/2542 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the sum of 33/41 and 83/62 is 5449/2542.

    ### Answer: 5449/2542

Expected answer: 5449/2542

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, simplify the expression inside the parentheses:
    (30 / 11) + (72 / 38) = (30 / 11) + (2 / 1) = (30 + 22) / 11 = 52 / 11

    Next, add the result to (81 / 34):
    (52 / 11) + (81 / 34) = (52 * 34) / (11 * 34) + (81 * 11) / (34 * 11) = (1768 + 891) / (374) = 2659 / 374

    Finally, simplify the fraction:
    2659 / 374 = 7 / 1

    ### Answer: 7

Expected answer: 49773/7106

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to simplify the fractions (64 / 34) and (3 / 24).

    (64 / 34) = <<64/34=18/11>>18/11
    (3 / 24) = <<3/24=1/8>>1/8

    Now, we can add the two fractions:

    (18/11) + (1/8) = (144/88) + (11/88) = <<144/88+11/88=155/88>>155/88

    Finally, we can add the result to (41 / 96):

    (155/88) + (41/96) = (155 * 96) / (88 * 96) + (41 * 88) / (96 * 88) = (14880/8448) + (3608/8448) = <<14880/8448+3608/8448=18488/8448>>18488/8448

    Simplifying the fraction, we get:

    18488/8448 = <<18488/8448=1155/528>>1155/528

    ### Answer: 1155/528

Expected answer: 3973/1632

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning:
    First, Daniel needs to add 83/73 and 53/77 to get 'w'. To add these fractions, he needs to find a common denominator. The least common multiple (LCM) of 73 and 77 is 5601.

    So, 83/73 = (83 * 77) / (73 * 77) = 6411/5601
    And, 53/77 = (53 * 73) / (77 * 73) = 3869/5601

    Now, Daniel can add these two fractions:
    w = 6411/5601 + 3869/5601 = (6411 + 3869) / 5601 = 10280/5601

    Next, Daniel needs to add 80/76 to 'w'. The LCM of 76 and 5601 is 424076.

    So, 80/76 = (80 * 5601) / (76 * 5601) = 448080/424076
    And, w = 10280/5601 = (10280 * 76) / (5601 * 76) = 780480/424076

    Now, Daniel can add these two fractions:
    Final answer = 448080/424076 + 780480/424076 = (448080 + 780480) / 424076 = 1228560/424076

    To simplify this fraction, Daniel can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1228560 and 424076 is 4.

    So, the simplified fraction is:
    Final answer = 1228560/4 / 424076/4 = 307140/106019

    ### Answer: 307140/106019

Expected answer: 307360/106799

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the fractions, we need a common denominator. The least common multiple of 20 and 66 is 660.

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

    Now we can add the fractions:

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

    The fraction 1031/660 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is 1031/660.

    ### Answer: 1031/660

Expected answer: 1031/660

Correct? Yes

🔗 Follow-up

Problem: You previously added the fractions 27/20 and 14/66. Now, add the result to the fraction 58/18 and simplify your answer.

Gemma 2B:

     Reasoning: We previously found that 27/20 + 14/66 = 1031/660.

    Now we need to add this result to 58/18. To do this, we need a common denominator. The least common multiple of 660 and 18 is 1980.

    1031/660 = (1031\*3)/(660\*3) = 3093/1980
    58/18 = (58\*110)/(18\*110) = 6380/1980

    Now we can add the fractions:

    3093/1980 + 6380/1980 = (3093+6380)/1980 = 9473/1980

    The fraction 9473/1980 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is 9473/1980.

    ### Answer: 9473/1980

Expected answer: 9473/1980

Correct? Yes

🔗 Follow-up

Problem: Previously, you added the fractions 27/20 and 14/66. Let's change the problem slightly. Now, instead of 14/66, consider a fraction of 14/41. Add 27/20 and 14/41 together and simplify your answer.

Gemma 2B:

     Reasoning: To add the fractions, we need a common denominator. The least common multiple of 20 and 41 is 820.

    27/20 = (27\*41)/(20\*41) = 1107/820
    14/41 = (14\*20)/(41\*20) = 280/820

    Now we can add the fractions:

    1107/820 + 280/820 = (1107+280)/820 = 1387/820

    The fraction 1387/820 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is 1387/820.

    ### Answer: 1387/820

Expected answer: 1387/820

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we simplify the fractions 32/14 and 22/47.
    32/14 = <<32/14=16/7>>16/7
    22/47 = <<22/47=22/47>>22/47
    Now, we subtract the second fraction from the first:
    16/7 - 22/47 = (16*47 - 22*7) / (7*47) = (752 - 154) / 329 = <<(752 - 154) / 329=598/329>>598/329
    ### Answer: 598/329

Expected answer: 598/329

Correct? Yes

🔗 Follow-up

Problem: If you take the result of ((32 / 14) - (22 / 47)) you calculated earlier, what would be the value you get when you add this result to itself? Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: We already calculated the result of ((32 / 14) - (22 / 47)) as 598/329.
    Now, we add this result to itself:
    598/329 + 598/329 = (598 + 598) / 329 = <<(598 + 598) / 329=1196/329>>1196/329
    ### Answer: 1196/329

Expected answer: 1196/329

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of having 32/14 part of the original mixture, you actually had 71/14 part, and the same fraction (22/47) was subtracted from it. In that case, what would be the new result of the calculation: ((71 / 14) - (22 / 47))? Write your answer as a simplified fraction.

Gemma 2B:

     Reasoning: First, we simplify the fraction 71/14.
    71/14 = <<71/14=71/14>>71/14
    Now, we subtract the second fraction from the first:
    71/14 - 22/47 = (71*47 - 22*14) / (14*47) = (3337 - 308) / 658 = <<(3337 - 308) / 658=3029/658>>3029/658
    ### Answer: 3029/658

Expected answer: 3029/658

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of 74/61 and 41/53, we need to find a common denominator. The least common multiple of 61 and 53 is 3233.

    So, we convert 74/61 to 3794/3233 and 41/53 to 2623/3233.

    Now, we can add the two fractions: 3794/3233 + 2623/3233 = 6417/3233.

    ### Answer: 6417/3233

Expected answer: 6423/3233

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, calculate 94 / 2 = <<94/2=47>>47 and 74 / 57 = <<74/57=1.3>>1.3 (rounded to one decimal place).
    Then, subtract 1.3 from 47 = <<47-1.3=45.7>>45.7 (rounded to one decimal place).
    Next, calculate 56 / 97 = <<56/97=0.57732>>0.57732 (rounded to five decimal places).
    Finally, add 0.57732 to 45.7 = <<45.7+0.57732=46.27732>>46.27732 (rounded to five decimal places).
    The fraction is 46.27732 / 1 = <<46.27732/1=46.27732>>46.27732.
    ### Answer: 46.27732

Expected answer: 255877/5529

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: The sum of 14/89 and the sum of 24/34 and 44/87 is (14/89) + (24/34 + 44/87).
    First, we need to find the sum of 24/34 and 44/87. To do this, we need to find a common denominator. The least common multiple of 34 and 87 is 2918.
    So, 24/34 = (24 \* 87)/(34 \* 87) = 2088/2918 and 44/87 = (44 \* 34)/(87 \* 34) = 1496/2918.
    Now, we can find the sum of 24/34 and 44/87: 2088/2918 + 1496/2918 = 3584/2918.
    Now, we can find the sum of 14/89 and 3584/2918. To do this, we need to find a common denominator. The least common multiple of 89 and 2918 is 259602.
    So, 14/89 = (14 \* 2918)/(89 \* 2918) = 40852/259602 and 3584/2918 = (3584 \* 89)/(2918 \* 89) = 319616/259602.
    Now, we can find the sum of 14/89 and 3584/2918: 40852/259602 + 319616/259602 = 360468/259602.
    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.
    So, 360468/259602 = 180234/129801.
    ### Answer: 180234/129801

Expected answer: 180194/131631

Correct? No

🔗 Problem

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

Gemma 2B:

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

    73/30 = (73*2)/(30*2) = 146/60
    8/60 = 8/60

    Now we can add the fractions:

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

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

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

    ### Answer: 77/30

Expected answer: 77/30

Correct? Yes

🔗 Follow-up

Problem: If you take the result of adding 73/30 to 8/60 and then add it to itself again, what fraction do you get?

Gemma 2B:

     Reasoning: We already know that 73/30 + 8/60 = 77/30.

    Now we need to add this result to itself:

    77/30 + 77/30 = (77+77)/30 = 154/30

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    154/30 = (154/2)/(30/2) = 77/15

    ### Answer: 77/15

Expected answer: 77/15

Correct? Yes

🔗 Follow-up

Problem: Suppose you originally had a fraction of 73/30. Now, instead of adding 8/60 to it, you decide to add 49/60. What fraction will you get in this case?

Gemma 2B:

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

    73/30 = (73*2)/(30*2) = 146/60
    49/60 = 49/60

    Now we can add the fractions:

    146/60 + 49/60 = (146+49)/60 = 195/60

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 15:

    195/60 = (195/15)/(60/15) = 13/4

    ### Answer: 13/4

Expected answer: 13/4

Correct? Yes

🔗 Problem

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.

Gemma 2B:

     Reasoning:
    First, we simplify the second fraction 45/60 = <<45/60=3/4>>3/4.
    Then, we add the first fraction (82/49) with the simplified second fraction (3/4):
    82/49 + 3/4 = (82*4 + 3*49)/(49*4) = (328 + 147)/196 = 475/196.
    Now, we add the result 'd' (475/196) to the third fraction (99/59):
    475/196 + 99/59 = (475*59 + 99*196)/(196*59) = (28075 + 19404)/11584 = 47479/11584.
    Finally, we simplify the resulting fraction 47479/11584 = <<47479/11584=1186975/28960>>1186975/28960.
    ### Answer: 1186975/28960

Expected answer: 47429/11564

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning:
    First, subtract 76/30 from 91/16.
    To subtract fractions, we need a common denominator. The least common multiple of 30 and 16 is 240.
    So, we convert 76/30 to 240/30 * 76/240 = 152/240 and 91/16 to 240/16 * 91/240 = 546/240.
    Now, we can subtract 152/240 from 546/240 to get 394/240.
    Next, we add the answer to 18/44.
    To add fractions, we need a common denominator. The least common multiple of 240 and 44 is 1320.
    So, we convert 394/240 to 1320/240 * 394/1320 = 1970/1320 and 18/44 to 1320/44 * 18/1320 = 540/1320.
    Now, we can add 1970/1320 to 540/1320 to get 2510/1320.
    Finally, we round the answer to the nearest hundredth.
    2510/1320 = 1.9015151515151515, which rounds to 1.90.
    ### Answer: 1.90

