Gemma 2B on 7.NS.A.2
Common Core Standard 7.NS.A.2
This standard covers the following:
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Problem: Calculate the product of (29/2) and (19/28) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (29/2) x (19/28) = <<(29/2) x (19/28) = (29/28)>>14.5. The final answer is 14.5.
Expected answer: 551/56
Correct? No
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:
Reasoning: 7 * (27/12) = 7 * 27/12 = 105/12. ### Answer: 105/12
Expected answer: 63/4
Correct? No
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: Since the proportions of flour and water are equal, if Susan uses 29 parts of flour, she will use the same amount of water. ### Answer: 29
Expected answer: 29/27
Correct? No
Problem: Calculate the result of the following operation: ((24 / 22) * (24 / 17)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The operation is a division of fractions, which can be simplified by finding a common multiple of the denominators and dividing them out. The common multiple of 22 and 17 is 34, so we can rewrite the fractions as: (24/22) = 12/11 (24/17) = 16/17 Therefore, the result of the operation is 12/11 = 16/17.
Expected answer: 288/187
Correct? No
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 divided by 16/6 is equal to 25/4 * 6/16 = 25/64. ### Answer: 0.390625
Expected answer: 75/32
Correct? No
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: Multiply the numerators and multiply the denominators: 3/7 x 26/6 = <<(3/7) x (26/6) = 3/1>>3/1. Therefore, 3/7 x 26/6 = 3/1.
Expected answer: 13/7
Correct? No
Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.
Gemma 2B:
Reasoning: (17/10) * (28/10) = 17/10 * 28/10 = 440/100 = 4.4. ### Answer: 4.4
Expected answer: 119/25
Correct? No
Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))
Gemma 2B:
Reasoning: (29/14) * (23/6) = (29/14) * (7/2) = (29/14) * 7/2 = 29/2 = 14.5 ### Answer: 14.5
Expected answer: 667/84
Correct? No
Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.
Gemma 2B:
Reasoning: (18/19) * (19/6) = (18/6) = 3. Therefore, the answer is 3.
Expected answer: 3
Correct? Yes
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 (20/6) = 380/72. ### Answer: 380/72
Expected answer: 95/18
Correct? Yes
Problem: Taking the answer from the previous problem (19/12 * 20/6), multiply this result with itself. What is the resulting fraction when simplified?
Gemma 2B:
### Answer: 735/72
Expected answer: 9025/324
Correct? No
Problem: In the original problem, you multiplied the fractions 19/12 and 20/6. Now suppose you replace 19/12 with 10/12 and redo the calculation. What is the resulting fraction when it is simplified?
Gemma 2B:
### Answer: 5/3
Expected answer: 25/9
Correct? No
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 load is (28/21) + (22/4) = 28/42 + 22/42 = 50/42. The total fractional representation is 50/42.
Expected answer: 22/3
Correct? No
Problem: Determine the result of the following mathematical expression: (16 / 4) / (24 / 21). Write your answer as a simplified fraction or decimal.
Gemma 2B:
Reasoning: (16 / 4) / (24 / 21) = 4/1 = 4. ### Answer: 4
Expected answer: 7/2
Correct? No
Problem: Calculate the product of the fractions 5/27 and 15/2. Write your answer in the simplest form.
Gemma 2B:
Reasoning: 5/27 x 15/2 = 75/54. The answer is 75/54.
Expected answer: 25/18
Correct? Yes
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:
Reasoning: Multiply the numerators and multiply the denominators. (15/13) * (19/7) = 255/91. ### Answer: 255/91
Expected answer: 285/91
Correct? No
Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: 23/22 x 27/20 = <<23/22 x 27/20=63/40>>63/40. ### Answer: 63/40
Expected answer: 621/440
Correct? No
Problem: Calculate the result of the following operation: (12 / 25) * (20 / 4). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (12 / 25) * (20 / 4) = 12/25 * 20/4 = 24/100 = 0.24. ### Answer: 0.24
Expected answer: 12/5
Correct? No
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: Multiply the numerators and multiply the denominators. 14/10 * 30/5 = <<14/10 * 30/5=7>>7 The final answer is 7.
