LLemma 34B 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 34B:
Reasoning: (29/2) * (19/28) = <<(29/2)*(19/28)=(29*19)/(2*28)=(551)/(56)>>(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.
LLemma 34B:
Reasoning: (551)/(56) * (8/28) = <<(551)/(56)*(8/28)=(551*8)/(56*28)=(4408)/(1568)>>(4408)/(1568) ### Answer: (4408)/(1568)
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.
LLemma 34B:
Reasoning: (29/2) * (19/14) = <<(29/2)*(19/14)=(29*19)/(2*14)=(551)/(28)>>(551)/(28) ### Answer: (551)/(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.
LLemma 34B:
Reasoning: 7*27/12 = <<7*27/12=189/12>>189/12 ### Answer: 189/12
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 34B:
Reasoning: 7*26/12 = <<7*26/12=182/12>>182/12 ### Answer: 182/12
Expected answer: 91/6
Correct? Yes
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 34B:
Reasoning: Susan will use 29/27 = <<29/27=1.0740740740740741>>1.0740740740740741 parts of water. ### Answer: 1.0740740740740741
Expected answer: 29/27
Correct? Yes
Problem: Following on from the last question: If Susan made 23/4 batches of her recipe, how would the amount of water she used change? Calculate this using fraction multiplication: ((23 / 4) * ((30 / 30) * (29 / 27))).
LLemma 34B:
Reasoning: Susan will use 23/4 * 29/27 = <<23/4*29/27=1.0740740740740741>>1.0740740740740741 parts of water. ### Answer: 1.0740740740740741
Expected answer: 667/108
Correct? No
Problem: Following on from the last question: What happens if Susan decides to use 30 parts of flour out of an available 12, while still keeping the water proportion the same? Calculate this using fraction multiplication: ((30 / 12) * (29 / 27)).
LLemma 34B:
Reasoning: Susan will use 29/27 = <<29/27=1.0740740740740741>>1.0740740740740741 parts of water. ### Answer: 1.0740740740740741
Expected answer: 145/54
Correct? No
Problem: Calculate the result of the following operation: ((24 / 22) * (24 / 17)). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((24 / 22) * (24 / 17)) = (1 * 1) = 1 ### Answer: 1
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 34B:
Reasoning: 25/4 = <<25/4=6.25>>6.25 16/6 = <<16/6=2.6666666666666665>>2.6666666666666665 6.25/2.6666666666666665 = <<6.25/2.6666666666666665=2.3529411764705882>>2.3529411764705882 ### Answer: 2.3529411764705882
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 34B:
Reasoning: 3/7 * 26/6 = <<3/7*26/6=13/7>>13/7 ### Answer: 13/7
Expected answer: 13/7
Correct? Yes
Problem: In the previous question, you found the result of (3 / 7) * (26 / 6). Now, take that result and multiply it by the fraction 23/2. What's the result of this calculation, expressed as a simplified fraction?
LLemma 34B:
Reasoning: 13/7 * 23/2 = <<13/7*23/2=299/14>>299/14 ### Answer: 299/14
Expected answer: 299/14
Correct? Yes
Problem: In the previous problem, you multiplied the fraction 3/7 by the fraction 26/6. Now, let's change the fraction a bit. Instead of 3/7, use 7/7 (which is actually 1). Multiply this new fraction 7/7 by the same fraction 26/6. What is the result of this new calculation, expressed as a simplified fraction?
LLemma 34B:
Reasoning: 7/7 * 26/6 = <<7/7*26/6=26/6>>26/6 ### Answer: 26/6
Expected answer: 13/3
Correct? Yes
Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.
LLemma 34B:
Reasoning: (17 / 10) * (28 / 10) = <<(17/10)*(28/10)=(17*28)/(10*10)=456/100=4.56>>4.56 ### Answer: 4.56
Expected answer: 119/25
Correct? No
Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))
LLemma 34B:
Reasoning: ((29 / 14) * (23 / 6)) = <<(29/14)*(23/6)=(29*23)/(14*6)=627/84>>627/84 ### Answer: 627/84
Expected answer: 667/84
Correct? No
Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.
LLemma 34B:
Reasoning: ((18 / 19) * (19 / 6)) = (18 / 6) = <<18/6=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 34B:
Reasoning: ((18 / 19) * (19 / 6)) = (18 / 6) = <<18/6=3>>3 ((18 / 19) * (19 / 6)) * ((18 / 19) * (19 / 6)) = (18 / 6) * (18 / 6) = <<(18/6)*(18/6)=(18*18)/(6*6)=324/36=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 34B:
Reasoning: ((9 / 19) * (19 / 6)) = (9 / 6) = <<9/6=3/2>>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.