Expected answer: 9407/2640

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, we calculate the result of ((8 / 91) + (49 / 5)).
    To add these fractions, we need a common denominator. The least common multiple of 91 and 5 is 455.
    So, we convert the fractions to have the same denominator:
    (8 / 91) = (8 * 5) / (91 * 5) = 40 / 455
    (49 / 5) = (49 * 91) / (5 * 91) = 4459 / 455
    Now, we can add the fractions:
    (40 / 455) + (4459 / 455) = (40 + 4459) / 455 = 4499 / 455
    Next, we subtract (32 / 76) from the result.
    To subtract these fractions, we need a common denominator. The least common multiple of 455 and 76 is 34520.
    So, we convert the fractions to have the same denominator:
    (4499 / 455) = (4499 * 76) / (455 * 76) = 342304 / 34520
    (32 / 76) = (32 * 455) / (76 * 455) = 14560 / 34520
    Now, we can subtract the fractions:
    (342304 / 34520) - (14560 / 34520) = (342304 - 14560) / 34520 = 327744 / 34520
    Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8.
    (327744 / 34520) / (8 / 8) = 40968 / 4315
    ### Answer: 40968 / 4315

Expected answer: 81841/8645

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, calculate the value of ((75 / 45) + (5 / 49)).
    (75 / 45) = <<75/45=5/3>>5/3
    (5 / 49) = <<5/49>>5/49
    ((75 / 45) + (5 / 49)) = (5/3) + (5/49) = (145/147)
    Next, add this value with 3 / 58.
    (145/147) + (3/58) = (145/147) + (3/58) = (145/147) \* (58/58) + (3/58) \* (147/147) = (8410/8526) + (441/8526) = (8851/8526)
    ### Answer: 8851/8526

Expected answer: 15521/8526

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we calculate the two fractions separately:
    43 / 15 = <<43/15=2.8666666666666665>>2.8666666666666665
    33 / 95 = <<33/95=0.34736842105263156>>0.34736842105263156
    Next, we subtract the second fraction from the first:
    2.8666666666666665 - 0.34736842105263156 = <<2.8666666666666665-0.34736842105263156=2.519298245614035>>2.519298245614035
    To simplify this to its lowest terms, we can convert it to a fraction:
    2.519298245614035 = <<2.519298245614035*

Expected answer: 718/285

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find the sum of ((78 / 45) + (89 / 36)).

    (78 / 45) + (89 / 36) = (78 * 36 + 89 * 45) / (45 * 36)

    = (2808 + 3960) / 1620

    = 6768 / 1620

    Now, we need to add this sum to itself.

    6768 / 1620 + 6768 / 1620 = 2 * (6768 / 1620)

    = 13536 / 1620

    Simplifying the fraction, we get:

    13536 / 1620 = 11 * (1236 / 1620)

    = 11 * (206 / 270)

    = 11 * (103 / 135)

    = 1133 / 135

    ### Answer: 1133/135

Expected answer: 757/90

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning: 93 divided by 34 is equal to 2.7352941176470588.
    77 divided by 74 is equal to 1.0405405405405406.
    Subtracting the second fraction from the first gives us 1.6947535771065182.
    To express this as a fraction, we can multiply the numerator and denominator by 10000000000000000 to get rid of the decimal point and simplify the fraction.
    This gives us 16947535771065182/10000000000000000.
    Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2, gives us 8473767885532591/5000000000000000.
    ### Answer: 8473767885532591/5000000000000000

Expected answer: 1066/629

Correct? Yes

🔗 Follow-up

Problem: Continuing from our previous problem, let's now take our previous result and add it to the fraction 64/70. What would we get as a simplified fraction as the final answer?

Gemma 2B:

     Reasoning: The previous result was 8473767885532591/5000000000000000.
    Adding 64/70 to this gives us (8473767885532591/5000000000000000) + (64/70).
    To add these fractions, we need to find a common denominator. The least common multiple of 5000000000000000 and 70 is 350000000000000000.
    Multiplying the first fraction by 7/7 and the second fraction by 5000000000000000/5000000000000000 gives us (59316375208728137/350000000000000000) + (320000000000000000/350000000000000000).
    Adding these fractions gives us 409316375208728137/350000000000000000.
    Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7, gives us 58473767885532591/50000000000000000.
    ### Answer: 58473767885532591/50000000000000000

Expected answer: 57438/22015

Correct? No

🔗 Follow-up

Problem: Recall the previous problem where we had 93 divided by 34 and subtracted the fraction 77/74 from it. Now, let's slightly adjust the scenario. Suppose instead of subtracting 77/74, we subtract 77/51 from the result of 93 divided by 34. What would be the result as a simplified fraction under this new circumstance?

Gemma 2B:

     Reasoning: 93 divided by 34 is equal to 2.7352941176470588.
    77 divided by 51 is equal to 1.5098039215686274.
    Subtracting the second fraction from the first gives us 1.2254901960784314.
    To express this as a fraction, we can multiply the numerator and denominator by 10000000000000000 to get rid of the decimal point and simplify the fraction.
    This gives us 12254901960784314/10000000000000000.
    Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2, gives us 6127450980392157/5000000000000000.
    ### Answer: 6127450980392157/5000000000000000

Expected answer: 125/102

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of 86/35 and 68/85, we need to find a common denominator. The least common multiple of 35 and 85 is 595.

    86/35 = (86 \* 17)/(35 \* 17) = 1462/595

    68/85 = (68 \* 7)/(85 \* 7) = 476/595

    Now, we can add the two fractions:

    1462/595 + 476/595 = (1462 + 476)/595 = 1938/595

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 17.

    1938/595 = (1938/17)/(595/17) = 114/35

    ### Answer: 114/35

Expected answer: 114/35

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 86/35 and 68/85, add the result to 86/35 again. Express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: We have already found that the sum of 86/35 and 68/85 is 114/35.

    Now, we need to add 86/35 to 114/35.

    86/35 + 114/35 = (86 + 114)/35 = 200/35

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5.

    200/35 = (200/5)/(35/5) = 40/7

    ### Answer: 40/7

Expected answer: 40/7

Correct? Yes

🔗 Follow-up

Problem: Reconsider the previous problem where you found the sum of 86/35 and 68/85. What if there were a mistake and the original fraction was actually 86/75, not 86/35? Find the sum of the revised fraction, 86/75, with 68/85. Express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: To find the sum of 86/75 and 68/85, we need to find a common denominator. The least common multiple of 75 and 85 is 1275.

    86/75 = (86 \* 17)/(75 \* 17) = 1462/1275

    68/85 = (68 \* 15)/(85 \* 15) = 1020/1275

    Now, we can add the two fractions:

    1462/1275 + 1020/1275 = (1462 + 1020)/1275 = 2482/1275

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 17.

    2482/1275 = (2482/17)/(1275/17) = 146/75

    ### Answer: 146/75

Expected answer: 146/75

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 53 and 94 is 53*94.

    99/53 = (99*94)/(53*94) = 9306/5002

    67/94 = (67*53)/(94*53) = 3551/5002

    Now we can add the two fractions:

    9306/5002 + 3551/5002 = (9306+3551)/5002 = 12857/5002

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the sum of 99/53 and 67/94 in simplest form is 12857/5002.

    ### Answer: 12857/5002

Expected answer: 12857/4982

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To subtract the fractions, we need a common denominator. The least common multiple of 27 and 33 is 297.

    74/27 = (74*11)/(27*11) = 814/297
    56/33 = (56*9)/(33*9) = 504/297

    Now we can subtract the fractions:

    814/297 - 504/297 = (814-504)/297 = 310/297

    The fraction 310/297 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the simplified form of the fraction is 310/297.

    ### Answer: 310/297

Expected answer: 310/297

Correct? Yes

🔗 Follow-up

Problem: If you then add 92/70 to the result of 74/27 minus 56/33, what fraction do you now have? Please answer as a simplified fraction.

Gemma 2B:

     Reasoning: From the previous question, we know that the result of 74/27 - 56/33 is 310/297.

    Now we need to add 92/70 to this result. To add the fractions, we need a common denominator. The least common multiple of 297 and 70 is 20790.

    310/297 = (310*70)/(297*70) = 21700/20790
    92/70 = (92*297)/(70*297) = 27384/20790

    Now we can add the fractions:

    21700/20790 + 27384/20790 = (21700+27384)/20790 = 49084/20790

    The fraction 49084/20790 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

    Therefore, the simplified form of the fraction is 24542/10395.

    ### Answer: 24542/10395

Expected answer: 24512/10395

Correct? No

🔗 Follow-up

Problem: What if we had 77/27 instead of 74/27 in the beginning? What would the fraction be if you subtracted 56/33 from this? Please answer as a simplified fraction.

Gemma 2B:

     Reasoning: To subtract the fractions, we need a common denominator. The least common multiple of 27 and 33 is 297.

    77/27 = (77*11)/(27*11) = 847/297
    56/33 = (56*9)/(33*9) = 504/297

    Now we can subtract the fractions:

    847/297 - 504/297 = (847-504)/297 = 343/297

    The fraction 343/297 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 7.

    Therefore, the simplified form of the fraction is 49/42.

    ### Answer: 49/42

Expected answer: 343/297

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: First, we need to find the sum of 96/40 and 11/99. To do this, we need to find a common denominator. The least common multiple of 40 and 99 is 3960.

    So, we convert 96/40 to 96*99/40*99 = 9486/3960 and 11/99 to 11*40/99*40 = 440/3960.

    Now, we can add the two fractions: 9486/3960 + 440/3960 = 9926/3960.

    Next, we need to subtract 91/65 from this sum. To do this, we need to find a common denominator for 9926/3960 and 91/65. The least common multiple of 3960 and 65 is 257400.

    So, we convert 9926/3960 to 9926*65/3960*65 = 645290/257400 and 91/65 to 91*3960/65*3960 = 360240/257400.

    Now, we can subtract the two fractions: 645290/257400 - 360240/257400 = 285050/257400.

    Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 10.

    So, the result is 28505/25740.

    ### Answer: 28505/25740

Expected answer: 10/9

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning:
    1) To find h, we first divide 10 by 5, which equals 2. Then we divide 35 by 27, which equals approximately 1.296. Adding these two results together, we get h = 2 + 1.296 = <<2+1.296=3.296>>3.296.
    2) To find p, we add 47 divided by 99 to h. Dividing 47 by 99 equals approximately 0.475. Adding this to h, we get p = 3.296 + 0.475 = <<3.296+0.475=3.771>>3.771.
    ### Answer: 3.771

Expected answer: 1120/297

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, simplify the fraction 2/66 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us 1/33.
    Next, add the two fractions 90/81 and 1/33. To do this, we need to find a common denominator. The least common multiple of 81 and 33 is 2673.
    So, we convert 90/81 to 300/2673 and 1/33 to 81/2673.
    Adding these two fractions gives us 381/2673.
    Finally, simplify the fraction 381/2673 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. This gives us 127/891.
    ### Answer: 127/891

Expected answer: 113/99

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning: Oliver has a piece of ribbon that is 56/41 yards long. If he gets another piece of the same length, then the total length of both pieces of ribbon would be 2*(56/41) = <<2*(56/41)=2.8 yards>>2.8 yards.
    ### Answer: 2.8 yards

Expected answer: 112/41

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 75 and 92 is 75 \* 92.

