LLemma 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.
LLemma 7B:
Reasoning: (29/2) x (19/28) = (29 x 19)/(2 x 28) = <<(29*19)/(2*28)=(531)/(56)>>(531)/(56) ### Answer: (531)/(56)
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.
LLemma 7B:
Reasoning: 27/12 = <<27/12=2.25>>2.25 7*2.25 = <<7*2.25=15.75>>15.75 ### Answer: 15.75
Expected answer: 63/4
Correct? Yes
Problem: Let's reconsider the previous question. Instead of multiplying 7 by the result of dividing 27 by 12, calculate the result when you multiply 7 by the division of 26 by 12. Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 26/12 = <<26/12=2.1666666666666665>>2.1666666666666665 7*2.1666666666666665 = <<7*2.1666666666666665=15.199999999999999>>15.199999999999999 ### Answer: 15.199999999999999
Expected answer: 91/6
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)).
LLemma 7B:
Reasoning: 30/27 = <<30/27=1.074>>1.074 29/27 = <<29/27=1.074>>1.074 (30 / 30) * (29 / 27) = <<(30/30)*(29/27)=1.074>>1.074 ### Answer: 1.074
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.
LLemma 7B:
Reasoning: 24 / 22 = <<24/22=2/1>>2/1 24 / 17 = <<24/17=4/1>>4/1 (24 / 22) * (24 / 17) = <<(24/22)*(24/17)=(2/1)*(4/1)>>2*4 = 8 ### Answer: 8
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.
LLemma 7B:
Reasoning: 25/4 = <<25/4=6.25>>6.25 and 16/6 = <<16/6=2.6666666666666665>>2.6666666666666665 25/4 by 16/6 = <<6.25/2.6666666666666665=2.3076923076923074>>2.3076923076923074 ### Answer: 2.3076923076923074
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.
LLemma 7B:
Reasoning: 3/7 x 26/6 = <<3/7 x 26/6>> = <<3 x 26/7 x 6>> = <<3 x 26/7 x 6>> = <<26/7>> ### Answer: 26/7
Expected answer: 13/7
Correct? No
Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.
LLemma 7B:
Reasoning: (17 / 10) * (28 / 10) = <<17/10*28/10=4.4>>4.4 ### Answer: 4.4
Expected answer: 119/25
Correct? No
Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))
LLemma 7B:
29/14 = <<29/14=2>>2 23/6 = <<23/6=3.8333333333333335>>3.8333333333333335 (2 * 3.8333333333333335) = <<2*3.8333333333333335=7.666666666666667>>7.666666666666667
Expected answer: 667/84
Correct? No
Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.
LLemma 7B:
Reasoning: 18/19 is a fraction that is less than 1. 19/6 is a fraction that is greater than 1. 18/19 is approximately <<18/19=0.947368421>>0.95. 19/6 is approximately <<19/6=3.166666667>>3.17. 0.95 * 3.17 = <<0.95*3.17=2.9925>>2.99. 2.99 is approximately <<2.99=3>>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.
LLemma 7B:
Reasoning: 18/19 is a fraction that is less than 1. 19/6 is a fraction that is greater than 1. 18/19 is approximately <<18/19=0.947368421>>0.95. 19/6 is approximately <<19/6=3.166666667>>3.17. 0.95 * 3.17 = <<0.95*3.17=2.9925>>2.99. 2.99 is approximately <<2.99=3>>3. 3 * 3 = <<3*3=9>>9. 9 is approximately <<9=9>>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.
LLemma 7B:
Reasoning: 9/19 is a fraction that is less than 1. 19/6 is a fraction that is greater than 1. 9/19 is approximately <<9/19=0.47368421>>0.47. 19/6 is approximately <<19/6=3.166666667>>3.17. 0.47 * 3.17 = <<0.47*3.17=1.52175>>1.52. 1.52 is approximately <<1.52=1>>1. ### Answer: 1
Expected answer: 3/2
Correct? No
Problem: Calculate the result of the multiplication of the fraction 19/12 by 20/6. Write your final answer as a simplified fraction.
LLemma 7B:
Reasoning: 19/12 = <<19/12=1 7/12>>1 7/12 and 20/6 = <<20/6=3 2/6=3 1/3>>3 1/3. 1 7/12 x 3 1/3 = <<1 7/12 x 3 1/3=5 1/4>>5 1/4 ### Answer: 5 1/4
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.
LLemma 7B:
Reasoning: 28/21 = <<28/21=1.36363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636
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.
LLemma 7B:
Reasoning: 16/4 = <<16/4=4>>4, 24/21 = <<24/21=2/3>>2/3 (16 / 4) / (24 / 21) = <<4/(2/3)=12>>12 ### Answer: 12
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.
LLemma 7B:
Reasoning: 5/27 = <<5/27=5/(27/3)=5/9>>5/9 15/2 = <<15/2=15/(2/2)=15/1>>15/1 5/9 x 15/1 = <<5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=5/9 x 15/1=
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.
LLemma 7B:
Reasoning: (15 / 13) * (19 / 7) = (15 * 19) / (13 * 7) = <<15*19/13*7>>15*19/13*7 = <<15*19/13*7>>285/91 = <<285/91>>285/91 = <<285/91>>285/91 ### Answer: 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.