Expected answer: 42/5
Correct? No
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 can make (26/1) ÷ (29/14) = <<(26/1) ÷ (29/14) = (26 × 14) / (1 × 29) = 36/29>> batches of cookies. ### Answer: 36/29
Expected answer: 364/29
Correct? No
Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (27 / 10) * (9 / 4) = 27/40. ### Answer: 0.675
Expected answer: 243/40
Correct? No
Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The expression is equal to (24/11) * (27/26) = (24 * 27) / (11 * 26) = 630/294 = 2.15. ### Answer: 2.15
Expected answer: 324/143
Correct? No
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:
Reasoning: To multiply fractions with different denominators, we first need to rewrite them with a common denominator. The least common multiple of 9 and 13 is 63. So, 26/9 = 26/9 and 17/13 = 17/13. Now we can multiply the fractions: 26/9 x 17/13 = <<26/9 x 17/13=2>>2. ### Answer: 2
Expected answer: 34/9
Correct? No
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) = 7/9. ### Answer: 7/9
Expected answer: 14/9
Correct? No
Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The first step is to simplify the fractions within the parentheses: (15/3) * (19/26) = 15/3 * 19/26 = 15/26. The final answer is 15/26.
Expected answer: 95/26
Correct? No
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: 19/28 = 0.6875. 30/4 = 0.75. Therefore, they will need 0.6875 * 0.75 = <<0.53>>0.53 of the ingredient. ### Answer: 0.53
Expected answer: 285/56
Correct? No
Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.
Gemma 2B:
Reasoning: 5/2 = <<5/2=25/10>>25/10, and 26/15 = <<26/15=19/10>>19/10. Therefore, (5/2) / (26/15) = 25/10 ÷ 19/10 = 25/19. ### Answer: 125/19
Expected answer: 75/52
Correct? No
Problem: Calculate the result of the expression (9/3) * (27/28) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (9/3) * (27/28) = (9/3) * (9/4) = (9/4). The final answer is 9/4.
Expected answer: 81/28
Correct? No
Problem: Calculate the solution to the following equation and write your answer as a simplified fraction: ((15 / 13) * (24 / 24))
Gemma 2B:
Reasoning: The equation is (15/13) * (24/24). The fractions can be simplified by canceling out the common factor of 24: (15/13) * (24/24) = (15/13)
Expected answer: 15/13
Correct? Yes
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:
### Answer: 15/7
Expected answer: 330/91
Correct? No
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:
### Answer: 15/13
Expected answer: 15/2
Correct? No
Problem: Calculate the result of the following multiplication of fractions operation: (9 / 7) * (25 / 30). Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: The two fractions can be multiplied by multiplying the numerators and the denominators separately. (9 / 7) * (25 / 30) = (9 * 25) / (7 * 30) = 225 / 210. The simplified fraction is 5/6.
Expected answer: 15/14
Correct? No
Problem: Calculate the result of the problem ((9 / 8) / (20 / 18)). Write your final answer as a simplified fraction.
Gemma 2B:
Reasoning: The numerator of the left side is 9 / 8, and the denominator is 20 / 18. The result is (9 / 8) / (20 / 18) = (9/8) * (18/20) = 9/20. ### Answer: 9/20
Expected answer: 81/80
Correct? No
Problem: What is the result of performing the operation (30 / 6) / (13 / 9)? Write your answer as a simplified number or fraction.
Gemma 2B:
Reasoning: (30 / 6) / (13 / 9) = 5 / 13. The result of the operation is 5/13.
Expected answer: 45/13
Correct? No
Problem: If you divide 30 by 18 and then multiply the result by the fraction 18/6, what is the result?
Gemma 2B:
Reasoning: 30 ÷ 18 = <<30 ÷ 18=1.66>>1.66, and 1.66 × 18/6 = <<1.66 × 18/6=0.33>>0.33. Therefore, the result is 0.33.