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

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 13414 and 75 \* 92 is 2.

    13414/75 \* 92 = (13414/2)/(75 \* 92/2) = 6707/37 \* 46

    ### Answer: 6707/37 \* 46

Expected answer: 6707/3450

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of 32/65 and 73/22, we need to find a common denominator. The least common multiple of 65 and 22 is 1430.

    So, we convert 32/65 to 640/1430 and 73/22 to 4691/1430.

    Now, we can add the two fractions: 640/1430 + 4691/1430 = 5331/1430.

    ### Answer: 5331/1430

Expected answer: 5449/1430

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 51/34 - 12/86 = (51*86 - 12*34)/(34*86) = (4386 - 408)/(2924) = 4278/2924 = <<4278/2924=3/2>>3/2
    ### Answer: 3/2

Expected answer: 117/86

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning: First, convert the whole number 51 to a fraction with a denominator of 1, so 51 becomes 51/1.
    Next, add the fractions 51/1 and 93/8. To do this, find a common denominator, which is 8 in this case. So, 51/1 becomes 408/8.
    Now, add the fractions 408/8 and 93/8 to get 501/8.
    Next, add the fraction 501/8 to the fraction 58/44. To do this, find a common denominator, which is 88 in this case. So, 501/8 becomes 5512/88 and 58/44 becomes 116/88.
    Now, add the fractions 5512/88 and 116/88 to get 5628/88.
    Finally, simplify the fraction 5628/88 by dividing both the numerator and the denominator by their greatest common divisor, which is 8. So, 5628/88 becomes 678/11.
    ### Answer: 678/11

Expected answer: 5627/88

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To subtract the fractions, we need to find a common denominator. The least common multiple of 5 and 25 is 25.

    82/5 = (82*5)/(5*5) = 410/25

    98/25 = 98/25

    Now we can subtract the fractions:

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

    The fraction 312/25 is already in its simplest form.

    ### Answer: 312/25

Expected answer: 312/25

Correct? Yes

🔗 Follow-up

Problem: Given the result you obtained previously from calculating 82/5 - 98/25, what would you get if you added this result to itself?

Gemma 2B:

     Reasoning: The result of the previous calculation was 312/25.

    To find the result of adding this result to itself, we simply multiply it by 2:

    312/25 * 2 = (312*2)/25 = 624/25

    ### Answer: 624/25

Expected answer: 624/25

Correct? Yes

🔗 Follow-up

Problem: If you originally had 82/5 oranges and instead of taking away 98/25 of them, you took away 98/90 oranges, how many oranges would you have left? Write the answer in the simplest form.

Gemma 2B:

     Reasoning: To find out how many oranges are left, we need to subtract the number of oranges taken away from the original number of oranges.

    First, we need to find a common denominator for the fractions. The least common multiple of 5, 25, and 90 is 90.

    82/5 = (82*18)/(5*18) = 1476/90

    98/25 = (98*3.6)/(25*3.6) = 352.8/90

    98/90 = 98/90

    Now we can subtract the number of oranges taken away from the original number of oranges:

    1476/90 - 98/90 = (1476-98)/90 = 1378/90

    The fraction 1378/90 is not in its simplest form. To simplify it, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.

    1378/2 = 689

    90/2 = 45

    So the simplest form of the fraction is 689/45.

    ### Answer: 689/45

Expected answer: 689/45

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: (64 / 50) + (70 / 22) = (64 * 22 + 70 * 50) / (50 * 22) = (1408 + 3500) / 1100 = 4908 / 1100
    ### Answer: 4908/1100

Expected answer: 1227/275

Correct? Yes

🔗 Follow-up

Problem: In the previous question, we considered a situation where we added the fractions (64 / 50) and (70 / 22). Now imagine we made a slight error in our calculations, and the initial fraction was actually (64 / 49), not (64 / 50). How would that affect our total sum? Calculate (64 / 49) + (70 / 22) and provide your answer as an unsimplified fraction.

Gemma 2B:

     Reasoning: (64 / 49) + (70 / 22) = (64 * 22 + 70 * 49) / (49 * 22) = (1408 + 3430) / 1078 = 4838 / 1078
    ### Answer: 4838/1078

Expected answer: 2419/539

Correct? Yes

🔗 Problem

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?

Gemma 2B:

     Reasoning: John calculated s by adding 24/6 + 40/53.
    24/6 = <<24/6=4>>4 and 40/53 is approximately 0.7547.
    So, s = 4 + 0.7547 = <<4+0.7547=4.7547>>4.7547.
    John then added s to itself to get b, so b = s + s = 4.7547 + 4.7547 = <<4.7547+4.7547=9.5094>>9.5094.
    ### Answer: 9.5094

Expected answer: 504/53

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we calculate the two fractions separately.

    80/90 = <<80/90=8/9>>8/9

    52/11 = <<52/11=4 8/11>>4 8/11

    Now, we add the two fractions together.

    8/9 + 4 8/11 = <<8/9+4 8/11=1 16/99>>1 16/99

    ### Answer: 1 16/99

Expected answer: 556/99

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 18 and 74 is 666.

    12/18 = (12 * 37)/(18 * 37) = 444/666
    91/74 = (91 * 9)/(74 * 9) = 819/666

    Now we can add the two fractions:

    444/666 + 819/666 = (444 + 819)/666 = 1263/666

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 333:

    1263/666 = (1263/333)/(666/333) = 3.8/2

    So the sum of 12/18 and 91/74 is 3.8/2 or 1.9.

    ### Answer: 1.9

Expected answer: 421/222

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of the fractions 7/2 and 51/25, we need to find a common denominator. The least common multiple of 2 and 25 is 50.

    So, we convert the fractions to have the same denominator:

    7/2 = (7 \* 25) / (2 \* 25) = 175/50

    51/25 = (51 \* 2) / (25 \* 2) = 102/50

    Now, we can add the fractions:

    175/50 + 102/50 = (175 + 102) / 50 = 277/50

    ### Answer: 277/50

Expected answer: 277/50

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous question, add the fraction 86/39 to the sum of 7/2 and 51/25. Express your answer as a simple fraction.

Gemma 2B:

     Reasoning: We already found the sum of 7/2 and 51/25 to be 277/50. Now, we need to add the fraction 86/39 to this sum.

    First, we need to find a common denominator for 50 and 39. The least common multiple of 50 and 39 is 1950.

    So, we convert the fractions to have the same denominator:

    277/50 = (277 \* 39) / (50 \* 39) = 10803/1950

    86/39 = (86 \* 50) / (39 \* 50) = 4300/1950

    Now, we can add the fractions:

    10803/1950 + 4300/1950 = (10803 + 4300) / 1950 = 15103/1950

    ### Answer: 15103/1950

Expected answer: 15103/1950

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you were asked to find the sum of 7/2 and 51/25. Now suppose that instead of 7/2, the fraction was 7/22. How would this change the result? Calculate 7/22 + 51/25 as a simplified fraction.

Gemma 2B:

     Reasoning: To find the sum of the fractions 7/22 and 51/25, we need to find a common denominator. The least common multiple of 22 and 25 is 550.

    So, we convert the fractions to have the same denominator:

    7/22 = (7 \* 25) / (22 \* 25) = 175/550

    51/25 = (51 \* 22) / (25 \* 22) = 1122/550

    Now, we can add the fractions:

    175/550 + 1122/550 = (175 + 1122) / 550 = 1297/550

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1:

    1297/550 = 1297/550

    ### Answer: 1297/550

Expected answer: 1297/550

Correct? Yes

🔗 Problem

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.

Gemma 2B:

     Reasoning:

    First, we calculate the value of the expression inside the parentheses:

    (68 / 69) = <<68/69=0.9855072463768116>>0.9855072463768116

    (93 / 7) = <<93/7=13.285714285714285>>13.285714285714285

    Now, we add the two results:

    0.9855072463768116 + 13.285714285714285 = <<0.9855072463768116+13.285714285714285=14.271221532091096>>14.271221532091096

    Since the expression is a monomial, we can add it to (3 / 46):

    (3 / 46) = <<3/46=0.06521739130434783>>0.06521739130434783

    Now, we add the two results:

    14.271221532091096 + 0.06521739130434783 = <<14.271221532091096+0.06521739130434783=14.336438923395444>>14.336438923395444

    To provide the resulting value as a simple fraction, we can convert the decimal to a fraction:

    14.336438923395444 = <<14.336438923395444*1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Expected answer: 13849/966

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 98 and 4 is 196.

    31/98 = (31\*2)/(98\*2) = 62/196

    60/4 = (60\*49)/(4\*49) = 2940/196

    Now we can add the two fractions:

    62/196 + 2940/196 = (62+2940)/196 = 3002/196

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    3002/196 = (3002/2)/(196/2) = 1501/98

    ### Answer: 1501/98

Expected answer: 1501/98

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what's the result when you subtract 41/52 from the sum of 31/98 and 60/4? Answer as a simplified fraction.

Gemma 2B:

     Reasoning: From the previous problem, we know that the sum of 31/98 and 60/4 is 1501/98.

    Now we need to subtract 41/52 from this sum. To do this, we need to find a common denominator for the two fractions. The least common multiple of 98 and 52 is 2450.

    1501/98 = (1501\*25)/(98\*25) = 37525/2450

    41/52 = (41\*47)/(52\*47) = 1927/2450

    Now we can subtract the two fractions:

    37525/2450 - 1927/2450 = (37525-1927)/2450 = 35598/2450

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    35598/2450 = (35598/2)/(2450/2) = 17799/1225

    ### Answer: 17799/1225

Expected answer: 37017/2548

Correct? No

🔗 Follow-up

Problem: In the previous situation, instead of adding 31/98 to 60/4, what would happen if you added 31/98 to 83/4? What would the new sum be, in simplified fraction form?

Gemma 2B:

     Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 98 and 4 is 196.

    31/98 = (31\*2)/(98\*2) = 62/196

    83/4 = (83\*49)/(4\*49) = 4067/196

    Now we can add the two fractions:

    62/196 + 4067/196 = (62+4067)/196 = 4129/196

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1:

    4129/196 = (4129/1)/(196/1) = 4129/196

    ### Answer: 4129/196

Expected answer: 4129/196

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: First, simplify the second fraction (24/36) by dividing both the numerator and the denominator by their greatest common divisor, which is 12.

    (24/36) = (24 ÷ 12) / (36 ÷ 12) = 2/3

    Now, add the two fractions:

    (3/2) + (2/3)

    To add these fractions, find a common denominator, which is 6 in this case.

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

    Now, add the fractions:

    (9/6) + (4/6) = (9 + 4) / 6 = 13/6

    ### Answer: 13/6

Expected answer: 13/6

Correct? Yes

🔗 Follow-up

Problem: After completing the calculation for ((3 / 2) + (24 / 36)), add the result to 7/2 and give your answer as a simplified fraction.

Gemma 2B:

     Reasoning: From the previous calculation, we know that ((3 / 2) + (24 / 36)) = 13/6.

