InternLM-Math Base 7B 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.
InternLM-Math Base 7B:
Reasoning: 29/2*19/28 = 29*19/2*28 = 551/56 ### Answer: 551/56
Expected answer: 551/56
Correct? Yes
Problem: After finding the product of (29/2) and (19/28), multiply your result by (8/28). Write your final answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 551/56*8/28 = 551*8/56*28 = 44/7 ### Answer: 44/7
Expected answer: 551/196
Correct? No
Problem: After finding the product of (29/2) and (19/28), reconsider the calculation using (19/14) instead of (19/28). Recalculate the product of (29/2) and (19/14) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 29/2*19/14 = 29*19/2*14 = 565/28 ### Answer: 565/28
Expected answer: 551/28
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.
InternLM-Math Base 7B:
Reasoning: 7 ⋅ 27/12 = 7⋅(2⋅3/2⋅2) = 7⋅3/2 = 21/2 ### Answer: 21/2
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)).
InternLM-Math Base 7B:
You are correct.
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.
InternLM-Math Base 7B:
Reasoning: ((24/22) * (24/17)) = <<(24/22) * (24/17) = 576/374>>576/374 ### Answer: 576/374
Expected answer: 288/187
Correct? Yes
Problem: After finding the result of ((24 / 22) * (24 / 17)) in the previous problem, multiply the answer you found by (27 / 18). Write the result as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: <<576/374 * 27/18=576*27/374*18=15552/6612= 8/3>>8/3 ### Answer: 8/3
Expected answer: 432/187
Correct? No
Problem: Since the previous problem had you evaluating ((24 / 22) * (24 / 17)), consider this change: What if instead of multiplying (24 / 22) by (24 / 17), you multiplied it by (24 / 9)? Calculate the result of ((24 / 22) * (24 / 9)) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((24/22) * (24/9)) = <<(24/22) * (24/9) = 144/11>>144/11 ### Answer: 144/11
Expected answer: 32/11
Correct? No
Problem: What is the result when you divide 25/4 by 16/6? Please write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 25/4 ÷ 16/6 = <<25/4 ÷ 16/6= 25*6/4*16= 150/64= 25/8>>25/8 ### Answer: 25/8
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.
InternLM-Math Base 7B:
Expected answer: 13/7
Correct? No
Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.
InternLM-Math Base 7B:
Reasoning: (17/10) * (28/10) = <<(17/10) * (28/10) = 17*28/10*10 = 17*28/100 = 17.6>>17.6 ### Answer: 17.6
Expected answer: 119/25
Correct? No
Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))
InternLM-Math Base 7B:
Reasoning: (29/14) * (23/6) = <<(29/14) * (23/6) = 8.5 * 3.8 = 32.3>>32.3 ### Answer: 32.3
Expected answer: 667/84
Correct? No
Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((18 / 19) * (19 / 6)) = 18/6 = 3/1 = 3 ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: After calculating the solution for ((18 / 19) * (19 / 6)), take the result and multiply it by itself. What do you get? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((18 / 19) * (19 / 6)) = 3/1 (3/1) * (3/1) = 9/1 = 9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: After you've calculated the solution for ((18 / 19) * (19 / 6)), now consider what would happen if the fraction was instead ((9 / 19) * (19 / 6)). What would be the result? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((9 / 19) * (19 / 6)) = 9/6 = 3/2 ### Answer: 3/2
Expected answer: 3/2
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.
InternLM-Math Base 7B:
Reasoning: 19/12 ⋅ 20/6 = <<19/12⋅20/6=19⋅20/12⋅6=380/72=19/4>>19/4 ### Answer: 19/4
Expected answer: 95/18
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.
InternLM-Math Base 7B:
The total fractional representation of these two types of cargo hauled in one day is 2/3.
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.
InternLM-Math Base 7B:
Reasoning: (16/4) / (24/21) = <<(16/4) / (24/21) = 4/3>>4/3 ### Answer: 4/3
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.
InternLM-Math Base 7B:
Reasoning: 5/27 * 15/2 = 5*15/27*2 = <<5*15/27*2=75/54=5/3>>5/3 ### Answer: 5/3
Expected answer: 25/18
Correct? No
Problem: Calculate the result of the following product of fractions: (15 / 13) * (19 / 7). Make sure to write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/13) * (19/7) = 15*19/13*7 = <<15*19/13*7=285/91>>285/91.
Expected answer: 285/91
Correct? Yes
Problem: After finding the result of the product of fractions (15 / 13) * (19 / 7), multiply your result by another fraction (23/22). Write your final answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/13) * (19/7) = 15*19/13*7 = 285/91. 285/91 * 23/22 = 285*23/91*22 = <<285*23/91*22=6285/2018>>6285/2018.
Expected answer: 6555/2002
Correct? No
Problem: In the previous task, instead of calculating the product of fractions (15 / 13) * (19 / 7), now calculate the result of a slightly different operation: (15 / 29) * (19 / 7). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/29) * (19/7) = 15*19/29*7 = <<15*19/29*7=285/203>>285/203.
Expected answer: 285/203
Correct? Yes
Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 23/22⋅27/20= <<23/22⋅27/20= 621/440>>621/440 ### Answer: 621/440
Expected answer: 621/440
Correct? Yes
Problem: Calculate the result of the following operation: (12 / 25) * (20 / 4). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (12/25) * (20/4) = <<(12/25) * (20/4) = 2/5>>2/5 ### Answer: 2/5
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.
InternLM-Math Base 7B:
Reasoning: 14/10 · 30/5 = <<14*30/10*5=420/50=21/5>>21/5 ### Answer: 21/5
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.
