🔗 Problem

Problem: Calculate the product of (29/2) and (19/28) and write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (29/2) = 14.5
    (19/28) = 0.7

    Product: 14.5 x 0.7 = 10.85

    Simplified fraction: 10 11/14

    ### Answer: 10 11/14

Expected answer: 551/56

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem: multiply 7 by the result of dividing 27 by 12. Write your answer as a simplified fraction.

Gemma 2B:

      To calculate the result of the problem, we need to perform the following steps:

    1. Divide 27 by 12: 27 ÷ 12 = 2
    2. Multiply 7 by the result: 7 × 2 = 14

    Therefore, the result of the problem is 14.

    ### Answer: 14

Expected answer: 63/4

Correct? No

🔗 Problem

Problem: Susan has a recipe that calls for 30 parts of flour to 27 parts of water. If she decides to use 29 parts of flour instead, and she keeps the water proportion the same, how much water will she use? Calculate this using fraction multiplication: ((30 / 30) * (29 / 27)).

Gemma 2B:

      Reasoning:

    Susan wants to use 29 parts of flour instead of 30 parts. To keep the water proportion the same, she needs to use the same amount of water as before.

    The recipe calls for 30 parts of flour to 27 parts of water. To find the amount of water, we can use fraction multiplication:

    ((30 / 30) * (29 / 27)) = (1 / 1) * (29 / 27) = 29 / 27

    So, Susan will use 29 parts of flour and 27 parts of water.

Expected answer: 29/27

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: ((24 / 22) * (24 / 17)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (24 / 22) = 1

    (24 / 17) = 1.364

    (1 * 1.364) = 1.364

    ### Answer: 1.364

Expected answer: 288/187

Correct? No

🔗 Problem

Problem: What is the result when you divide 25/4 by 16/6? Please write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    25/4 = 6
    16/6 = 2

    When you divide 6 by 2, you get:

    6 ÷ 2 = 3

    So, the result when you divide 25/4 by 16/6 is 3.

    ### Answer: 3

Expected answer: 75/32

Correct? No

🔗 Problem

Problem: Determine the result of the following: Multiply the fraction 3/7 by the fraction 26/6 and express your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    3/7 x 26/6 = 3 x 26/42 = 78/42

    ### Answer: 78/42

Expected answer: 13/7

Correct? Yes

🔗 Follow-up

Problem: In the previous question, you found the result of (3 / 7) * (26 / 6). Now, take that result and multiply it by the fraction 23/2. What's the result of this calculation, expressed as a simplified fraction?

Gemma 2B:

      Reasoning:

    78/42 x 23/2 = 78 x 11 = 858

    ### Answer: 858/2

Expected answer: 299/14

Correct? No

🔗 Follow-up

Problem: In the previous problem, you multiplied the fraction 3/7 by the fraction 26/6. Now, let's change the fraction a bit. Instead of 3/7, use 7/7 (which is actually 1). Multiply this new fraction 7/7 by the same fraction 26/6. What is the result of this new calculation, expressed as a simplified fraction?

Gemma 2B:

      Reasoning:

    7/7 x 26/6 = 7 x 26/42 = 184/42

    ### Answer: 184/42

Expected answer: 13/3

Correct? No

🔗 Problem

Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.

Gemma 2B:

      The expression (17 / 10) * (28 / 10) can be evaluated as follows:

    1. First, we divide 17 by 10: 17 / 10 = 1.7
    2. Next, we divide 28 by 10: 28 / 10 = 2.8
    3. Finally, we multiply 1.7 and 2.8: 1.7 * 2.8 = 4.52

    Therefore, the result of the expression (17 / 10) * (28 / 10) is 4.52.

Expected answer: 119/25

Correct? No

🔗 Problem

Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))

Gemma 2B:

      Reasoning:

    1. ((29 / 14) * (23 / 6)) = (29 / 14) * (23 / 6)
    2. (29 / 14) = 2
    3. (23 / 6) = 3
    4. (2 * 3) = 6

    Therefore, the value of the given expression is 6.
    ### Answer: 6

Expected answer: 667/84

Correct? No

🔗 Problem

Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((18 / 19) * (19 / 6)) = (18/19) * (19/6)
    = (18/19) * (3/2)
    = (18/19) * (3)
    = (54/19)

    Therefore, the simplified fraction is 54/19.
    ### Answer: 54/19

Expected answer: 3

Correct? No

🔗 Problem

Problem: Calculate the result of the multiplication of the fraction 19/12 by 20/6. Write your final answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    19/12 x 20/6 = 19/12 x 32/6 = 576/72

    Simplifying:

    576/72 = 8/1

    ### Answer: 8/1

Expected answer: 95/18

Correct? No

🔗 Problem

Problem: A cargo ship carries 28/21 of its capacity in the morning, and 22/4 of its capacity in the afternoon. If the cargo in the morning represents the load allocated to consumer goods and the cargo in the afternoon represents industrial supplies, what is the total fractional representation of these two types of cargo hauled in one day? Calculate ((28 / 21) * (22 / 4)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    The total fractional representation of these two types of cargo hauled in one day can be calculated by multiplying the fractions for the morning and afternoon cargo loads.

    ((28 / 21) * (22 / 4)) = (28 / 21) * (22 / 4) = (56 / 84)

    Therefore, the total fractional representation of these two types of cargo hauled in one day is 56/84, or 67.5%.

    ### Answer: 67.5%

Expected answer: 22/3

Correct? No

🔗 Problem

Problem: Determine the result of the following mathematical expression: (16 / 4) / (24 / 21). Write your answer as a simplified fraction or decimal.

Gemma 2B:

      The expression is:

    (16 / 4) / (24 / 21)

    = (4) / (24 / 21)

    = (4) / (24 / 7)

    = (4) / (3)

    = 12 / 3

    = 4

    Therefore, the result of the expression is 4.