    Now, add this result to 7/2:

    (13/6) + (7/2)

    To add these fractions, find a common denominator, which is 6 in this case.

    (7/2) = (7 * 3) / (2 * 3) = 21/6

    Now, add the fractions:

    (13/6) + (21/6) = (13 + 21) / 6 = 34/6

    Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

    (34/6) = (34 ÷ 2) / (6 ÷ 2) = 17/3

    ### Answer: 17/3

Expected answer: 17/3

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of having 3/2, we had (32/36) as part of the calculation along with what you previously calculated. Can you determine the new total if you calculate ((3 / 2) + (32 / 36))? Answer as a simplified fraction.

Gemma 2B:

     Reasoning: First, simplify the second fraction (32/36) by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

    (32/36) = (32 ÷ 4) / (36 ÷ 4) = 8/9

    Now, add the two fractions:

    (3/2) + (8/9)

    To add these fractions, find a common denominator, which is 18 in this case.

    (3/2) = (3 * 9) / (2 * 9) = 27/18
    (8/9) = (8 * 2) / (9 * 2) = 16/18

    Now, add the fractions:

    (27/18) + (16/18) = (27 + 16) / 18 = 43/18

    ### Answer: 43/18

Expected answer: 43/18

Correct? Yes

🔗 Problem

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?

Gemma 2B:

     Reasoning:
    First, calculate the sum of 92/54 and 90/13.
    To add these fractions, we need a common denominator. The least common multiple of 54 and 13 is 54 \* 13 = <<54\*13=702>>702.
    So, we convert the fractions to have the same denominator:
    92/54 = (92 \* 13) / (54 \* 13) = <<92\*13=1196>>1196 / 702
    90/13 = (90 \* 54) / (13 \* 54) = <<90\*54=4860>>4860 / 702
    Now, we can add the fractions:
    1196/702 + 4860/702 = (1196 + 4860) / 702 = <<1196+4860=6056>>6056 / 702
    Next, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 6056 and 702 is 2.
    So, we divide both numbers by 2:
    6056 / 2 = <<6056/2=3028>>3028
    702 / 2 = <<702/2=351>>351
    Now, we have the simplified fraction: 3028/351
    Finally, we subtract 46/41 from this fraction.
    To subtract these fractions, we need a common denominator. The least common multiple of 351 and 41 is 351 \* 41 = <<351\*41=14391>>14391.
    So, we convert the fractions to have the same denominator:
    3028/351 = (3028 \* 41) / (351 \* 41) = <<3028\*41=124148>>124148 / 14391
    46/41 = (46 \* 351) / (41 \* 351) = <<46\*351=16186>>16186 / 14391
    Now, we can subtract the fractions:
    124148/14391 - 16186/14391 = (124148 - 16186) / 14391 = <<124148-16186=107962>>107962 / 14391
    Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 107962 and 14391 is 1.
    So, the fraction is already in its simplest form: 107962/14391.
    ### Answer: 107962/14391

Expected answer: 108002/14391

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: Twice the value of 29/23 is 2*(29/23) = <<2*(29/23)=58/23>>58/23.
    The fraction 58/23 is already in its simplest form.
    ### Answer: 58/23

Expected answer: 58/23

Correct? Yes

🔗 Follow-up

Problem: After calculating the value of 2*(29/23), subtract this result from 32/5. What is the resulting fraction in simplest form?

Gemma 2B:

     Reasoning: The value of 2*(29/23) is 58/23.
    Subtracting this from 32/5 gives 32/5 - 58/23 = <<(32/5) - (58/23)=(624-290)/115=334/115>>334/115.
    The fraction 334/115 is already in its simplest form.
    ### Answer: 334/115

Expected answer: 446/115

Correct? No

🔗 Follow-up

Problem: If the initial number was 36/23 instead of 29/23 in our previous problem, what would now be the value of two times this new fraction? Simplify your answer to the simplest form.

Gemma 2B:

     Reasoning: Two times the value of 36/23 is 2*(36/23) = <<2*(36/23)=72/23>>72/23.
    The fraction 72/23 is already in its simplest form.
    ### Answer: 72/23

Expected answer: 72/23

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 20 and 72 is 360.

    29/20 = (29\*18)/(20\*18) = 522/360

    17/72 = (17\*5)/(72\*5) = 85/360

    Now we can add the two fractions:

    522/360 + 85/360 = (522+85)/360 = 607/360

    The fraction 607/360 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the sum of 29/20 and 17/72 is 607/360.

    ### Answer: 607/360

Expected answer: 607/360

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 29/20 and 17/72 in the previous question, now subtract 9/68 from that sum to obtain a new value. What is the simplified fraction of this new answer?

Gemma 2B:

     Reasoning: The sum of 29/20 and 17/72 is 607/360.

    To subtract 9/68 from this sum, we need to find a common denominator. The least common multiple of 360 and 68 is 11040.

    607/360 = (607\*30)/(360\*30) = 18210/11040

    9/68 = (9\*162)/(68\*162) = 1458/11040

    Now we can subtract the two fractions:

    18210/11040 - 1458/11040 = (18210-1458)/11040 = 16752/11040

    The fraction 16752/11040 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 12. Therefore, the new value is 1404/920.

    ### Answer: 1404/920

Expected answer: 9509/6120

Correct? No

🔗 Follow-up

Problem: In the previous problem, you found the sum of 29/20 and 17/72. Now, imagine that instead of having 29/20 of a quantity, you only had 29/5. What would be the sum of 29/5 and 17/72? Keep your answer as a simplified fraction.

Gemma 2B:

     Reasoning: If we have 29/5 of a quantity instead of 29/20, we can convert 29/5 to a fraction with a denominator of 72 by multiplying both the numerator and the denominator by 14.4 (since 72/5 = 14.4).

    29/5 = (29\*14.4)/(5\*14.4) = 417.6/72

    Now we can add the two fractions:

    417.6/72 + 17/72 = (417.6+17)/72 = 434.6/72

    The fraction 434.6/72 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Therefore, the sum of 29/5 and 17/72 is 217.3/36.

    ### Answer: 217.3/36

Expected answer: 2173/360

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: First, simplify each fraction by dividing the numerator by the denominator.
    (36 / 27) = <<36/27=1.3333333333333333>>1.3333333333333333
    (80 / 10) = <<80/10=8>>8
    (73 / 79) = <<73/79=0.9240506329113924>>0.9240506329113924
    Next, add the first two fractions and subtract the third fraction.
    (1.3333333333333333 + 8) - 0.9240506329113924 = <<1.3333333333333333+8-0.9240506329113924=8.413282700422641>>8.413282700422641
    ### Answer: 8.413282700422641

Expected answer: 1993/237

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: (86 / 71) = <<86/71=1.2112676056338028>>1.21 (rounded to the nearest hundredth)
    (91 / 75) = <<91/75=1.2133333333333333>>1.21 (rounded to the nearest hundredth)
    (86 / 71) + (91 / 75) = 1.21 + 1.21 = <<1.21+1.21=2.42>>2.42 (rounded to the nearest hundredth)
    ### Answer: 2.42

Expected answer: 12911/5325

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find a common denominator for the fractions. The least common multiple of 75, 43, and 62 is 20225.

    (21 / 75) = (21 * 270) / (75 * 270) = 5670 / 20225
    (74 / 43) = (74 * 470) / (43 * 470) = 34780 / 20225
    (10 / 62) = (10 * 326) / (62 * 326) = 3260 / 20225

    Now, we can add the fractions:

    (5670 / 20225) + (34780 / 20225) + (3260 / 20225) = (5670 + 34780 + 3260) / 20225 = 43710 / 20225

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5.

    (43710 / 20225) / (5 / 5) = 8742 / 4045

    Therefore, the result is 8742 / 4045.

    ### Answer: 8742 / 4045

Expected answer: 72056/33325

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: ((75 / 66) + (81 / 61)) = (75 * 61 + 81 * 66) / (66 * 61) = (4575 + 5346) / (4026) = 9921 / 4026.
    To reduce the fraction to its lowest term, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 9921 and 4026 is 3.
    So, 9921 / 4026 = (9921 / 3) / (4026 / 3) = 3307 / 1342.
    ### Answer: 3307/1342

Expected answer: 3307/1342

Correct? Yes

🔗 Follow-up

Problem: After you have computed ((75 / 66) + (81 / 61)), what is the result if you additionally add (47 / 19) to that sum? Give your response as a simplified fraction.

Gemma 2B:

     Reasoning: The result of ((75 / 66) + (81 / 61)) is 3307 / 1342.
    Adding (47 / 19) to that sum, we get (3307 / 1342) + (47 / 19) = (3307 * 19 + 47 * 1342) / (1342 * 19) = (62833 + 62874) / (25498) = 125707 / 25498.
    To reduce the fraction to its lowest term, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 125707 and 25498 is 1.
    So, 125707 / 25498 = (125707 / 1) / (25498 / 1) = 125707 / 25498.
    ### Answer: 125707/25498

Expected answer: 125907/25498

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: First, let's find the value of t by adding the two fractions:

    t = 53/18 + 21/99

    To add these fractions, we need a common denominator. The least common multiple of 18 and 99 is 198. So we convert the fractions to have the same denominator:

    t = (53 * 11)/(18 * 11) + (21 * 2)/(99 * 2)
    t = 583/198 + 42/198
    t = (583 + 42)/198
    t = 625/198

    Now that we have the value of t, we can find the total sum, l, of the two identical fractions:

    l = t + t
    l = 625/198 + 625/198
    l = (625 + 625)/198
    l = 1250/198

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1250 and 198 is 2. So we divide both by 2:

    l = (1250/2) / (198/2)
    l = 625/99

    Therefore, the total sum of the two identical fractions is 625/99.

    ### Answer: 625/99

Expected answer: 625/99

Correct? Yes

🔗 Follow-up

Problem: Consider the previous situation where you calculated the sum of two identical fractions, t, both equal to the sum of 53/18 and 21/99. You found the total sum, l. Now, add the fraction 99/92 to l, and call this total c. What is c expressed as a simplified fraction?

Gemma 2B:

     Reasoning: We already found that the total sum of the two identical fractions, l, is 625/99. Now we need to add the fraction 99/92 to l:

    c = l + 99/92

    To add these fractions, we need a common denominator. The least common multiple of 99 and 92 is 891. So we convert the fractions to have the same denominator:

    c = (625 * 92)/(99 * 92) + (99 * 10)/(92 * 10)
    c = 57500/891 + 990/891
    c = (57500 + 990)/891
    c = 58490/891

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 58490 and 891 is 1. So the fraction is already in its simplest form.

    Therefore, the total sum of the two identical fractions and the fraction 99/92 is 58490/891.

    ### Answer: 58490/891

Expected answer: 67301/9108

Correct? No

🔗 Follow-up

Problem: Remember the earlier situation where you found the sum of two identical fractions, each equal to the sum of 53/18 and 21/99. Now, suppose that each fraction was instead equal to the sum of 76/18 and 21/99. You add these two identical fractions together to get a new total, which we will call w. What is w expressed as a simple fraction?