Expected answer: 5
Correct? No
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 = 10, and 10/18 = 5/9. Therefore, (20/2 * (2/18)) = 10 * 5/9 = 50/72. ### Answer: 50/72
Expected answer: 10/9
Correct? No
Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))
Gemma 2B:
Reasoning: (11/9) * (29/6) = (11/9) * (29/6) = 11/6. ### Answer: 11/6
Expected answer: 319/54
Correct? No
Problem: Calculate the result for the following mathematical operation: (30 / 7) * (16 / 19). Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: (30/7) * (16/19) = 30/7 * 16/19 = 48/19. ### Answer: 48/19
Expected answer: 480/133
Correct? No
Problem: Calculate the product of 25/22 and 20/3 and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 25/22 = <<25/22=5/4>>5/4 and 20/3 = <<20/3=4/3>>4/3. The product of 25/22 and 20/3 is 5/4 * 4/3 = 20/12. ### Answer: 20/12
Expected answer: 250/33
Correct? No
Problem: Calculate the result of the following problem and write your answer as a simplified fraction: ((29 / 2) / (23 / 19))
Gemma 2B:
Reasoning: The problem can be solved by first simplifying the fractions within the parentheses: (29/2) / (23/19) = (29/2) * (19/23) = 19/29. Therefore, the answer is 19/29.
Expected answer: 551/46
Correct? No
Problem: Calculate the solution for the following expression: (5 / 3) * (27 / 13) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (5 / 3) * (27 / 13) = (5/3) * (9/4) = 45/48. The simplified fraction is 45/48.
Expected answer: 45/13
Correct? No
Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.
Gemma 2B:
Reasoning: The answer is 1. The answer is 1 because 29 / 29 is equal to 1 and 1 / 1 is equal to 1.
Expected answer: 1
Correct? Yes
Problem: Now, use your answer from the last problem and multiply it by (27 / 27) to solve this follow-up problem. What is the result?
Gemma 2B:
### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Now, let's change the problem a little bit. Instead of (29 / 29) * (1 / 1), let's use (29 / 6) * (1 / 1). What will the result be?
Gemma 2B:
Reasoning: The answer is 29/6. The answer is 29/6 because 29 divided by 6 is equal to 4 with a remainder of 5, which is the same number of clips Natalia sold in April and May combined.
Expected answer: 29/6
Correct? Yes
Problem: Calculate the product of the fractions 11/19 and 22/7. Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: Multiply the numerators and multiply the denominators. 11/19 * 22/7 = 222/153. The answer is 222/153.
Expected answer: 242/133
Correct? No
Problem: What is the result of multiplying 21/30 by 19/5? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 21/30 x 19/5 = (21/30) x (19/5) = 377/150. ### Answer: 377/150
Expected answer: 133/50
Correct? No
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 x 23)/(15 x 8) = 243/120. ### Answer: 2.08
Expected answer: 253/120
Correct? No
Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.
Gemma 2B:
Reasoning: (29/16) * (21/27) = (29/16) * (3/9) = (29/16) * (1/3) = 9/16. ### Answer: 9/16
Expected answer: 203/144
Correct? No
Problem: What is the result when (28 / 1) is divided by (30 / 27)? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (28/1) ÷ (30/27) = (28 ÷ 30) ÷ (1 ÷ 27) = 0.9333. The result is 0.9333, which can be simplified to 3/4.
Expected answer: 126/5
Correct? No
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 * 2 = 2. Therefore, (25/25) * (20/7) = 2.
Expected answer: 20/7
Correct? No
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:
Reasoning: 5/1 * 16/27 = 80/81. ### Answer: 80/81
Expected answer: 80/27
Correct? No
Problem: Calculate the result of the expression ((27 / 3) / (12 / 12)) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The first step is to simplify the fractions within the parentheses: (27 / 3) / (12 / 12) = 9 / 1 = 9 Therefore, the final answer is 9.