InternLM-Math Base 7B:
Reasoning: The baker can only make 1/3 of a full batch of cookies. 1/3 of 26/1 = 1/3 * 26/1 = 26/3 = 8 2/3. ### Answer: 8 2/3
Expected answer: 364/29
Correct? No
Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Answer: 9/2
Expected answer: 243/40
Correct? No
Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: <<(24/11)*(27/26) = 9/11>>9/11 ### Answer: 9/11
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.
InternLM-Math Base 7B:
Reasoning: 26/9 * 17/13 = <<26/9*17/13=26*17/9*13=442/117>>442/117 ### Answer: 442/117
Expected answer: 34/9
Correct? Yes
Problem: Having solved the previous problem, now multiply your answer by the fraction 24/30. What is the result in simplest form?
InternLM-Math Base 7B:
Reasoning: 442/117 * 24/30 = <<442/117*24/30=442*24/117*30=10488/3510=3016/35>>3016/35 ### Answer: 3016/35
Expected answer: 136/45
Correct? No
Problem: If instead of multiplying the fraction 26/9 by the fraction 17/13, you multiplied 25/9 by 17/13, what would the result be in simplest form?
InternLM-Math Base 7B:
Reasoning: 25/9 * 17/13 = <<25/9*17/13=25*17/9*13=425/117>>425/117 ### Answer: 425/117
Expected answer: 425/117
Correct? Yes
Problem: Solve the following problem: What is the result of the expression (28 / 16) / (27 / 24)? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (28/16) / (27/24) = <<(28/16) / (27/24) = (1 3/4) / (1 3/8) = 7/8>>7/8 ### Answer: 7/8
Expected answer: 14/9
Correct? No
Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: The answer to the expression is 3/2. ### Answer: 3/2
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?
InternLM-Math Base 7B:
Reasoning: The bakers will need 19/28 × 30/4 = <<19/28 × 30/4=45/28>>45/28 of the ingredient. ### Answer: 45/28
Expected answer: 285/56
Correct? No
Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.
InternLM-Math Base 7B:
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.
InternLM-Math Base 7B:
Reasoning: (9/3) * (27/28) = <<(9/3) * (27/28) = 9*27/3*28 = 243/84 = 3*3*3*7/3*3*2*2*2*7 = 3*3*3/3*3*2*2*2 = 3*3*3/3*3*2*2*2*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7*7
Expected answer: 81/28
Correct? Yes
Problem: After you have calculated the result of the expression (9/3) * (27/28) from the previous problem, calculate the square of your answer. Write your final answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: The square of <<(9/3) * (27/28) = 3>>3 is 3*3 = 9. ### Answer: 9
Expected answer: 6561/784
Correct? No
Problem: In the previous problem, you multiplied the fractions (9/3) * (27/28). Now consider the case where the second fraction has changed from (27/28) to (23/28). How does this change your answer? Recalculate using (9/3) * (23/28) and write your new answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (9/3) * (23/28) = <<(9/3) * (23/28) = 9*23/3*28 = 207/84 = 3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*
Expected answer: 69/28
Correct? Yes
Problem: Calculate the solution to the following equation and write your answer as a simplified fraction: ((15 / 13) * (24 / 24))
InternLM-Math Base 7B:
Reasoning: ((15 / 13) * (24 / 24)) = 1 ### Answer: 1
Expected answer: 15/13
Correct? No
Problem: Calculate the result of the following multiplication of fractions operation: (9 / 7) * (25 / 30). Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Answer: 3/4
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.
InternLM-Math Base 7B:
Reasoning: (9/8) / (20/18) = <<(9/8) / (20/18) = (9/8) ⋅ (18/20) = (9⋅18) / (8⋅20) = 162/160 = 9/8 = 1 1/8 = 1.125>>1 1/8 = 1.125 ### Answer: 1 1/8
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.
InternLM-Math Base 7B:
Reasoning: (30/6) / (13/9) = <<30/6=5, 5/13=0.3846153846153846, 0.3846153846153846/9=0.0427272727272727>>0.0427272727272727. ### Answer: 0.0427272727272727
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?
InternLM-Math Base 7B:
Reasoning: 30/18 = <<30/18=1.6...>>1.6. 1.6*18/6 = <<1.6*18/6=3.2...>>3.2. ### Answer: 3.2
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.
InternLM-Math Base 7B:
Reasoning: ((20 / 2) * (2 / 18)) = 1/3 ### Answer: 1/3
Expected answer: 10/9
Correct? No
Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))
InternLM-Math Base 7B:
Reasoning: ((11 / 9) * (29 / 6)) = 11*29/9*6 = <<11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11*29/9*6= 11
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.
InternLM-Math Base 7B:
Reasoning: (30/7) * (16/19) = 30*16 / 7*19 = <<30*16/7*19=480/133>>480/133 ### Answer: 480/133
Expected answer: 480/133
Correct? Yes
Problem: Let's proceed with the result found in the previous fraction multiplication task. Now, take that result and multiply it by 22/7. What is the new result? Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 480/133 * 22/7 = 480*22/133*7 = <<480*22/133*7=5760/133>>5760/133 ### Answer: 5760/133
Expected answer: 10560/931
Correct? No
Problem: Recall the earlier problem where we performed a fraction multiplication. If we consider a slight change and now multiply 21/7 (instead of 30/7) with 16/19, what would be the result? Remember to express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 21/7 * 16/19 = 21*16/7*19 = <<21*16/7*19=336/133>>336/133 ### Answer: 336/133
Expected answer: 48/19
Correct? Yes
Problem: Calculate the product of 25/22 and 20/3 and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 25/22*20/3= <<25/22*20/3=5*20/22*3=5*20/66=100/66=5/3>>5/3 ### Answer: 5/3
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))
InternLM-Math Base 7B:
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.