Expected answer: 7/2

Correct? No

🔗 Problem

Problem: Calculate the product of the fractions 5/27 and 15/2. Write your answer in the simplest form.

Gemma 2B:

      Reasoning:

    5/27 = 1/5
    15/2 = 3/2

    Product:

    (1/5) x (3/2) = 3/10

    ### Answer: 3/10

Expected answer: 25/18

Correct? No

🔗 Problem

Problem: Calculate the result of the following product of fractions: (15 / 13) * (19 / 7). Make sure to write your answer as a simplified fraction.

Gemma 2B:

      (15 / 13) * (19 / 7) = (15 * 19) / (13 * 7)
    = (285) / (91)
    = 3 1/9

    Therefore, the result of the product of fractions (15 / 13) * (19 / 7) is 3 1/9.

Expected answer: 285/91

Correct? No

🔗 Problem

Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.

Gemma 2B:

      To calculate the product of the fractions 23/22 and 27/20, we need to multiply the numerators and denominators:

    23/22 x 27/20 = 23 x 27 / 22 x 20 = 649 / 440

    Therefore, the product of the fractions 23/22 and 27/20 is 649/440, or 15/11.

Expected answer: 621/440

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: (12 / 25) * (20 / 4). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (12 / 25) = 1/2
    (20 / 4) = 5

    (1/2) * (5) = 5/2

    ### Answer: 5/2

Expected answer: 12/5

Correct? No

🔗 Problem

Problem: Calculate the following operation: multiply the fraction 14/10 by the fraction 30/5. Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    14/10 = 14/10
    30/5 = 6

    Multiplying the fractions:

    14/10 x 6 = 84/50

    Simplifying the fraction:

    84/50 = 17/25

    ### Answer: 17/25

Expected answer: 42/5

Correct? No

🔗 Problem

Problem: A baker is preparing a large batch of cookies that requires 26 cups of sugar per each full batch. If he only has enough sugar to make a fraction of the batch, represented by 29/14 of a full batch, how many batches of cookies can the baker make? Calculate this as ((26 / 1) / (29 / 14)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning: The baker has 26 cups of sugar per full batch, and he only has enough sugar to make a fraction of the batch, represented by 29/14 of a full batch.

    To find out how many batches of cookies the baker can make, we need to divide the amount of sugar he has by the amount of sugar needed for one batch.

    ((26 / 1) / (29 / 14)) = (26 / 29) = 0.857

    So, the baker can make 0.857 batches of cookies.

    ### Answer: 0.857 batches

Expected answer: 364/29

Correct? No

🔗 Problem

Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (27 / 10) = 2 3/10
    (9 / 4) = 2 3/4

    (2 3/10) * (2 3/4) = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4 = 2 3/10 * 2 3/4

Expected answer: 243/40

Correct? No

🔗 Problem

Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (24 / 11) = 2
    (27 / 26) = 3/2

    (2 * 3/2) = 3/2

    ### Answer: 3/2

Expected answer: 324/143

Correct? No

🔗 Problem

Problem: Find the solution to the following multiplication problem: Multiply the fraction 26/9 by the fraction 17/13. Write your answer in simplest form.

Gemma 2B:

      To multiply the fractions 26/9 and 17/13, we need to follow the order of operations (PEMDAS):

    1. Multiply the numerators: 26 x 17 = 438
    2. Multiply the denominators: 9 x 13 = 117
    3. Simplify the fraction: 438/117

    Therefore, the product of the fractions 26/9 and 17/13 is 438/117.

Expected answer: 34/9

Correct? No

🔗 Problem

Problem: Solve the following problem: What is the result of the expression (28 / 16) / (27 / 24)? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (28 / 16) / (27 / 24) = (28 / 16) × (24 / 27)
    = (28 × 24) / (16 × 27)
    = (576) / (432)
    = 1 3/4

    ### Answer: 1 3/4

Expected answer: 14/9

Correct? No

🔗 Problem

Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.

Gemma 2B:

      The expression is:

    ((15 / 3) * (19 / 26)) = (5 * 19) / (3 * 26)

    = 95 / 82

    = 1 3/4

    So the simplified fraction is 1 3/4.

Expected answer: 95/26

Correct? No

🔗 Problem

Problem: The local bakery was making a special order for a customer. The recipe they are using requires 19/28, and they want to make exactly 30/4 of this recipe. How much of the ingredient will they require?

Gemma 2B:

      Reasoning: The recipe requires 19/28 of the ingredient, and they want to make exactly 30/4 of this recipe.

    To find the amount of ingredient required, we can multiply the recipe's ingredient requirement by the number of times they want to make the recipe.

    19/28 x 30/4 = 19/28 x 7.5 = 137.5/28

    So, the bakery will require 137.5/28 of the ingredient.

    ### Answer: 137.5/28

Expected answer: 285/56

Correct? No

🔗 Problem

Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((5 / 2) / (26 / 15)) = (5 / 2) / (26 / 15)
    = (5 / 2) * (15 / 26)
    = (5 / 2) * (3 / 5)
    = (3 / 2)

    Therefore, the result of the expression is 3/2.

Expected answer: 75/52

Correct? No

🔗 Problem

Problem: Calculate the result of the expression (9/3) * (27/28) and write your answer as a simplified fraction.

Gemma 2B:

      The expression (9/3) * (27/28) can be evaluated as follows:

    (9/3) = 3
    (27/28) = 9/4

    Therefore, the result of the expression is:

    (3) * (9/4) = 27/12

    Simplifying the fraction, we get:

    27/12 = 2 1/2

    So, the simplified fraction is 2 1/2.