Expected answer: 9
Correct? Yes
Problem: Calculate the result of the following operation: (15 / 16) * (29 / 2). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (15/16) * (29/2) = 15/16 * 29/2 = 405/320. ### Answer: 405/320
Expected answer: 435/32
Correct? No
Problem: Calculate the solution to this mathematical equation: ((6 / 2) / (13 / 9)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The equation is asking for the result of (6/2) divided by (13/9). (6/2) / (13/9) = (6/2) * (9/13) = 54/132. The final answer is 54/132.
Expected answer: 27/13
Correct? No
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:
Reasoning: 7/1 divided by 15/9 is equivalent to 7/1 * 9/15 = 63/150. ### Answer: 63/150
Expected answer: 21/5
Correct? No
Problem: What is the result when you multiply (23/10) by (9/1)?
Gemma 2B:
Reasoning: (23/10) x (9/1) = 207/100 = 2.07. ### Answer: 2.07
Expected answer: 207/10
Correct? No
Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (18/4) * (10/11) = 45/44. The answer is 45/44.
Expected answer: 45/11
Correct? No
Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?
Gemma 2B:
Reasoning: The fractions 24/23 and 23/3 are equivalent, meaning they have the same value. Therefore, 24/23 * 23/3 = 1. ### Answer: 1
Expected answer: 8
Correct? No
Problem: Determine the solution for the following division of fractions: (20 / 13) / (17 / 16) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (20/13) / (17/16) = (20/13) * (16/17) = 320/204. The simplified fraction is 320/204.
Expected answer: 320/221
Correct? No
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 is 1, and 4 divided by 1 is also 1. Therefore, (5 divided by 5) multiplied by (4 divided by 1) is 1 * 1 = <<1>>1. ### Answer: 1
Expected answer: 4
Correct? No
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) = 1.
Expected answer: 95/92
Correct? No
Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.
Gemma 2B:
Reasoning: (23/26) * (16/1) = (23 * 16) / (26 * 1) = 384/26 = 14.
Expected answer: 184/13
Correct? No
Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.
Gemma 2B:
Reasoning: The numerator of the fraction is 21/1, and the denominator is 26/20. Simplifying the fraction, we get: (21/1) / (26/20) = 21/1 * 20/26 = 45/52. The simplified fraction is 45/52.
Expected answer: 210/13
Correct? No
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 * 21/19 = 4/1. Therefore, 24/19 * 21/19 = 4/1.
Expected answer: 504/361
Correct? No
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: (12/2) * (17/14) = <<(12/2) * (17/14) = 85/56>>85/56. Therefore, Jim needs 85/56 cups of sugar and 85/56 cups of flour in total for a larger cake.
Expected answer: 51/7
Correct? No
Problem: Calculate the result of the following operation: ((21 / 16) / (27 / 23)) and represent the answer as a simplified fraction.
Gemma 2B:
Reasoning: The operation involves dividing fractions with different denominators. ((21 / 16) / (27 / 23)) = (21/16) * (23/27) = 21/27. The final answer is 21/27.
Expected answer: 161/144
Correct? No
Problem: Calculate the answer to the following problem and write the answer as a simplified fraction: (11 / 20) * (24 / 12)
Gemma 2B:
Reasoning: Multiply the numerators and multiply the denominators: (11/20) * (24/12) = 11 * 24/20 * 12 = 264/240. The answer is 11/80.
Expected answer: 11/10
Correct? No
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 * 28) / (19 * 2) = 168 / 38 = 4.5. ### Answer: 4.5
Expected answer: 84/19
Correct? No
Problem: Calculate the result of the following operation: (12 / 14) * (28 / 5). Simplify the resulting fraction to its lowest terms.