LLemma 34B:
Reasoning: 19/12 * 20/6 = <<19/12*20/6=190/72>>190/72 = <<190/72=25/4>>25/4 ### Answer: 25/4
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 34B:
Reasoning: The cargo ship carries 28/21 = <<28/21=14/7>>14/7 of its capacity in the morning, and 22/4 = <<22/4=11/2>>11/2 of its capacity in the afternoon. The total fractional representation of these two types of cargo hauled in one day is ((28 / 21) * (22 / 4)) = ((14 / 7) * (11 / 2)) = <<(14/7)*(11/2)=154/14>>154/14. ### Answer: 154/14
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 34B:
Reasoning: (16 / 4) / (24 / 21) = (4) / (24 / 21) = (4) / (12 / 21) = (4) / (4 / 7) = (4) / (1 / 7) = 4 * (7 / 1) = 28 ### Answer: 28
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 34B:
Reasoning: 5/27 * 15/2 = <<5/27*15/2=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.
LLemma 34B:
Reasoning: (15 / 13) * (19 / 7) = <<15/13*19/7>>190/91 ### Answer: 190/91
Expected answer: 285/91
Correct? No
Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.
LLemma 34B:
Reasoning: 23/22 * 27/20 = <<23/22*27/20=23*27/22*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.
LLemma 34B:
Reasoning: (12 / 25) * (20 / 4) = (12 * 20) / (25 * 4) = <<12*20=240>>240 / <<25*4=100>>100 = <<240/100=2.4>>2.4 ### Answer: 2.4
Expected answer: 12/5
Correct? Yes
Problem: After finding the result of (12 / 25) * (20 / 4), now multiply this result by (17 / 17). Report your final answer as a simplified fraction.
LLemma 34B:
Reasoning: (12 / 25) * (20 / 4) * (17 / 17) = (12 / 25) * (20 / 4) = <<12/25=0.48>>0.48 ### Answer: 0.48
Expected answer: 12/5
Correct? No
Problem: After resolving the previous problem, let us consider a slightly different situation. Now, calculate the result of (10 / 25) * (20 / 4) instead of (12 / 25) * (20 / 4). What difference does this make to the result? Write your new answer as a simplified fraction.
LLemma 34B:
Reasoning: (10 / 25) * (20 / 4) = (10 * 20) / (25 * 4) = <<10*20=200>>200 / <<25*4=100>>100 = <<200/100=2>>2 ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: Calculate the following operation: multiply the fraction 14/10 by the fraction 30/5. Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 14/10 * 30/5 = <<14/10*30/5=9/2>>9/2 ### Answer: 9/2
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.
LLemma 34B:
Reasoning: The baker can make 26/29 of a full batch. ### Answer: 26/29
Expected answer: 364/29
Correct? No
Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: (27 / 10) * (9 / 4) = (27 / 10) * (9 / 4) = (27 * 9) / (10 * 4) = <<27*9=243>>243 / <<10*4=40>>40 = <<243/40=6.075>>6.075 ### Answer: 6.075
Expected answer: 243/40
Correct? Yes
Problem: After solving for s in the previous problem, now calculate a new value o, where o = (9 / 13) * s. Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: o = (9 / 13) * s = (9 / 13) * <<243/40=6.075>>6.075 = (9 / 13) * <<243/40=6.075>>6.075 = <<9*6.075=54.675>>54.675 / <<13*40=520>>520 = <<54.675/520=0.105>>0.105 ### Answer: 0.105
Expected answer: 2187/520
Correct? No
Problem: After having calculated the previous problem where you multiplied (27 / 10) * (9 / 4), consider what would happen if instead of multiplying by (9 / 4), you multiplied by (9 / 11). Calculate the new value of s = ((27 / 10) * (9 / 11)) and write your answer as a simplified fraction.
LLemma 34B:
Reasoning: s = ((27 / 10) * (9 / 11)) = (27 / 10) * (9 / 11) = (27 * 9) / (10 * 11) = <<27*9=243>>243 / <<10*11=110>>110 = <<243/110=2.2>>2.2 ### Answer: 2.2
Expected answer: 243/110
Correct? No
Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((24 / 11) * (27 / 26)) = ((24 / 11) * (27 / 26)) = ((24 * 27) / (11 * 26)) = <<(24*27)/(11*26)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24*3)/(11*2)=(24
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 34B:
Reasoning: 26/9 * 17/13 = <<26/9*17/13=418/117>>418/117 418/117 = <<418/117=27/7>>27/7 ### Answer: 27/7
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 34B:
Reasoning: (28 / 16) / (27 / 24) = (28 / 16) * (24 / 27) = (28 * 24) / (16 * 27) = <<28*24=672>>672 / <<16*27=432>>432 = <<672/432=1.55>>1.55 ### Answer: 1.55
Expected answer: 14/9
Correct? No
Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((15 / 3) * (19 / 26)) = ((5 * 3) / (3 * 26)) = (5 / 26) ### Answer: 5/26
Expected answer: 95/26
Correct? No
Problem: The local bakery was making a special order for a customer. The recipe they are using requires 19/28, and they want to make exactly 30/4 of this recipe. How much of the ingredient will they require?