Expected answer: 81/28

Correct? No

🔗 Problem

Problem: Calculate the solution to the following equation and write your answer as a simplified fraction: ((15 / 13) * (24 / 24))

Gemma 2B:

      Reasoning:

    ((15 / 13) * (24 / 24)) = (15 / 13) * 1

    = 15 / 13

    = 15/13

    ### Answer: 15/13

Expected answer: 15/13

Correct? Yes

🔗 Follow-up

Problem: After calculating the solution to ((15 / 13) * (24 / 24)), multiply your answer with (22 / 7) and write that answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((15 / 13) * (24 / 24)) = 15/13

    (15/13) * (22/7) = 15/13 * 3

    = 45/13

    ### Answer: 45/13

Expected answer: 330/91

Correct? No

🔗 Follow-up

Problem: After calculating the solution to ((15 / 2) * (24 / 24)), consider what would happen if you originally had 15 halves instead of 15 thirteenths. Multiply this new fraction with 1 (represented by (24 / 24)) and write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    If you originally had 15 halves instead of 15 thirteenths, the fraction would be:

    15/2

    Multiplying this fraction with 1 (represented by (24 / 24)) gives us:

    15/2 * 24/24 = 15/2 * 1 = 15/2

    ### Answer: 15/2

Expected answer: 15/2

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following multiplication of fractions operation: (9 / 7) * (25 / 30). Express your answer as a simplified fraction.

Gemma 2B:

      To perform the multiplication of fractions operation, we need to follow the order of operations (PEMDAS):

    1. Multiply the numerators: 9 × 25 = 225
    2. Multiply the denominators: 7 × 30 = 210
    3. Simplify the fraction: 225/210 = 4 3/5

    Therefore, the result of the multiplication of fractions operation is 4 3/5.

Expected answer: 15/14

Correct? Yes

🔗 Follow-up

Problem: Using the answer you obtained from the previous problem, multiply it by 15/15. What simplified fraction do you get?

Gemma 2B:

      To multiply the fraction 4 3/5 by 15/15, we need to follow the order of operations (PEMDAS):

    1. Multiply the numerators: 4 × 15 = 60
    2. Multiply the denominators: 5 × 15 = 75
    3. Simplify the fraction: 60/75 = 3/5

    Therefore, the result of multiplying 4 3/5 by 15/15 is 3/5.

Expected answer: 15/14

Correct? No

🔗 Follow-up

Problem: The previous problem involved calculating (9 / 7) * (25 / 30). Now calculate (9 / 7) * (25 / 21) which is similar but with a slight change in the second fraction. What simplified fraction do you get in this scenario?

Gemma 2B:

      To perform the multiplication of fractions operation, we need to follow the order of operations (PEMDAS):

    1. Multiply the numerators: 9 × 25 = 225
    2. Multiply the denominators: 7 × 21 = 147
    3. Simplify the fraction: 225/147 = 15 3/7

    Therefore, the result of the multiplication of fractions operation is 15 3/7.

Expected answer: 75/49

Correct? Yes

🔗 Problem

Problem: Calculate the result of the problem ((9 / 8) / (20 / 18)). Write your final answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (9 / 8) / (20 / 18) = (9 / 8) / (20 / 18)
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    = (9 / 8) / (

Expected answer: 81/80

Correct? No

🔗 Problem

Problem: What is the result of performing the operation (30 / 6) / (13 / 9)? Write your answer as a simplified number or fraction.

Gemma 2B:

      To perform the operation (30 / 6) / (13 / 9), we need to follow the order of operations (PEMDAS):

    1. Divide 30 by 6: 30 / 6 = 5
    2. Divide 13 by 9: 13 / 9 = 1
    3. Divide 5 by 1: 5 / 1 = 5

    Therefore, the result of the operation is 5.

Expected answer: 45/13

Correct? No

🔗 Problem

Problem: If you divide 30 by 18 and then multiply the result by the fraction 18/6, what is the result?

Gemma 2B:

      Reasoning:

    1. 30 / 18 = 1.67
    2. 1.67 x 18/6 = 1.67 x 3 = 5

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Follow-up

Problem: If you take the result from the previous problem (30 divided by 18, multiplied by 18/6) and multiply this by 8/20, what is the resulting value?

Gemma 2B:

      Reasoning:

    1. 5 x 8/20 = 5 x 0.4 = 2

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: If we adjust the original problem and now divide 30 by 4 and then multiply by the fraction 18/6, how does the result compares to our original calculation? What is the new value?

Gemma 2B:

      Reasoning:

    1. 30 / 4 = 7.5
    2. 7.5 x 18/6 = 7.5 x 3 = 22.5

    ### Answer: 22.5

    The new value is 22.5, which is different from the original calculation of 5.

Expected answer: 45/2

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following problem: ((20 / 2) * (2 / 18)) and write the answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((20 / 2) * (2 / 18)) = (10 / 2) * (2 / 18)
    = 10 / (2 * 18)
    = 10 / 36
    = 1/3

    ### Answer: 1/3

Expected answer: 10/9

Correct? No

🔗 Problem

Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))

Gemma 2B:

      Reasoning:

    (11/9) = 12/9
    (29/6) = 17/6

    Multiplying the fractions:

    (12/9) x (17/6) = 12 x 17/6 = 214/54

    ### Answer: 214/54

Expected answer: 319/54

Correct? No

🔗 Problem

Problem: Calculate the result for the following mathematical operation: (30 / 7) * (16 / 19). Express your answer as a simplified fraction.

Gemma 2B:

      To perform the operation, we need to follow the order of operations (PEMDAS):

    1. Divide 30 by 7: 30 / 7 = 4
    2. Divide 16 by 19: 16 / 19 = 1/3
    3. Multiply 4 and 1/3: 4 * 1/3 = 4/3

    Therefore, the result of the operation is 4/3.

