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

    ### Answer: 2967/812

Expected answer: 7702/2093

Correct? No

🔗 Problem

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

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

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

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

    ### Answer: 7345/755

Expected answer: 210434/21645

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 16277/1025

Expected answer: 2477/1025

Correct? No

🔗 Problem

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

    ### Answer: 7148/3157

Expected answer: 7148/3157

Correct? Yes

🔗 Follow-up

Problem: In the same scenario as before, imagine that John had less cake initially, only 28/41 of his cake was left instead of 71/41. If Emily still added 41/77 of another cake to it, how much cake is there now in total? Give your answer as a simplified fraction.

Gemma 2B:

    Reasoning: We'll follow a similar process as before, starting by finding a common denominator for our fractions. The least common denominator for 41 and 77 is their product, 3157.
    We can rewrite 28/41 as (28 * 77) / (41 * 77) = 2156 / 3157.
    We already know from the previous problem that 41/77 is equivalent to 1681 / 3157.
    Adding these two fractions, we get (2156 + 1681) / 3157 = 3837 / 3157.

    ### Answer: 3837/3157

Expected answer: 3837/3157

Correct? Yes

🔗 Problem

Problem: Calculate the result of 10/65 + 56/35. 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 65 (5*13) and 35 (5*7) is 5*7*13 = 455.

     To get a denominator of 455 for 10/65, we multiply both numerator and denominator by 7: (10*7)/(65*7) = 70/455.

     To get a denominator of 455 for 56/35, we multiply both numerator and denominator by 13: (56*13)/(35*13) = 728/455.

     Now we can add the two fractions:  70/455 + 728/455 = 798/455

     ### Answer: 798/455

Expected answer: 114/65

Correct? Yes

🔗 Follow-up

Problem: Following the result of the previous calculation (10/65 + 56/35), subtract your answer from 34. What's the resultant value? Answer as a simple fraction.

Gemma 2B:

    Reasoning:
    We need to subtract 798/455 from 34.

    First, convert 34 to a fraction with a denominator of 455: (34 * 455) / 455 = 15470/455

    Now, subtract 798/455 from that: 15470/455 - 798/455 = 14672/455

    ### Answer: 14672/455

Expected answer: 2096/65

Correct? Yes

🔗 Follow-up

Problem: Given your previous calculation with the 10/65 + 56/35, imagine instead that you started with 25 instead of 10 in the first fraction. What would be the outcome of 25/65 + 56/35? Answer as a simplified fraction.

Gemma 2B:

    Reasoning:
     We follow a similar approach as before, keeping in mind that the only change is the numerator of the first fraction.

     We already know the least common denominator for 65 and 35 is 455.

     To get a denominator of 455 for 25/65, we multiply both numerator and denominator by 7: (25*7)/(65*7) = 175/455

     We also know from before that 56/35 is equivalent to 728/455

     Now we can add the two fractions: 175/455 + 728/455 = 903/455

     This fraction can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 151: (903/151)/(455/151) = 6/3

     Finally, 6/3 simplifies to 2.
     ### Answer: 2

Expected answer: 129/65

Correct? No

🔗 Problem

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

Gemma 2B:

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

    Then we adjust the numerators accordingly:

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

    This gives us:

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

    Now, we can add the numerators:

    (3525 + 7857)/(3807)

    ### Answer: 11382/3807

Expected answer: 3794/1269

Correct? Yes

🔗 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:

    We already know from the previous problem that (75/81) + (97/47) = 11382/3807.

    Now we need to add 52/71 to that result.

    To do this, we need to find a common denominator for 3807 and 71.  We can do this by multiplying them together: 3807 * 71 = 269297

    Next, we adjust the numerators accordingly:

    (11382/3807) + (52/71) = (11382 * 71)/(3807 * 71) + (52 * 3807)/(71 * 3807)

    This simplifies to:

    (808122 / 269297) + (197964 / 269297)

    Finally, we add the numerators:

    (808122 + 197964) / 269297

    ### Answer: 1006086/269297

Expected answer: 335362/90099

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 4626/53

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of 88/1 - 38/53, add it to 25/79. What is the final value, and answer as a simplified fraction?

Gemma 2B:

    Reasoning: We know from the previous problem that 88/1 - 38/53 = 4626/53.  Therefore we need to solve for 4626/53 + 25/79.
    To add these fractions, they must have a common denominator. The least common denominator of 53 and 79 (which are both prime numbers) is 53 * 79 = 4187.
    We can rewrite both fractions with this denominator:
    (4626/53) * (79/79) = 365454 / 4187
    (25/79) * (53/53) = 1325 / 4187
    Finally, we add the two fractions: (365454 / 4187) + (1325/4187) = 366779/4187
    ### Answer: 366779/4187

Expected answer: 366779/4187

Correct? Yes

🔗 Follow-up

Problem: Previous problem: What is 88/1 - 38/53? Now consider if the second fraction (38/53) was changed to 38/93 instead. So, what is 88/1 - 38/93? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: To subtract fractions, they must have a common denominator. The least common denominator of 1 and 93 is 93. We can rewrite 88/1 as a fraction over 93: (88/1)*(93/93) = 8184/93.
    Therefore the problem becomes 8184/93 - 38/93.
    This simplifies to (8184 - 38)/93 = 8146/93.
    ### Answer: 8146/93

Expected answer: 8146/93

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 6026/2773

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 3569/1400

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 89/56 and 48/50, add the result to 2/65. What is the final simplified fraction?

Gemma 2B:

    Reasoning: From the previous problem, the sum of 89/56 and 48/50 is 3569/1400.  The least common denominator for 1400 and 65 is 18200.  Converting the fractions to this denominator gives us (3569/1400)*(13/13) = 46397/18200 and (2/65)*(280/280) = 560/18200. Finally, adding those two fractions, we get 46397/18200 + 560/18200 = 46957/18200
    ### Answer: 46957/18200

Expected answer: 46957/18200

Correct? Yes

🔗 Follow-up

Problem: Suppose in the original problem, instead of having 89/12, we only have 89/12, and the number of parts out of 50 remain the same. So, what is the sum of 89/12 and 48/50 this time? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: I believe you meant to state that the first fraction is different from the original problem, while the second fraction remains as 48/50.

    First find the least common denominator: 300. Then convert the fractions: (89/12)*(25/25)=2225/300 and (48/50)*(6/6)=288/300. Finally, add the fractions: 2225/300 + 288/300 = 2513/300.
    ### Answer: 2513/300

Expected answer: 2513/300

Correct? Yes

🔗 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 add fractions, they must have a common denominator. The least common denominator of 11 and 5 is 55.
    Therefore:
    96/11 + 12/5 = (96/11)*(5/5) + (12/5)*(11/11) = 480/55 + 132/55 = 612/55

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

    ### Answer: 51154/4785

Expected answer: 51154/4785

Correct? Yes

🔗 Follow-up

Problem: After you find the result subtracting 38/87 from the sum of 96/11 and 12/5, add that result back to the initial sum of 96/11 and 12/5. What is the final result? Please leave your answer as a fraction.

Gemma 2B:

    Reasoning:
    From the previous problem, we know that the result of subtracting 38/87 from the sum of 96/11 and 12/5 is 51154/4785.

    Now we need to add this result back to the initial sum of 96/11 + 12/5 = 612/55.

    Again, we need a common denominator:
    612/55 + 51154/4785 = (612/55)*(87/87) + 51154/4785 = 53244/4785 + 51154/4785 = 104398/4785

    ### Answer: 104398/4785

Expected answer: 104398/4785

Correct? Yes

🔗 Follow-up

Problem: After considering the fruit you have, suppose you actually started off with a fraction of the fruits, having 96/58 oranges, and still having 12/5 apples. If you subtracted 38/87 of your total fruits for charity, what fraction of fruits would you have left? Please leave your answer as a fraction.

Gemma 2B:

    Reasoning:
    First, find the total number of fruits you started with by adding the fractions of oranges and apples.  The least common denominator of 58 and 5 is 290.

    96/58 + 12/5 = (96/58)*(5/5) + (12/5)*(58/58) = 480/290 + 696/290 = 1176/290

    Now, simplify this fraction: 1176/290 = 588/145

    Next, determine what fraction of your total fruit you gave to charity.  The problem specifies this is 38/87.

    To find the fraction of fruit remaining, subtract the fraction donated to charity (38/87) from 1 (representing the whole of your fruit before donating any).

    1 - 38/87 = 87/87 - 38/87 = 49/87

    Finally, multiply the fraction of your total fruit (588/145) by the fraction remaining after the donation (49/87) to find the fraction of fruit you have left.