InternLM-Math Base 7B:
Reasoning: (5/3) * (27/13) = 5*27 / 3*13 = <<5*27/3*13= 135/39= 5/1>>5/1 ### Answer: 5/1
Expected answer: 45/13
Correct? No
Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.
InternLM-Math Base 7B:
Reasoning: 1/1 = 1 29/29 = 1 (1*1) = 1 ### Answer: 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?
InternLM-Math Base 7B:
Reasoning: 27/27 = 1 (1*1) = 1 ### 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?
InternLM-Math Base 7B:
Reasoning: 1/1 = 1 6/6 = 1 29/6 = 4.833333333 (4.833333333*1) = 4.833333333 ### Answer: 4.833333333
Expected answer: 29/6
Correct? No
Problem: Calculate the product of the fractions 11/19 and 22/7. Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 11/19 ⋅ 22/7 = 11⋅22/19⋅7 = <<11⋅22/19⋅7=242/133>>242/133 ### Answer: 242/133
Expected answer: 242/133
Correct? Yes
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?
InternLM-Math Base 7B:
Reasoning: 242/133 ⋅ 25/4 = 242⋅25/133⋅4 = <<242⋅25/133⋅4=6100/532>>6100/532 ### Answer: 6100/532
Expected answer: 3025/266
Correct? No
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.
InternLM-Math Base 7B:
Reasoning: 11/19 ⋅ 25/7 = 11⋅25/19⋅7 = 275/133 ### Answer: 275/133
Expected answer: 275/133
Correct? Yes
Problem: What is the result of multiplying 21/30 by 19/5? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 21/30 * 19/5 = <<21*19/30*5= 399/150>>399/150 ### Answer: 399/150
Expected answer: 133/50
Correct? Yes
Problem: If you further multiply the result you got from the last problem ((21/30) * (19/5)) by 16/12, what would be the final result? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 21/30 * 19/5 = 399/150 399/150 * 16/12 = <<399*16/150*12= 6,384/1,800>>6,384/1,800 ### Answer: 6,384/1,800
Expected answer: 266/75
Correct? Yes
Problem: If in the previous problem, instead of multiplying 21/30 by 19/5, you had to multiply 9/30 by 19/5, what would be the new result? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 9/30 * 19/5 = <<9*19/30*5= 171/150>>171/150 ### Answer: 171/150
Expected answer: 57/50
Correct? Yes
Problem: What is the result when you multiply the fraction 11/15 by the fraction 23/8? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 11/15 × 23/8 = 11 × 23/15 × 8 = 253/120. 253/120 = 1 × 253/1 × 120 = 1 × 253 × 1/1 × 3 × 4 × 2 × 2 × 5 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/1 × 3 × 4 × 2 × 2 × 5 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/1 × 3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/1 × 3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4 × 2 × 2 × 5 × 11 × 23/3 × 2 × 2 × 2 × 2 × 3 × 5 × 11 × 23 = 1 × 3 × 4
Expected answer: 253/120
Correct? No
Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (29 / 16) * (21 / 27) = 3/8 ### Answer: 3/8
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.
InternLM-Math Base 7B:
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.
InternLM-Math Base 7B:
Reasoning: 1 * 20/7 = 20/7 ### Answer: 20/7
Expected answer: 20/7
Correct? Yes
Problem: After finding the result of ((25 / 25) * (20 / 7)), what is the result when you multiply this product by itself? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 20/7 * 20/7 = 20*20/7*7 = 400/49 ### Answer: 400/49
Expected answer: 400/49
Correct? Yes
Problem: After reevaluating the previous problem, if you found the result of ((25 / 25) * (11 / 7)) instead of ((25 / 25) * (20 / 7)), what would be the new result? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 1*11/7 = 11/7 ### Answer: 11/7
Expected answer: 11/7
Correct? Yes
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.
InternLM-Math Base 7B:
Reasoning: 5/1 ⋅ 16/27 = <<5⋅16/1⋅27=80/27>>80/27 ### Answer: 80/27
Expected answer: 80/27
Correct? Yes
Problem: Suppose you initially started with 30 (instead of 5), which is equivalent to the fraction 30/1. You are then required to multiply this with the fraction 16/27. How does this change the result from the previous problem? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 30/1 ⋅ 16/27 = <<30⋅16/1⋅27=480/27=16⋅30/3⋅9=16⋅10/3⋅3=16⋅10/3=16⋅10⋅3/3⋅3⋅3=16⋅10⋅3/3⋅9=16⋅10⋅3⋅9/9⋅9⋅9=16⋅10⋅3⋅9/729=16⋅10⋅27/27⋅27⋅3=16⋅10⋅27⋅3/27⋅27⋅9⋅3=16⋅10⋅27⋅3/2187=16⋅10⋅27⋅3/2187=16⋅10⋅27⋅3⋅3/3⋅3⋅3⋅3⋅3⋅3⋅3⋅3=16⋅10⋅27⋅9⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3/3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3=16⋅10⋅27⋅9⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅
Expected answer: 160/9
Correct? Yes
Problem: Calculate the result of the expression ((27 / 3) / (12 / 12)) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((27/3) / (12/12)) = <<(27/3) / (12/12) = 9/4>>9/4 ### Answer: 9/4
Expected answer: 9
Correct? No
Problem: Calculate the result of the following operation: (15 / 16) * (29 / 2). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/16) * (29/2) = <<(15/16) * (29/2) = (15*29)/(16*2) = 435/32>>435/32 ### Answer: 435/32
Expected answer: 435/32
Correct? Yes
Problem: If the result from the previous problem is multiplied by (18/18), what is the new result? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (435/32) * (18/18) = <<(435/32) * (18/18) = 435*18/32*18 = 7830/576 = 3*5*11*3*2*3*2*2*3*2*2*2*3*2*3*2*2*3*2*2*3*2*3*2*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3
Expected answer: 435/32
Correct? Yes
Problem: In the previous problem, instead of multiplying (15/16) by (29/2), what would be the result if we multiply it by (13/2) instead? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/16) * (13/2) = <<(15/16) * (13/2) = (15*13)/(16*2) = 195/32>>195/32 ### Answer: 195/32
Expected answer: 195/32
Correct? Yes
Problem: Calculate the solution to this mathematical equation: ((6 / 2) / (13 / 9)). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((6/2) / (13/9)) = <<(6/2) / (13/9) = 3/2 * 9/13 = 27/13>>27/13 ### Answer: 27/13
Expected answer: 27/13
Correct? Yes
Problem: Following your previous calculation, how would the result change if the first fraction was actually ((6 / 2) / 3) instead of ((6 / 2) / (13 / 9))? Calculate and write your answer as a simplfied fraction.