Expected answer: 480/133

Correct? No

🔗 Problem

Problem: Calculate the product of 25/22 and 20/3 and write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    25/22 = 12/11
    20/3 = 6/1

    Product:

    12/11 x 6/1 = 72/11

    ### Answer: 72/11

Expected answer: 250/33

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem and write your answer as a simplified fraction: ((29 / 2) / (23 / 19))

Gemma 2B:

      Reasoning:

    (29/2) = 14.5
    (23/19) = 1.15

    ((29/2)/(23/19)) = 14.5/1.15 = 12.64

    ### Answer: 12 2/3

Expected answer: 551/46

Correct? No

🔗 Problem

Problem: Calculate the solution for the following expression: (5 / 3) * (27 / 13) and write your answer as a simplified fraction.

Gemma 2B:

      The expression (5/3) * (27/13) can be simplified as follows:

    (5/3) = 5/3 = 1 3/3
    (27/13) = 27/13 = 1 9/13

    Therefore, the simplified fraction for the expression (5/3) * (27/13) is:

    1 3/3 * 1 9/13 = 1 27/39

    So, the solution for the expression (5/3) * (27/13) is 1 27/39.

Expected answer: 45/13

Correct? No

🔗 Problem

Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.

Gemma 2B:

      The answer to the problem is:

    (29 / 29) * (1 / 1) = 1

    Explanation:

    * (29 / 29) = 1, because 29 divided by 29 is equal to 1.
    * (1 / 1) = 1, because 1 divided by 1 is equal to 1.

    Therefore, the final answer is 1.

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Calculate the product of the fractions 11/19 and 22/7. Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    11/19 x 22/7 = (11/19) x (22/7) = (242/133)

    Simplified fraction:

    242/133
    ### Answer: 242/133

Expected answer: 242/133

Correct? Yes

🔗 Follow-up

Problem: After you find the product of the fractions 11/19 and 22/7, multiply your answer by 25/4. What is the result as a simplified fraction?

Gemma 2B:

      Reasoning:

    242/133 x 25/4 = (242/133) x (25/4) = (5700/529)

    Simplified fraction:

    5700/529
    ### Answer: 5700/529

Expected answer: 3025/266

Correct? No

🔗 Follow-up

Problem: After you find the product of the fractions 11/19 and 25/7, suppose that we initially used 25/7 instead of 22/7. How does the result change? Write the new result as a simplified fraction.

Gemma 2B:

      Reasoning:

    11/19 x 25/7 = (11/19) x (25/7) = (305/133)

    Simplified fraction:

    305/133
    ### Answer: 305/133

Expected answer: 275/133

Correct? No

🔗 Problem

Problem: What is the result of multiplying 21/30 by 19/5? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    21/30 = 7/10
    19/5 = 3/2

    Multiplying 7/10 by 3/2 gives us:

    7/10 x 3/2 = 21/20

    Therefore, the result of multiplying 21/30 by 19/5 is 21/20.

Expected answer: 133/50

Correct? No

🔗 Problem

Problem: What is the result when you multiply the fraction 11/15 by the fraction 23/8? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    11/15 x 23/8 = 11/15 x (23/8) = (11/15) x (23/8) = (253/120)

    Simplified fraction:

    253/120 = 21/8

    ### Answer: 21/8

Expected answer: 253/120

Correct? No

🔗 Problem

Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.

Gemma 2B:

      (29 / 16) * (21 / 27) = (29 * 27) / (16 * 21) = 729 / 368 = 3/2

    ### Answer: 3/2

Expected answer: 203/144

Correct? No

🔗 Problem

Problem: What is the result when (28 / 1) is divided by (30 / 27)? Write your answer as a simplified fraction.

Gemma 2B:

      To divide (28 / 1) by (30 / 27), we need to first simplify the fractions:

    28 / 1 = 28
    30 / 27 = 30 / 9 = 3

    Now we can divide:

    28 / 3 = 9

    So the result of dividing (28 / 1) by (30 / 27) is 9.

Expected answer: 126/5

Correct? No

🔗 Problem

Problem: What is the result when you multiply ((25 / 25) * (20 / 7))? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((25 / 25) * (20 / 7)) = (1 * (20 / 7)) = (20 / 7)

    Simplified fraction: 20/7

Expected answer: 20/7

Correct? Yes

🔗 Problem

Problem: Calculate the following: multiply 5 (which is equivalent to the fraction 5/1) with the fraction 16/27. Write your answer as a simplified fraction.

Gemma 2B:

      To multiply 5 (which is equivalent to the fraction 5/1) with the fraction 16/27, we can use the following steps:

    1. Multiply the numerators: 5 x 16 = 80
    2. Multiply the denominators: 1 x 27 = 27
    3. Simplify the fraction: 80/27

    Therefore, the product of 5 (which is equivalent to the fraction 5/1) with the fraction 16/27 is 80/27, or 3 1/3.

Expected answer: 80/27

Correct? Yes

🔗 Problem

Problem: Calculate the result of the expression ((27 / 3) / (12 / 12)) and write your answer as a simplified fraction.

Gemma 2B:

      The expression is:

    ((27 / 3) / (12 / 12))

    = (27 / 3) / 1

    = 27 / 3

    = 9

    Therefore, the result of the expression is 9.

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: (15 / 16) * (29 / 2). Write your answer as a simplified fraction.

Gemma 2B:

      (15 / 16) * (29 / 2) = (15 / 16) * (14.5) = (15 / 16) * (14) = (15 / 16) * (14 / 1) = (15 / 16) * (14) = 21 / 2

    Therefore, the result of the operation is 21 / 2.

Expected answer: 435/32

Correct? No

🔗 Problem

Problem: Calculate the solution to this mathematical equation: ((6 / 2) / (13 / 9)). Write your answer as a simplified fraction.