    (588/145) * (49/87) = 28812/12615

    ### Answer: 28812/12615

Expected answer: 1574/435

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

Expected answer: 164/21

Correct? Yes

🔗 Follow-up

Problem: In our previous question, we originally had a value of 82 divided by 9 and subtracted 82 divided by 63 from it. Now let's change it up. What would have been the result if, originally, the number we subtracted wasn't 82 divided by 63 but instead 37 divided by 63? What's the new result? Please provide your answer as a simplified fraction.

Gemma 2B:

    Reasoning: 82 divided by 9 is 82/9, and 37 divided by 63 is 37/63.
    Therefore, the required value is 82/9 - 37/63 = (82*7 - 37)/63 = (574-37)/63 = 537/63 = 179/21
    ### Answer: 179/21

Expected answer: 179/21

Correct? Yes

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

Expected answer: 6229/1092

Correct? Yes

🔗 Follow-up

Problem: In the earlier problem you calculated the value of 23/3 minus the sum of 80/91 and 26/24. Now, add 45/94 to the result. What's your answer? Answer as a simple fraction.

Gemma 2B:

    Reasoning: We previously found that 23/3 minus the sum of 80/91 and 26/24 is 6229/1092.  We need to add 45/94 to this.
    Let's find a common denominator for 1092 and 94.  Both numbers are divisible by 2, and 1092 is also divisible by 4, so their least common multiple, and our common denominator, is 4 * 546 = 2184.
    Converting to this denominator we get 6229/1092 + 45/94 = (6229 * 2)/(1092 * 2) + (45 * 23)/(94 * 23) = 12458/2184 + 1035/2184 = 13493/2184.
    ### Answer: 13493/2184

Expected answer: 317333/51324

Correct? No

🔗 Follow-up

Problem: Previously, you calculated the result of 23/3 minus the sum of 80/91 and 26/24. This time, consider if there were originally 76/24 instead of 26/24. How would this affect the calculation? Find the result of the new expression, which is 23/3 minus the sum of 80/91 and 76/24. Provide your answer in its simplest fraction form.

Gemma 2B:

    Reasoning:  Let's analyze the impact of changing 26/24 to 76/24. The new sum, 80/91 + 76/24, will be larger than the previous sum. Therefore, subtracting this new sum from 23/3 will yield a smaller result compared to the previous calculation.

    Now, let's calculate the new expression:

    1. **Calculate the sum:**
       - Find a common denominator for 80/91 and 76/24 (again, 91*24 = 2184):
         - (80 * 24)/(91 * 24) = 1920/2184
         - (76 * 91)/(24 * 91) = 6916/2184
       - Add the fractions: (1920 + 6916)/2184 = 8836/2184

    2. **Subtract the sum from 23/3:**
       - Convert 23/3 to a fraction with a denominator of 2184: (23 * 728)/(3 * 728) = 16744/2184
       - Subtract the fractions: 16744/2184 - 8836/2184 = 7908/2184

    3. **Simplify:** 7908/2184 simplifies to 1977/546

    ### Answer: 1977/546

Expected answer: 659/182

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 221/90

Correct? Yes

🔗 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: We already know from the previous problem that the simplified sum of 37/18 and 24/60 is 221/90.
    To add 221/90 to 92/28, we need to find a common denominator. The least common denominator for 90 and 28 is 1260.
    221/90 is equivalent to 3094/1260, and 92/28 is equivalent to 4140/1260.
    Therefore, 3094/1260 + 4140/1260 = 7234/1260, which simplifies to 12057/2100.
    ### Answer: 12057/2100

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: First, we simplify 24/72 to its lowest terms, which is 1/3.  Next, we need to find a common denominator for 37/18 and 1/3, which is 18. 1/3 is equivalent to 6/18.
    Therefore, 37/18 + 6/18 = 43/18.
    ### Answer: 43/18

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

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

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

    ### Answer: 5941/2542

Expected answer: 5941/2542

Correct? Yes

🔗 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 already know from the previous problem that the sum of 33/41 and 95/62 is 5941/2542. Now we need to add that to 95/62.

    First, rewrite 95/62 with the denominator 2542:
    * 95/62 = (95 * 41) / (62 * 41) = 3895/2542

    Now we can add: 5941/2542 + 3895/2542 = 9836/2542

    Finally, simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2:
    * 9836/2542 = (9836 / 2) / (2542 / 2) = 4918/1271

    ### Answer: 4918/1271

Expected answer: 4918/1271

Correct? Yes

🔗 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: Similar to the previous problem, we need a common denominator to add these fractions.  The least common denominator for 41 and 62 is still their product, 2542.  Let's rewrite the fractions:

    * 33/41 = (33 * 62) / (41 * 62) = 2046/2542
    * 83/62 = (83 * 41) / (62 * 41) = 3403/2542

    Adding the fractions: 2046/2542 + 3403/2542 = 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, we simplify (30/11) + (72/38). Both 30 and 11 are prime numbers so (30/11) remains as it is. We can simplify (72/38) to (36/19). Our expression now becomes (30/11) + (36/19). To add the two fractions, we need to find a common denominator. The least common denominator for 11 and 19 is their product, which is 209. We can rewrite (30/11) as (570/209) and (36/19) as (396/209). Our expression now becomes (570/209)+(396/209), which simplifies to 966/209.

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

    Therefore, the simplified answer is 49935/7106.

    ### Answer: 49935/7106

Expected answer: 49773/7106

Correct? No

🔗 Problem

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

Expected answer: 3973/1632

Correct? No

🔗 Problem

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

    ### Answer: 880/307

Expected answer: 307360/106799

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 1031/660

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 598/329

Correct? Yes

🔗 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 found that ((32 / 14) - (22 / 47)) = 598/329. Adding this fraction to itself is the same as multiplying by 2: (598/329) * 2 = 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:  We follow the same steps as before, but with 71/14 instead of 32/14.

    1. **Simplify:** 71/14 cannot be simplified further. 22/47 also cannot be simplified.

    2. **Common Denominator:** The least common denominator for 14 and 47 is their product, 658. So we have:
       * (71/14) - (22/47) = (71*47)/(14*47) - (22*14)/(47*14) = 3337/658 - 308/658

    3. **Subtract:** 3337/658 - 308/658 = 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 get the sum of the two fractions, we first need to find their least common denominator (LCD).
    The LCD is the least common multiple (LCM) of 61 and 53, which is 3233.
    Next, we express the fractions using the LCD:
    74/61 = (74 x 53)/(61 x 53) = 3922/3233
    41/53 = (41 x 61)/(53 x 61) = 2501/3233
    Finally, we add the two fractions: 3922/3233 + 2501/3233 = (3922+2501)/3233 = 6423/3233
    ### Answer: 6423/3233

Expected answer: 6423/3233

Correct? Yes

🔗 Follow-up

Problem: Assuming you already calculated the sum of 74/61 and 41/53, what would be the total if you added 83/4 to the result? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: From the previous calculation, we know the sum of 74/61 and 41/53 is 6423/3233. To add 83/4 to this, we need to find a common denominator.
    The least common denominator for 3233 and 4 is 12932. We can express the fractions with this denominator:
    6423/3233 = (6423 x 4)/(3233 x 4) = 25692/12932
    83/4 = (83 x 3233)/(4 x 3233) = 268339/12932
    Finally, we add these two fractions: 25692/12932 + 268339/12932 = 294031/12932. This fraction cannot be simplified further.
    ### Answer: 294031/12932

Expected answer: 294031/12932

Correct? Yes

🔗 Follow-up

Problem: Previously you calculated the sum of 74/61 and 41/53. Now, let's consider if the second fraction was actually 41/88 instead of 41/53. What would be the new total of 74/61 and 41/88? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: First, we need to find the least common denominator (LCD) of 61 and 88.
    The LCD is the least common multiple (LCM) of 61 and 88, which is 5368.
    Next, we express both fractions with the denominator of 5368:
    74/61 = (74 * 88)/(61 * 88) = 6512/5368
    41/88 = (41 * 61)/(88 * 61) = 2501/5368
    Finally, we add the two fractions: 6512/5368 + 2501/5368 = (6512 + 2501)/5368 = 9013/5368
    ### Answer: 9013/5368

Expected answer: 9013/5368

Correct? Yes

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

    ### Answer: 46.279 (approximately)

Expected answer: 255877/5529

Correct? No

🔗 Problem

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

Expected answer: 180194/131631

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 154/60

Expected answer: 77/30

Correct? Yes

🔗 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 from the previous problem that 73/30 + 8/60 = 154/60.
    Adding this fraction to itself is the same as multiplying by 2: (154/60) * 2 = 308/60.