LLemma 7B:
Reasoning: (15 / 13) * (19 / 7) * (23 / 22) = (15 * 19 * 23) / (13 * 7 * 22) = <<15*19*23/13*7*22>>15*19*23/13*7*22 = <<15*19*23/13*7*22>>4115/1826 = <<4115/1826>>4115/1826 = <<4115/1826>>4115/1826 ### Answer: 4115/1826
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.
LLemma 7B:
Reasoning: (15 / 29) * (19 / 7) = (15 * 19) / (29 * 7) = <<15*19/29*7>>15*19/29*7 = <<15*19/29*7>>285/193 = <<285/193>>285/193 = <<285/193>>285/193 ### Answer: 285/193
Expected answer: 285/203
Correct? No
Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 23/22 = <<23/22=11/11>>11/11 27/20 = <<27/20=3/4>>3/4 11/11 x 3/4 = <<11/11*3/4=33/44>>33/44 33/44 = <<33/44=11/22>>11/22 ### Answer: 11/22
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.
LLemma 7B:
Reasoning: (12 / 25) * (20 / 4) = (12 * 20) / (25 * 4) = <<12*20/25*4>>48/100 = <<48/100=4/10>>4/10 ### Answer: 4/10
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.
LLemma 7B:
Reasoning: 14/10 = <<14/10=7/5>>7/5 and 30/5 = <<30/5=6>>6. 14/10 x 30/5 = 7/5 x 6 = <<7/5 x 6 = 42/5>>42/5 ### Answer: 42/5
Expected answer: 42/5
Correct? Yes
Problem: After calculating the multiplication of 14/10 by 30/5, multiply that result by the fraction 13/15. Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 14/10 x 30/5 = 42/5 and 13/15 = <<13/15=13/15>>13/15 42/5 x 13/15 = <<42/5 x 13/15 = 42/5 x 13/15 = 546/75>>546/75 ### Answer: 546/75
Expected answer: 182/25
Correct? Yes
Problem: In the previous problem, suppose that instead of 14/10 we had 30/10. Now, the problem becomes: calculate the multiplication of 30/10 by 30/5. What would be the simplified fraction as an answer?
LLemma 7B:
Reasoning: 30/10 = <<30/10=3>>3 and 30/5 = <<30/5=6>>6. 30/10 x 30/5 = 3/10 x 6 = <<3/10 x 6 = 18/5>>18/5 ### Answer: 18/5
Expected answer: 18
Correct? Yes
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.
LLemma 7B:
Reasoning: 26/29 = <<26/29=0.91529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352
Expected answer: 364/29
Correct? No
Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 27/10 = <<27/10=3/5>>3/5, 9/4 = <<9/4=2 1/4>>2 1/4 (27 / 10) * (9 / 4) = <<(27/10)*(9/4)=(3/5)*(2 1/4)=(3/5)*(9/4)=(3*9)/(5*4)=27/20>>27/20 ### Answer: 27/20
Expected answer: 243/40
Correct? No
Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 24/11 = <<24/11=2>>2, 27/26 = <<27/26=1>>1. (24 / 11) * (27 / 26) = <<2*1=2>>2. ### Answer: 2
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.
LLemma 7B:
Reasoning: 26/9 = <<26/9=2.888888888888889>>2.888888888888889 17/13 = <<17/13=1.230769230769231>>1.230769230769231 2.888888888888889 x 1.230769230769231 = <<2.888888888888889 x 1.230769230769231=3.539130434782609>>3.539130434782609 ### Answer: 3.539130434782609
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.
LLemma 7B:
Reasoning: 28/16 = <<28/16=1.5>>1.5 27/24 = <<27/24=1.0416666666666667>>1.0416666666666667 (28 / 16) / (27 / 24) = <<1.5/1.0416666666666667=1.443067796610169>>1.443067796610169 ### Answer: 1.443067796610169
Expected answer: 14/9
Correct? No
Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 15/3 = <<15/3=5>>5, 19/26 = <<19/26=3/13>>3/13 (5 * 3/13) = <<5*3/13=15/13>>15/13 ### Answer: 15/13
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?
LLemma 7B:
Reasoning: 30/4 = <<30/4=7.5>>7.5 recipes. They will require 7.5*19/28 = <<7.5*19/28=10.5>>10.5 of the ingredient. ### Answer: 10.5
Expected answer: 285/56
Correct? No
Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.
LLemma 7B:
Reasoning: 5/2 = <<5/2=2.5>>2.5 2.5 / (26/15) = <<2.5/26*15/1>><<2.5/26*15/1=1.25/26>>1.25/26 ### Answer: 1.25/26
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.
LLemma 7B:
Reasoning: 9/3 = 3, 27/28 = 3/4. (9/3) * (27/28) = 3 * (3/4) = 9/4 = <<9/4=2 1/4>>2 1/4 ### Answer: 2 1/4
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))
LLemma 7B:
Reasoning: 15/13 = <<15/13=1.1538461538461538>> 24/24 = <<24/24=1>>1 1.1538461538461538 * 1 = <<1.1538461538461538*1=1.1538461538461538>> ### Answer: 1.1538461538461538
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.
LLemma 7B:
Reasoning: 1.1538461538461538 * 22/7 = <<1.1538461538461538*22/7=3.142857142857143>> ### Answer: 3.142857142857143
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.