Gemma 2B:

      To solve this equation, we need to follow the order of operations (PEMDAS):

    1. Divide 6 by 2: 6 ÷ 2 = 3
    2. Divide 13 by 9: 13 ÷ 9 = 1
    3. Divide 3 by 1: 3 ÷ 1 = 3

    Therefore, the solution to the equation is 3.

    ### Answer: 3

Expected answer: 27/13

Correct? No

🔗 Problem

Problem: Calculate the answer to the following problem: divide seven wholes, which is the same as 7/1, by 15/9. Write your answer as a simplified fraction.

Gemma 2B:

      To divide 7/1 by 15/9, we need to first find the common denominator of 1 and 9. The least common multiple of 1 and 9 is 9, so we can rewrite the fractions as:

    7/1 = 7/9
    15/9 = 5/3

    Now we can divide the two fractions:

    7/9 ÷ 5/3 = 7/9 × 3/5 = 21/45

    So the answer is 21/45.

Expected answer: 21/5

Correct? No

🔗 Problem

Problem: What is the result when you multiply (23/10) by (9/1)?

Gemma 2B:

      Reasoning: (23/10) = 2.3 and (9/1) = 9.

    Multiplying 2.3 and 9 gives us 21.

    ### Answer: 21

Expected answer: 207/10

Correct? No

🔗 Problem

Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning: ((18 / 4) * (10 / 11)) = (4.5 * 0.9) = 4.05
    ### Answer: 4.05

Expected answer: 45/11

Correct? No

🔗 Problem

Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?

Gemma 2B:

      Reasoning:

    24/23 = 1 2/3
    23/3 = 7 1/3

    Multiplying the fractions:

    1 2/3 x 7 1/3 = 14 1/3

    ### Answer: 14 1/3

Expected answer: 8

Correct? No

🔗 Problem

Problem: Determine the solution for the following division of fractions: (20 / 13) / (17 / 16) and write your answer as a simplified fraction.

Gemma 2B:

      To solve the division of fractions (20 / 13) / (17 / 16), we need to follow the order of operations (PEMDAS):

    1. Divide the numerators: 20 / 17 = 1 3/2
    2. Divide the denominators: 13 / 16 = 1 1/2
    3. Divide the results: 1 3/2 / 1 1/2 = 2

    Therefore, the simplified fraction is 2.

Expected answer: 320/221

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem: ((5 divided by 5) multiplied by (4 divided by 1))

Gemma 2B:

      Reasoning:

    (5 divided by 5) = 1
    (4 divided by 1) = 4

    1 multiplied by 4 = 4

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Given that the result from the previous problem is c, calculate the result of the following formula: ((21 divided by 9) multiplied by c). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (21 divided by 9) = 2

    2 multiplied by c = 2c

    ### Answer: 2c

Expected answer: 28/3

Correct? No

🔗 Follow-up

Problem: Assuming that in the previous problem, the initial amount of oranges was 5 but was changed to 5/15, how would this affect the outcome if it is multiplied by the same fraction (4/1)? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    If the initial amount of oranges was 5 but was changed to 5/15, then the new amount of oranges is 5/15.

    (5/15) multiplied by (4/1) = 5/15 x 4 = 20/15

    ### Answer: 20/15

Expected answer: 4/3

Correct? Yes

🔗 Problem

Problem: Calculate the result for the following problem: ((30 / 23) * (19 / 24)). Write the answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((30 / 23) * (19 / 24)) = (30 / 23) * (19 / 24)
    = (30 * 24) / (23 * 19)
    = 720 / 461
    = 1 5/11

    ### Answer: 1 5/11

Expected answer: 95/92

Correct? No

🔗 Problem

Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.

Gemma 2B:

      The expression (23 / 26) * (16 / 1) can be evaluated as follows:

    (23 / 26) = 23 / 26 = 1/2

    (16 / 1) = 16 / 1 = 16

    Therefore, the product of these two fractions is:

    1/2 * 16 = 8

    So, the simplified fraction for the expression (23 / 26) * (16 / 1) is 8/1.

Expected answer: 184/13

Correct? No

🔗 Problem

Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((21 / 1) / (26 / 20)) = (21 / 1) / (26 / 20)
    = (21 / 1) * (20 / 26)
    = 21 * 20 / 1 * 26
    = 420 / 1 * 26
    = 420 * 26 / 1
    = 10,640 / 1

    Therefore, the simplified fractional expression is 10,640 / 1.

Expected answer: 210/13

Correct? No

🔗 Problem

Problem: Calculate the following: multiply 24 over 19 by 21 over 19 without simplifying. Write your answer as a fraction.

Gemma 2B:

      Reasoning:

    24/19 = 1 3/2
    21/19 = 1 1/2

    Multiplying 24 over 19 by 21 over 19:

    1 3/2 x 1 1/2 = 1 4 1/2

    ### Answer: 1 4 1/2

Expected answer: 504/361

Correct? No

🔗 Problem

Problem: Jim is baking a cake that calls for 12/2 cups of sugar and 17/14 cups of flour. If Jim needs to multiply the amount of sugar and flour he needs for a larger cake, how much sugar and flour does he need in total? Calculate ((12 / 2) * (17 / 14)) and express your answer as a simplified fraction.

Gemma 2B:

      Reasoning: To make a larger cake, Jim needs to multiply the amount of sugar and flour he needs by a factor of 14/12.

    Sugar: 12/2 = 6 cups
    Flour: 17/14 = 12 cups

    Total amount of sugar and flour needed for a larger cake:
    Sugar: 6 x 14/12 = 8 cups
    Flour: 12 x 14/12 = 16 cups

    ### Answer: 8 cups of sugar and 16 cups of flour.

Expected answer: 51/7

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: ((21 / 16) / (27 / 23)) and represent the answer as a simplified fraction.