Gemma 2B:
Reasoning: (12/14) * (28/5) = 12/14 * 28/5 = 32/70. The fraction can be simplified to its lowest terms by dividing both numerator and denominator by 4, resulting in 8/35. ### Answer: 8/35
Expected answer: 24/5
Correct? No
Problem: Calculate the result of the following expression: (19 / 3) * (8 / 15). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (19 / 3) * (8 / 15) = 19/3 * 8/15 = 19/15. ### Answer: 1
Expected answer: 152/45
Correct? No
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) = (5 * 7)/(3 * 25) = 35/75. The simplified fraction is 7/15.
Expected answer: 7/5
Correct? No
Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.
Gemma 2B:
Reasoning: The equation is (20/10) * (10/1) = 20. Therefore, the answer is 20.
Expected answer: 20
Correct? Yes
Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.
Gemma 2B:
Reasoning: The numerator of the fraction is 27 / 18, and the denominator is 19 / 8. The fraction can be simplified by dividing both the numerator and denominator by 3, which gives 9/6. Therefore, the final answer is 9/6.
Expected answer: 57/16
Correct? No
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 * 13/24 = (29 * 13)/(5 * 24) = 377/120. ### Answer: 377/120
Expected answer: 377/120
Correct? Yes
Problem: After finding the result of multiplying 29/5 by 13/24, what is the result if you then multiply this answer by 25/11? Please write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (377/120) * 25/11 = (377 * 25)/(120 * 11) = 955/1320. ### Answer: 0.75
Expected answer: 1885/264
Correct? No
Problem: After recalculating the early problem, suppose we only had 29/8 instead of 29/5. In that case, what would be the result of multiplying the fraction 29/8 by 13/24? Please write your answer in its simplest form.
Gemma 2B:
### Answer: 377/120
Expected answer: 377/192
Correct? No
Problem: Calculate the value of the expression ((29 / 17) / (27 / 22)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The expression can be simplified as follows: ((29 / 17) / (27 / 22)) = (29/17) * (22/27) = 29/27 = 10/9. ### Answer: 10/9
Expected answer: 638/459
Correct? No
Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?
Gemma 2B:
Reasoning: (27 / 6) * (25 / 5) = 27/5 = 5.4. ### Answer: 5.4
Expected answer: 45/2
Correct? No
Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).
Gemma 2B:
Reasoning: The answer is 13/6 = 2.5. (13/1) * (1/6) = 2.5.
Expected answer: 13/6
Correct? Yes
Problem: Calculate the value of the following, given that e = 13/6: (13 / 2) * e. Write your final answer as a simplified fraction. This is a follow-up question to a previous problem.
Gemma 2B:
Reasoning: (13/2) * e = (13/2) * (13/6) = 13/2. (13/2) * e = 13/2.
Expected answer: 169/12
Correct? No
Problem: Calculate the value of the following, given the modification to the previous problem: (11 / 1) * (1 / 6). What happens to the result if instead of having 13 of an item as in the previous problem, you only had 11 of it now? Write your new final answer as a simplified fraction.
Gemma 2B:
Reasoning: The answer is 11/6 = 1.83. (11/1) * (1/6) = 1.83.
Expected answer: 11/6
Correct? Yes
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 = <<25/20=5/4>>5/4 and 11/6 = <<11/6=1/6>>1/6. Multiplying these fractions gives 5/4 x 1/6 = <<5/4 x 1/6=5/24>>5/24. ### Answer: 5/24
Expected answer: 55/24
Correct? No
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) * (10/25) = 70/50 = 14/10. ### Answer: 14/10
Expected answer: 7/5
Correct? Yes
Problem: After determining the value of ((7 / 2) / (25 / 10)), now calculate the result when this value is multiplied by (5 / 3). Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: (7 / 2) / (25 / 10) * (5/3) = (7/2) * (5/3) / (25/10) = 35/60. ### Answer: 7/12
Expected answer: 7/3
Correct? No
Problem: Calculate the multiplication of two fractions: Multiply 15/16 by 29/27. Give your answer as a simplified fraction.
Gemma 2B:
Reasoning: 15/16 x 29/27 = <<15/16 x 29/27 = 405/432>>405/432. ### Answer: 405/432
Expected answer: 145/144
Correct? No
Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.