LLemma 7B:
Reasoning: 15/2 = <<15/2=7.5>> 24/24 = <<24/24=1>>1 7.5 * 1 = <<7.5*1=7.5>> ### Answer: 7.5
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.
LLemma 7B:
Reasoning: 9/7 = <<9/7=1 2/7>>1 2/7 and 25/30 = <<25/30=5/6>>5/6 (9 / 7) * (25 / 30) = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 5/6>><<1 2/7 * 5/6>> = <<1 2/7 * 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.
LLemma 7B:
Reasoning: 9/8 = <<9/8=11/8>>11/8 20/18 = <<20/18=10/9>>10/9 (9 / 8) / (20 / 18) = <<(9/8)/(20/18)=(11/8)/(10/9)=(11*9)/(8*10)=(99)/(80)>>(99)/(80) ### Answer: (99)/(80)
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.
LLemma 7B:
Reasoning: (30 / 6) / (13 / 9) = <<30/6/13/9>><<30/6/13/9=30/6*9/13>><<30/6*9/13=5*9/13>><<5*9/13=45/13>><<45/13=3>>3 ### Answer: 3
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?
LLemma 7B:
Reasoning: 30/18 = <<30/18=1.6666666666666667>>1.6666666666666667 1.6666666666666667*18/6 = <<1.6666666666666667*18/6=6>>6 ### Answer: 6
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.
LLemma 7B:
Reasoning: 20/2 = <<20/2=10>>10, 2/18 = <<2/18=1/9>>1/9 ((20 / 2) * (2 / 18)) = <<(20/2)*(2/18)=10*1/9>>10/9 ### Answer: 10/9
Expected answer: 10/9
Correct? Yes
Problem: After calculating the result of ((20 / 2) * (2 / 18)), now find the answer for ((27 / 4) * that result). Write your final answer as a simplified fraction.
LLemma 7B:
Reasoning: ((20 / 2) * (2 / 18)) = <<(20/2)*(2/18)=10*1/9>>10/9 ((27 / 4) * (10 / 9)) = <<(27/4)*(10/9)=27*10/4*9>>270/36 ### Answer: 270/36
Expected answer: 15/2
Correct? Yes
Problem: After calculating the result of ((20 / 2) * (2 / 18)), reconsider your calculation, but this time using (15 / 18) instead of (2 / 18). Thus, find the answer for ((20 / 2) * (15 / 18)). Write your final answer as a simplified fraction.
LLemma 7B:
Reasoning: 20/2 = <<20/2=10>>10, 15/18 = <<15/18=5/9>>5/9 ((20 / 2) * (15 / 18)) = <<(20/2)*(15/18)=10*5/9>>50/18 ### Answer: 50/18
Expected answer: 25/3
Correct? No
Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))
LLemma 7B:
Reasoning: 11/9 = <<11/9=1.2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222
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.
LLemma 7B:
Reasoning: (30 / 7) * (16 / 19) = <<30/7*16/19>> = <<(30*16)/(7*19)>> = <<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.
LLemma 7B:
Reasoning: (480/133) * (22/7) = <<480/133*22/7>> = <<(480*22)/(133*7)>> = <<10560/951>> ### Answer: 10560/951
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.
LLemma 7B:
Reasoning: (21 / 7) * (16 / 19) = <<21/7*16/19>> = <<(21*16)/(7*19)>> = <<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.
LLemma 7B:
Reasoning: 25/22 x 20/3 = <<(25/22)*(20/3)>> = <<(25*20)/(22*3)>> = <<(500)/(66)>> = <<500/66=7.5>>7.5 ### Answer: 7.5
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))
LLemma 7B:
Reasoning: 29/2 = <<29/2=14.5>>14.5 23/19 = <<23/19=1.2>>1.2 ((29 / 2) / (23 / 19)) = <<14.5/1.2=12.25>>12.25 ### Answer: 12.25
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.
LLemma 7B:
Reasoning: 5/3 = <<5/3=1.666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
Expected answer: 45/13
Correct? No
Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.
LLemma 7B:
Reasoning: (29 / 29) * (1 / 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?
LLemma 7B:
Reasoning: (27 / 27) * (1 / 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?
LLemma 7B:
Reasoning: (29 / 6) * (1 / 1) = 4.8333333333333335 * 1 = 4.8333333333333335 ### Answer: 4.8333333333333335
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.
LLemma 7B:
Reasoning: 11/19 x 22/7 = <<11*22/19*7>>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?
LLemma 7B:
Reasoning: 25/4 x 242/133 = <<25*242/4*133>>1505/532 ### Answer: 1505/532
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.
LLemma 7B:
Reasoning: 11/19 x 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.
LLemma 7B:
Reasoning: 21/30 = <<21/30=7/10>>7/10 19/5 = <<19/5=3.8>>3.8 7/10 x 3.8 = <<7/10*3.8=2.56>>2.56 ### Answer: 2.56
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.
LLemma 7B:
Reasoning: 11/15 = <<11/15=0.7333333333333333>>0.7333333333333333 and 23/8 = <<23/8=2.875>>2.875. 11/15 x 23/8 = <<11/15*23/8=0.7333333333333333*2.875=2.111111111111111>>2.111111111111111 ### Answer: 2.111111111111111
Expected answer: 253/120
Correct? No
Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.