LLemma 34B:
Reasoning: 30/4 of 19/28 is 30/4 * 19/28 = <<30/4*19/28=19/8>>19/8. They will require 19/8 of the ingredient. ### Answer: 19/8
Expected answer: 285/56
Correct? No
Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.
LLemma 34B:
Reasoning: ((5 / 2) / (26 / 15)) = (5 / 2) * (15 / 26) = <<(5/2)*(15/26)=5/13>>5/13 ### Answer: 5/13
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 34B:
Reasoning: (9/3) * (27/28) = <<9/3*27/28=3*27/3*28=27/28>>27/28 ### Answer: 27/28
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 34B:
Reasoning: ((15 / 13) * (24 / 24)) = <<(15/13)*(24/24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*
Expected answer: 15/13
Correct? Yes
Problem: After calculating the solution to ((15 / 13) * (24 / 24)), multiply your answer with (22 / 7) and write that answer as a simplified fraction.
LLemma 34B:
Reasoning: ((15 / 13) * (24 / 24)) = <<(15/13)*(24/24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*24)=(15*24)/(13*
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 34B:
Reasoning: ((15 / 2) * (24 / 24)) = <<(15/2)*(24/24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15*24)/(2*24)=(15
Expected answer: 15/2
Correct? Yes
Problem: Calculate the result of the following multiplication of fractions operation: (9 / 7) * (25 / 30). Express your answer as a simplified fraction.
LLemma 34B:
Reasoning: (9 / 7) * (25 / 30) = <<(9/7)*(25/30)=(9*25)/(7*30)=225/210>>225/210 = <<225/210=25/21>>25/21 ### Answer: 25/21
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 34B:
Reasoning: ((9 / 8) / (20 / 18)) = (9 / 8) * (18 / 20) = (9 * 18) / (8 * 20) = <<9*18=162>>162 / <<8*20=160>>160 = <<162/160=11/10>>11/10 ### Answer: 11/10
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 34B:
Reasoning: (30 / 6) / (13 / 9) = (30 / 6) * (9 / 13) = (30 * 9) / (6 * 13) = <<30*9=270>>270 / <<6*13=78>>78 = <<270/78=3.4285714285714284>>3.4285714285714284 ### Answer: 3.4285714285714284
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 34B:
Reasoning: 30/18 = <<30/18=1.6666666666666667>>1.6666666666666667 1.6666666666666667 * 18/6 = <<1.6666666666666667*18/6=3>>3 ### Answer: 3
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 34B:
Reasoning: ((20 / 2) * (2 / 18)) = (<<20/2=10>>10 * (2 / 18)) = (<<10*2/18=10/9>>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 34B:
Reasoning: ((27 / 4) * that result) = (<<27/4=6.75>>6.75 * (<<10/9>>10/9)) = (<<6.75*10/9=7.5>>7.5) ### Answer: 7.5
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 34B:
Reasoning: ((20 / 2) * (15 / 18)) = (<<20/2=10>>10 * (15 / 18)) = (<<10*15/18=5/2>>5/2) ### Answer: 5/2
Expected answer: 25/3
Correct? No
Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))
LLemma 34B:
Reasoning: ((11 / 9) * (29 / 6)) = ((11 * 29) / (9 * 6)) = <<(11*29)/(9*6)=319/54>>319/54 ### Answer: 319/54
Expected answer: 319/54
Correct? Yes
Problem: After finding the result of ((11 / 9) * (29 / 6)), multiply your answer by the fraction (11 / 5). Write your final answer as a simplified fraction.
LLemma 34B:
Reasoning: ((11 / 9) * (29 / 6)) = ((11 * 29) / (9 * 6)) = <<(11*29)/(9*6)=319/54>>319/54 ((11 / 9) * (29 / 6)) * (11 / 5) = ((319 / 54) * (11 / 5)) = <<(319/54)*(11/5)=319/27>>319/27 ### Answer: 319/27
Expected answer: 3509/270
Correct? No
Problem: After finding the result of ((21 / 9) * (29 / 6)), consider what would have happened if the initial calculation involved (21 / 9) instead of (11 / 9). Calculate the new result and write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((21 / 9) * (29 / 6)) = ((21 * 29) / (9 * 6)) = <<(21*29)/(9*6)=589/54>>589/54 ### Answer: 589/54
Expected answer: 203/18
Correct? No
Problem: Calculate the result for the following mathematical operation: (30 / 7) * (16 / 19). Express your answer as a simplified fraction.
LLemma 34B:
Reasoning: (30 / 7) * (16 / 19) = <<(30/7)*(16/19)=(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.