Gemma 2B:
Reasoning: (30/25) * (25/10) = 6/1 = 6. The final answer is 6.
Expected answer: 3
Correct? No
Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.
Gemma 2B:
Reasoning: 27/10 = 27 ÷ 10 = 2.7, and 27/3 = 27 ÷ 3 = 9. The product of 27/10 and 27/3 is 2.7 x 9 = <<2.7 x 9=24.3>>24.3.
Expected answer: 243/10
Correct? Yes
Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (10/8) * (30/26) = 10/8 * 30/26 = 150/224. ### Answer: 150/224
Expected answer: 75/52
Correct? No
Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: (20/22) * (14/11) = 20/22 * 14/11 = 280/262. ### Answer: 1.06
Expected answer: 140/121
Correct? No
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:
Answer: (25/8)*(3/4) = 25/32. This result signifies a division operation where 25 is divided by 8, resulting in 3.125, which is then multiplied by 3 to get 9.75.
Expected answer: 75/32
Correct? No
Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).
Gemma 2B:
Reasoning: The expression is equal to 29/15 = 1.93. ### Answer: 1.93
Expected answer: 232/15
Correct? No
Problem: What is the result when you multiply (29/17) by (26/15)?
Gemma 2B:
Reasoning: (29/17) x (26/15) = <<(29/17) x (26/15) =1>>1. The result is 1.
Expected answer: 754/255
Correct? No
Problem: Calculate the value of the expression ((25 / 5) * (16 / 8)) and provide your answer as a simplified fraction.
Gemma 2B:
Reasoning: The expression is equal to (5/2) * (4/8) = 5/4. Therefore, the answer is 5/4.
Expected answer: 10
Correct? No
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) * (10/12) = 230/480 = 0.4625. ### Answer: 0.4625
Expected answer: 115/24
Correct? No
Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form.
Gemma 2B:
Reasoning: The fractions can be simplified by finding a common denominator. The least common multiple of 26 and 9 is 198. Dividing both numerator and denominator by 2, we get (21/26) = (10.5/13) and (20/9) = (2.22). Multiplying these simplified fractions, we get (21/26) * (20/9) = 10.5/13 * 2.22 = 22/39. ### Answer: 22/39
Expected answer: 70/39
Correct? No
Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The expression can be simplified as follows: ((17 / 13) * (15 / 6)) = (17/13 * 15/6) = 17/6 = 3/1. ### Answer: 3/1
Expected answer: 85/26
Correct? No
Problem: Calculate the result of the following equation: (25 / 18) * (17 / 6). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The numerator of the first fraction is 25/18, and the numerator of the second fraction is 17/6. The denominator of both fractions is 6. Multiplying the numerators together, we get 25/18 * 17/6 = 25/108. Simplifying this fraction by dividing both numerator and denominator by 5, we get 5/21. ### Answer: 5/21
Expected answer: 425/108
Correct? No
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: 9/1 * 2/17 = (9 * 2)/(17 * 9) = 18/153. ### Answer: 0.125
Expected answer: 18/17
Correct? No
Problem: Calculate the result of the multiplication: (27 / 14) * (19 / 14). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The first fraction represents the number of people who bought the first item, and the second fraction represents the number of people who bought the second item. Combining them, we get the total number of items bought, which is 27/14 * 19/14 = 51/14. ### Answer: 51/14
Expected answer: 513/196
Correct? No
Problem: Calculate the result for the expression: (16 / 5) * (5 / 15) and write your answer as a simplified fraction.
Gemma 2B:
Reasoning: The expression can be simplified by canceling out the common factor of 16 and 5: (16/5) * (5/15) = 16/15 = 16/15. ### Answer: 16/15
Expected answer: 16/15
Correct? Yes
Problem: After finding the solution to the previous problem, which was (16 / 5) * (5 / 15), multiply your answer with the fraction (30 / 24) and again write your result as a simplified fraction.