LLemma 7B:
Reasoning: 29/16 = <<29/16=1 13/16>>1 13/16 21/27 = <<21/27=1 4/27>>1 4/27 (29 / 16) * (21 / 27) = <<(29/16)*(21/27)>>(1 13/16)*(1 4/27) = <<(1 13/16)*(1 4/27)>>(1 13/16)*(1 4/27) = <<(1 13/16)*(1 4/27)>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 13/16 + 4/27>>1 13/16 + 4/27 = <<1 1
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.
LLemma 7B:
Reasoning: 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/27=10/3>>10/3. 28/1 = <<28/1=28>>28 and 30/27 = <<30/2
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.
LLemma 7B:
Reasoning: 25/25 = 1, so 25/25 * 20/7 = 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.
LLemma 7B:
Reasoning: 20/7 * 20/7 = 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.
LLemma 7B:
Reasoning: 25/25 = 1, so 25/25 * 11/7 = 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.
LLemma 7B:
Reasoning: 5 x 16/27 = <<5*16/27=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.
LLemma 7B:
Reasoning: 30 x 16/27 = <<30*16/27=480/27>>480/27 ### Answer: 480/27
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.
LLemma 7B:
Reasoning: 27/3 = <<27/3=9>>9, 12/12 = <<12/12=1>>1. ((27 / 3) / (12 / 12)) = <<(27/3)/(12/12)=9/1=9>>9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: You previously calculated the result of ((27 / 3) / (12 / 12)) and labeled that answer as 's'. Now, compute the result of multiplying your answer 's' by the fraction (21/17) and report the result as a simplified fraction. This new result will be labeled as 'b'.
LLemma 7B:
Reasoning: s = <<27/3=9>>9, 21/17 = <<21/17=1>>1. b = <<s*(21/17)=9*(21/17)=9*1=9>>9 ### Answer: 9
Expected answer: 189/17
Correct? No
Problem: Earlier, you calculated the result of ((27 / 3) / (12 / 12)) and labeled that answer as 's'. Consider the same scenario, but this time, instead of having 27 items, you only have 24. Calculate the result of (24 / (12 / 12)) and report the answer as a simplified fraction. What effect does this change have on the answer 's'?
LLemma 7B:
Reasoning: 24/12 = <<24/12=2>>2. (24 / (12 / 12)) = <<24/(12/12)=24/1=24>>24 ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: Calculate the result of the following operation: (15 / 16) * (29 / 2). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 15/16 = <<15/16=0.9375>>0.9375, 29/2 = <<29/2=14.5>>14.5 (15 / 16) * (29 / 2) = <<15/16*29/2=0.9375*14.5=13.4375>>13.4375 ### Answer: 13.4375
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.
LLemma 7B:
Reasoning: 6/2 = <<6/2=3>>3 13/9 = <<13/9=1.444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444
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.
LLemma 7B:
Reasoning: 7/1 divided by 15/9 = (7/1) / (15/9) = (7/1) * (9/15) = (7*9)/(1*15) = 63/15 = <<63/15=4 1/5>>4 1/5 ### Answer: 4 1/5
Expected answer: 21/5
Correct? Yes
Problem: Following up on the last question, once you have found the result of dividing seven wholes by 15/9, multiply your answer by the fraction 10/5. What do you get as a simplified fraction?
LLemma 7B:
Reasoning: 4 1/5 * 10/5 = (4*10)/(5*5) = 40/25 = <<40/25=1 15/25>>1 15/25 = <<1 15/25=1 3/5>>1 3/5 ### Answer: 1 3/5
Expected answer: 42/5
Correct? No
Problem: Previously, you evaluated the result of dividing seven wholes, or 7/1, by 15/9. Now, consider what would happen if instead of seven whole, there were twenty wholes, or 20/1. What would be the result if you divide twenty wholes by 15/9? Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 20/1 divided by 15/9 = (20/1) / (15/9) = (20/1) * (9/15) = (20*9)/(1*15) = 180/15 = <<180/15=12 0/1>>12 0/1 ### Answer: 12 0/1
Expected answer: 12
Correct? Yes
Problem: What is the result when you multiply (23/10) by (9/1)?
LLemma 7B:
Reasoning: (23/10) is the same as 2.3. (9/1) is the same as 9. 2.3 x 9 = <<2.3*9=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?
LLemma 7B:
Reasoning: (23/10) is the same as 2.3. (9/1) is the same as 9. (1/16) is the same as 0.0625. 2.3 x 9 x 0.0625 = <<2.3*9*0.0625=1.3125>>1.3125 ### Answer: 1.3125
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?
LLemma 7B:
Reasoning: (9/6) is the same as 1.5. 2.3 x 1.5 = <<2.3*1.5=3.45>>3.45 ### Answer: 3.45
Expected answer: 69/20
Correct? No
Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 18/4 = <<18/4=4.5>>4.5 10/11 = <<10/11=0.9090909090909091>>0.9090909090909091 4.5 * 0.9090909090909091 = <<4.5*0.9090909090909091=4.054054054054054>>4.054054054054054 ### Answer: 4.054054054054054
Expected answer: 45/11
Correct? No
Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?
LLemma 7B:
Reasoning: 24/23 x 23/3 = 24/3 = <<24/3=8>>8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Continuing from the previous problem, if the result is then multiplied by the fraction 30/21, what is the final numerical outcome?