Gemma 2B:

     Reasoning: First, let's find the value of the new fraction by adding the two fractions:

    t = 76/18 + 21/99

    To add these fractions, we need a common denominator. The least common multiple of 18 and 99 is 198. So we convert the fractions to have the same denominator:

    t = (76 * 11)/(18 * 11) + (21 * 2)/(99 * 2)
    t = 836/198 + 42/198
    t = (836 + 42)/198
    t = 878/198

    Now that we have the value of t, we can find the total sum, w, of the two identical fractions:

    w = t + t
    w = 878/198 + 878/198
    w = (878 + 878)/198
    w = 1756/198

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1756 and 198 is 2. So we divide both by 2:

    w = (1756/2) / (198/2)
    w = 878/99

    Therefore, the total sum of the two identical fractions is 878/99.

    ### Answer: 878/99

Expected answer: 878/99

Correct? Yes

🔗 Problem

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?

Gemma 2B:

     Reasoning:
    First, calculate the result of 58/49 + 31/34.
    To add these fractions, we need a common denominator. The least common multiple of 49 and 34 is 1666.
    So, we convert the fractions to have the same denominator:
    58/49 = (58 \* 34)/(49 \* 34) = 1972/1666
    31/34 = (31 \* 49)/(34 \* 49) = 1519/1666
    Now, we can add the fractions:
    1972/1666 + 1519/1666 = (1972 + 1519)/1666 = 3491/1666
    Next, add that result to the fraction 74/38.
    To add these fractions, we need a common denominator. The least common multiple of 1666 and 38 is 1666.
    So, we convert the fraction 74/38 to have the same denominator:
    74/38 = (74 \* 44)/(38 \* 44) = 3256/1666
    Now, we can add the fractions:
    3491/1666 + 3256/1666 = (3491 + 3256)/1666 = 6747/1666
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
    So, the final result is 6747/1666.
    ### Answer: 6747/1666

Expected answer: 127971/31654

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 100 divided by 76 is equal to 1.3157894736842105 (repeating).
    29 divided by 14 is equal to 2.0714285714285714 (repeating).
    The sum of these two numbers is 1.3157894736842105 + 2.0714285714285714 = 3.3872179451127819 (repeating).
    ### Answer: 3.3872179451127819 (repeating) or 3 17/49 as a simplified fraction.

Expected answer: 901/266

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: Evan has read 51/18 of his novel.
    Olivia has read the same amount as Evan, which is also 51/18 of her novel.
    After reading the same amount as Evan, Olivia has read an additional (8/42) of her novel.
    To find out how much of the novel Olivia has read in total, we need to add the two fractions together:
    51/18 + 8/42 = (51/18) \* (42/42) + (8/42) \* (18/18) = (51 \* 42)/(18 \* 42) + (8 \* 18)/(42 \* 18) = (2142 + 144)/(756) = 2286/756
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6:
    2286/756 = (2286/6)/(756/6) = 381/126
    Therefore, Olivia has read 381/126 of her novel in total.
    ### Answer: 381/126

Expected answer: 127/42

Correct? Yes

🔗 Follow-up

Problem: Building off of the previous question and given that Evan then continues to read and finishes the same amount of his novel as Olivia had read in total, how much of the novel has Evan read now? Answer as a simplified fraction.

Gemma 2B:

     Reasoning: Olivia has read 381/126 of her novel in total.
    Evan has read 51/18 of his novel, which is the same amount as Olivia had read before she read the additional (8/42).
    To find out how much of the novel Evan has read now, we need to add the amount he has already read to the amount Olivia has read in total:
    51/18 + 381/126 = (51/18) \* (126/126) + (381/126) \* (18/18) = (51 \* 126)/(18 \* 126) + (381 \* 18)/(126 \* 18) = (6426 + 6858)/(2268) = 13284/2268
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 18:
    13284/2268 = (13284/18)/(2268/18) = 738/126
    Therefore, Evan has read 738/126 of his novel now.
    ### Answer: 738/126

Expected answer: 41/7

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, let's now instead assume that Olivia initially read 3/42 of her novel, instead of 8/42, before reading the same amount as Evan. Now how much of the novel has Olivia read altogether? Answer as a simplified fraction.

Gemma 2B:

     Reasoning: Olivia initially read 3/42 of her novel.
    After reading the same amount as Evan, Olivia has read an additional 51/18 of her novel.
    To find out how much of the novel Olivia has read in total, we need to add the two fractions together:
    3/42 + 51/18 = (3/42) \* (18/18) + (51/18) \* (42/42) = (3 \* 18)/(42 \* 18) + (51 \* 42)/(18 \* 42) = (54 + 2142)/(756) = 2196/756
    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6:
    2196/756 = (2196/6)/(756/6) = 366/126
    Therefore, Olivia has read 366/126 of her novel in total.
    ### Answer: 366/126

Expected answer: 61/21

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: 48 divided by 13 is equal to 48/13.
    31 divided by 22 is equal to 31/22.
    The sum of 48/13 and 31/22 is equal to (48/13) + (31/22).
    To add these fractions, we need a common denominator. The least common multiple of 13 and 22 is 286.
    So, we convert 48/13 to 1104/286 and 31/22 to 403/286.
    The sum of 1104/286 and 403/286 is equal to 1507/286.
    ### Answer: 1507/286 or 5.27

Expected answer: 1459/286

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, we find the value of 24/86 + 76/77.
    24/86 = <<24/86=0.27906976744186046511627906976744>>0.27906976744186046511627906976744
    76/77 = <<76/77=0.98701298701298701298701298701298>>0.98701298701298701298701298701298
    24/86 + 76/77 = 0.27906976744186046511627906976744 + 0.98701298701298701298701298701298 = <<0.27906976744186046511627906976744+0.98701298701298701298701298701298=1.26608275445484747800329105678042>>1.26608275445484747800329105678042
    Next, we subtract this value from 27/6.
    27/6 = <<27/6=4.5>>4.5
    27/6 - (24/86 + 76/77) = 4.5 - 1.26608275445484747800329105678042 = <<4.5-1.26608275445484747800329105678042=3.23391724554515252199670894321958>>3.23391724554515252199670894321958
    ### Answer: 3.23391724554515252199670894321958

Expected answer: 21415/6622

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous question where you found the value of 24/86 + 76/77 and subtracted that from 27/6, please subtract the original value of 24/86 + 76/77 from your most recent answer. Remember to simplify your answer to the lowest terms.

Gemma 2B:

     Reasoning:
    First, we find the value of 24/86 + 76/77.
    24/86 = <<24/86=0.27906976744186046511627906976744>>0.27906976744186046511627906976744
    76/77 = <<76/77=0.98701298701298701298701298701298>>0.98701298701298701298701298701298
    24/86 + 76/77 = 0.27906976744186046511627906976744 + 0.98701298701298701298701298701298 = <<0.27906976744186046511627906976744+0.98701298701298701298701298701298=1.26608275445484747800329105678042>>1.26608275445484747800329105678042
    Next, we subtract this value from 27/6.
    27/6 = <<27/6=4.5>>4.5
    27/6 - (24/86 + 76/77) = 4.5 - 1.26608275445484747800329105678042 = <<4.5-1.26608275445484747800329105678042=3.23391724554515252199670894321958>>3.23391724554515252199670894321958
    Now, we subtract the original value of 24/86 + 76/77 from our most recent answer.
    3.23391724554515252199670894321958 - (24/86 + 76/77) = 3.23391724554515252199670894321958 - 1.26608275445484747800329105678042 = <<3.23391724554515252199670894321958-1.26608275445484747800329105678042=1.96783449109030504399341788643916>>1.96783449109030504399341788643916
    To simplify this answer to the lowest terms, we can see that the decimal repeats after the 14th digit, so we can round it to the nearest hundredth.
    1.96783449109030504399341788643916 ≈ <<1.9678344

Expected answer: 13031/6622

Correct? No

🔗 Follow-up

Problem: Following the previous task, suppose instead of adding 76/77, we add 61/77 to 24/86. Then, subtract this total from 27/6. Please write out the process and show your work for this new problem.

Gemma 2B:

     Reasoning:
    First, we find the value of 24/86 + 61/77.
    24/86 = <<24/86=0.27906976744186046511627906976744>>0.27906976744186046511627906976744
    61/77 = <<61/77=0.79220779220779220779220779220779>>0.79220779220779220779220779220779
    24/86 + 61/77 = 0.27906976744186046511627906976744 + 0.79220779220779220779220779220779 = <<0.27906976744186046511627906976744+0.79220779220779220779220779220779=1.07127755964965267290848636197523>>1.07127755964965267290848636197523
    Next, we subtract this value from 27/6.
    27/6 = <<27/6=4.5>>4.5
    27/6 - (24/86 + 61/77) = 4.5 - 1.07127755964965267290848636197523 = <<4.5-1.07127755964965267290848636197523=3.42872244035034732709151363802477>>3.42872244035034732709151363802477
    ### Answer: 3.42872244035034732709151363802477

Expected answer: 22705/6622

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of 73/39 and 49/14, we first need to find a common denominator. The least common multiple of 39 and 14 is 133.

    73/39 = (73 \* 3)/(39 \* 3) = 219/117
    49/14 = (49 \* 9)/(14 \* 9) = 441/126

    Now we can add the two fractions:

    219/117 + 441/126 = (219 \* 126)/(117 \* 126) + (441 \* 117)/(126 \* 117) = (27594 + 51597)/(14742) = 79191/14742

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    79191/14742 = (79191/3)/(14742/3) = 26397/4914

    ### Answer: 26397/4914

Expected answer: 419/78

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 73/39 and 49/14 (the last problem), now add the result to 21/80. What is the new total? Express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: The sum of 73/39 and 49/14 is 26397/4914.

    To add this result to 21/80, we first need to find a common denominator. The least common multiple of 4914 and 80 is 393120.

    26397/4914 = (26397 \* 80)/(4914 \* 80) = 2111760/393120
    21/80 = (21 \* 4914)/(80 \* 4914) = 103209/393120

    Now we can add the two fractions:

    2111760/393120 + 103209/393120 = (2111760 + 103209)/393120 = 2214969/393120

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    2214969/393120 = (2214969/3)/(393120/3) = 738323/131040

    ### Answer: 738323/131040

Expected answer: 17579/3120

Correct? No

🔗 Follow-up

Problem: After finding the sum of 73/6 and 49/14 (instead of 73/39 as in the previous question), what would be the new total? Please express it as a simplified fraction.

Gemma 2B:

     Reasoning: To find the sum of 73/6 and 49/14, we first need to find a common denominator. The least common multiple of 6 and 14 is 42.

    73/6 = (73 \* 7)/(6 \* 7) = 511/42
    49/14 = (49 \* 3)/(14 \* 3) = 147/42

    Now we can add the two fractions:

    511/42 + 147/42 = (511 + 147)/42 = 658/42

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    658/42 = (658/2)/(42/2) = 329/21

    ### Answer: 329/21

Expected answer: 47/3

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 65 and 39 is 2535.