LLemma 34B:
Reasoning: (480/133) * (22/7) = <<(480/133)*(22/7)=(480*22)/(133*7)=960/961>>960/961 ### Answer: 960/961
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 34B:
Reasoning: (21 / 7) * (16 / 19) = <<(21/7)*(16/19)=(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.
LLemma 34B:
Reasoning: 25/22 * 20/3 = <<25/22*20/3=500/66>>500/66 ### Answer: 500/66
Expected answer: 250/33
Correct? Yes
Problem: Following the previous calculation, take the product result of 25/22 and 20/3. Now multiply that result with 28/29 and write your final answer as a simplified fraction.
LLemma 34B:
Reasoning: 25/22 * 20/3 * 28/29 = <<25/22*20/3*28/29=1000/299>>1000/299 ### Answer: 1000/299
Expected answer: 7000/957
Correct? No
Problem: After reconsidering the calculation from the previous step, if we actually had 25/15 instead of 25/22. Recalculate the product with these new quantities. What is the product of 25/15 and 20/3? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 25/15 * 20/3 = <<25/15*20/3=100/9>>100/9 ### Answer: 100/9
Expected answer: 100/9
Correct? Yes
Problem: Calculate the result of the following problem and write your answer as a simplified fraction: ((29 / 2) / (23 / 19))
LLemma 34B:
Reasoning: ((29 / 2) / (23 / 19)) = ((29 / 2) * (19 / 23)) = (29 * 19) / (2 * 23) = <<29*19=551>>551 / <<2*23=46>>46 = <<551/46=12>>12 ### Answer: 12
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 34B:
Reasoning: (5 / 3) * (27 / 13) = (5 * 27) / (3 * 13) = <<5*27=135>>135 / <<3*13=39>>39 = <<135/39=3.5>>3.5 ### Answer: 3.5
Expected answer: 45/13
Correct? No
Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.
LLemma 34B:
Reasoning: (29 / 29) * (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?
LLemma 34B:
Reasoning: (29 / 29) * (1 / 1) * (27 / 27) = <<(29/29)*(1/1)*(27/27)=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 34B:
Reasoning: (29 / 6) * (1 / 1) = <<(29/6)*(1/1)=4.833333333333333>>4.833333333333333 ### Answer: 4.833333333333333
Expected answer: 29/6
Correct? Yes
Problem: Calculate the product of the fractions 11/19 and 22/7. Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 11/19 * 22/7 = <<11/19*22/7=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?
LLemma 34B:
Reasoning: 242/133 * 25/4 = <<242/133*25/4=10050/532>>10050/532 ### Answer: 10050/532
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 34B:
Reasoning: 11/19 * 25/7 = <<11/19*25/7=275/133>>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 34B:
Reasoning: 21/30 * 19/5 = <<21/30*19/5=19/10>>19/10 ### Answer: 19/10
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 34B:
Reasoning: 11/15 * 23/8 = <<11/15*23/8=23/20>>23/20 ### Answer: 23/20
Expected answer: 253/120
Correct? No
Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.
LLemma 34B:
Reasoning: (29 / 16) * (21 / 27) = <<(29/16)*(21/27)=(29*21)/(16*27)>>(29*21)/(16*27) = <<(29*21)/(16*27)=(29*3)/(16*9)>>(29*3)/(16*9) = <<(29*3)/(16*9)=(29*1)/(16*3)>>(29*1)/(16*3) = <<(29*1)/(16*3)=29/48>>29/48 = <<29/48=1/2>>1/2 ### Answer: 1/2
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 34B:
Reasoning: (28 / 1) / (30 / 27) = (28 / 1) * (27 / 30) = (28 * 27) / (1 * 30) = <<28*27=756>>756 / <<1*30=30>>30 = <<756/30=25.2>>25.2 ### Answer: 25.2
Expected answer: 126/5
Correct? Yes
Problem: After finding the result of (28 / 1) divided by (30 / 27), what is the new result when this is multiplied by (6 / 19)? Write your final answer as a simplified fraction.
LLemma 34B:
Reasoning: (28 / 1) / (30 / 27) = (28 / 1) * (27 / 30) = (28 * 27) / (1 * 30) = <<28*27=756>>756 / <<1*30=30>>30 = <<756/30=25.2>>25.2 (28 / 1) / (30 / 27) * (6 / 19) = (25.2) * (6 / 19) = (25.2 * 6) / (19) = <<25.2*6=151.2>>151.2 / <<19=19>>19 = <<151.2/19=7.95>>7.95 ### Answer: 7.95
Expected answer: 756/95
Correct? No
Problem: Suppose instead of the original calculation, we now have to perform (28 / 1) divided by 11, how would the result change? Write your updated answer as a simplified fraction.