    ### Answer: 308/60

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: Let's find the least common denominator of 30 and 60, which is 60.
    We'll convert 73/30 to have a denominator of 60: (73 * 2) / (30 * 2) = 146/60
    Now, we can add the fractions: 146/60 + 49/60 = 195/60

    ### Answer: 195/60

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

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

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

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

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

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

    ### Answer: 805/196

Expected answer: 47429/11564

Correct? No

🔗 Problem

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

Expected answer: 9407/2640

Correct? No

🔗 Problem

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

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

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

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

    ### Answer: 81841/8645

Expected answer: 81841/8645

Correct? Yes

🔗 Follow-up

Problem: Let's extend the previous problem. After you have calculated ((8 / 91) + (49 / 5)) and subtracted (32 / 76), now subtract (58 / 49) from the result. Provide your new answer as a simplified fraction.

Gemma 2B:

    Reasoning:
    From the previous calculation, we know that ((8/91) + (49/5)) - (32/76) = 81841/8645.

    Now we need to subtract 58/49 from 81841/8645.  First, we find a common denominator for these two fractions. The least common multiple of 8645 and 49 is 423605:

    * (81841/8645) - (58/49) = (81841 * 49)/(8645 * 49) - (58 * 8645)/(49 * 8645)
    * = 4010209/423605 - 501810/423605
    * = 3508399/423605

    ### Answer: 3508399/423605

Expected answer: 501257/60515

Correct? No

🔗 Follow-up

Problem: Let's make a slight change to the previous problem. Instead of starting with ((8 / 91) + (49 / 5)), let's use ((26 / 91) + (49 / 5)) instead, still subtracting (32 / 76) from the result. What would be the new outcome? Provide your answer as a simplified fraction.

Gemma 2B:

    Reasoning:

    First, we need to simplify the expressions inside the parentheses:

    * 26/91 can be simplified to 2/7 (dividing both numerator and denominator by 13)
    * 49/5 is already in its simplest form.

    Next, we need to find a common denominator for 2/7 and 49/5 to add them. The least common multiple of 7 and 5 is 35:

    * (2/7) + (49/5) = (2 * 5)/(7 * 5) + (49 * 7)/(5 * 7) = 10/35 + 343/35 = 353/35

    Now we need to subtract 32/76 from 353/35. First, we simplify 32/76 to 8/19. Then, we find a common denominator for 353/35 and 8/19. The least common multiple of 35 and 19 is 665:

    * (353/35) - (8/19) = (353 * 19)/(35 * 19) - (8 * 35)/(19 * 35) = 6707/665 - 280/665 = 6427/665

    ### Answer: 6427/665

Expected answer: 6427/665

Correct? Yes

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

Expected answer: 15521/8526

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 718/285

Correct? No

🔗 Problem

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

Gemma 2B:

    Reasoning:  First, find the sum of (78/45) + (89/36). The least common multiple of 45 and 36 is 180. Therefore:
     (78/45) + (89/36) = (78 * 4 / 180) + (89 * 5 / 180) = (312 / 180) + (445 / 180) = 757/180

     Next, add the fraction to itself:
     (757 / 180) + (757 / 180) = 1514 / 180

     Finally, simplify the resulting fraction by dividing both numerator and denominator by their greatest common divisor, which is 18:
     (1514 / 18) / (180 / 18) = 841/100

    ### Answer: 841/100

Expected answer: 757/90

Correct? No

🔗 Problem

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

    ### Answer: 1066/629

Expected answer: 1066/629

Correct? Yes

🔗 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:
    * We need to add 1066/629 to 64/70. To add fractions, we need a common denominator.
    * First, simplify the fraction 64/70 by dividing both numerator and denominator by 2: 64/2 = 32 and 70/2 = 35, resulting in 32/35.
    * The least common denominator for 629 and 35 is their product, 22015.
    * We convert 1066/629 to an equivalent fraction with a denominator of 22015: (1066 * 35) / (629 * 35) = 37310/22015.
    * We convert 32/35 to an equivalent fraction with a denominator of 22015: (32 * 629) / (35 * 629) = 20128/22015.
    * Finally, we perform the addition: 37310/22015 + 20128/22015 = 57438/22015.

    ### Answer: 57438/22015

Expected answer: 57438/22015

Correct? Yes

🔗 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:
    * We already know from the previous calculation that 93 divided by 34 is 93/34.
    *  We need to subtract 77/51 from 93/34. To do this, we need a common denominator. The least common denominator for 34 and 51 is 102.
    * We convert 93/34 to an equivalent fraction with a denominator of 102: (93 * 3) / (34 * 3) = 279/102
    * We convert 77/51 to an equivalent fraction with a denominator of 102: (77 * 2) / (51 * 2) = 154/102
    * Now we subtract: 279/102 - 154/102 = 125/102

    ### Answer: 125/102

Expected answer: 125/102

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

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

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

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

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

    ### Answer: 17/5

Expected answer: 114/35

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 12857/4982

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 310/297

Correct? No

🔗 Problem

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

Expected answer: 10/9

Correct? No

🔗 Problem

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

Expected answer: 1120/297

Correct? No

🔗 Problem

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

Expected answer: 113/99

Correct? Yes

🔗 Follow-up

Problem: Imagine again the fraction 90/81. We already added it to 2/66. Now, pretend to add that sum to another fraction, 77/62. If you have to simplify your answer to the simplest form, what would be the result?

Gemma 2B:

    Reasoning: First, simplify the fractions: 90/81 = 10/9, 2/66 = 1/33, and 77/62 is already in its simplest form.
    Next, find a common denominator for 10/9 and 1/33: 10/9 + 1/33 = 110/99 + 3/99 = 113/99.
    Then, find a common denominator for 113/99 and 77/62: 113/99 + 77/62 = 7006/6138 + 7623/6138 = 14629/6138.
    The fraction cannot be simplified any further.
    ### Answer: 14629/6138

Expected answer: 14629/6138

Correct? Yes

🔗 Follow-up

Problem: Previously, you calculated the sum of the fraction 90/81 and 2/66. In a new scenario, what if you started with 90/39 instead of 90/81 then added it with 2/66? What would be the result in the simplest form?

Gemma 2B:

    Reasoning: First, we need to simplify the fractions. 90/39 simplifies to 30/13.  The fraction 2/66 simplifies to 1/33.
    Next, find a common denominator for 30/13 and 1/33. The least common denominator is 429.
    Then, rewrite the fractions with the common denominator: 30/13 = 990/429 and 1/33 = 13/429.
    Now, add the fractions:  990/429 + 13/429 = 1003/429.
    The fraction cannot be simplified any further.
    ### Answer: 1003/429

Expected answer: 1003/429

Correct? Yes

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

Expected answer: 112/41

Correct? Yes

🔗 Follow-up

Problem: If Oliver receives two more pieces of ribbon, with each being 56/41 yards long, how long would all the pieces of ribbon be when added together?

Gemma 2B:

    Reasoning: Oliver starts with two pieces of ribbon that total 112/41 yards in length. He gets two more of the same length, meaning we add (56/41) + (56/41) to his current total. That means he has 112/41 + 56/41 + 56/41 = 224/41 yards of ribbon.
    ### Answer: 224/41 yards

Expected answer: 224/41

Correct? Yes

🔗 Follow-up

Problem: If Oliver initially had a piece of ribbon that was 63/41 yards long instead of 56/41 yards, and he still receives a second piece of the same length, how long would both pieces of ribbon be when put together?

Gemma 2B:

    Reasoning: Since Oliver has two pieces of ribbon that are each 63/41 yards long, we find the total length by adding them together: (63/41) + (63/41) = 126/41 yards.
    ### Answer: 126/41 yards

Expected answer: 126/41

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

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

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

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

    ### Answer: 6707/3450

Expected answer: 6707/3450

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, what is the result of 97/17 minus the sum of 92/75 + 66/92? Give your answer as a simplified fraction.

Gemma 2B:

    From the previous problem, we know the sum of 92/75 + 66/92 is 6707/3450.  So the problem becomes:

    97/17 - 6707/3450

    To subtract fractions, they must have a common denominator.  The least common denominator for 17 and 3450 is 3450 (since 3450 is divisible by 17).  We can convert 97/17 to have a denominator of 3450:

    97/17 = (97 * 203)/(17 * 203) = 19691/3450

    Now we can subtract:

    19691/3450 - 6707/3450 = 12984/3450

    Finally, we simplify by finding the greatest common factor of 12984 and 3450, which is 6:

    12984/3450 = (6 * 2164) / (6 * 575) = 2164/575

    ### Answer: 2164/575

Expected answer: 220631/58650

Correct? No

🔗 Follow-up

Problem: Following the previous problem, consider instead if there were 83/75 of something instead of 92/75. What would be the new total when you add 66/92 to it? Please provide your answer as a simplified fraction.