InternLM-Math Base 7B:
Reasoning: ((6/2) / 3) = <<(6/2) / 3 = 3/2 * 1/3 = 3/6 = 1/2>>1/2 ### Answer: 1/2
Expected answer: 1
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.
InternLM-Math Base 7B:
Reasoning: 7/1 ÷ 15/9 = <<7/1 ÷ 15/9=7/9>>7/9 ### Answer: 7/9
Expected answer: 21/5
Correct? No
Problem: What is the result when you multiply (23/10) by (9/1)?
InternLM-Math Base 7B:
Reasoning: 23/10*9/1=<<23/10*9/1=207/10=20.7>>20.7 ### Answer: 20.7
Expected answer: 207/10
Correct? Yes
Problem: You have already calculated the result of (23/10) multiplied by (9/1). Now, multiply this result by (1/16). What is your answer?
InternLM-Math Base 7B:
Reasoning: 20.7*1/16=<<20.7*1/16=1.3>>1.3 ### Answer: 1.3
Expected answer: 207/160
Correct? No
Problem: Previously, you computed the result of (23/10) multiplied by (9/1). Now, consider what would have happened if instead of (9/1), you had (9/6). Multiply (23/10) by this new fraction. What is your answer?
InternLM-Math Base 7B:
Reasoning: 23/10*9/6=<<23/10*9/6=11.5>>11.5 ### Answer: 11.5
Expected answer: 69/20
Correct? No
Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (18/4) * (10/11) = <<(18/4) * (10/11) = 9/2 * 1/11 = 9/22>>9/22 ### Answer: 9/22
Expected answer: 45/11
Correct? No
Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?
InternLM-Math Base 7B:
Reasoning: 24/23 * 23/3 = 24*23/23*3 = <<24*23/23*3=24*23/69=24*23*1/69*1=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69=24*23*1/69*1=24*23/69
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.
InternLM-Math Base 7B:
Reasoning: (20 / 13) / (17 / 16) = 20*16 / 13*17 = <<20*16/13*17=160/221>>160/221 ### Answer: 160/221
Expected answer: 320/221
Correct? No
Problem: Calculate the result of the following problem: ((5 divided by 5) multiplied by (4 divided by 1))
InternLM-Math Base 7B:
Reasoning: <<(5/5*4/1=8)>>
Expected answer: 4
Correct? No
Problem: Calculate the result for the following problem: ((30 / 23) * (19 / 24)). Write the answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (30/23) * (19/24) = 30*19 / 23*24 = <<30*19/23*24=285/552>>285/552 ### Answer: 285/552
Expected answer: 95/92
Correct? No
Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (23 / 26) * (16 / 1) = <<23/26*16/1=23*16/26*1=368/26=14/1=14>>14 ### Answer: 14
Expected answer: 184/13
Correct? No
Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((21 / 1) / (26 / 20)) = <<(21/1)/(26/20)=(21*20)/(1*26)=(21*20)/(1*26)=(420/26)=16>>16 ### Answer: 16
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.
InternLM-Math Base 7B:
Reasoning: 24/19 * 21/19 = <<24/19*21/19=504/361>>504/361 ### Answer: 504/361
Expected answer: 504/361
Correct? Yes
Problem: Considering the previous problem, let's make a small change to it. Instead of multiplying 24 over 19, let's multiply 20 over 19 by 21 over 19 but without simplifying. Write your answer as a fraction.
InternLM-Math Base 7B:
Reasoning: 20/19 * 21/19 = <<20/19*21/19=420/361>>420/361 ### Answer: 420/361
Expected answer: 420/361
Correct? Yes
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.
InternLM-Math Base 7B:
Reasoning: 12/2 = <<12/2=6>>6, 17/14 = <<17/14=1 3/7>>1 3/7, 6 * 1 3/7 = <<6*1 3/7=6 18/7>>6 18/7, 6 18/7 = <<6 18/7=6 3/7>>6 3/7 ### Answer: 6 3/7
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.
InternLM-Math Base 7B:
Reasoning: ((21 / 16) / (27 / 23)) = 21/16 ⋅ 23/27 = 3/4 ### Answer: 3/4
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)
InternLM-Math Base 7B:
Reasoning: (11/20) * (24/12) = 11/20 * 2/1 = <<11/20*2/1=11/20*2=11/20*1/1=11/20*1=11/20>>11/20 ### Answer: 11/20
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.