LLemma 7B:
Reasoning: 8 x 30/21 = 8 x 30/21 = <<8 x 30/21=120/21=5.769230769>>5.769230769 ### Answer: 5.769230769
Expected answer: 80/7
Correct? No
Problem: Continuing from the previous problem, if we replace the original fraction of 23/3 with 18/3 and keep the 24/23 fraction the same, what now happens to the numerical result when we perform the multiplication?
LLemma 7B:
Reasoning: 24/23 x 18/3 = 24/3 = <<24/3=8>>8 ### Answer: 8
Expected answer: 144/23
Correct? No
Problem: Determine the solution for the following division of fractions: (20 / 13) / (17 / 16) and write your answer as a simplified fraction.
LLemma 7B:
Reasoning: (20 / 13) / (17 / 16) = <<20/13>> / <<17/16>> = <<20*16>> / <<13*17>> = <<320>> / <<221>> ### Answer: 320/221
Expected answer: 320/221
Correct? Yes
Problem: After finding the solution for the division of fractions (20 / 13) / (17 / 16), now multiply that result by the fraction (20 / 26). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: (20 / 13) / (17 / 16) * (20 / 26) = <<20/13>> / <<17/16>> * <<20/26>> = <<20*16>> / <<13*17>> * <<20/26>> = <<320>> / <<221>> * <<20/26>> = <<320*20>> / <<221*26>> = <<6400>> / <<5766>> ### Answer: 6400/5766
Expected answer: 3200/2873
Correct? No
Problem: Calculate the result of the following problem: ((5 divided by 5) multiplied by (4 divided by 1))
LLemma 7B:
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.
LLemma 7B:
30/23 * 19/24 = <<30/23 * 19/24>> = <<(30 * 19) / (23 * 24)>> = <<(30 * 19) / (23 * 24)>> = <<(570) / (522)>> = <<570 / 522>> = <<1.15>> ### Answer: 1.15
Expected answer: 95/92
Correct? No
Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 23/26 = <<23/26=1/2>>1/2 16/1 = <<16/1=16>>16 (23/26) * (16/1) = <<(23/26)*(16/1)=(1/2)*(16/1)=16/2=8>>8 ### Answer: 8
Expected answer: 184/13
Correct? No
Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 21/1 = <<21/1=21>>21, 26/20 = <<26/20=13/10>>13/10 ((21 / 1) / (26 / 20)) = <<21/1/26/20=21*20/1*13=420/13=32 1/13>>32 1/13 ### Answer: 32 1/13
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.
LLemma 7B:
Reasoning: 24/19 x 21/19 = <<24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=24*21/361=24*21/19*19=2
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.
LLemma 7B:
Reasoning: Jim needs to multiply the amount of sugar and flour he needs for a larger cake. ((12 / 2) * (17 / 14)) = <<(12/2)*(17/14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*7)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(14)>> ((12 / 2) * (17 / 14)) = <<(12*17)/(2*
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.
LLemma 7B:
Reasoning: 21/16 = <<21/16=1.25>>1.25, 27/23 = <<27/23=1.1538461538461538>>1.1538461538461538 ((21 / 16) / (27 / 23)) = <<(21/16)/(27/23)=1.25/1.1538461538461538>>1.25/1.1538461538461538 = <<1.25/1.1538461538461538=1.0892857142857142>>1.0892857142857142 ### Answer: 1.0892857142857142
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)
LLemma 7B:
Reasoning: 11/20 = <<11/20=3/5>>3/5 24/12 = <<24/12=2>>2 (11/20) * (24/12) = <<3/5*2=6/5>>6/5 ### Answer: 6/5
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.
LLemma 7B:
Reasoning: 6/19 = <<6/19=2/19>>2/19 28/2 = <<28/2=14>>14 (2/19) * (14) = <<2/19*14=28/19>>28/19 (6/19) * (28/2) = <<6/19*28/2=28/19>>28/19 ### Answer: 28/19
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.
LLemma 7B:
Reasoning: (12 / 14) * (28 / 5) = <<12/14*28/5>><<12*28/14*5>><<12*28/70>><<2*28/10>><<28/5>> ### Answer: 28/5
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.
LLemma 7B:
Reasoning: 19/3 = <<19/3=6.333333333333333>>6.333333333333333 8/15 = <<8/15=0.5333333333333333>>0.5333333333333333 6.333333333333333 * 0.5333333333333333 = <<6.333333333333333*0.5333333333333333=3.333333333333333>>3.333333333333333 ### Answer: 3.333333333333333
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.
LLemma 7B:
Reasoning: 15/3 = <<15/3=5>>5, 7/25 = <<7/25=0.28>>0.28 ((15 / 3) * (7 / 25)) = <<(15/3)*(7/25)=(5*0.28)=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.
LLemma 7B:
Reasoning: 28/16 = <<28/16=1.75>>1.75 ((15 / 3) * (7 / 25)) * (28 / 16) = <<(15/3)*(7/25)*(28/16)=(5*0.28)*1.75=(1.4*1.75)=2.52>>2.52 ### Answer: 2.52
Expected answer: 49/20
Correct? No
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?