Gemma 2B:

    Similar to before, we need a common denominator to add these fractions.  We can use the product of the denominators, 75 * 92:

    83/75 + 66/92 = (83 * 92)/(75 * 92) + (66 * 75)/(92 * 75)
                       = 7636/6900 + 4950/6900
                       = 12586/6900

    Now we simplify by finding the greatest common factor of 12586 and 6900, which is 2:

    12586/6900 = (2 * 6293) / (2 * 3450)
                      = 6293/3450

    ### Answer: 6293/3450

Expected answer: 6293/3450

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 5449/1430

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous question, what is the sum of your answer from that problem and 24/71? Leave your answer as an unsimplified fraction.

Gemma 2B:

    Reasoning: Our previous answer was 5449/1430.  To add it to 24/71 we need to find a common denominator.  Notice that 1430 is a multiple of 71: 1430=20*71.  Therefore, a common denominator is 1430.

    24/71 is equivalent to (24*20)/(71*20)=480/1430

    The sum of 5449/1430 and 480/1430 is (5449+480)/1430 = 5929/1430.

    ### Answer: 5929/1430

Expected answer: 421199/101530

Correct? No

🔗 Follow-up

Problem: In the earlier problem, we considered the sum of 32/65 and 73/22. But what if the fraction was 53/65 instead of 32/65? What would the new sum be? Please leave your answer as an unsimplified fraction.

Gemma 2B:

    Reasoning: Following the same process as before, we need to make both fractions have a common denominator. The least common denominator is still 1430 (65 * 22).

     So, 53/65 is equivalent to (53*22)/(65*22) = 1166/1430

     And, 73/22 remains equivalent to (73*65)/(22*65) = 4745/1430

     The sum of 1166/1430 and 4745/1430 is (1166+4745)/1430 = 5911/1430.
    ### Answer: 5911/1430

Expected answer: 5911/1430

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 117/86

Correct? No

🔗 Problem

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

Expected answer: 5627/88

Correct? Yes

🔗 Follow-up

Problem: After completing the initial calculation, you realize there was an extra component to your math problem. You must now also add the fraction 38/53 to your previous result. What is the new total, expressed as a simplified fraction?

Gemma 2B:

    Reasoning:
    We need to add 38/53 to our previous result of 5627/88.
    To do this, we need to find a common denominator for these two fractions. The least common multiple of 88 and 53 is 4664 (88 * 53).
    We get a common denominator for 5627/88 and 38/53 by multiplying the numerator and denominator of the first fraction by 53 and the numerator and denominator of the second fraction by 88: (5627/88)*(53/53)=298131/4664 and (38/53)*(88/88)=3344/4664
    Now we can add 5627/88 and 38/53: 298131/4664 + 3344/4664 = 301475/4664.
    The fraction 301475/4664 cannot be simplified as it doesn’t have any common factors.
    ### Answer: 301475/4664

Expected answer: 301575/4664

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

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

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

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

    ### Answer: 312/25

Expected answer: 312/25

Correct? Yes

🔗 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 we obtained previously was 312/25. Adding this result to itself means calculating (312/25) + (312/25). Since both fractions have the same denominator, we simply add the numerators: (312 + 312) / 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:  First, find a common denominator for the fractions. The least common denominator for 5 and 90 is 90. To get 90 in the denominator of 82/5, multiply both numerator and denominator by 18: (82 * 18) / (5 * 18) = 1476/90

    Now we have: 1476/90 - 98/90

    Since the fractions have the same denominator, subtract the numerators: (1476-98)/90 = 1378/90

    This can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 2: (1378/2)/(90/2) = 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:

    We begin by individually simplifying the fractions:

     $64/50 = (8*8)/(2*25) = (2*4*2*4)/(2*25) = (4*4*2)/25 = 32/25$

     $70/22 = (2*5*7)/(2*11) = (5*7)/11 = 35/11$

     Next, we find a common denominator for the two fractions. The least common denominator is $25\times11=275$. We can re-express our fractions as:

     $32/25 = (32\times11)/(25\times11) = 352/275$

     $35/11 = (35\times25)/(11\times25)=875/275$

     Now we can add the fractions:

     $(352/275) + (875/275) = 1227/275$

     ### Answer: 1227/275

Expected answer: 1227/275

Correct? Yes

🔗 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:

    Let's calculate the sum with the adjusted fraction:

    First, we simplify the first fraction:

    $64/49$ is already in its simplest form, as 64 and 49 share no common factors other than 1.

    Next, we simplify the second fraction (which remains the same as before):

    $70/22 = (2*5*7)/(2*11) = (5*7)/11 = 35/11$

    Now, we need to find a common denominator for our two fractions, 64/49 and 35/11.  The least common denominator is 49 * 11 = 539.

    Let's express both fractions with the common denominator:

    *  $64/49 = (64 * 11) / (49 * 11) = 704/539$
    *  $35/11 = (35 * 49) / (11 * 49) = 1715/539$

    Finally, we add the two fractions:

    * $704/539 + 1715/539 = 2419/539$

    ### Answer: 2419/539

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

Expected answer: 504/53

Correct? No

🔗 Problem

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

Gemma 2B:

    Reasoning:

     First, simplify 80/90: 80/90 = 8/9.

     Then simplify 52/11: 52/11 = 4 8/11.

     Now add the two simplified fractions: 8/9 + 4 8/11

     To add these fractions, we need a common denominator. The least common denominator for 9 and 11 is 99.

     Convert 8/9 to a fraction with a denominator of 99: (8/9) * (11/11) = 88/99.

     Convert 4 8/11 to a fraction with a denominator of 99: (4 8/11) * (9/9) = 44/99 + 72/99 = 116/99.

     Now, add the fractions with the common denominator: 88/99 + 116/99 = 204/99.

     Simplify the fraction 204/99: 204/99 = 2 6/99 = 2 2/33.
     ### Answer: 2 2/33

Expected answer: 556/99

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 421/222

Correct? Yes

🔗 Follow-up

Problem: You previously calculated the sum of 12/18 and 91/74. Now, double that result. What is the new sum? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: You are asking to double the result we got previously, which was 421/222. Doubling a fraction is the same as multiplying by 2/1.
    That means we need to calculate (421/222)*(2/1).
    (421/222)*(2/1) = 842/222
    842/222 can be simplified to 421/111.
    ### Answer: 421/111

Expected answer: 421/111

Correct? Yes

🔗 Follow-up

Problem: You originally added 12/18 and 91/74. Instead, what if we added 78/18 and 91/74? What is the new sum? Answer as a simplified fraction.

Gemma 2B:

    Reasoning: First find the least common multiple of 18 and 74, which is 666.
    To get 666 in the denominator of 78/18, we need to multiply it by 37/37, so 78/18 is equivalent to (78/18)*(37/37) = 2886/666
    To get 666 in the denominator of 91/74, we need to multiply by 9/9, so 91/74 is equivalent to (91/74)*(9/9) = 819/666
    The sum of 78/18 and 91/74 is equivalent to 2886/666 + 819/666 = 3705/666
    3705/666 can be simplified to 1235/222
    ### Answer: 1235/222

Expected answer: 1235/222

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

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

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

    ### Answer: 277/50

Expected answer: 277/50

Correct? Yes

🔗 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: From the previous question, we know the sum of 7/2 and 51/25 is 277/50.  Now we need to add 86/39 to this sum.

    To add fractions, we need a common denominator. The least common denominator for 50 and 39 is 1950.

    * 277/50 is equivalent to (277 * 39) / (50 * 39) = 10803/1950
    * 86/39 is equivalent to (86 * 50) / (39 * 50) = 4300/1950

    Now we can add the fractions: 10803/1950 + 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: Now the least common denominator for 22 and 25 is their product, which is 550.

    * 7/22 is equivalent to (7 * 25) / (22 * 25) = 175/550
    * 51/25 is equivalent to (51 * 22) / (25 * 22) = 1122/550

    Now we add the fractions: 175/550 + 1122/550 = 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: Let's first simplify (68/69) + (93/7).  Note that these fractions can't be simplified as they share no common factors in their numerator and denominator. We get a common denominator through multiplication:
    (68/69)*(7/7) + (93/7)*(69/69) = 476/483 + 6417/483 = 6893/483.