LLemma 34B:
Reasoning: (28 / 1) / 11 = (28 / 1) * (1 / 11) = (28 * 1) / (1 * 11) = <<28*1=28>>28 / <<1*11=11>>11 = <<28/11=2.55>>2.55 ### Answer: 2.55
Expected answer: 28/11
Correct? No
Problem: What is the result when you multiply ((25 / 25) * (20 / 7))? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((25 / 25) * (20 / 7)) = <<(25/25)*(20/7)=(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 34B:
Reasoning: ((25 / 25) * (20 / 7)) = <<(25/25)*(20/7)=(20/7)>>(20/7) ((20/7) * (20/7)) = <<(20/7)*(20/7)=(400/49)>>(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 34B:
Reasoning: ((25 / 25) * (11 / 7)) = <<(25/25)*(11/7)=(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 34B:
Reasoning: 5/1 * 16/27 = <<5/1*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 34B:
Reasoning: 30/1 * 16/27 = <<30/1*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 34B:
Reasoning: ((27 / 3) / (12 / 12)) = ((27 / 3) / 1) = (27 / 3) = <<27/3=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 34B:
Reasoning: b = s * (21/17) = (9 * (21/17)) = <<9*(21/17)=183/17>>183/17 ### Answer: 183/17
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 34B:
Reasoning: (24 / (12 / 12)) = (24 / 1) = <<24/1=24>>24 The answer 's' is now 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 34B:
Reasoning: (15 / 16) * (29 / 2) = (15 * 29) / (16 * 2) = <<15*29=435>>435 / <<16*2=32>>32 = <<435/32=13.5625>>13.5625 ### Answer: 13.5625
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 34B:
Reasoning: ((6 / 2) / (13 / 9)) = (3 / (13 / 9)) = (3 * 9 / 13) = (27 / 13) = 2. ### Answer: 2
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 34B:
Reasoning: 7/1 = <<7/1=7>>7. 7/1 ÷ 15/9 = 7 ÷ 15/9 = <<7/15*9/1=63/15>>63/15. ### Answer: 63/15
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 34B:
Reasoning: 63/15 × 10/5 = <<63/15*10/5=630/75>>630/75. ### Answer: 630/75
Expected answer: 42/5
Correct? Yes
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 34B:
Reasoning: 20/1 = <<20/1=20>>20. 20/1 ÷ 15/9 = 20 ÷ 15/9 = <<20/15*9/1=360/15>>360/15. ### Answer: 360/15
Expected answer: 12
Correct? No
Problem: What is the result when you multiply (23/10) by (9/1)?
LLemma 34B:
Reasoning: (23/10) * (9/1) = <<(23/10)*(9/1)=(207/10)>>207/10 ### Answer: 207/10
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 34B:
Reasoning: (207/10) * (1/16) = <<(207/10)*(1/16)=(207/160)>>207/160 ### Answer: 207/160
Expected answer: 207/160
Correct? Yes
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 34B:
Reasoning: (23/10) * (9/6) = <<(23/10)*(9/6)=(207/30)>>207/30 ### Answer: 207/30
Expected answer: 69/20
Correct? No
Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((18 / 4) * (10 / 11)) = ((18 * 10) / (4 * 11)) = <<(18*10)/(4*11)=90/44>>90/44 ### Answer: 90/44
Expected answer: 45/11
Correct? No
Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?
LLemma 34B:
Reasoning: 24/23 * 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 34B:
Reasoning: 8 * 30/21 = 8/3 * 30/21 = 8/7 * 30/3 = <<8/7*30/3=40>>40. ### Answer: 40
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 34B:
Reasoning: 24/23 * 18/3 = 24/3 * 18/3 = <<24/3*18/3=8*18/3=144/3=48>>48. ### Answer: 48
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 34B:
Reasoning: (20 / 13) / (17 / 16) = (20 / 13) * (16 / 17) = (20 * 16) / (13 * 17) = <<20*16=320>>320 / <<13*17=221>>221 = <<320/221=160/110>>160 / 110 = <<160/110=16/11>>16 / 11 ### Answer: 16 / 11
Expected answer: 320/221
Correct? No
Problem: Calculate the result of the following problem: ((5 divided by 5) multiplied by (4 divided by 1))
LLemma 34B:
Reasoning: (5 divided by 5) = <<5/5=1>>1 (4 divided by 1) = <<4/1=4>>4 ((5 divided by 5) multiplied by (4 divided by 1)) = <<1*4=4>>4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Given that the result from the previous problem is c, calculate the result of the following formula: ((21 divided by 9) multiplied by c). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((21 divided by 9) multiplied by c) = <<(21/9)*4=8/3>>8/3 ### Answer: 8/3
Expected answer: 28/3
Correct? No
Problem: Assuming that in the previous problem, the initial amount of oranges was 5 but was changed to 5/15, how would this affect the outcome if it is multiplied by the same fraction (4/1)? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: (5/15 divided by 5/15) = <<5/15/5/15=1>>1 (4/1 multiplied by 5/15 divided by 5/15) = <<4/1*1=4>>4 ### Answer: 4
Expected answer: 4/3
Correct? No
Problem: Calculate the result for the following problem: ((30 / 23) * (19 / 24)). Write the answer as a simplified fraction.