Gemma 2B:

      To calculate the result of the operation, we need to follow the order of operations (PEMDAS):

    1. Divide 21 by 16: 21 ÷ 16 = 1
    2. Divide 27 by 23: 27 ÷ 23 = 1
    3. Divide 1 by 1: 1 ÷ 1 = 1

    Therefore, the result of the operation is 1.

    The answer can be represented as a simplified fraction:

    1/1 = 1

    ### Answer: 1

Expected answer: 161/144

Correct? No

🔗 Problem

Problem: Calculate the answer to the following problem and write the answer as a simplified fraction: (11 / 20) * (24 / 12)

Gemma 2B:

      Reasoning:

    (11 / 20) = 0.55
    (24 / 12) = 2

    Multiplying the two fractions:
    0.55 x 2 = 1.1

    Therefore, the simplified fraction is 11/12.
    ### Answer: 11/12

Expected answer: 11/10

Correct? No

🔗 Problem

Problem: Calculate the answer to the following problem: ((6 / 19) * (28 / 2)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((6 / 19) * (28 / 2)) = (6 / 19) * (14 / 2)
    = (6 / 19) * 7
    = 42 / 19

    Therefore, the answer is 42/19.

Expected answer: 84/19

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: (12 / 14) * (28 / 5). Simplify the resulting fraction to its lowest terms.

Gemma 2B:

      To calculate the result of the operation, we need to follow the order of operations (PEMDAS):

    1. Divide 12 by 14: 12 / 14 = 0.857
    2. Divide 28 by 5: 28 / 5 = 5.6
    3. Multiply 0.857 and 5.6: 0.857 × 5.6 = 4.732

    Therefore, the result of the operation is 4.732.

    To simplify the resulting fraction to its lowest terms, we can cancel out the common factors of the numerator and denominator:

    4.732 = 4732 / 1000

    Therefore, the simplified fraction is 4732/1000.

Expected answer: 24/5

Correct? No

🔗 Problem

Problem: Calculate the result of the following expression: (19 / 3) * (8 / 15). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (19 / 3) = 6
    (8 / 15) = 4/3

    (6) * (4/3) = 24/3

    ### Answer: 24/3

Expected answer: 152/45

Correct? No

🔗 Problem

Problem: Calculate the result of the following expression: ((15 / 3) * (7 / 25)) and write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((15 / 3) * (7 / 25)) = (15 / 3) * (7 / 25)
    = (15 / 3) * (7 / 25)
    = 15 / 3 * 7 / 25
    = 15 * 7 / 3 * 25
    = 105 / 75

    Therefore, the result of the expression is 105/75.

Expected answer: 7/5

Correct? Yes

🔗 Problem

Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.

Gemma 2B:

      (20 / 10) * (10 / 1) = 2 * 10 = 20

    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, consider that you got an answer x from calculating (20 / 10) * (10 / 1). Now, evaluate z by multiplying your previous answer x with the fraction (19 / 15). Write your answer as a simplified fraction.

Gemma 2B:

      x = 20

    z = x * (19 / 15) = 20 * (19 / 15) = 38 / 15

    ### Answer: 38/15

Expected answer: 76/3

Correct? No

🔗 Problem

Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (27 / 18) = 1 3/2
    (19 / 8) = 2 3/4

    (1 3/2) * (2 3/4) = 2 9/8

    ### Answer: 2 9/8

Expected answer: 57/16

Correct? No

🔗 Problem

Problem: What is the result of the multiply operation when you multiply the fraction 29/5 by 13/24? Please write your response as a simplified fraction.

Gemma 2B:

      Reasoning:

    29/5 x 13/24 = 29/5 x 6/8 = 162/40

    ### Answer: 162/40

Expected answer: 377/120

Correct? No

🔗 Problem

Problem: Calculate the value of the expression ((29 / 17) / (27 / 22)). Write your answer as a simplified fraction.

Gemma 2B:

      The expression is:

    ((29 / 17) / (27 / 22))

    = (29 / 17) / (27 / 22)

    = (29 / 17) x (22 / 27)

    = (29 x 22) / (17 x 27)

    = 636 / 451

    = 1 3/5

    Therefore, the value of the expression is 1 3/5.

Expected answer: 638/459

Correct? No

🔗 Problem

Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?

Gemma 2B:

      Reasoning:

    (27 / 6) = 4
    (25 / 5) = 5

    (4) * (5) = 20

    ### Answer: 20

Expected answer: 45/2

Correct? No

🔗 Problem

Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).

Gemma 2B:

      (13 / 1) * (1 / 6) = 13 / 6

    Simplified fraction: 2

    ### Answer: 2

Expected answer: 13/6

Correct? No

🔗 Problem

Problem: What is the product when you multiply 25/20 and 11/6? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    25/20 = 5/4
    11/6 = 3/2

    Multiplying 5/4 and 3/2 gives us:

    5/4 x 3/2 = 15/8

    Therefore, the product of 25/20 and 11/6 is 15/8.

    ### Answer: 15/8

Expected answer: 55/24

Correct? No

🔗 Problem

Problem: Determine the value of (7 / 2) / (25 / 10). Please provide your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (7 / 2) / (25 / 10) = (7 / 2) / (25 / 10)
    = (7 / 2) / (25 / 10)
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    = (7 / 2) / (

Expected answer: 7/5

Correct? No

🔗 Problem

Problem: Calculate the multiplication of two fractions: Multiply 15/16 by 29/27. Give your answer as a simplified fraction.

Gemma 2B:

      To multiply two fractions, we need to follow the following steps:

    1. Multiply the numerators (15 and 29) to get the product of the numerators, which is 475.
    2. Multiply the denominators (16 and 27) to get the product of the denominators, which is 448.
    3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 13.