     Now let's add 3/46 to our previous result. Again, we need a common denominator:
    (6893/483)*(46/46) + (3/46)*(483/483) = 317078/22218 + 1449/22218 = 318527/22218. This fraction can't be simplified further.

     While 318527/22218 is technically a monomial (a monomial can be a constant, a variable or a product of a constant and variables) the problem statement is technically incorrect. (68 / 69) + (93 / 7) is not a monomial, it is a binomial.  It is only after the addition operation is performed that it becomes a monomial.

    ### Answer: 318527/22218

Expected answer: 13849/966

Correct? Yes

🔗 Follow-up

Problem: After you calculated the sum of ((68 / 69) + (93 / 7)) and (3 / 46) in the previous problem, continue the calculation by subtracting (54 / 12) from that total. What's the resulting value in a simplified fraction form?

Gemma 2B:

    Reasoning: From the previous problem, we know the sum of ((68 / 69) + (93 / 7)) and (3 / 46) is 318527/22218. Now we need to subtract (54/12).

    First, simplify (54/12) to its simplest form, which is 9/2.

    Now, we need a common denominator to subtract 9/2 from 318527/22218:
    (318527/22218) - (9/2) = (318527/22218) - (9/2)*(11109/11109)

    This gives us: (318527/22218) - (99981/22218) = 218546/22218

    Finally, simplify the resulting fraction: 218546/22218 = 109273/11109

    ### Answer: 109273/11109

Expected answer: 4751/483

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 1501/98

Correct? Yes

🔗 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: We already know the sum of 31/98 and 60/4 is 1501/98. To subtract 41/52, we need a common denominator:

    1501/98 - 41/52 = 78052/5096 - 3918/5096 = 74134/5096

    This simplifies by dividing both numerator and denominator by their greatest common factor, 2:

    74134/5096 = (74134/2) / (5096/2) = 37067/2548

    ### Answer: 37067/2548

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, find a common denominator for the fractions:
    31/98 + 83/4 = 31/98 + 2075/98 = 2106/98
    Then, we can simplify this fraction by dividing both numerator and denominator by 2: 2106/98 = 1053/49
    ### Answer: 1053/49

Expected answer: 4129/196

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 13/6

Expected answer: 13/6

Correct? Yes

🔗 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 we need to add that result to 7/2:  (13/6) + (7/2).
    The least common denominator for 6 and 2 is 6.
    Convert 7/2 to a fraction with denominator 6: (7/2)*(3/3) = 21/6.
    Now we can add the fractions: (13/6) + (21/6) = 34/6.
    Finally, simplify the fraction by dividing numerator and denominator by their greatest common factor, 2: (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 (32/36) by dividing both numerator and denominator by their greatest common factor, 4. This gives us (32/4)/(36/4) = 8/9.
    Now we have (3/2) + (8/9). To add these fractions, we need a common denominator. The least common denominator for 2 and 9 is 18.
    Convert (3/2) to a fraction with denominator 18: (3/2)*(9/9) = 27/18
    Convert (8/9) to a fraction with denominator 18: (8/9)*(2/2) = 16/18
    Now we can add the fractions: (27/18) + (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, we simplify the fractions: 92/54 = 46/27 and 90/13 = 30/13
    Adding the first two fractions: 46/27 + 30/13 = (46*13)/(27*13) + (30*27)/(13*27) = 1398/351
    Now, subtract the third fraction from the sum: 1398/351 - 46/41 = (1398*41)/(351*41) - (46*351)/(41*351) = (57318-16146)/14491 = 41172/14491
    The simplified form of 41172/14491 is 1144/403
    ### Answer: 1144/403

Expected answer: 108002/14391

Correct? No

🔗 Problem

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 the same as 29/23 * 2 = 58/23.
    ### 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:
    First, calculate 2*(29/23) = 58/23.
    Then, subtract 58/23 from 32/5:  (32/5)-(58/23).
    To subtract fractions, find a common denominator: (32*23)/(5*23)-(58*5)/(23*5) = 736/115 - 290/115
    Finally, subtract the numerators: 446/115
    ### Answer: 446/115

Expected answer: 446/115

Correct? Yes

🔗 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: Twice the value of 36/23 is the same as 36/23 * 2 = 72/23.
    ### 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 fractions, they must have the same denominator.  The least common denominator of 20 and 72 is 360.  Therefore, 29/20 is equivalent to 29*18 / 20*18 = 522/360, and 17/72 is equivalent to 17*5 / 72*5 = 85/360. So, 29/20 + 17/72 = 522/360 + 85/360 = 607/360.
    ### Answer: 607/360

Expected answer: 607/360

Correct? Yes

🔗 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: From the previous question, the sum of 29/20 and 17/72 is 607/360. The least common denominator of 360 and 68 is 6120. So 607/360 is equivalent to 607*17/360*17 = 10319/6120, and 9/68 is equivalent to 9*90 / 68*90 = 810/6120.  Therefore, 607/360 - 9/68 = 10319/6120 - 810/6120 = 9509/6120.
    ### Answer: 9509/6120

Expected answer: 9509/6120

Correct? Yes

🔗 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: To add fractions, they must have the same denominator.  The least common denominator of 5 and 72 is 360.  Therefore, 29/5 is equivalent to 29*72 / 5*72 = 2088/360, and 17/72 is equivalent to 17*5 / 72*5 = 85/360.  So, 29/5 + 17/72 = 2088/360 + 85/360 = 2173/360.
    ### Answer: 2173/360

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

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

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

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

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

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

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

    ### Answer: 1993/237

Expected answer: 1993/237

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, after you have found the value of that expression, add it to 17/88. What do you get? Please simplify your answer as much as possible.

Gemma 2B:

    Reasoning: We need to add 1993/237 to 17/88.

    To add these fractions, we need a common denominator. Let's find the least common multiple of 237 and 88:

    * Prime factorize 237: 3 x 79
    * Prime factorize 88: 2 x 2 x 2 x 11
    * LCM(237, 88) = 2 x 2 x 2 x 3 x 11 x 79 = 20904

    Now, let's convert our fractions to have this denominator:

    * (1993/237) = (1993 * 88) / (237 * 88) = 175384 / 20904
    * (17/88) = (17 * 237) / (88 * 237) = 4029 / 20904

    Finally, we can add them:
    175384/20904 + 4029/20904 = 179413/20904

    This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1.  Therefore, the fraction is already in its simplest form.

    ### Answer: 179413/20904

Expected answer: 179413/20856

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 12911/5325

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 72039/33325

Expected answer: 72056/33325

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 3307/1342

Correct? Yes

🔗 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: From the previous calculation, we know that (75/66) + (81/61) = 3307/1342.
    * Now we need to add 47/19 to this result.
    * First, find a common denominator for 1342 and 19, which is their least common multiple: 25498
    * Rewrite 3307/1342 with a denominator of 25498:  (3307/1342) = (3307*19)/(1342*19) = 62833/25498
    * Rewrite 47/19 with a denominator of 25498: (47/19) = (47*1342)/(19*1342) = 63074/25498
    * Now we can add the fractions: (62833/25498) + (63074/25498) = (62833+63074)/25498 = 125907/25498
    ### Answer: 125907/25498

Expected answer: 125907/25498

Correct? Yes

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

    ### Answer: 1250/198

Expected answer: 625/99

Correct? Yes

🔗 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 previously found that l = 1250/198.  To find c, we need to add 99/92 to l:

    c = l + 99/92 = 1250/198 + 99/92

    To add these fractions, we need a common denominator. The least common denominator for 198 and 92 is 8976. Let's rewrite both fractions with this denominator:

    1250/198 = (1250 * 46) / (198 * 46) = 57500 / 8976
    99/92 = (99 * 98) / (92 * 98) = 9702 / 8976

    Now we can add the fractions:

    c = 57500/8976 + 9702/8976 = 67202/8976

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

    c = (67202 / 2) / (8976 / 2) = 33601/4488

    ### Answer: 33601/4488

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, we simplify 76/18 to 38/9.
    Then, we find the sum of 38/9 and 21/99:
    38/9 + 21/99 = (38*11)/(9*11) + 21/99 = 418/99 + 21/99 = 439/99
    Then we double 439/99 to find the sum of the two identical fractions:
    2*(439/99) = 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 find a common denominator for 58/49 and 31/34. The least common denominator is 1666.
    We get: (58 * 34)/(49 * 34) + (31 * 49)/(34 * 49) = 1972/1666 + 1519/1666 = 3491/1666
    Now we need to add 74/38 to that result. Let's find the least common denominator for these two fractions, which is 3193:
    (3491 * 19)/(1666 * 19) + (74 * 84)/(38 * 84) = 66329/31934 + 6216/31934
    The result of this addition is (66329 + 6216)/31934 = 72545/31934
    Finally, we can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 17:
    (72545/17) / (31934/17) = 4267/1879
    ### Answer: 4267/1879