LLemma 34B:
Reasoning: ((30 / 23) * (19 / 24)) = <<(30/23)*(19/24)=(30*19)/(23*24)=570/552>>570/552 ### Answer: 570/552
Expected answer: 95/92
Correct? Yes
Problem: After calculating the previous problem of ((30 / 23) * (19 / 24)) and getting the result, now proceed to multiply this result with (28 / 4). What is your new answer when written as a simplified fraction?
LLemma 34B:
Reasoning: ((30 / 23) * (19 / 24)) * (28 / 4) = <<((30/23)*(19/24))*(28/4)=(570/552)*(28/4)=(570*28)/(552*4)=15400/22112>>15400/22112 ### Answer: 15400/22112
Expected answer: 665/92
Correct? No
Problem: After calculating the previous problem and getting a result, let's change the condition. Instead of (30 / 23) which you used last time, now use (30 / 11). Repeat the multiplication with (19 / 24). What is the new result when you write it as a simplified fraction?
LLemma 34B:
Reasoning: ((30 / 11) * (19 / 24)) = <<(30/11)*(19/24)=(30*19)/(11*24)=570/264>>570/264 ### Answer: 570/264
Expected answer: 95/44
Correct? Yes
Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.
LLemma 34B:
Reasoning: (23 / 26) * (16 / 1) = <<(23/26)*(16/1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(23*16)/(26*1)=(23*16)/(26*1)=(23*16)/(26*1)>>(23*16)/(26*1) = <<(
Expected answer: 184/13
Correct? Yes
Problem: Given that you previously calculated (23 / 26) * (16 / 1) as 'g', now find the value of (4 / 7) * g. Express your answer as a simplified fraction.
LLemma 34B:
Reasoning: (4 / 7) * g = <<(4/7)*g=(4/7)*(23*16)/(26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(7*26*1)=(4*23*16)/(
Expected answer: 736/91
Correct? No
Problem: In the previous problem, you calculated (23 / 26) * (16 / 1) as 'g'. Now assume that instead of 23/26, you had 2/26. How would that change the value of 'g'? Compute g as (2 / 26) * (16 / 1) and express your answer as a simplified fraction.
LLemma 34B:
Reasoning: (2 / 26) * (16 / 1) = <<(2/26)*(16/1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16)/(26*1) = <<(2*16)/(26*1)=(2*16)/(26*1)=(2*16)/(26*1)>>(2*16
Expected answer: 16/13
Correct? No
Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((21 / 1) / (26 / 20)) = (21 / (26 / 20)) = (21 * 20 / 26) = (21 * 10 / 13) = (210 / 13) = (210 / 13) = (150 / 13) = (150 / 13) = (112 / 13) = (112 / 13) = (91 / 13) = (91 / 13) = (78 / 13) = (78 / 13) = (65 / 13) = (65 / 13) = (52 / 13) = (52 / 13) = (41 / 13) = (41 / 13) = (30 / 13) = (30 / 13) = (19 / 13) = (19 / 13) = (8 / 13) = (8 / 13) = (5 / 13) = (5 / 13) = (2 / 13) = (2 / 13) = (1 / 13) = (1 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0 / 13) = (0
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 34B:
Reasoning: 24/19 * 21/19 = <<24/19*21/19=24/19*21/19>>24/19*21/19 ### Answer: 24/19*21/19
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 34B:
Reasoning: Jim needs to multiply the amount of sugar and flour he needs for a larger cake. Jim needs ((12 / 2) * (17 / 14)) = <<(12/2)*(17/14)=(12*17)/(2*14)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*17)/(2*7)=(12*1
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 34B:
Reasoning: ((21 / 16) / (27 / 23)) = (21 / 16) * (23 / 27) = (21 * 23) / (16 * 27) = <<21*23=483>>483 / <<16*27=432>>432 = <<483/432=15/14>>15/14 ### Answer: 15/14
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 34B:
Reasoning: (11 / 20) * (24 / 12) = (11 * 24) / (20 * 12) = <<11*24=264>>264 / <<20*12=240>>240 = <<264/240=13/10>>13 / 10 ### Answer: 13 / 10
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 34B:
Reasoning: ((6 / 19) * (28 / 2)) = <<(6/19)*(28/2)=(6*28)/(19*2)=(6*14)/(19*1)=(6*7)/(19*1)=(6*7)/19>>(6*7)/19 ### Answer: (6*7)/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 34B:
Reasoning: (12 / 14) * (28 / 5) = <<(12/14)*(28/5)=(12*28)/(14*5)=336/70>>336/70 = <<336/70=11/2>>11/2 = <<11/2=5.5>>5.5 ### Answer: 5.5
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 34B:
Reasoning: (19 / 3) * (8 / 15) = (19 * 8) / (3 * 15) = <<19*8=152>>152 / <<3*15=45>>45 = <<152/45=3>>3 ### Answer: 3
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 34B:
Reasoning: ((15 / 3) * (7 / 25)) = (5 * (7 / 25)) = (5 * 0.28) = <<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 34B:
Reasoning: ((15 / 3) * (7 / 25)) = (5 * (7 / 25)) = (5 * 0.28) = <<5*0.28=1.4>>1.4 ((15 / 3) * (7 / 25)) * (28 / 16) = (1.4 * (28 / 16)) = (1.4 * 1.75) = <<1.4*1.75=2.45>>2.45 ### Answer: 2.45
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 34B:
Reasoning: (13 / 3) * (7 / 25) = (13 * 7) / (3 * 25) = <<13*7=91>>91 / <<3*25=75>>75 = 91 / 75 = <<91/75=1.22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222
Expected answer: 91/75
Correct? No
Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.