Gemma 2B:
Reasoning: (16/5) * (5/15) * (30/24) = 16/24 = 4/6. ### Answer: 4/6
Expected answer: 4/3
Correct? No
Problem: The previous problem involved calculating an expression (16 / 5) * (5 / 15). But what if the situation changed slightly and instead of (16 / 5) * (5 / 15), you now have to calculate (16 / 5) * (5 / 7). What would the result be now? Write your answer as a simplified fraction.
Gemma 2B:
### Answer: 16/7
Expected answer: 16/7
Correct? Yes
Problem: Calculate the result of the following fraction multiplication: (8 / 3) * (18 / 21). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: Multiply the numerators and multiply the denominators. (8/3) * (18/21) = 8 * 3/3 * 18/21 = 24/63. The simplified fraction is 24/63.
Expected answer: 16/7
Correct? No
Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))
Gemma 2B:
Answer: 7/11
Expected answer: 56/33
Correct? No
Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)
Gemma 2B:
Reasoning: The two fractions can be multiplied by multiplying the numerators and the denominators separately: (16/3) * (25/26) = 16 * 25 / 3 * 26 = 400/808 = 0.48 ### Answer: 0.48
Expected answer: 200/39
Correct? No
Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)
Gemma 2B:
Reasoning: Both 16 and 22 are divisible by 2, so we can simplify the fractions to 1 and 11 respectively. (16/16) * (26/22) = 1 * 11 = 11
Expected answer: 13/11
Correct? No
Problem: Calculate the result of the following operation: (17 / 5) * (5 / 14). Write your answer as a simplest form fraction.
Gemma 2B:
Reasoning: (17/5) * (5/14) = 17/14. ### Answer: 17/14
Expected answer: 17/14
Correct? Yes
Problem: After calculating the result of the previous operation: (17 / 5) * (5 / 14), now take that result and multiply it by the fraction 21 / 25. What is your final answer, written as a simplified fraction?
Gemma 2B:
### Answer: 17/25
Expected answer: 51/50
Correct? No
Problem: After performing the prior operation: (17 / 5) * (5 / 14), consider what would happen if instead of multiplying the value by 5 / 14, we multiplied it by 5 / 12. What would be the result, written as a simplified fraction, in this case?
Gemma 2B:
### Answer: 17/12
Expected answer: 17/12
Correct? Yes
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) * (29/27) = 16/27. The fraction in simplest form is 16/27.
Expected answer: 232/81
Correct? No
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 will consume 16/10 * 13/17 = <<16/10 * 13/17=4/7>>4/7 gallons of petrol when you finish the drive. ### Answer: 4/7
Expected answer: 104/85
Correct? No
Problem: Calculate the result of the following problem and express your answer as a simplified fraction: (29 / 10) / (18 / 16)
Gemma 2B:
Reasoning: The problem can be solved by dividing the numerator and denominator by the same denominator. (29 / 10) / (18 / 16) = (29/10) * (16/18) = 44/36 = 44/36 with a common denominator of 12. Therefore, the answer is 44/36.
Expected answer: 116/45
Correct? No
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:
Reasoning: (15/12) x (27/3) = (15/12) x (9/3) = 15/3 = 5/1. Therefore, Jeremy's final answer is 5/1.
Expected answer: 45/4
Correct? No
Problem: Calculate the answer to the following math problem: (7 / 7) * (12 / 12)
Gemma 2B:
Reasoning: The answer is 1. The answer is 1 because 7/7 = 1 and 12/12 = 1.
Expected answer: 1
Correct? Yes
Problem: Given your previous answer, now multiply it by the fraction 27/15. What is the resulting value when simplified?
Gemma 2B:
### Answer: 1.8
Expected answer: 9/5
Correct? Yes
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:
### Answer: 1
Expected answer: 4/3
Correct? No
Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 28/6 = <<28/6=4>>4, and 16/24 = <<16/24=0.625>>0.625. Therefore, (28/6 * 16/24) = 4 * 0.625 = 2.5. ### Answer: 2.5
Expected answer: 28/9
Correct? No