    75/65 = (75 \* 39)/(65 \* 39) = 2925/2535

    7/39 = (7 \* 65)/(39 \* 65) = 455/2535

    Now we can add the two fractions:

    2925/2535 + 455/2535 = (2925 + 455)/2535 = 3380/2535

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5.

    3380/2535 = (3380/5)/(2535/5) = 676/507

    ### Answer: 676/507

Expected answer: 4/3

Correct? Yes

🔗 Follow-up

Problem: You previously calculated the sum of 75/65 and 7/39. Now, add the fraction 65/97 to your result. What is your new total?

Gemma 2B:

     Reasoning: We previously found that the sum of 75/65 and 7/39 is 676/507.

    Now we need to add the fraction 65/97 to this result. To do this, we need to find a common denominator for the two fractions. The least common multiple of 507 and 97 is 49179.

    676/507 = (676 \* 97)/(507 \* 97) = 65612/49179

    65/97 = (65 \* 507)/(97 \* 507) = 32905/49179

    Now we can add the two fractions:

    65612/49179 + 32905/49179 = (65612 + 32905)/49179 = 98517/49179

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.

    98517/49179 = (98517/3)/(49179/3) = 32839/16393

    ### Answer: 32839/16393

Expected answer: 583/291

Correct? No

🔗 Follow-up

Problem: In a previous calculation, you found the sum of 75/65 and 7/39. Now, suppose we had originally used 75/65 and 7/47 instead. What would be the sum of these two fractions?

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 65 and 47 is 3055.

    75/65 = (75 \* 47)/(65 \* 47) = 3525/3055

    7/47 = (7 \* 65)/(47 \* 65) = 455/3055

    Now we can add the two fractions:

    3525/3055 + 455/3055 = (3525 + 455)/3055 = 3980/3055

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5.

    3980/3055 = (3980/5)/(3055/5) = 796/611

    ### Answer: 796/611

Expected answer: 796/611

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: 79/1 - 30/92 = <<79/1=79>>79 - <<30/92=0.3260869565217391>>0.3260869565217391 = <<79-0.3260869565217391=78.67391304347826>>78.67391304347826
    78.67391304347826 - 61/63 = <<78.67391304347826-61/63=78.67391304347826-0.9682539682539683>>77.70565907522429
    ### Answer: 77.70565907522429

Expected answer: 225191/2898

Correct? Yes

🔗 Follow-up

Problem: After you've calculated 79/1 - 30/92, and then subtracted 61/63 from the result, further subtract 59/7 from that resultant value. What fraction do you end up with?

Gemma 2B:

     Reasoning: 79/1 - 30/92 = <<79/1=79>>79 - <<30/92=0.3260869565217391>>0.3260869565217391 = <<79-0.3260869565217391=78.67391304347826>>78.67391304347826
    78.67391304347826 - 61/63 = <<78.67391304347826-61/63=78.67391304347826-0.9682539682539683>>77.70565907522429
    77.70565907522429 - 59/7 = <<77.70565907522429-59/7=77.70565907522429-8.428571428571429>>69.27708764665286
    ### Answer: 69.27708764665286

Expected answer: 200765/2898

Correct? No

🔗 Follow-up

Problem: After recalculating the previous problem, let's change the first fraction: instead of subtracting 30/92 from 79/1, we're going to subtract 3/92 instead. After that, we still need to subtract 61/63 from the result. What is the value after these operations?

Gemma 2B:

     Reasoning: 79/1 - 3/92 = <<79/1=79>>79 - <<3/92=0.03260869565217391>>0.03260869565217391 = <<79-0.03260869565217391=78.96739130434783>>78.96739130434783
    78.96739130434783 - 61/63 = <<78.96739130434783-61/63=78.96739130434783-0.9682539682539683>>77.99913733609386
    ### Answer: 77.99913733609386

Expected answer: 452083/5796

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: (58 / 26) + (58 / 26) = 2 * (58 / 26) = 2 * 2 = <<2*2=4>>4.
    ### Answer: 4

Expected answer: 58/13

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning:
    First, let's find the total amount of orange juice Alex had after buying additional orange juice.

    Alex had 69/63 + 77/5 = <<69/63+77/5=1.1+15.4=16.5>>16.5 gallons of orange juice.

    Then, Alex received another 47/71 gallons from Sally.

    So, the total amount of orange juice Alex had is 16.5 + 47/71 = <<16.5+47/71=16.5+0.662=17.162>>17.162 gallons.

    Since we are looking for the total amount of orange juice Alex had in gallons, we can round the answer to the nearest hundredth.

    ### Answer: 17.16 gallons

Expected answer: 127907/7455

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    First, we simplify the fractions inside the parentheses:
    (100 / 61) = <<100/61=100/61>>100/61
    (39 / 6) = <<39/6=13/2>>13/2
    (67 / 49) = <<67/49=67/49>>67/49

    Next, we add the fractions inside the parentheses:
    (13/2) + (67/49) = (637/98) + (67/49) = (637+67)/98 = <<(637+67)/98=704/98>>704/98

    Finally, we add the result to the first fraction:
    (100/61) + (704/98) = (9800/5958) + (704/98) = (9800+704)/5958 = <<(9800+704)/5958=10504/5958>>10504/5958

    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
    10504/5958 = (10504/2)/(5958/2) = <<(10504/2)/(5958/2)=5252/2979>>5252/2979

    ### Answer: 5252/2979

Expected answer: 56831/5978

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: 85/1 = <<85/1=85>>85
    83/69 = <<83/69=1.2028985507246377>>1.2028985507246377 (rounded to 10 decimal places)
    85 + 1.2028985507246377 = <<85+1.2028985507246377=86.20289855072463>>86.20289855072463 (rounded to 10 decimal places)
    ### Answer: 86.20289855072463 (rounded to 10 decimal places)

Expected answer: 5948/69

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 13 and 86 is 104.

    92/13 = (92 * 8) / (13 * 8) = 736/104
    43/86 = (43 * 1) / (86 * 1) = 43/104

    Now we can add the two fractions:

    736/104 + 43/104 = (736 + 43) / 104 = 779/104

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    779/104 is already in its simplest form.

    ### Answer: 779/104

Expected answer: 197/26

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 32 and 98 is 224.

    67/32 = (67\*7)/(32\*7) = 469/224

    10/98 = (10\*2)/(98\*2) = 20/196 = (20\*1)/(196\*1) = 20/224

    Now we can add the two fractions:

    469/224 + 20/224 = (469+20)/224 = 489/224

    The fraction 489/224 is already in its simplest form.

    ### Answer: 489/224

Expected answer: 3443/1568

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 52 and 32 is 1664.

    59/52 = (59\*32)/(52\*32) = 1888/1664

    70/32 = (70\*52)/(32\*52) = 3640/1664

    Now we can add the two fractions:

    1888/1664 + 3640/1664 = (1888+3640)/1664 = 5528/1664

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 16:

    5528/1664 = (5528/16)/(1664/16) = 346/104

    We can further simplify the fraction by dividing both the numerator and the denominator by 2:

    346/104 = (346/2)/(104/2) = 173/52

    ### Answer: 173/52

Expected answer: 691/208

Correct? No

🔗 Problem

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?

Gemma 2B:

     Reasoning: 48 divided by 5 = <<48/5=9.6>>9.6
    11 divided by 65 = <<11/65=0.16923076923076923>>0.16923076923076923
    9.6 - 0.16923076923076923 = <<9.6-0.16923076923076923=9.430769230769231>>9.430769230769231
    28 divided by 2 = <<28/2=14>>14
    9.430769230769231 + 14 = <<9.430769230769231+14=23.430769230769231>>23.430769230769231
    ### Answer: 23.430769230769231

Expected answer: 1523/65

Correct? Yes

🔗 Follow-up

Problem: After recalculating the operation considering the new fraction 28/87 instead of 28/2, add the previous result, which is 48/5 minus 11/65. What will be the new outcome?

Gemma 2B:

     Reasoning: 28 divided by 87 = <<28/87=0.32183907961783435>>0.32183907961783435
    9.430769230769231 + 0.32183907961783435 = <<9.430769230769231+0.32183907961783435=9.752608310387065>>9.752608310387065
    ### Answer: 9.752608310387065

Expected answer: 55151/5655

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 52 and 82 is 2124.

    20/52 = (20 \* 41)/(52 \* 41) = 820/2124
    75/82 = (75 \* 26)/(82 \* 26) = 1950/2124

    Now we can add the two fractions:

    820/2124 + 1950/2124 = (820 + 1950)/2124 = 2770/2124

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 26.

    2770/2124 = (2770/26)/(2124/26) = 106.53846153846154/81.69230769230769

    Since we are looking for the smallest possible fraction, we can round the decimal to the nearest whole number.

    106.53846153846154 ≈ 107
    81.69230769230769 ≈ 82

    So the simplified fraction is 107/82.

    ### Answer: 107/82

Expected answer: 1385/1066

Correct? No

🔗 Problem

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

Gemma 2B:

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

    So, we convert the fractions to have the same denominator:

    92/84 = (92 \* 5) / (84 \* 5) = 460/420

    31/5 = (31 \* 84) / (5 \* 84) = 2604/420

    Now, we can subtract the two fractions:

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

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 8:

    2144/420 = (2144/8) / (420/8) = 268/52.5

    Since 52.5 is not an integer, we can multiply both the numerator and the denominator by 2 to get an integer denominator:

    268/52.5 = (268 \* 2) / (52.5 \* 2) = 536/105

    Therefore, the result of subtracting 92/84 from 31/5 is 536/105.

    ### Answer: 536/105

Expected answer: 536/105

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we subtracted 67/84 from 31/5. The result was a certain simplified fraction, but what if instead of 92/84, we had only subtracted 67/84 from 31/5? What would the result be as a simplified fraction with this modification?

Gemma 2B:

     Reasoning: We can follow the same steps as before, but this time we subtract 67/84 instead of 92/84.

    First, we find a common denominator for the two fractions, which is 420.

    So, we convert the fractions to have the same denominator:

    67/84 = (67 \* 5) / (84 \* 5) = 335/420

    31/5 = (31 \* 84) / (5 \* 84) = 2604/420

    Now, we can subtract the two fractions:

    2604/420 - 335/420 = (2604 - 335) / 420 = 2269/420

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1:

    2269/420 = (2269/1) / (420/1) = 2269/420

    Therefore, the result of subtracting 67/84 from 31/5 is 2269/420.

    ### Answer: 2269/420

Expected answer: 2269/420

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find the sum of 81/90 and 94/49.
    81/90 + 94/49 = <<81/90+94/49=1.75>>1.75
    Then, we need to double this sum.
    2 * 1.75 = <<2*1.75=3.5>>3.5
    ### Answer: 3.5

Expected answer: 1381/245

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 21 and 92 is 644.