InternLM-Math Base 7B:
Reasoning: ((6/19)*(28/2)) = 2/19 ### Answer: 2/19
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.
InternLM-Math Base 7B:
Reasoning: (12/14) * (28/5) = <<(12/14) * (28/5) = 8/5>>8/5 ### Answer: 8/5
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.
InternLM-Math Base 7B:
Reasoning: (19/3) * (8/15) = 19*8 / 3*15 = <<19*8/3*15=19*8/3*3*5=19*8/9*5=19*8/45=19*8*1/45*1=19*8*1/45*1*1=19*8*1/45*1*1*1=19*8*1*1/45*1*1*1*1=19*8*1*1*1/45*1*1*1*1*1=19*8*1*1*1*1/45*1*1*1*1*1*1=19*8*1*1*1*1*1/45*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1=19*8*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1*1/45*1*1*1*1*1*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.
InternLM-Math Base 7B:
Reasoning: 15/3 = <<15/3=5>>5, 7/25 = <<7/25=0.28>>0.28, 5*0.28 = <<5*0.28=1.4>>1.4, 1.4/1 = <<1.4/1=1.4>>1.4 ### Answer: 1.4
Expected answer: 7/5
Correct? Yes
Problem: After finding the result of ((15 / 3) * (7 / 25)), take that result and multiply it by (28 / 16). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 1.4*28/16 = 1.4*1.75 = <<1.4*1.75=2.45>>2.45, 2.45/1 = <<2.45/1=2.45>>2.45 ### Answer: 2.45
Expected answer: 49/20
Correct? Yes
Problem: Given the result of the previous problem, let's consider a new scenario. Suppose instead of (15 / 3), we have (13 / 3). Now, multiply (13 / 3) * (7 / 25) and write your answer as a simplified fraction. How does this change in scenario affect the final result?
InternLM-Math Base 7B:
Reasoning: 13/3 = <<13/3=4.3>>4.3, 4.3*0.28 = <<4.3*0.28=1.204>>1.204, 1.204/1 = <<1.204/1=1.204>>1.204 The result of the new scenario is 1.204, which is different from 1.4.
Expected answer: 91/75
Correct? No
Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.
InternLM-Math Base 7B:
Reasoning: 2 * 10 = <<2*10=20>>20 ### Answer: 20
Expected answer: 20
Correct? Yes
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.
InternLM-Math Base 7B:
Reasoning: 2 * 1.3 = <<2*1.3=2.6>>2.6 ### Answer: 2.6
Expected answer: 76/3
Correct? No
Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 27/18 = <<27/18=3/2>>3/2, 19/8 = <<19/8=19/8>>19/8, 3/2 * 19/8 = <<3/2 * 19/8=57/16>>57/16. ### Answer: 57/16
Expected answer: 57/16
Correct? Yes
Problem: Now, multiplying the result from the previous calculation by the fraction (28 / 16), what do you get? Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 57/16 * 28/16 = <<57/16 * 28/16=1608/256>>1608/256. ### Answer: 1608/256
Expected answer: 399/64
Correct? No
Problem: If we change the situation from the previous problem, and instead of the fraction (19 / 8), we now have (19 / 17), what will be the result of the calculation [(27 / 18) * (19 / 17)]? Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 27/18 = <<27/18=3/2>>3/2, 19/17 = <<19/17=19/17>>19/17, 3/2 * 19/17 = <<3/2 * 19/17=57/34>>57/34. ### Answer: 57/34
Expected answer: 57/34
Correct? Yes
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.
InternLM-Math Base 7B:
Reasoning: 29/5 * 13/24 = 29*13/5*24 = <<29*13/5*24=377/120>>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.
InternLM-Math Base 7B:
Reasoning: 377/120 * 25/11 = 377*25/120*11 = <<377*25/120*11= 9275/1320>>9275/1320 ### Answer: 9275/1320
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.
InternLM-Math Base 7B:
Reasoning: 29/8 * 13/24 = 29*13/8*24 = 377/96 ### Answer: 377/96
Expected answer: 377/192
Correct? No
Problem: Calculate the value of the expression ((29 / 17) / (27 / 22)). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((29/17) / (27/22)) = <<(29/17) / (27/22) = (29/17) * (22/27) = (22*29) / (17*27) = 608/513>>608/513 ### Answer: 608/513
Expected answer: 638/459
Correct? No
Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?
InternLM-Math Base 7B:
Reasoning: (27/6) * (25/5) = <<27/6*25/5=25*25/6*5=625/30=21.6>>21.6 ### Answer: 21.6
Expected answer: 45/2
Correct? No
Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).
InternLM-Math Base 7B:
Reasoning: (13 / 1) * (1 / 6) = <<13/1*1/6=13/6>>13/6 ### Answer: 13/6
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.
InternLM-Math Base 7B:
Reasoning: (13 / 2) * e = (13/2)*(13/6) = <<(13/2)*(13/6)=169/12>>169/12 ### Answer: 169/12
Expected answer: 169/12
Correct? Yes
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.
InternLM-Math Base 7B:
Reasoning: (11 / 1) * (1 / 6) = 11/6 The result is 1/6 less than the previous one because 11/6 is 1/6 less than 13/6. ### Answer: 11/6
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.
InternLM-Math Base 7B:
Reasoning: 25/20*11/6= <<25*11/20*6=275/120>>275/120.