Expected answer: 127971/31654

Correct? No

🔗 Problem

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

Expected answer: 901/266

Correct? No

🔗 Problem

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

    ### Answer: 3/1

Expected answer: 127/42

Correct? No

🔗 Problem

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

Gemma 2B:

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

    Then we add the results: 3.69 + 1.41 = 5.1

    ### Answer: 5.1

Expected answer: 1459/286

Correct? No

🔗 Problem

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

Expected answer: 21415/6622

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 419/78

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 4/3

Correct? Yes

🔗 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: Our previous result was 52/39. To add 65/97, we need a common denominator.
    The least common denominator for 39 and 97 is 3783.
    We can rewrite 52/39 as 5096/3783, since (52 x 97)/(39 x 97) = 5096/3783.
    We can rewrite 65/97 as 2535/3783, since (65 x 39)/(97 x 39) = 2535/3783.
    Therefore, 52/39 + 65/97 = 5096/3783 + 2535/3783 = 7631/3783.
    ### Answer: 7631/3783

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 fractions, they must have the same denominator. The least common denominator of 65 and 47 is 3055.
    We can rewrite 75/65 as 3485/3055, since (75 x 47)/(65 x 47) = 3485/3055.
    We can rewrite 7/47 as 455/3055, since (7 x 65)/(47 x 65) = 455/3055.
    Therefore, 75/65 + 7/47 = 3485/3055 + 455/3055 = 3940/3055.
    ### Answer: 3940/3055

Expected answer: 796/611

Correct? No

🔗 Problem

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

Gemma 2B:

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

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

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

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

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

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

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

    ### Answer: 225351/2898

Expected answer: 225191/2898

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 58/13

Expected answer: 58/13

Correct? Yes

🔗 Follow-up

Problem: After you have calculated twice the fraction (58 / 26), what would be the result if you then added (49 / 66) to that sum? Express your final answer as a simplified fraction.

Gemma 2B:

    Reasoning: We already know from the previous problem that twice the fraction (58/26) is 58/13.
    Now we need to add (49/66) to 58/13. To add fractions, we need a common denominator.
    The least common denominator for 13 and 66 is their product, 858.
    To get 858 in the denominator of 58/13, we multiply both numerator and denominator by 66: (58 * 66) / (13 * 66) = 3828/858
    To get 858 in the denominator of 49/66, we multiply both numerator and denominator by 13: (49 * 13) / (66 * 13) = 637/858
    Now we can add the two fractions: 3828/858 + 637/858 = 4465/858
    This fraction can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 9: (4465 / 9) / (858 / 9) = 496/94.

    ### Answer: 496/94

Expected answer: 4465/858

Correct? No

🔗 Follow-up

Problem: If originally instead of 58 parts, there were 54 parts in every batch of 26, and two such fractions were added, what would be the sum? Express your answer in simplest form.

Gemma 2B:

    Reasoning: We start with the fraction 54/26.  Both numerator and denominator are divisible by 2, so we simplify to 27/13.
    The problem asks us to add two of this fraction: (27/13) + (27/13).
    Since the fractions share the same denominator, we simply add the numerators: (27+27)/13 = 54/13.

    ### Answer: 54/13

Expected answer: 54/13

Correct? Yes

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

Expected answer: 127907/7455

Correct? No

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 7213/2989

Expected answer: 56831/5978

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 5948/69

Correct? Yes

🔗 Follow-up

Problem: After calculating the sum of 85/1 and 83/69, what is the result if you then add 21/86 to that sum?

Gemma 2B:

    Reasoning: We previously determined the sum of 85/1 and 83/69 to be 86 and 14/69.
    Adding 21/86 to 86 and 14/69, we get: 86 and 14/69 + 21/86
    To add fractions, we need a common denominator.  The least common denominator for 69 and 86 is their product, as they share no common factors. However, we are only asked for the sum, not a simplified answer.
    Therefore, 86 and 14/69 + 21/86 = 86 + 14/69 + 21/86
    ### Answer: 86 and 14/69 + 21/86

Expected answer: 512977/5934

Correct? No

🔗 Follow-up

Problem: In the previous problem, instead of adding 83/69, what would be the result if you added 83/52 to 85/1 instead?

Gemma 2B:

    Reasoning: 85/1 is equivalent to 85
    To add the fractions, they must share a common denominator. The least common denominator is 52.
    85/1 * 52/52 = 4420/52
    4420/52 + 83/52 = 4503/52
    The result can remain as an improper fraction or be changed to a mixed number.
    4503/52 = 86 and 31/52
    ### Answer: 4503/52 or 86 and 31/52

Expected answer: 4503/52

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

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

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

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

    ### Answer: 8471/1118

Expected answer: 197/26

Correct? Yes

🔗 Follow-up

Problem: You solved the sum of 92/13 and 43/86 in the previous problem. Now, additional 36/72 to that sum. What is the total as a simplified fraction?

Gemma 2B:

    Reasoning:  We know from before that the sum of 92/13 and 43/86 is 8471/1118. We need to add 36/72 to this.

    First, simplify 36/72 by dividing both numerator and denominator by their greatest common factor, 36: (36/36)/(72/36) = 1/2

    Now find the least common multiple of 1118 and 2, which is 1118.

    Rewrite 1/2 with a denominator of 1118: (1/2) * (559/559) = 559/1118

    Finally, add the two fractions: 8471/1118 + 559/1118 = 9030/1118

    Simplify this fraction by dividing both numerator and denominator by their greatest common factor, 2: (9030/2)/(1118/2) = 4515/559

    ### Answer: 4515/559

Expected answer: 105/13

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you found the sum of 92/13 and 43/86. Now suppose the original problem actually was about adding 61/13, not 92/13, to 43/86. What would be the new sum as a simplified fraction?

Gemma 2B:

    Reasoning: We already know from the previous problem that 43/86 is equivalent to 559/1118.

    To get a denominator of 1118 for 61/13, we multiply the numerator and denominator by 86: (61/13) * (86/86) = 5246/1118.

    Now we can add the two fractions: 5246/1118 + 559/1118 = 5805/1118

    ### Answer: 5805/1118

Expected answer: 135/26

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 3443/1568

Correct? Yes

🔗 Follow-up

Problem: Now, to the sum of 67/32 and 10/98, add 14/59. What is the final result as a simplified fraction?

Gemma 2B:

    Reasoning: We found that the sum of the first two fractions is 3443/1568.  To add 14/59, we need to find a common denominator for these two fractions.  The least common multiple of 1568 and 59 is 92512.
    Since 92512 / 1568 = 59, the fraction 3443/1568 is equivalent to (3443 * 59) / (1568 * 59) = 203137 / 92512. Since 92512 / 59 = 1568, the fraction 14/59 is equivalent to (14 * 1568) / (59 * 1568) = 21952 / 92512.
    The sum of the three fractions is therefore (203137 + 21952) / 92512 = 225089 / 92512.
    ### Answer: 225089/92512

Expected answer: 225089/92512

Correct? Yes

🔗 Follow-up

Problem: Let's reconsider the previous problem. Instead of a fraction of 67/32, consider a fraction of 43/32. Keeping the second fraction of 10/98 the same, what would be the new sum expressed as a simplified fraction?

Gemma 2B:

    Reasoning: Similar to before, the least common multiple of 32 and 98 is 1568.
    Since 1568 / 32 = 49, the fraction 43/32 is equivalent to (43 * 49) / (32 * 49) = 2107/1568. We already know from the previous problem that 10/98 is equivalent to 160/1568.
    Therefore, the sum of 43/32 and 10/98 is (2107 + 160)/1568 = 2267/1568.
    ### Answer: 2267/1568

Expected answer: 2267/1568

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 691/208

Expected answer: 691/208

Correct? Yes

🔗 Follow-up

Problem: After finding the sum of 59/52 and 70/32, add this to 42/41. What is the final sum as a simplified fraction?