LLemma 34B:
Reasoning: (20 / 10) * (10 / 1) = <<(20/10)*(10/1)=2>>2 ### Answer: 2
Expected answer: 20
Correct? No
Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.
LLemma 34B:
Reasoning: [(27 / 18) * (19 / 8)] = <<(27/18)*(19/8)=(27*19)/(18*8)=45/12>>45/12 ### Answer: 45/12
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 34B:
Reasoning: 29/5 * 13/24 = <<29/5*13/24=29/10>>29/10 ### Answer: 29/10
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 34B:
Reasoning: ((29 / 17) / (27 / 22)) = (29 / 17) * (22 / 27) = (29 * 22) / (17 * 27) = <<29*22=618>>618 / <<17*27=459>>459 = <<618/459=1.3496236559139>>1.3496236559139 ### Answer: 1.3496236559139
Expected answer: 638/459
Correct? No
Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?
LLemma 34B:
Reasoning: (27 / 6) * (25 / 5) = (27 / 6) * (5 / 5) = (27 / 6) * 1 = 27 / 6 = <<27/6=4.5>>4.5 ### Answer: 4.5
Expected answer: 45/2
Correct? No
Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).
LLemma 34B:
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 34B:
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 34B:
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 34B:
Reasoning: 25/20 = 5/4 and 11/6 = 11/6. The product is 5/4 * 11/6 = <<5/4*11/6=11/8>>11/8. ### Answer: 11/8
Expected answer: 55/24
Correct? No
Problem: Determine the value of (7 / 2) / (25 / 10). Please provide your answer as a simplified fraction.
LLemma 34B:
Reasoning: (7 / 2) / (25 / 10) = (7 / 2) * (10 / 25) = (7 * 10) / (2 * 25) = <<7*10=70>>70 / <<2*25=50>>50 = <<70/50=1.4>>1.4 ### Answer: 1.4
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 34B:
Reasoning: (5 / 3) * (7 / 2) / (25 / 10) = (5 / 3) * (7 / 2) * (10 / 25) = (5 * 7 * 10) / (3 * 2 * 25) = <<5*7*10=350>>350 / <<3*2*25=150>>150 = <<350/150=2.3333333333333335>>2.3333333333333335 ### Answer: 2.3333333333333335
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 34B:
Reasoning: 15/16 * 29/27 = <<15/16*29/27=15*29/16*27>>15*29/16*27 = <<15*29=435>>435/<<16*27=432>>432 = <<435/432=5/4>>5/4 ### Answer: 5/4
Expected answer: 145/144
Correct? No
Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.
LLemma 34B:
Reasoning: ((30 / 25) * (25 / 10)) = ((30 / 25) * (1 / 2)) = (12 / 25) = 0.48 ### Answer: 0.48
Expected answer: 3
Correct? No
Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.
LLemma 34B:
Reasoning: 27/10 * 27/3 = <<27/10*27/3=9/10>>9/10 ### Answer: 9/10
Expected answer: 243/10
Correct? No
Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: (10 / 8) * (30 / 26) = (10 * 30) / (8 * 26) = <<10*30=300>>300 / <<8*26=208>>208 = <<300/208=15/13>>15/13 ### Answer: 15/13
Expected answer: 75/52
Correct? No
Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 20/22 = <<20/22=10/11>>10/11 and 14/11 = <<14/11=14/11>>14/11. 10/11 * 14/11 = <<10/11*14/11=140/121>>140/121. ### Answer: 140/121
Expected answer: 140/121
Correct? Yes
Problem: After evaluating the expression ((20 / 22) * (14 / 11)), multiply your result by (17/3). Write your final answer as a simplified fraction.