Expected answer: 55/24
Correct? Yes
Problem: After finding the product of 25/20 and 11/6, now multiply that result by the fraction 20/26. What do you get? Remember to write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 275/120*20/26= <<275*20/120*26=1100/312>>1100/312.
Expected answer: 275/156
Correct? No
Problem: After calculating the product of 25/20 and 11/6 and multiplying that result by 20/26, now consider what would happen if you initially multiplied 25/17 instead of 25/20 by 11/6. What new result do you get? Please write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 25/20*11/6*20/26= <<25*11*20/20*6*26=1100/156=25/3>>25/3.
Expected answer: 275/102
Correct? No
Problem: Determine the value of (7 / 2) / (25 / 10). Please provide your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (7/2) / (25/10) = <<(7/2) / (25/10) = (7/2) * (10/25) = 7/5>>7/5 ### Answer: 7/5
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.
InternLM-Math Base 7B:
Reasoning: (7/2) / (25/10) = 7/5 (7/2) / (25/10) * 5/3 = <<(7/2) / (25/10) * 5/3 = 7/5 * 5/3 = 7/3>>7/3 ### Answer: 7/3
Expected answer: 7/3
Correct? Yes
Problem: Calculate the multiplication of two fractions: Multiply 15/16 by 29/27. Give your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 15/16 × 29/27 = 15 × 29/16 × 27 = <<15 × 29/16 × 27= 435/432>>435/432 ### Answer: 435/432
Expected answer: 145/144
Correct? Yes
Problem: After calculating the multiplication of the fractions 15/16 by 29/27, multiply that answer by the fraction 27/4. What is the result as a simplified fraction?
InternLM-Math Base 7B:
Reasoning: 15/16 × 29/27 × 27/4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16 × 27 × 4 = 15 × 29 × 27/16
Expected answer: 435/64
Correct? No
Problem: In the previous problem, you calculated the multiplication of the fractions 15/16 and 29/27. Now, let's imagine that you initially had a fraction with 15 as the numerator and 10 as the denominator instead of 15/16. How would the result differ if you multiply 15/10 by 29/27? Give your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 15/10 × 29/27 = 15 × 29/10 × 27 = <<15 × 29/10 × 27= 285/270>>285/270 ### Answer: 285/270
Expected answer: 29/18
Correct? No
Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.
InternLM-Math Base 7B:
Reasoning: 3/2*2/1 = <<3/2*2/1=3>>3 ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: After calculating the answer to ((30 / 25) * (25 / 10)), multiply your answer by (5 / 9). What is the result? Be sure to simplify your final answer.
InternLM-Math Base 7B:
Reasoning: 3*5/9 = <<3*5/9=15/9>>15/9 15/9 = <<15/9=1 4/9>>1 4/9 ### Answer: 1 4/9
Expected answer: 5/3
Correct? No
Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.
InternLM-Math Base 7B:
Reasoning: 27/3 = 9 (27/10)⋅(27/3) = (27/10)⋅9 (27/10)⋅9 = 27⋅9/10 27⋅9/10 = 243/10 ### Answer: 243/10
Expected answer: 243/10
Correct? Yes
Problem: First, calculate the product of the fractions 27/10 and 27/3. Then, multiply the result by 9/20. Write your answer in simplest form.
InternLM-Math Base 7B:
Reasoning: 27/3 = 9 (27/10)⋅(27/3) = (27/10)⋅9 (27/10)⋅9 = 27⋅9/10 27⋅9/10 = 243/10 243/10⋅(9/20) = 243⋅9/10⋅20 243⋅9/10⋅20 = 2187/20 ### Answer: 2187/20
Expected answer: 2187/200
Correct? No
Problem: First, calculate the product of the fractions 27/10 and 27/21, instead of 27/3 as we had in the previous question. Write your answer in simplest form.
InternLM-Math Base 7B:
Reasoning: 27/21 = 3/7 (27/10)⋅(27/21) = (27/10)⋅(3/7) (27/10)⋅(3/7) = 27⋅3/10⋅7 27⋅3/10⋅7 = 81/70 ### Answer: 81/70
Expected answer: 243/70
Correct? No
Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (10/8) * (30/26) = 5/4 ### Answer: 5/4
Expected answer: 75/52
Correct? No
Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: <<(20 / 22) * (14 / 11) = (1/2) * (14/11) = 7/11>>
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?
InternLM-Math Base 7B:
Reasoning: ((25 / 8) * (3 / 4)) = <<(25/8)*(3/4) = 3/8>>3/8 The result 3/8 signifies a division of 8 into 3 parts.
Expected answer: 75/32
Correct? No
Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).
InternLM-Math Base 7B:
Reasoning: (29 / 1) = <<29/1=29>>29, and 8/15 = <<8/15=0.5>>0.5.
Expected answer: 232/15
Correct? No
Problem: What is the result when you multiply (29/17) by (26/15)?
InternLM-Math Base 7B:
Reasoning: (29/17) * (26/15) = 29*26/17*15 = <<29*26/17*15= 754/255>>754/255 ### Answer: 754/255
Expected answer: 754/255
Correct? Yes
Problem: Using the previous result ((29/17) * (26/15)), multiply this answer by (21/9). What is the result when you simplify the final fraction?
InternLM-Math Base 7B:
Reasoning: (29/17) * (26/15) * (21/9) = 754*21/255*9 = <<754*21/255*9= 15774/2295>>15774/2295 ### Answer: 15774/2295
Expected answer: 5278/765
Correct? No
Problem: If the original fraction were (15/17) instead of (29/17), what would be the result when you multiply (15/17) by (26/15)?