    69/21 = (69 \* 31)/(21 \* 31) = 2139/644

    10/92 = (10 \* 7)/(92 \* 7) = 70/644

    Now, we can find the difference between the two fractions:

    2139/644 - 70/644 = (2139 - 70)/644 = 2069/644

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    Therefore, the difference between 69/21 and 10/92 is 2069/644.

    ### Answer: 2069/644

Expected answer: 1023/322

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:
    (26 / 87) + (92 / 88) = <<26/87+92/88=1.0563>>1.0563
    (26 / 57) = <<26/57=0.4561>>0.4561
    1.0563 + 0.4561 = <<1.0563+0.4561=1.5124>>1.5124
    ### Answer: 1.5124

Expected answer: 21825/12122

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, simplify each fraction:
    78/66 = <<78/66=1.1818181818181819>>1.1818181818181819 (rounded to 12 decimal places)
    28/6 = <<28/6=4.666666666666667>>4.666666666666667 (rounded to 12 decimal places)
    90/34 = <<90/34=2.6470588235294117>>2.6470588235294117 (rounded to 12 decimal places)
    Next, add the fractions together:
    1.1818181818181819 + 4.666666666666667 + 2.6470588235294117 = <<1.1818181818181819+4.666666666666667+2.6470588235294117=8.495543671914259>>8.495543671914259 (rounded to 12 decimal places)
    Finally, convert the decimal to a fraction:
    8.495543671914259 = <<8.495543671914259*1000000000000=8495543671914259>>8495543671914259/1000000000000 (rounded to 12 decimal places)
    ### Answer: 8495543671914259/1000000000000

Expected answer: 4766/561

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To calculate (12 / 7) - (9 / 23), we first find a common denominator for the two fractions. The least common multiple of 7 and 23 is 161.

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

    Now we can subtract the two fractions:

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

    The fraction 213 / 161 is already in its simplest form, as 213 and 161 have no common factors other than 1.

    ### Answer: 213 / 161

Expected answer: 213/161

Correct? Yes

🔗 Follow-up

Problem: After finding the result of (12 / 7) - (9 / 23), use your answer as t. Then, calculate (40 / 11) - t. What do you find? Please express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: From the previous question, we found that t = 213 / 161.

    Now we need to calculate (40 / 11) - t.

    First, we find a common denominator for the two fractions. The least common multiple of 11 and 161 is 1771.

    (40 / 11) = (40 * 161) / (11 * 161) = 6440 / 1771
    (213 / 161) = (213 * 11) / (161 * 11) = 2343 / 1771

    Now we can subtract the two fractions:

    (6440 / 1771) - (2343 / 1771) = (6440 - 2343) / 1771 = 4097 / 1771

    The fraction 4097 / 1771 is not in its simplest form, as both the numerator and the denominator can be divided by 11.

    4097 / 11 = 372.45454545454544
    1771 / 11 = 161

    So the simplified fraction is 372.45454545454544 / 161.

    ### Answer: 372.45454545454544 / 161

Expected answer: 4097/1771

Correct? No

🔗 Follow-up

Problem: In the previous problem, you calculated (12 / 7) - (9 / 23) which accounted for certain quantities of two different fruits. Now suppose you actually had 12/7th of a crate of oranges but only 9/48th of a crate of apples. In that case, what would be the resulting difference in fractions between the two fruit quantities? Simplify your answer to the lowest terms.

Gemma 2B:

     Reasoning: In this case, we have 12/7th of a crate of oranges and 9/48th of a crate of apples. To find the difference between the two quantities, we first simplify the fraction for the apples:

    (9 / 48) = (9 / (9 * 5)) = 1 / 5

    Now we can find the difference between the two fractions:

    (12 / 7) - (1 / 5)

    To subtract these fractions, we need a common denominator. The least common multiple of 7 and 5 is 35.

    (12 / 7) = (12 * 5) / (7 * 5) = 60 / 35
    (1 / 5) = (1 * 7) / (5 * 7) = 7 / 35

    Now we can subtract the two fractions:

    (60 / 35) - (7 / 35) = (60 - 7) / 35 = 53 / 35

    The fraction 53 / 35 is already in its simplest form, as 53 and 35 have no common factors other than 1.

    ### Answer: 53 / 35

Expected answer: 171/112

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 18 and 61 is 1098.

    95/18 = (95 \* 61) / (18 \* 61) = 5795 / 1098

    51/61 = (51 \* 18) / (61 \* 18) = 918 / 1098

    Now we can add the two fractions:

    5795/1098 + 918/1098 = (5795 + 918) / 1098 = 6713 / 1098

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 13.

    6713 / 1098 = (6713 / 13) / (1098 / 13) = 516 / 84

    We can simplify this fraction further by dividing both the numerator and the denominator by 4.

    516 / 84 = (516 / 4) / (84 / 4) = 129 / 21

    ### Answer: 129/21

Expected answer: 6713/1098

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To subtract the fractions, we need to find a common denominator. The least common multiple of 46 and 84 is 23 * 4 = 92.

    (93 / 46) = (93 * 2) / (46 * 2) = 186 / 92
    (51 / 84) = (51 * 1) / (84 * 1) = 51 / 92

    Now we can subtract the fractions:

    186 / 92 - 51 / 92 = (186 - 51) / 92 = 135 / 92

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    135 / 3 = 45
    92 / 3 = 30.666...

    Since the denominator cannot be a decimal, we can multiply both the numerator and the denominator by 3 to get rid of the decimal:

    45 * 3 = 135
    30.666... * 3 = 92

    So the simplified fraction is 135 / 92.

    ### Answer: 135 / 92

Expected answer: 911/644

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the fractions, we need a common denominator. The least common multiple of 70 and 9 is 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

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6:

    5988/630 = (5988/6) / (630/6) = 998/105

    ### Answer: 998/105

Expected answer: 998/105

Correct? Yes

🔗 Follow-up

Problem: If you remember, you previously calculated the sum of the fractions 12/70 and 84/9. Now, add this new fraction to the result: 21/86. What is the new total? Again, please present your answer in simplified form.

Gemma 2B:

     Reasoning: The sum of the fractions 12/70 and 84/9 is 998/105.

    To add the fraction 21/86 to this result, we need a common denominator. The least common multiple of 105 and 86 is 86 * 105 = 9030.

    998/105 = (998 * 86) / (105 * 86) = 85828/9030
    21/86 = (21 * 105) / (86 * 105) = 2205/9030

    Now we can add the fractions:

    85828/9030 + 2205/9030 = (85828 + 2205) / 9030 = 88033/9030

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1:

    88033/9030 = (88033/1) / (9030/1) = 88033/9030

    ### Answer: 88033/9030

Expected answer: 88033/9030

Correct? Yes

🔗 Follow-up

Problem: Let's rethink a detail from your previous calculation. Instead of adding the fractions 12/70 and 84/9, suppose you need to consider a situation where you add 12/70 and 40/9 instead. What is the sum of these two fractions? Provide your answer as a simplified fraction.

Gemma 2B:

     Reasoning: To add the fractions, we need a common denominator. The least common multiple of 70 and 9 is 630.

    12/70 = (12 * 9) / (70 * 9) = 108/630
    40/9 = (40 * 70) / (9 * 70) = 2800/630

    Now we can add the fractions:

    108/630 + 2800/630 = (108 + 2800) / 630 = 2908/630

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

    2908/630 = (2908/2) / (630/2) = 1454/315

    ### Answer: 1454/315

Expected answer: 1454/315

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: First, subtract 40/92 from 32/3.
    32/3 - 40/92 = (32*92 - 40*3)/(3*92) = (3008 - 120)/276 = 2888/276 = <<2888/276=10.463777777777778>>10.463777777777778
    Then, double the result: 10.463777777777778 * 2 = <<10.463777777777778*2=20.927555555555556>>20.927555555555556
    ### Answer: 20.927555555555556

Expected answer: 1412/69

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: The sum of 79/24 and 79/24 is (79/24) + (79/24) = 2*(79/24) = <<2*(79/24)=79/12>>79/12.
    ### Answer: 79/12

Expected answer: 79/12

Correct? Yes

🔗 Follow-up

Problem: In continuation to the previous problem, now find out what is the sum of two times the previously found sum. In other words, calculate (79/24 + 79/24) + (79/24 + 79/24). Please answer as a simplified fraction.

Gemma 2B:

     Reasoning: The sum of two times the previously found sum is (79/24 + 79/24) + (79/24 + 79/24) = 2*(79/24) + 2*(79/24) = 4*(79/24) = <<4*(79/24)=79/6>>79/6.
    ### Answer: 79/6

Expected answer: 79/6

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you added together two fractions of 79/24. Now, consider if those were fractions of 79/20 instead. What would be the total if you added together two fractions of 79/20? Please express your answer as a simplified fraction.

Gemma 2B:

     Reasoning: The sum of 79/20 and 79/20 is (79/20) + (79/20) = 2*(79/20) = <<2*(79/20)=79/10>>79/10.
    ### Answer: 79/10

Expected answer: 79/10

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 76 and 22 is 184.

    91/76 = (91\*2)/(76\*2) = 182/152
    12/22 = (12\*8)/(22\*8) = 96/176

    Now we can add the two fractions:

    182/152 + 96/176 = (182\*176)/(152\*176) + (96\*152)/(176\*152) = (32032+14688)/(26880) = 46720/26880

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 160:

    46720/26880 = (46720/160)/(26880/160) = 292/168

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

    292/168 = (292/4)/(168/4) = 73/42

    ### Answer: 73/42

Expected answer: 1457/836

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, convert the fractions to have a common denominator. The least common multiple of 93, 47, and 4 is 186.

    88/93 = (88 * 2) / (93 * 2) = 176/186
    6/47 = (6 * 4) / (47 * 4) = 24/186

    Now, add the two fractions:

    176/186 + 24/186 = (176 + 24) / 186 = 200/186

    Next, convert 92/4 to have the same denominator:

    92/4 = (92 * 46.5) / (4 * 46.5) = 4260/186

    Now, add the two results:

    200/186 + 4260/186 = (200 + 4260) / 186 = 4460/186

    ### Answer: 4460/186

Expected answer: 105227/4371

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to calculate the sum of 52/21 and 75/67.
    52/21 + 75/67 = (52\*67 + 75\*21) / (21\*67) = (3484 + 1575) / (1407) = 5059 / 1407
    Now, we can add this result to 95/83.
    95/83 + 5059/1407 = (95\*1407 + 5059\*83) / (83\*1407) = (133665 + 420717) / (116121) = 554382 / 116121
    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
    The GCD of 554382 and 116121 is 3.
    So, the simplified fraction is 554382/3 / 116121/3 = 184794 / 38707
    ### Answer: 184794/38707

Expected answer: 553562/116781

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: The expression can be simplified by finding the common denominator of 27 and 48, which is 216.

    (73 / 27) = (73 * 8) / (27 * 8) = 584 / 216

    (23 / 48) = (23 * 4.5) / (48 * 4.5) = 103.5 / 216

    Now, subtract the two fractions:

    584 / 216 - 103.5 / 216 = (584 - 103.5) / 216 = 480.5 / 216

    The fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 108.