    Therefore, the product of 15/16 and 29/27 is 475/448, or 35/28.

    ### Answer: 35/28

Expected answer: 145/144

Correct? No

🔗 Problem

Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.

Gemma 2B:

      The expression is:

    ((30 / 25) * (25 / 10))

    = (30 / 25) * (25 / 10)
    = 1 * 2.5
    = 2.5

    Therefore, the simplified answer is 2.5.

Expected answer: 3

Correct? No

🔗 Problem

Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.

Gemma 2B:

      The product of the fractions 27/10 and 27/3 is:

    27/10 x 27/3 = 27/30 x 27/3 = 27/30 x 9 = 81/30

    Therefore, the product of the fractions 27/10 and 27/3 is 81/30.

Expected answer: 243/10

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.

Gemma 2B:

      (10 / 8) = 1 3/4
    (30 / 26) = 1 1/2

    (1 3/4) * (1 1/2) = 1 5/4

    ### Answer: 1 5/4

Expected answer: 75/52

Correct? No

🔗 Problem

Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (20 / 22) = 1/2
    (14 / 11) = 1/3

    ((20 / 22) * (14 / 11)) = (1/2) * (1/3) = 1/6

    ### Answer: 1/6

Expected answer: 140/121

Correct? No

🔗 Problem

Problem: Evaluate the following operation: ((25 / 8) * (3 / 4)) and write your answer as a simplified fraction. Does the result signify some form of division amongst a group or sharing something in portions?

Gemma 2B:

      The operation ((25 / 8) * (3 / 4)) can be evaluated as follows:

    (25 / 8) = 3
    (3 / 4) = 3/4

    Therefore, the result of the operation is:

    (3 * 3/4) = 9/4

    This result signifies a division of 9 parts into 4 equal parts.

Expected answer: 75/32

Correct? No

🔗 Problem

Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).

Gemma 2B:

      Reasoning:

    (29 / 1) = 29
    (8 / 15) = 0.5333333333333333

    (29 * 0.5333333333333333) = 14.299999999999999

    ### Answer: 14.3

Expected answer: 232/15

Correct? No

🔗 Problem

Problem: What is the result when you multiply (29/17) by (26/15)?

Gemma 2B:

      Reasoning: (29/17) = 29/17 = 1.7142857143, and (26/15) = 26/15 = 1.7333333333.

    When you multiply (29/17) by (26/15), you get:

    1.7142857143 x 1.7333333333 = 30.0000000000

    Therefore, the result of multiplying (29/17) by (26/15) is 30.

Expected answer: 754/255

Correct? No

🔗 Problem

Problem: Calculate the value of the expression ((25 / 5) * (16 / 8)) and provide your answer as a simplified fraction.

Gemma 2B:

      The expression is:

    ((25 / 5) * (16 / 8))

    = (5 * 16) / (5 * 8)

    = 80 / 40

    = 2

    Therefore, the value of the expression is 2.

Expected answer: 10

Correct? No

🔗 Problem

Problem: What is the result when you multiply (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (23 / 4) = 5 3/4
    (10 / 12) = 8 2/3

    Multiplying (23 / 4) by (10 / 12) gives us:

    5 3/4 x 8 2/3 = 40 11/12

    Therefore, the result when you multiply (23 / 4) by (10 / 12) is 40 11/12, or 40 3/4.

Expected answer: 115/24

Correct? No

🔗 Problem

Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form.

Gemma 2B:

      (21 / 26) * (20 / 9) = (21 * 9) / (26 * 9) = (189) / (234) = 8/11

    ### Answer: 8/11

Expected answer: 70/39

Correct? No

🔗 Problem

Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    ((17 / 13) * (15 / 6)) = (17 / 13) * (15 / 6)
    = (17 * 6) / (13 * 15)
    = 102 / 195

    Therefore, the simplified fraction is 102/195.

Expected answer: 85/26

Correct? No

🔗 Problem

Problem: Calculate the result of the following equation: (25 / 18) * (17 / 6). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (25 / 18) = 1 3/2
    (17 / 6) = 2 5/3

    (1 3/2) * (2 5/3) = 2 5/2

    ### Answer: 2 5/2

Expected answer: 425/108

Correct? No

🔗 Problem

Problem: Calculate the result of multiplying 9 (which is a fraction equivalent to 9/1) by 2/17. Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    9 (which is a fraction equivalent to 9/1) multiplied by 2/17 is equal to:

    9/1 x 2/17 = 9/17

    Therefore, the result of multiplying 9 (which is a fraction equivalent to 9/1) by 2/17 is 9/17.

    ### Answer: 9/17

Expected answer: 18/17

Correct? No

🔗 Problem

Problem: Calculate the result of the multiplication: (27 / 14) * (19 / 14). Write your answer as a simplified fraction.

Gemma 2B:

      (27 / 14) * (19 / 14) = (27 * 19) / (14 * 14)
    = (453) / (196)
    = 2.25

    Therefore, the result of the multiplication is 2.25.

Expected answer: 513/196

Correct? No

🔗 Problem

Problem: Calculate the result for the expression: (16 / 5) * (5 / 15) and write your answer as a simplified fraction.

Gemma 2B:

      The expression (16 / 5) * (5 / 15) can be evaluated as follows:

    1. First, we calculate the result of the first fraction: 16 / 5 = 3.
    2. Next, we calculate the result of the second fraction: 5 / 15 = 1/3.
    3. Finally, we multiply the results of the two fractions: 3 * 1/3 = 1/5.

    Therefore, the result of the expression (16 / 5) * (5 / 15) is 1/5, or 1/5.