LLemma 7B:
Reasoning: 13/3 = <<13/3=4.333333333333333>>4.333333333333333, 7/25 = <<7/25=0.28>>0.28 ((13 / 3) * (7 / 25)) = <<(13/3)*(7/25)=(4.333333333333333*0.28)=1.211111111111111>>1.211111111111111 ### Answer: 1.211111111111111
Expected answer: 91/75
Correct? No
Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.
LLemma 7B:
Reasoning: 20/10 = <<20/10=2>>2, 10/1 = <<10/1=10>>10. (20 / 10) * (10 / 1) = <<20/10*10/1=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.
LLemma 7B:
Reasoning: x = <<20/10*10/1=2*10=20>>20, (19 / 15) = <<19/15=19/5>>19/5. z = x * (19 / 15) = <<20/10*10/1*19/5=2*10*19/5=20*19/5=380/5=76/1>>76/1. ### Answer: 76/1
Expected answer: 76/3
Correct? No
Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 27/18 = <<27/18=1/2>>1/2 and 19/8 = <<19/8=19/8>>19/8. (1/2) * (19/8) = <<(1/2)*(19/8)=(19/16)>>19/16 ### Answer: 19/16
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.
LLemma 7B:
Reasoning: 29/5 = <<29/5=5.8>>5.8 and 13/24 = <<13/24=0.5416666666666667>>0.5416666666666667. 5.8 x 0.5416666666666667 = <<5.8*0.5416666666666667=2.999999999999999>>2.999999999999999 ### Answer: 2.999999999999999
Expected answer: 377/120
Correct? No
Problem: Calculate the value of the expression ((29 / 17) / (27 / 22)). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 29/17 = <<29/17=1.6153846153846154>> 27/22 = <<27/22=1.2727272727272727>> (29 / 17) / (27 / 22) = <<(29/17)/(27/22)=1.5>> ### Answer: 1.5
Expected answer: 638/459
Correct? No
Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?
LLemma 7B:
27/6 = <<27/6=4.5>>4.5 25/5 = <<25/5=5>>5 4.5 * 5 = <<4.5*5=22.5>>22.5 ### Answer: 22.5
Expected answer: 45/2
Correct? Yes
Problem: If the result of (27 / 6) * (25 / 5) was multiplied by (20 / 27), what would be the outcome?
LLemma 7B:
27/6 = <<27/6=4.5>>4.5 25/5 = <<25/5=5>>5 4.5 * 5 = <<4.5*5=22.5>>22.5 20/27 = <<20/27=0.740740740740741>>0.740740740740741 22.5 * 0.740740740740741 = <<22.5*0.740740740740741=16.875>>16.875 ### Answer: 16.875
Expected answer: 50/3
Correct? No
Problem: If instead of the initial calculation with (27 / 6), we used (11 / 6) and repeated the multiplication with (25 / 5), what would the new result be?
LLemma 7B:
11/6 = <<11/6=1.8333333333333333>>1.8333333333333333 25/5 = <<25/5=5>>5 1.8333333333333333 * 5 = <<1.8333333333333333*5=9.166666666666667>>9.166666666666667 ### Answer: 9.166666666666667
Expected answer: 55/6
Correct? No
Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).
LLemma 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.
LLemma 7B:
Reasoning: 13/2 * e = <<13/2 * 13/6 = 13/4>>13/4 ### Answer: 13/4
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.
LLemma 7B:
Reasoning: 11/1 * 1/6 = <<11/1 * 1/6 = 11/6>>11/6 ### 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.
LLemma 7B:
Reasoning: 25/20 = <<25/20=5/4>>5/4 and 11/6 = <<11/6=11/6>>11/6 5/4 x 11/6 = <<5/4*11/6=55/24>>55/24 ### Answer: 55/24
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.
LLemma 7B:
Reasoning: 25/20 = <<25/20=5/4>>5/4 and 11/6 = <<11/6=11/6>>11/6 5/4 x 11/6 = <<5/4*11/6=55/24>>55/24 55/24 x 20/26 = <<55/24*20/26=550/612>>550/612 ### Answer: 550/612
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.
LLemma 7B:
Reasoning: 25/17 = <<25/17=25/17>>25/17 and 11/6 = <<11/6=11/6>>11/6 25/17 x 11/6 = <<25/17*11/6=275/102>>275/102 ### Answer: 275/102
Expected answer: 275/102
Correct? Yes
Problem: Determine the value of (7 / 2) / (25 / 10). Please provide your answer as a simplified fraction.
LLemma 7B:
Reasoning: (7 / 2) / (25 / 10) = (7 / 2) * (10 / 25) = (7 * 10) / (2 * 25) = 70 / 50 = 70 / 50 = 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.
LLemma 7B:
Reasoning: ((7 / 2) / (25 / 10)) * (5 / 3) = (7 / 2) / (25 / 10) * (5 / 3) = (7 / 2) * (10 / 25) * (5 / 3) = (7 * 10 * 5) / (2 * 25 * 3) = 70 / 150 = 70 / 150 = 7 / 15 ### Answer: 7/15
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.
LLemma 7B:
Reasoning: 15/16 x 29/27 = <<15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x 29/27=15/16 x
Expected answer: 145/144
Correct? No
Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.
LLemma 7B:
Reasoning: 30/25 = <<30/25=1.2>>1.2, 25/10 = <<25/10=2.5>>2.5 ((30 / 25) * (25 / 10)) = <<(30/25)*(25/10)=1.2*2.5=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.