InternLM-Math Base 7B:
Reasoning: (15/17) * (26/15) = 15*26/17*15 = 390/17*15 = 390/255 ### Answer: 390/255
Expected answer: 26/17
Correct? Yes
Problem: Calculate the value of the expression ((25 / 5) * (16 / 8)) and provide your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: ((25/5) * (16/8)) = 5/1 * 2/1 = 10/1 = 10 ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: In the previous problem, we used the numbers 25 and 5, and 16 and 8 in our calculations. Now consider a slight change where we keep the '25 and '5', but instead of '16 and 8', we use '19 and 8'. Recalculate the value of k using this new information: ((25 / 5) * (19 / 8)). What is the value of k in this scenario?
InternLM-Math Base 7B:
Reasoning: ((25/5) * (19/8)) = 5/1 * 19/8 = 95/8 ### Answer: 95/8
Expected answer: 95/8
Correct? Yes
Problem: What is the result when you multiply (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (23 / 4) ⋅ (10 / 12) = 23⋅10/4⋅12 = 230/48 = 115/24 ### Answer: 115/24
Expected answer: 115/24
Correct? Yes
Problem: What would be the result if you changed the previous problem by multiplying (28 / 4) by (10 / 12) instead of (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (28 / 4) ⋅ (10 / 12) = 28⋅10/4⋅12 = 280/48 = 70/12 ### Answer: 70/12
Expected answer: 35/6
Correct? Yes
Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form.
InternLM-Math Base 7B:
Reasoning: (21 / 26) * (20 / 9) = 21*20 / 26*9 = <<21*20/26*9=420/234>>420/234 (21 / 26) * (20 / 9) = 21*20 / 26*9 = <<21*20/26*9=420/234>>420/234
Expected answer: 70/39
Correct? Yes
Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form. Then, take that result and multiply it by the fraction (15 / 21). Write the final answer in simplest form.
InternLM-Math Base 7B:
Reasoning: (21 / 26) * (20 / 9) = 21*20 / 26*9 = <<21*20/26*9=420/234>>420/234 (15 / 21) * (420 / 234) = 15*420 / 21*234 = <<15*420/21*234=3000/3=1000>>1000 ### Answer: 1000
Expected answer: 50/39
Correct? No
Problem: Recalculate the previous problem, but this time change the second fraction in the initial multiplication to (20 / 4) instead of (20 / 9). So, your new problem would be to calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 4). Write your answer in simplest form.
InternLM-Math Base 7B:
Reasoning: (21 / 26) * (20 / 4) = 21*20 / 26*4 = <<21*20/26*4=420/104>>420/104 (21 / 26) * (20 / 4) = 21*20 / 26*4 = <<21*20/26*4=420/104>>420/104
Expected answer: 105/26
Correct? Yes
Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: <<(17/13) * (15/6) = (17*15) / (13*6) = 255/78 = 15/4>>. ### Answer: 15/4
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.
InternLM-Math Base 7B:
Reasoning: (25 / 18) * (17 / 6) = 25*17 / 18*6 = <<25*17/18*6=175/108>>175/108 ### Answer: 175/108
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.
InternLM-Math Base 7B:
Reasoning: 9/1 * 2/17 = <<9/1 * 2/17=18/17>>18/17 ### Answer: 18/17
Expected answer: 18/17
Correct? Yes
Problem: After solving the earlier problem, you found a result by multiplying the fraction 9/1 by 2/17. Let's denote this result as t. Now, find what happens when you multiply the result with itself (t * t). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: t * t = <<t * t=18/17*18/17=324/289>>324/289 ### Answer: 324/289
Expected answer: 324/289
Correct? Yes
Problem: In the earlier problem, you multiplied the fraction 9/1 by 2/17. Now, we consider a similar scenario, but with a change: Instead of starting with 9 (or 9/1), you now start with 12 (or 12/1). Calculate the result of multiplying 12 by the fraction 2/17. Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 12/1 * 2/17 = <<12/1 * 2/17=24/17>>24/17 ### Answer: 24/17
Expected answer: 24/17
Correct? Yes
Problem: Calculate the result of the multiplication: (27 / 14) * (19 / 14). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (27/14) * (19/14) = 27*19/14*14 = <<27*19/14*14=27*19/196>>27*19/196 ### Answer: 27*19/196
Expected answer: 513/196
Correct? Yes
Problem: Having found the value of z from the previous problem ((27 / 14) * (19 / 14)), now multiply your answer by the fraction 17/23. Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 27*19/196*17/23 = <<27*19/196*17/23=27*19*17/196*23>>27*19*17/196*23 ### Answer: 27*19*17/196*23
Expected answer: 8721/4508
Correct? No
Problem: Previously, you calculated the result of the multiplication (27 / 14) * (19 / 14). Now, what if instead of 27, we had a value of 15? So calculate the new result for the multiplication problem (15 / 14) * (19 / 14). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (15/14) * (19/14) = 15*19/14*14 = 15*19/196 = <<15*19/196=15*19/196>>15*19/196 ### Answer: 15*19/196
Expected answer: 285/196
Correct? Yes
Problem: Calculate the result for the expression: (16 / 5) * (5 / 15) and write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (16/5) * (5/15) = <<(16/5) * (5/15) = (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.
InternLM-Math Base 7B:
Reasoning: 16/15 * 30/24 = <<16/15 * 30/24 = 16*30/15*24 = 480/360 = 8/5>>8/5 ### Answer: 8/5
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.
InternLM-Math Base 7B:
Reasoning: (16/5) * (5/7) = <<(16/5) * (5/7) = (16*5) / (5*7) = 16/7>>16/7 ### 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.