Gemma 2B:

    Reasoning:
    * We know from the previous problem that the sum of 59/52 and 70/32 is 691/208.
    * To add 691/208 to 42/41, we need to find a common denominator. The least common multiple of 208 and 41 is 208.
    * We can rewrite 42/41 as an equivalent fraction with a denominator of 208 by multiplying by 5/5:  (42/41)*(5/5) = 210/208.
    * Now we can add the fractions: 691/208 + 210/208 = 901/208

    ### Answer: 901/208

Expected answer: 37067/8528

Correct? No

🔗 Follow-up

Problem: After recalculating the original problem with 74/52 instead of 59/52 and still adding this to 70/32, what is the new sum as a simplified fraction?

Gemma 2B:

    Reasoning:
    * First, find the least common multiple (LCM) of the denominators, 52 and 32. The LCM of 52 and 32 is 416.
    * To get a denominator of 416 in the first fraction, we multiply by 8/8: (74/52)*(8/8) = 592/416.
    * To get a denominator of 416 in the second fraction, we multiply by 13/13: (70/32)*(13/13) = 910/416.
    * Now we can add the fractions: 592/416 + 910/416 = 1502/416
    * This simplifies to 751/208.

    ### Answer: 751/208

Expected answer: 751/208

Correct? Yes

🔗 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:

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

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

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

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

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

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

    ### Answer: 23.431

Expected answer: 1523/65

Correct? No

🔗 Problem

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

Expected answer: 1385/1066

Correct? Yes

🔗 Follow-up

Problem: What will the result be if you take the sum obtained from adding 20/52 to 75/82, and then add 41/75 to it? Simplify your answer to the smallest possible fraction.

Gemma 2B:

    Reasoning: We already know from the previous problem that 20/52 + 75/82 = 1385/1066. Now we need to add 41/75 to this result.

    First, find a common denominator for 1066 and 75. The least common denominator is 53300.

    Next, rewrite the fractions with this common denominator:
    * 1385/1066 = (1385 * 50)/(1066 * 50) = 69250/53300
    * 41/75 = (41 * 710)/(75 * 710) = 29110/53300

    Finally, add the fractions: 69250/53300 + 29110/53300 = 98360/53300. This fraction can be simplified to 4918/2665.

    ### Answer: 4918/2665

Expected answer: 147581/79950

Correct? No

🔗 Follow-up

Problem: What would the result be if you initially had 20/9 instead of 20/52, and you added this to 75/82? Remember to simplify your answer to the smallest possible fraction.

Gemma 2B:

    Reasoning: First, find the least common denominator for 9 and 82, which is 738. Next, rewrite both fractions with this common denominator: 20/9 becomes 1640/738 and 75/82 becomes 675/738. Finally, add the two fractions: 1640/738 + 675/738 = 2315/738. This fraction cannot be simplified further.
    ### Answer: 2315/738

Expected answer: 2315/738

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 536/105

Expected answer: 536/105

Correct? Yes

🔗 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:
    * First, we simplify 67/84.  Since 67 is prime, the fraction cannot be simplified.
    * Next, we need to find a common denominator for 31/5 and 67/84. The least common multiple of 5 and 84 is 420.
    * We convert both fractions to have this denominator: (31/5)*(84/84) = 2604/420 and (67/84)*(5/5) = 335/420
    * Now we can subtract: 2604/420 - 335/420 = 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 the two fractions: 81/90 + 94/49. To add fractions, they need a common denominator. The least common denominator for 90 and 49 is 4410. We get: (81*49)/(90*49) + (94*90)/(49*90) = 3969/4410 + 8460/4410 = 12429/4410.
    * Next, we simplify the fraction 12429/4410 by dividing both numerator and denominator by their greatest common divisor, which is 49. This gives us: 253/90.
    * Finally, we double the result: 2 * (253/90) = 253/45.

    ### Answer: 253/45

Expected answer: 1381/245

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 1023/322

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 21825/12122

Correct? No

🔗 Problem

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

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

    ### Answer: 553/171

Expected answer: 4766/561

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 213/161

Correct? No

🔗 Problem

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

Gemma 2B:

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

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

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

    (5795 + 918)/1188 = 6713/1188

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

Expected answer: 6713/1098

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 911/644

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 998/105

Correct? Yes

🔗 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: Our previous sum was 998/105. We need to add 21/86 to this.
    First, we simplify 21/86 (divide both numerator and denominator by 7) = 3/12.
    To add fractions, they must have the same denominator. The least common multiple of 105 and 12 is 420.
    Thus, we have 998/105 (multiply both numerator and denominator by 4) = 3992/420 and 3/12 (multiply both numerator and denominator by 35) = 105/420.
    Finally, 3992/420 + 105/420 = 4097/420. This fraction cannot be simplified further.
    ### Answer: 4097/420

Expected answer: 88033/9030

Correct? No

🔗 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: First, we need to simplify the fraction 12/70 (divide both numerator and denominator by 2) = 6/35.
    To add fractions, they must have the same denominator. The least common multiple of 35 and 9 is 315.
    Thus, we have 6/35 (multiply both numerator and denominator by 9) = 54/315 and 40/9 (multiply both numerator and denominator by 35) = 1400/315.
    Finally, 54/315 + 1400/315 = 1454/315. This fraction can be simplified by dividing both numerator and denominator by 3: 1454/315 = 484/105
    ### Answer: 484/105

Expected answer: 1454/315

Correct? No

🔗 Problem

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

Gemma 2B:

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

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

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

    ### Answer: 1412/69

Expected answer: 1412/69

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, now add your answer to 79/60. What is the result?

Gemma 2B:

    Reasoning:
    We need to add 1412/69 to 79/60. To do this, we need to find a common denominator.

    *  The least common multiple of 69 and 60 is 1380.
    *  Converting 1412/69 to a fraction with a denominator of 1380: (1412 * 20) / (69 * 20) = 28240/1380
    *  Converting 79/60 to a fraction with a denominator of 1380: (79 * 23) / (60 * 23) = 1817/1380
    *  Adding the two fractions: 28240/1380 + 1817/1380 = 30057/1380

    ### Answer: 30057/1380

Expected answer: 10019/460

Correct? Yes

🔗 Follow-up

Problem: If instead of subtracting 40/92 from 32/3, we subtract it from 65/3 and then double the result as before, what would be the new result?

Gemma 2B:

    Reasoning:
    We already simplified 40/92 to 10/23 from the previous problem.

    Now, let's subtract 10/23 from 65/3. To do this, we need a common denominator:
    * The least common multiple of 3 and 23 is 69.
    * Converting 65/3 to a fraction with a denominator of 69: (65 * 23) / (3 * 23) = 1495/69
    * Converting 10/23 to a fraction with a denominator of 69: (10 * 3) / (23 * 3) = 30/69
    * Subtracting the two fractions: 1495/69 - 30/69 = 1465/69

    Finally, let's double the result: (1465/69) * 2 = 2930/69

    ### Answer: 2930/69

Expected answer: 2930/69

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

Expected answer: 79/12

Correct? Yes

🔗 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: We already know from the previous problem that (79/24 + 79/24) = 79/12. So, the problem becomes (79/12) + (79/12). This equals (79+79)/12 = 158/12, which simplifies to 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:  79/20 + 79/20 is the same as (79 + 79)/20 = 158/20. This simplifies to 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: First, find the simplest form of 12/22 by dividing the numerator and denominator by 2: 12/2 = 6,  22/2 = 11, so 12/22 = 6/11
    To add fractions, they must have the same denominator. The least common denominator of 76 and 11 is 836.
    To get a denominator of 836 in the first fraction, multiply the numerator and denominator by 11: 91/76 * 11/11 = 1001/836
    To get a denominator of 836 in the second fraction, multiply the numerator and denominator by 76: 6/11 * 76/76 = 456/836
    Now, add the two fractions: 1001/836 + 456/836 = 1457/836
    The fraction can be simplified by dividing the numerator and denominator by 11: 1457/11 = 132  836/11 = 76
    So, 1457/836 = 132/76
    The fraction can be further simplified by dividing the numerator and denominator by 4: 132/4 = 33, 76/4 = 19, so 132/76 = 33/19
    ### Answer: 33/19

Expected answer: 1457/836

Correct? No

🔗 Problem

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

Gemma 2B:

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

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

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

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

    ### Answer: 149/44

Expected answer: 105227/4371

Correct? No

🔗 Problem

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

Expected answer: 553562/116781

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 961/432

Correct? Yes

🔗 Follow-up

Problem: What is the value of the original expression ((73 / 27) - (23 / 48)) minus the fraction 61/59? Answer as a simplified fraction.

Gemma 2B:

    Reasoning:
    From the previous problem, we know (73/27) - (23/48) is equivalent to 961/432.  So the problem is now (961/432) - (61/59).