LLemma 7B:
Reasoning: 5/9 = <<5/9=0.5555555555555555>>0.5555555555555555 ((30 / 25) * (25 / 10)) * (5 / 9) = <<(30/25)*(25/10)*(5/9)=3*2.5*0.5555555555555555=3.8333333333333333>>3.8333333333333333 ### Answer: 3.8333333333333333
Expected answer: 5/3
Correct? No
Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.
LLemma 7B:
Reasoning: 27/10 x 27/3 = <<27/10 x 27/3>> = <<(27 x 27)/(10 x 3)>> = <<729/30>> ### Answer: 729/30
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.
LLemma 7B:
Reasoning: 27/10 x 27/3 x 9/20 = <<27/10 x 27/3 x 9/20>> = <<(27 x 27 x 9)/(10 x 3 x 20)>> = <<(27 x 27 x 9)/(10 x 3 x 20)>> = <<(729 x 9)/(30 x 20)>> = <<(6561/600)>> ### Answer: 6561/600
Expected answer: 2187/200
Correct? Yes
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.
LLemma 7B:
Reasoning: 27/10 x 27/21 = <<27/10 x 27/21>> = <<(27 x 27)/(10 x 21)>> = <<729/210>> ### Answer: 729/210
Expected answer: 243/70
Correct? Yes
Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: (10 / 8) * (30 / 26) = (10 * 30) / (8 * 26) = <<10*30/8*26>>300 / 208 = <<300/208=15/14>>15/14 ### Answer: 15/14
Expected answer: 75/52
Correct? No
Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 20/22 = <<20/22=10/11>>10/11 14/11 = <<14/11=2/1>>2/1 (20/22) * (14/11) = <<(20/22)*(14/11)=(10/11)*(2/1)=20/11>>20/11 ### Answer: 20/11
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?
LLemma 7B:
Reasoning: 25/8 = <<25/8=3.125>>3.125 3/4 = <<3/4=0.75>>0.75 (25/8)*(3/4) = <<25/8*3/4=0.6875>>0.6875 The result signifies sharing something in portions. ### Answer: 0.6875
Expected answer: 75/32
Correct? No
Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).
LLemma 7B:
Reasoning: 29/1 = <<29/1=29>>29, 8/15 = <<8/15=0.5333333333333333>>0.5333333333333333, 29*0.5333333333333333 = <<29*0.5333333333333333=14.833333333333333>>14.833333333333333 ### Answer: 14.833333333333333
Expected answer: 232/15
Correct? No
Problem: What is the result when you multiply (29/17) by (26/15)?
LLemma 7B:
Reasoning: 29/17 = <<29/17=1.647058823529411764705882352941>> 26/15 = <<26/15=1.7333333333333333333333333333333>> 1.647058823529411764705882352941 * 1.7333333333333333333333333333333 = <<1.647058823529411764705882352941*1.7333333333333333333333333333333=2.9132291322913229132291322913229>> ### Answer: 2.9132291322913229132291322913229
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.
LLemma 7B:
Reasoning: 25/5 = <<25/5=5>>5, 16/8 = <<16/8=2>>2. ((25 / 5) * (16 / 8)) = <<(25/5)*(16/8)>>(5*2) = <<5*2>>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?
LLemma 7B:
Reasoning: 25/5 = <<25/5=5>>5, 19/8 = <<19/8=2.375>>2.375. ((25 / 5) * (19 / 8)) = <<(25/5)*(19/8)>>(5*2.375) = <<5*2.375>>11.875. ### Answer: 11.875
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.
LLemma 7B:
Reasoning: 23/4 = <<23/4=5.75>>5.75 and 10/12 = <<10/12=0.8333333333333334>>0.8333333333333334. 5.75 * 0.8333333333333334 = <<5.75*0.8333333333333334=4.75>>4.75 ### Answer: 4.75
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.
LLemma 7B:
Reasoning: 21/26 = <<21/26=3/4>>3/4 20/9 = <<20/9=2/3>>2/3 (21/26) * (20/9) = <<3/4*2/3=1/2>>1/2 ### Answer: 1/2
Expected answer: 70/39
Correct? No
Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 17/13 = <<17/13=1.1538461538461538>> 15/6 = <<15/6=2.5>> 1.1538461538461538 * 2.5 = <<2.8392857142857144>> ### Answer: 2.8392857142857144
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.
LLemma 7B:
Reasoning: 25/18 = <<25/18=5/3>>5/3 17/6 = <<17/6=17/6>>17/6 (25 / 18) * (17 / 6) = <<(25/18)*(17/6)=(5/3)*(17/6)=(5*17)/(3*6)=85/18>>85/18 ### Answer: 85/18
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.
LLemma 7B:
Reasoning: 9/1 = <<9/1=9>>9 9 x 2/17 = <<9*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.
LLemma 7B:
Reasoning: t = <<9*2/17=18/17>>18/17 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.
LLemma 7B:
Reasoning: 12/1 = <<12/1=12>>12 12 x 2/17 = <<12*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.
LLemma 7B:
Reasoning: 27/14 = <<27/14=1.5>>1.5 and 19/14 = <<19/14=1.3>>1.3. (27 / 14) * (19 / 14) = <<1.5*1.3=2.025>>2.025 ### Answer: 2.025
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.