InternLM-Math Base 7B:
Reasoning: (8 / 3) * (18 / 21) = 8*18 / 3*21 = 144 / 63 = 8/3 ### Answer: 8/3
Expected answer: 16/7
Correct? No
Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))
InternLM-Math Base 7B:
Reasoning: ((14 / 6) / (22 / 16)) = 7/11 ### Answer: 7/11
Expected answer: 56/33
Correct? No
Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)
InternLM-Math Base 7B:
Reasoning: (16/3) * (25/26) = 16*25/3*26 = <<16*25/3*26=400/78>>400/78 = 5/1 = 5 ### Answer: 5
Expected answer: 200/39
Correct? No
Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)
InternLM-Math Base 7B:
Reasoning: (16/16) * (26/22) = 26/22 ### Answer: 26/22
Expected answer: 13/11
Correct? Yes
Problem: Now, consider what happens when you square the result of the previous problem. Solve for (a * a), where 'a' is the answer to the previous problem: (16 / 16) * (26 / 22). Write the answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (a * a) = a^2 ### Answer: 26/22
Expected answer: 169/121
Correct? No
Problem: Now, modify the previous problem by changing the numerator of the first fraction. Instead of following the first procedure using (16 / 16), consider what would happen if we used (16 / 12) instead. Solve (16 / 12) * (26 / 22) and write the result as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: (16/12) * (26/22) = 104/66 ### Answer: 104/66
Expected answer: 52/33
Correct? Yes
Problem: Calculate the result of the following operation: (17 / 5) * (5 / 14). Write your answer as a simplest form fraction.
InternLM-Math Base 7B:
Reasoning: (17/5) * (5/14) = <<17/5 * 5/14=17/14=1 3/14>>1 3/14 ### Answer: 1 3/14
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?
InternLM-Math Base 7B:
Reasoning: (17/5) * (5/14) * (21/25) = <<17/5 * 5/14 * 21/25=17/14 * 21/25=17*21/5*14*25=357/350=3 7/35>>3 7/35 ### Answer: 3 7/35
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?
InternLM-Math Base 7B:
Reasoning: (17/5) * (5/12) = <<17/5 * 5/12=17/12=1 5/12>>1 5/12 ### Answer: 1 5/12
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.
InternLM-Math Base 7B:
Reasoning: (16/6) * (29/27) = 16*29 / 6*27 = <<16*29/6*27=464/162=29/9>>29/9 ### Answer: 29/9
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.
InternLM-Math Base 7B:
Reasoning: The car will have consumed 16/10*13/17= <<16/10*13/17=208/170>>208/170 gallons of petrol when you finish the drive. ### Answer: 208/170
Expected answer: 104/85
Correct? Yes
Problem: In the previous scenario, you drove a route that was 13/17 miles long. This time, suppose that you have to drive a route that is slightly longer, at 13/7 miles long. If your car still consumes 16/10 gallons of petrol every mile, calculate how many gallons of petrol will the car have consumed when you finish this drive? Express your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: The car will have consumed 16/10*13/7= <<16/10*13/7=208/70>>208/70 gallons of petrol when you finish the drive. ### Answer: 208/70
Expected answer: 104/35
Correct? Yes
Problem: Calculate the result of the following problem and express your answer as a simplified fraction: (29 / 10) / (18 / 16)
InternLM-Math Base 7B:
Reasoning: (29 / 10) / (18 / 16) = 29/10 × 16/18 = <<29/10 × 16/18=29 × 16/10 × 18=464/180=23/9>>23/9 ### Answer: 23/9
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.
InternLM-Math Base 7B:
Reasoning: 15/12 = <<15/12=5/4>>5/4 5/4 × 27/3 = <<5/4 × 27/3=5 × 27/4 × 3=5 × 9/4=45/4>>45/4 ### Answer: 45/4
Expected answer: 45/4
Correct? Yes
Problem: Following up on Jeremy's previous question, he now faces another complex problem. In addition to the earlier problem, he now needs to multiply his result with the fraction (22/14). Can you help Jeremy solve this problem? Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Reasoning: 45/4 × 22/14 = <<45/4 × 22/14=45 × 22/4 × 14=45 × 11/4 × 2=45 × 11/8=495/8>>495/8 ### Answer: 495/8
Expected answer: 495/28
Correct? No
Problem: Jeremy realized he made a mistake in his calculations. Instead of multiplying the fraction (15/12) by (27/3) as previously thought, he actually needs to multiply it by (27/5). What is the resulting simplified fraction, now that Jeremy has corrected his mistake?
InternLM-Math Base 7B:
Reasoning: 15/12 × 27/5 = <<15/12 × 27/5=15 × 27/12 × 5=15 × 9/12 × 5=135/60>>135/60 ### Answer: 135/60
Expected answer: 27/4
Correct? No
Problem: Calculate the answer to the following math problem: (7 / 7) * (12 / 12)
InternLM-Math Base 7B:
Reasoning: (7/7) * (12/12) = <<7/7*12/12=1*1=1>>1 ### Answer: 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?
InternLM-Math Base 7B:
Reasoning: 1* <<27/15=3/1>>3/1 = <<3*3/3*1=9/3=3>>3 ### Answer: 3
Expected answer: 9/5
Correct? No
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)?
InternLM-Math Base 7B:
Reasoning: (7/7) * (16/12) = <<7/7*16/12=1*4/3=4/3>>4/3 ### Answer: 4/3
Expected answer: 4/3
Correct? Yes
Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.
InternLM-Math Base 7B:
Expected answer: 28/9
Correct? No