    480.5 / 216 = (480.5 / 108) / (216 / 108) = 4.45 / 2

    Therefore, the value of the expression is 4.45 / 2.

    ### Answer: 4.45 / 2

Expected answer: 961/432

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: (78 / 2) = <<78/2=39>>39
    (70 / 23) = <<70/23=3.0434782608695652>>3.0434782608695652 (rounded to 10 decimal places)
    (78 / 2) - (70 / 23) = 39 - 3.0434782608695652 = <<39-3.0434782608695652=35.956521739130435>>35.956521739130435
    ### Answer: 35.956521739130435 or 35 19/23 as a simplified fraction.

Expected answer: 827/23

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, convert 34/1 to a mixed number, which is 34.
    Next, convert 53/4 to a mixed number, which is 13 1/4.
    Now, add the two mixed numbers: 34 + 13 1/4 = 47 1/4.
    ### Answer: 47 1/4

Expected answer: 189/4

Correct? Yes

🔗 Follow-up

Problem: Following the result of the previous problem, what is the sum of 24/67 and the result you got from adding 34/1 to 53/4? Express your answer as a mixed number.

Gemma 2B:

     Reasoning: First, convert 24/67 to a decimal, which is approximately 0.3582.
    Next, add this decimal to the mixed number 47 1/4, which is 47.25.
    The sum is approximately 47.6082.
    To express this as a mixed number, we can convert the decimal part to a fraction: 0.6082 is approximately 3/5.
    So, the sum is 47 3/5.
    ### Answer: 47 3/5

Expected answer: 12759/268

Correct? No

🔗 Follow-up

Problem: Let's reconsider the problem where you were adding fractions. Previously, it was asked to add 34/1 to 53/4. Now consider whether it may have been 34/97 instead of 34/1. What will be the result if you add 34/97 to 53/4? Write your answer as a mixed number.

Gemma 2B:

     Reasoning: First, convert 34/97 to a decimal, which is approximately 0.3505.
    Next, convert 53/4 to a mixed number, which is 13 1/4.
    Now, add the decimal to the mixed number: 0.3505 + 13 1/4 = 13.3505.
    Since the problem asks for a mixed number, we can convert 13.3505 to a mixed number by taking the whole number part (13) and the decimal part (0.3505).
    The decimal part can be converted to a fraction by dividing it by 1: 0.3505/1 = 3505/10000.
    Now, simplify the fraction: 3505/10000 = 701/2000.
    So, the mixed number is 13 701/2000.
    ### Answer: 13 701/2000

Expected answer: 5277/388

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 36 and 96 is 144.

    3/36 = 12/144
    97/96 = 145.5/144

    Now we can add the two fractions:

    12/144 + 145.5/144 = 157.5/144

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    157.5/144 = 52.5/48

    Now we can simplify the fraction further by dividing both the numerator and the denominator by 3:

    52.5/48 = 17.5/16

    ### Answer: 17.5/16

Expected answer: 35/32

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 3/36 and 97/96, add your answer to 55/69. What is your result reduced to its simplest form?

Gemma 2B:

     Reasoning: We have already found that the sum of 3/36 and 97/96 is 17.5/16.

    Now we need to add this result to 55/69. To do this, we need to find a common denominator. The least common multiple of 16 and 69 is 1104.

    17.5/16 = 122.5/1104
    55/69 = 805/1104

    Now we can add the two fractions:

    122.5/1104 + 805/1104 = 927.5/1104

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1:

    927.5/1104 = 927.5/1104

    ### Answer: 927.5/1104

Expected answer: 4175/2208

Correct? No

🔗 Follow-up

Problem: After the initial calculation with 3/36 and 97/96, now consider you made an error and the actual fraction was 3/38 not 3/36. Recalculate the sum of 3/38 and 97/96. What is the new sum as a simplified fraction?

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 38 and 96 is 144.

    3/38 = 12/144
    97/96 = 145.5/144

    Now we can add the two fractions:

    12/144 + 145.5/144 = 157.5/144

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:

    157.5/144 = 52.5/48

    Now we can simplify the fraction further by dividing both the numerator and the denominator by 3:

    52.5/48 = 17.5/16

    ### Answer: 17.5/16

Expected answer: 1987/1824

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning:

    First, simplify the fractions:

    92/95 is already in its simplest form.

    4/74 can be simplified by dividing both the numerator and the denominator by 2:

    4/74 = (4/2) / (74/2) = 2/37

    Now, add the fractions:

    (92/95) + (2/37)

    To add these fractions, we need a common denominator. The least common multiple (LCM) of 95 and 37 is 3515.

    So, we convert the fractions to have the same denominator:

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

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

    Now, add the fractions:

    3404/3515 + 190/3515 = (3404 + 190) / 3515 = 3594/3515

    This fraction is already in its simplest form.

    ### Answer: 3594/3515

Expected answer: 3594/3515

Correct? Yes

🔗 Problem

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.

Gemma 2B:

     Reasoning: The value of 'v' is 69/47.
    The value of 'd' is 88/72 + 69/47.
    To add these fractions, we need a common denominator. The least common multiple of 72 and 47 is 3456.
    So, we convert the fractions to have the same denominator:
    88/72 = (88 \* 48) / (72 \* 48) = 4224/3456
    69/47 = (69 \* 73) / (47 \* 73) = 5037/3456
    Now we can add the fractions:
    d = 4224/3456 + 5037/3456 = (4224 + 5037) / 3456 = 9261/3456
    We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 243:
    d = (9261/243) / (3456/243) = 38.111... / 14.222...
    So, the value of 'd' is approximately 2.68.
    ### Answer: 38.111... / 14.222... or approximately 2.68

Expected answer: 1138/423

Correct? No

🔗 Problem

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.

Gemma 2B:

     Reasoning: The wholesaler had 41/26 barrels of olive oil initially. They sold 41/72 barrels of oil.
    To find out how much oil they have now, we need to subtract the amount sold from the initial amount.
    41/26 - 41/72 = (41*3)/(26*3) - 41/72 = 123/78 - 41/72 = (123*2)/(78*2) - 41/72 = 246/156 - 41/72 = (246-41)/156 = 205/156
    Simplifying the fraction, we get 205/156 = 5/4
    ### Answer: 5/4

Expected answer: 943/936

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To find the sum of 85/75 and 88/56, we first need to find a common denominator. The least common multiple of 75 and 56 is 2100.

    85/75 = (85 \* 28)/(75 \* 28) = 2380/2100

    88/56 = (88 \* 37.5)/(56 \* 37.5) = 3300/2100

    Now we can add the two fractions:

    2380/2100 + 3300/2100 = (2380 + 3300)/2100 = 5680/2100

    To convert this fraction to decimal form, we divide 5680 by 2100:

    5680/2100 = <<5680/2100=2.7047619047619047>>2.7047619047619047

    ### Answer: 2.7047619047619047

Expected answer: 284/105

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: First, we need to find a common denominator for the two fractions. The least common multiple of 33 and 2 is 66.

    12/33 = (12*2)/(33*2) = 24/66
    49/2 = (49*33)/(2*33) = 1617/66

    Now we can add the two fractions:

    24/66 + 1617/66 = (24+1617)/66 = 1641/66

    To convert the improper fraction to a mixed fraction, we divide the numerator by the denominator:

    1641 ÷ 66 = 24 with a remainder of 51

    So the result is 24 51/66.

    ### Answer: 24 51/66

Expected answer: 547/22

Correct? No

🔗 Problem

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

Gemma 2B:

     Reasoning: To add two fractions, you can add the numerators and keep the denominator the same.
    78/65 + 78/65 = (78+78)/65 = <<(78+78)/65=156/65>>156/65
    ### Answer: 156/65

Expected answer: 12/5

Correct? Yes

🔗 Follow-up

Problem: After obtaining the result from the previous problem, where you added two fractions both equal to 78/65, what would you get if you add the result to 71/32?

Gemma 2B:

     Reasoning: To add two fractions, you can find a common denominator and then add the numerators.
    The common denominator of 65 and 32 is 65\*32 = <<65\*32=2080>>2080.
    The first fraction, 156/65, becomes 156\*32/65\*32 = <<156\*32/65\*32=5088/2080>>5088/2080.
    The second fraction, 71/32, becomes 71\*65/32\*65 = <<71\*65/32\*65=4615/2080>>4615/2080.
    Adding the two fractions, 5088/2080 + 4615/2080 = (5088+4615)/2080 = <<(5088+4615)/2080=9703/2080>>9703/2080
    ### Answer: 9703/2080

Expected answer: 739/160

Correct? No

🔗 Follow-up

Problem: Suppose that instead of having two fractions both equal to 78/65 like in the previous problem, they were both equal to 78/78. What would be the result of adding these two fractions together?

Gemma 2B:

     Reasoning: To add two fractions, you can add the numerators and keep the denominator the same.
    78/78 + 78/78 = (78+78)/78 = <<(78+78)/78=156/78>>156/78
    Since 156 and 78 are both divisible by 78, the fraction can be simplified to 2/1.
    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

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

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 7 and 90 is 630.

    16/7 = (16 \* 90) / (7 \* 90) = 1440/630
    11/90 = (11 \* 7) / (90 \* 7) = 77/630

    Now we can add the two fractions:

    1440/630 + 77/630 = (1440 + 77) / 630 = 1517/630

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    1517/630 is already in its simplest form.

    ### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 16/7 and 11/90, add your answer to 38/69. What is this new sum, expressed as a simplified fraction?

Gemma 2B:

     Reasoning: We have already found that the sum of 16/7 and 11/90 is 1517/630.

    Now we need to add this sum to 38/69.

    To add the two fractions, we need to find a common denominator. The least common multiple of 630 and 69 is 43470.

    1517/630 = (1517 \* 69) / (630 \* 69) = 104653/43470
    38/69 = (38 \* 630) / (69 \* 630) = 23940/43470

    Now we can add the two fractions:

    104653/43470 + 23940/43470 = (104653 + 23940) / 43470 = 128593/43470

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.

    128593/43470 is already in its simplest form.

    ### Answer: 128593/43470

Expected answer: 42871/14490

Correct? No

🔗 Follow-up

Problem: In the previous problem, you calculated the sum of 16/7 and 11/90. Now, let's consider if there were actually 99 parts out of 90 (as strange as that might sound) instead of 11 parts out of 90. What would be the sum of 16/7 and 99/90, expressed as a simplified fraction?

Gemma 2B:

     Reasoning: To add the two fractions, we need to find a common denominator. The least common multiple of 7 and 90 is 630.

    16/7 = (16 \* 90) / (7 \* 90) = 1440/630
    99/90 = (99 \* 7) / (90 \* 7) = 693/630

    Now we can add the two fractions:

    1440/630 + 693/630 = (1440 + 693) / 630 = 2133/630

    To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.

    2133/630 = (2133 ÷ 3) / (630 ÷ 3) = 711/210

    ### Answer: 711/210

Expected answer: 237/70

Correct? Yes