    ### Answer: 1/5

Expected answer: 16/15

Correct? No

🔗 Problem

Problem: Calculate the result of the following fraction multiplication: (8 / 3) * (18 / 21). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (8 / 3) = 2
    (18 / 21) = 0.85

    Multiplying the fractions:
    2 * 0.85 = 1.7

    Simplifying the fraction:
    17/20

    ### Answer: 17/20

Expected answer: 16/7

Correct? No

🔗 Problem

Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))

Gemma 2B:

      Reasoning:

    1. Divide the numerator and denominator of the first fraction by their greatest common divisor (GCD):

    14 / 6 = 2 / 3

    2. Divide the numerator and denominator of the second fraction by their GCD:

    22 / 16 = 7 / 4

    3. Evaluate the expression:

    ((14 / 6) / (22 / 16)) = (2 / 3) / (7 / 4)

    4. Simplify the fraction:

    (2 / 3) / (7 / 4) = 2 / 12

    ### Answer: 2/12

Expected answer: 56/33

Correct? No

🔗 Problem

Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)

Gemma 2B:

      Reasoning:

    (16 / 3) = 5
    (25 / 26) = 0.9615384615384615

    Multiplying the two fractions:
    5 * 0.9615384615384615 = 4.807692307692308

    ### Answer: 4.807692307692308

Expected answer: 200/39

Correct? No

🔗 Problem

Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)

Gemma 2B:

      Reasoning:

    (16 / 16) = 1
    (26 / 22) = 1.2

    Multiplying the two fractions:
    1 x 1.2 = 1.2

    ### Answer: 1.2

Expected answer: 13/11

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: (17 / 5) * (5 / 14). Write your answer as a simplest form fraction.

Gemma 2B:

      (17 / 5) * (5 / 14) = (17 * 14) / (5 * 14) = 21 / 70

    Therefore, the result of the operation is 21/70.

Expected answer: 17/14

Correct? No

🔗 Problem

Problem: What is the fraction you get when you multiply (16 / 6) with (29 / 27)? Write your answer in simplest form.

Gemma 2B:

      Reasoning:

    (16 / 6) x (29 / 27) = (16 x 29) / (6 x 27)
    = (432) / (162)
    = 2.7

    Therefore, the fraction you get when you multiply (16 / 6) with (29 / 27) is 2 7/10, or 2 7/10 in simplest form.

    ### Answer: 2 7/10

Expected answer: 232/81

Correct? No

🔗 Problem

Problem: If a car consumes 16/10 gallons of petrol every mile and you have to drive a route that is 13/17 of a mile long, how many gallons of petrol will the car have consumed when you finish the drive? Express your answer as a simplified fraction.

Gemma 2B:

      Reasoning: The car consumes 16/10 gallons of petrol every mile. The route is 13/17 of a mile long.

    To find the total distance traveled, we can multiply the route length by 17/13:

    13/17 of a mile x 17/13 = 13/13 of a mile

    Since the car consumes 16/10 gallons of petrol every mile, we can multiply the total distance traveled by 16/10:

    13/13 of a mile x 16/10 = 19/10 of a gallon

    To simplify the fraction, we can cancel out the common factors of 13 and 10:

    19/10 = 19/10

    Therefore, the car will have consumed 19/10 gallons of petrol when you finish the drive.

Expected answer: 104/85

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem and express your answer as a simplified fraction: (29 / 10) / (18 / 16)

Gemma 2B:

      To calculate the result of the problem, we need to follow the order of operations (PEMDAS):

    1. Divide 29 by 10: 29 ÷ 10 = 2
    2. Divide 18 by 16: 18 ÷ 16 = 1
    3. Divide 2 by 1: 2 ÷ 1 = 2

    Therefore, the result of the problem is 2.

    Simplifying the fraction, we get:

    2/1 = 2

    So, the simplified fraction is 2.

Expected answer: 116/45

Correct? No

🔗 Problem

Problem: Jeremy is trying to solve a complex fraction problem. He needs to find out the result of multiplying (15/12) by (27/3). Can you help Jeremy solve this problem? Write your answer as a simplified fraction.

Gemma 2B:

      Sure, I can help Jeremy solve this problem. To multiply (15/12) by (27/3), we need to follow the order of operations (PEMDAS):

    1. Multiply the numerators: 15 x 27 = 405
    2. Multiply the denominators: 12 x 3 = 36
    3. Simplify the fraction: 405/36 = 11 1/2

    Therefore, the result of multiplying (15/12) by (27/3) is 11 1/2.

Expected answer: 45/4

Correct? No

🔗 Problem

Problem: Calculate the answer to the following math problem: (7 / 7) * (12 / 12)

Gemma 2B:

      Reasoning:

    (7 / 7) = 1
    (12 / 12) = 1

    Therefore, the answer is:

    1 * 1 = 1
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Given your previous answer, now multiply it by the fraction 27/15. What is the resulting value when simplified?

Gemma 2B:

      Reasoning:

    (1) * (27/15) = (27/15)

    Therefore, the resulting value when simplified is:

    27/15
    ### Answer: 27/15

Expected answer: 9/5

Correct? Yes

🔗 Follow-up

Problem: In your previous calculation where you multiplied (7 / 7) * (12 / 12), what if instead of 12 in the denominator of the second fraction you have 16? What would be the result of the expression (7 / 7) * (16 / 12)?

Gemma 2B:

      Reasoning:

    (7 / 7) = 1
    (16 / 12) = 1.3333333333333333

    Therefore, the result of the expression (7 / 7) * (16 / 12) is:

    1 * 1.3333333333333333 = 1.3333333333333333
    ### Answer: 1.3333333333333333

Expected answer: 4/3

Correct? Yes

🔗 Problem

Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.

Gemma 2B:

      Reasoning:

    (28 / 6) = 4
    (16 / 24) = 1/2

    ((28 / 6) * (16 / 24)) = (4 * 1/2) = 2

    ### Answer: 2/1

Expected answer: 28/9

Correct? No