    The least common multiple of 432 and 59 is 25488.

    We can rewrite (961/432) as (961 * 59)/(432 * 59) = 56699/25488.
    We can rewrite (61/59) as (61 * 432) / (59 * 432) = 26352 / 25488.

    Now the expression becomes: (56699/25488) - (26352/25488).

    Subtracting the numerators, we get (56699 - 26352)/25488 = 30347/25488.

    ### Answer: 30347/25488

Expected answer: 30347/25488

Correct? Yes

🔗 Follow-up

Problem: In the previous question, we calculated the value of the expression ((73 / 27) - (23 / 48)). Now, suppose we made a mistake and the original fraction was actually 65/27, not 73/27. What would the value of the new expression be? Answer as a simplified fraction.

Gemma 2B:

    Reasoning:
    Following the same steps as before, we need to find a common denominator for 65/27 and 23/48, which is still 432.
    We can rewrite 65/27 as (65 * 16) / (27 * 16) = 1040/432
    We already know 23/48 is equivalent to 207/432
    Now the new expression becomes: (1040/432) - (207/432)
    Subtracting the numerators, we get: (1040-207)/432 = 833/432
    ### Answer: 833/432

Expected answer: 833/432

Correct? Yes

🔗 Problem

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

Gemma 2B:

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

    ### Answer: 35.96

Expected answer: 827/23

Correct? No

🔗 Problem

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

Gemma 2B:

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

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

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

    ### Answer: 47 1/4

Expected answer: 189/4

Correct? Yes

🔗 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: In the previous problem, we found that 34/1 + 53/4 = 47 1/4.  Now we need to add 24/67 to that result.

    First, let's convert 47 1/4 to an improper fraction: (47 * 4 + 1) / 4 = 189/4

    To add 189/4 and 24/67, we need a common denominator:
    - The least common multiple of 4 and 67 is 268.
    - 189/4 is equivalent to (189 * 67) / (4 * 67) = 12663/268
    - 24/67 is equivalent to (24 * 4) / (67 * 4) = 96/268

    Now we can add: 12663/268 + 96/268 = 12759/268

    Finally, convert 12759/268 to a mixed number: 12759 divided by 268 is 47 with a remainder of 153.

    ### Answer: 47 153/268

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, find a common denominator for 97 and 4. The least common multiple is their product: 97 * 4 = 388.
    - Convert 34/97 to a fraction with a denominator of 388: (34 * 4) / (97 * 4) = 136/388
    - Convert 53/4 to a fraction with a denominator of 388: (53 * 97) / (4 * 97) = 5141/388

    Now, add the two fractions: 136/388 + 5141/388 = 5277/388

    Finally, convert the improper fraction 5277/388 to a mixed number:
    - 5277 divided by 388 equals 13 with a remainder of 241.

    ### Answer: 13 241/388

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

    We can then rewrite the fractions as:
    * 3/36 = 24/288
    * 97/96 = 291/288

    Then we can add the fractions: 24/288 + 291/288 = 315/288.
    Finally, we can simplify 315/288 to 105/96, and then to 35/32.
    ### Answer: 35/32

Expected answer: 35/32

Correct? Yes

🔗 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 know from the previous problem that the sum of 3/36 and 97/96 is 35/32.  To add 35/32 + 55/69, we need to find a common denominator. The least common denominator of 32 and 69 (which share no common factors) is their product: 32 * 69 = 2208.

    Next, we'll convert our fractions to have this common denominator:
    * (35/32)*(69/69) = 2415/2208
    * (55/69)*(32/32) = 1760/2208

    Now, we can add the fractions: (2415/2208) + (1760/2208) = 4175/2208

    The fraction 4175/2208 cannot be simplified further as there are no common factors between the numerator and denominator.

    ### Answer: 4175/2208

Expected answer: 4175/2208

Correct? Yes

🔗 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 get the sum of the two fractions, we first need to find their least common denominator. The least common denominator of 38 and 96 is 1824.

    We can then rewrite the fractions as:
    * 3/38 = 144/1824
    * 97/96 = 1843/1824

    Then we can add the fractions: 144/1824 + 1843/1824 = 1987/1824
    Because 1987 is a prime number, the fraction cannot be further simplified.
    ### Answer: 1987/1824

Expected answer: 1987/1824

Correct? Yes

🔗 Problem

Problem: Calculate ((92 / 95) + (4 / 74)). 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 95 and 74 is 7030.
     We can rewrite (92/95) as (92 * 74) / (95 * 74) = 6808 / 7030.
     We can rewrite (4/74) as (4 * 95) / (74 * 95) = 380 / 7030.
     Now, we can add the two fractions: (6808 / 7030) + (380 / 7030) = 7188 / 7030
     This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 2: 7188/2 / 7030/2 = 3594 / 3515.
    ### Answer: 3594/3515

Expected answer: 3594/3515

Correct? Yes

🔗 Problem

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

Expected answer: 1138/423

Correct? No

🔗 Problem

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

Expected answer: 943/936

Correct? Yes

🔗 Follow-up

Problem: The wholesaler, after their sale, receives a new shipment of olive oil. This shipment contains 68/47 barrels of oil. After adding the new shipment to their existing stock, how much olive oil does the wholesaler have in total? Express your answer as a simple fraction.

Gemma 2B:

    Reasoning:
    The wholesaler currently has 943/936 barrels and receives a shipment of 68/47 barrels.
    First, find a common denominator for 936 and 47. The least common multiple of 936 and 47 is 43992.
    We can rewrite 943/936 as (943 * 47) / (936 * 47) = 44321/43992
    We can rewrite 68/47 as (68 * 936) / (47 * 936) = 63648/43992
    Adding the two amounts: 44321/43992 + 63648/43992 = 107969/43992
    This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, 23: (107969/23) / (43992/23) = 4694.3/1912.7
    Since we need the answer as a simple fraction, we round the numerator and denominator to the nearest whole number: 4694/1913
    ### Answer: 4694/1913

Expected answer: 107969/43992

Correct? No

🔗 Follow-up

Problem: Let's change the start of our olive oil wholesaler's scenario. Now, they originally had 71/26 barrels of olive oil in their warehouse. They still 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:
    First, we need to find a common denominator for 26 and 72. The least common multiple of 26 and 72 is 936.
    We can rewrite 71/26 as (71 * 36) / (26 * 36) = 2556/936
    We can rewrite 41/72 as (41 * 13) / (72 * 13) = 533/936
    The wholesaler has 2556/936 - 533/936 = 2023/936 barrels of olive oil left.
    We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 13. This gives us 155/72.
    ### Answer: 155/72

Expected answer: 2023/936

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 284/105

Correct? No

🔗 Problem

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

    ### Answer: 36 57/66

Expected answer: 547/22

Correct? No

🔗 Problem

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

Gemma 2B:

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

Expected answer: 12/5

Correct? Yes

🔗 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: The problem asks us to add 71/32 to 156/65.  To add fractions, they must share a common denominator.  The least common denominator is the least common multiple of 65 and 32, which is 2080.  Therefore, we must convert both fractions to equivalent fractions that have 2080 as a denominator. Since 2080/65 = 32, we multiply the first fraction by 32/32 to get (156*32)/(65*32) = 4992/2080.  Since 2080/32 = 65, we multiply the second fraction by 65/65 to get (71*65)/(32*65) = 4615/2080.  The sum of these two fractions is (4992+4615)/2080 = 9607/2080
    ### Answer: 9607/2080

Expected answer: 739/160

Correct? Yes

🔗 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: Any number divided by itself is equal to 1. Therefore, 78/78 = 1.  The problem is then simplified to 1 + 1 = 2.
    ### 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 fractions, they must have the same denominator. The least common multiple of 7 and 90 is 630.  We can rewrite 16/7 as 1440/630 and 11/90 as 77/630.
    1440/630 + 77/630 = 1517/630
    ### Answer: 1517/630

Expected answer: 1517/630

Correct? Yes

🔗 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 found that the sum of 16/7 and 11/90 is 1517/630.  To add this to 38/69, we need to find a common denominator. The least common multiple of 630 and 69 is 14490. We can rewrite 1517/630 as 36406/14490 and 38/69 as 8050/14490.
    36406/14490 + 8050/14490 = 44456/14490. This simplifies to 24698/7245.
    ### Answer: 24698/7245

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:  First, simplify 99/90, which simplifies to 11/10. Then, find a common denominator for 16/7 and 11/10, which is 70.
    Rewriting the fractions, we get 160/70 + 77/70 = 237/70
    ### Answer: 237/70

Expected answer: 237/70

Correct? Yes