LLemma 7B:
Reasoning: 16/5 = <<16/5=3.2>>3.2, 5/15 = <<5/15=0.3333333333333333>>0.3333333333333333, 3.2 * 0.3333333333333333 = <<3.2*0.3333333333333333=1.0666666666666666>>1.0666666666666666 ### Answer: 1.0666666666666666
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.
LLemma 7B:
Reasoning: 1.0666666666666666 * 30/24 = <<1.0666666666666666*30/24=1.52>>1.52 ### Answer: 1.52
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.
LLemma 7B:
Reasoning: 16/5 = <<16/5=3.2>>3.2, 5/7 = <<5/7=0.7142857142857143>>0.7142857142857143, 3.2 * 0.7142857142857143 = <<3.2*0.7142857142857143=2.299206349206349>>2.299206349206349 ### Answer: 2.299206349206349
Expected answer: 16/7
Correct? No
Problem: Calculate the result of the following fraction multiplication: (8 / 3) * (18 / 21). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: (8 / 3) * (18 / 21) = (8 * 18) / (3 * 21) = <<8*18/3*21=12/7>>12/7 ### Answer: 12/7
Expected answer: 16/7
Correct? No
Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))
LLemma 7B:
Reasoning: 14/6 = <<14/6=7/3>>7/3 22/16 = <<22/16=11/8>>11/8 (7/3) / (11/8) = <<(7/3) / (11/8)=(7/3) * (8/11)=(56/33)=18/11>>18/11 ### Answer: 18/11
Expected answer: 56/33
Correct? No
Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)
LLemma 7B:
(16 / 3) * (25 / 26) = <<16*25>>/<<3*26>> = <<400>>/<<78>> = <<400/78>> = <<5 14/39>> ### Answer: 5 14/39
Expected answer: 200/39
Correct? No
Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)
LLemma 7B:
Reasoning: 16/16 = 1, so (16/16) * (26/22) = 1 * (26/22) = (26/22) (26/22) = (2 * 13)/(2 * 11) = 13/11 ### Answer: 13/11
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.
LLemma 7B:
Reasoning: (16/16) * (26/22) = (26/22) (26/22) * (26/22) = (26 * 26)/(22 * 22) = 676/484 ### Answer: 676/484
Expected answer: 169/121
Correct? Yes
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.
LLemma 7B:
Reasoning: 16/12 = 4/3, so (16/12) * (26/22) = (4/3) * (26/22) = (4 * 26)/(3 * 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.
LLemma 7B:
Reasoning: (17 / 5) * (5 / 14) = <<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?
LLemma 7B:
Reasoning: (17 / 5) * (5 / 14) * (21 / 25) = <<17/5*5/14*21/25>>17/25 ### 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?
LLemma 7B:
Reasoning: (17 / 5) * (5 / 12) = <<17/5*5/12>>17/12 ### 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.
LLemma 7B:
Reasoning: (16/6) = <<16/6=2.6666666666666665>>2.6666666666666665 (29/27) = <<29/27=1.0740740740740741>>1.0740740740740741 (16/6) * (29/27) = <<2.6666666666666665*1.0740740740740741>>2.911111111111111 (16/6) * (29/27) = <<2.911111111111111>>2.911111111111111 ### Answer: 2.911111111111111
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.
LLemma 7B:
Reasoning: 16/10 gallons of petrol every mile means that the car consumes 16/10 * 13/17 = <<16/10 * 13/17 = 224/170>>224/170 gallons of petrol every mile. The car will have consumed 224/170 * 13/17 = <<224/170 * 13/17 = 224/17>>224/17 gallons of petrol when you finish the drive. ### Answer: 224/17
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)
LLemma 7B:
Reasoning: 29/10 = <<29/10=2.9>>2.9, 18/16 = <<18/16=0.5>>0.5 (29 / 10) / (18 / 16) = <<2.9/0.5=5.8>>5.8 ### Answer: 5.8
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.
LLemma 7B:
Reasoning: 15/12 = <<15/12=1.25>>1.25 and 27/3 = <<27/3=9>>9. (15/12) x (27/3) = <<1.25*9=11.25>>11.25 ### Answer: 11.25
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.
LLemma 7B:
Reasoning: 11.25 x (22/14) = <<11.25*22/14=18.5>>18.5 ### Answer: 18.5
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?
LLemma 7B:
Reasoning: 15/12 = <<15/12=1.25>>1.25 and 27/5 = <<27/5=5.4>>5.4. (15/12) x (27/5) = <<1.25*5.4=6.75>>6.75 ### Answer: 6.75
Expected answer: 27/4
Correct? No
Problem: Calculate the answer to the following math problem: (7 / 7) * (12 / 12)
LLemma 7B:
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?
LLemma 7B:
1 * 27/15 = <<1*27/15=1.8>>1.8 ### 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)?
LLemma 7B:
2 ### Answer: 2
Expected answer: 4/3
Correct? No
Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.
LLemma 7B:
Reasoning: 28/6 = <<28/6=4>>4, 16/24 = <<16/24=1/1.5>>1/1.5 ((28 / 6) * (16 / 24)) = <<(28/6)*(16/24)>>(4 * 1/1.5) = <<4*1/1.5>>4/1.5 = <<4/1.5=2.6666666666666665>>2.6666666666666665 ### Answer: 2.6666666666666665
Expected answer: 28/9
Correct? No