LLemma 34B:
Reasoning: 140/121 * 17/3 = <<140/121*17/3=140/4>>140/4. ### Answer: 140/4
Expected answer: 2380/363
Correct? No
Problem: Previously, you evaluated ((20 / 22) * (14 / 11)) and multiplied the result by (17/3). Now consider changing the second fraction in the initial multiplication to (14 / 2). Now how does the expression ((20 / 22) * (14 / 2)) differ from the original? Evaluate the new expression and write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 20/22 = <<20/22=10/11>>10/11 and 14/2 = <<14/2=7>>7. 10/11 * 7 = <<10/11*7=70/11>>70/11. ### Answer: 70/11
Expected answer: 70/11
Correct? Yes
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 34B:
Reasoning: ((25 / 8) * (3 / 4)) = (<<25/8=3.125>>3.125 * (3 / 4)) = (<<3.125*3/4=2.375>>2.375) ### Answer: 2.375
Expected answer: 75/32
Correct? No
Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).
LLemma 34B:
Reasoning: (29 / 1) * (8 / 15) = (29 * 8) / (1 * 15) = <<29*8=232>>232 / <<1*15=15>>15 = <<232/15=15.4>>15.4 ### Answer: 15.4
Expected answer: 232/15
Correct? No
Problem: What is the result when you multiply (29/17) by (26/15)?
LLemma 34B:
Reasoning: (29/17) * (26/15) = (29*26)/(17*15) = <<29*26=754>>754/<<17*15=255>>255 = <<754/255=3>>3 ### Answer: 3
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 34B:
Reasoning: ((25 / 5) * (16 / 8)) = (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 34B:
Reasoning: ((25 / 5) * (19 / 8)) = (5 * 19/8) = 19/2 = 9.5 ### Answer: 9.5
Expected answer: 95/8
Correct? No
Problem: What is the result when you multiply (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: (23 / 4) * (10 / 12) = (23 * 10) / (4 * 12) = <<23*10=230>>230 / <<4*12=48>>48 = <<230/48=5/2>>5/2 ### Answer: 5/2
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 34B:
Reasoning: (21 / 26) * (20 / 9) = <<(21/26)*(20/9)=(21*20)/(26*9)=(210)/(234)=(210/2)/(234/2)=(105)/(117)>>(105)/(117) ### Answer: (105)/(117)
Expected answer: 70/39
Correct? No
Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((17 / 13) * (15 / 6)) = <<(17/13)*(15/6)=(17*15)/(13*6)=255/78>>255/78 ### Answer: 255/78
Expected answer: 85/26
Correct? Yes
Problem: In the previous problem, you calculated the product of ((17 / 13) * (15 / 6)) and found it as a simplified fraction. Now, use that answer and further multiply it by (8 / 15). Write your final answer as a simplified fraction.
LLemma 34B:
Reasoning: ((17 / 13) * (15 / 6)) = <<(17/13)*(15/6)=(17*15)/(13*6)=255/78>>255/78 ((255 / 78) * (8 / 15)) = <<(255/78)*(8/15)=(255*8)/(78*15)=105/13>>105/13 ### Answer: 105/13
Expected answer: 68/39
Correct? No
Problem: Calculate the result of the following equation: (25 / 18) * (17 / 6). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: (25 / 18) * (17 / 6) = (25 * 17) / (18 * 6) = <<25*17=425>>425 / <<18*6=108>>108 = <<425/108=4>>4 ### Answer: 4
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 34B:
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.
LLemma 34B:
Reasoning: t * t = (9/1 * 2/17) * (9/1 * 2/17) = <<(9/1*2/17)*(9/1*2/17)=18/17*18/17>>18/17 * 18/17 = <<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 34B:
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.
LLemma 34B:
Reasoning: (27 / 14) * (19 / 14) = (27 * 19) / (14 * 14) = <<27*19=513>>513 / <<14*14=196>>196 = <<513/196=2>>2 ### Answer: 2
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 34B:
Reasoning: (16 / 5) * (5 / 15) = (16 * 5) / (5 * 15) = <<16*5=80>>80 / <<5*15=75>>75 = <<80/75=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.
LLemma 34B:
Reasoning: (16 / 5) * (5 / 15) * (30 / 24) = (16 / 15) * (30 / 24) = <<16/15*30/24=4/3*5/4>>4/3 * 5/4 = <<4*5=20>>20 / <<3*4=12>>12 = <<20/12=5/3>>5/3 ### Answer: 5/3
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 34B:
Reasoning: (16 / 5) * (5 / 7) = (16 * 5) / (5 * 7) = <<16*5=80>>80 / <<5*7=35>>35 = <<80/35=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.
LLemma 34B:
Reasoning: (8 / 3) * (18 / 21) = (8 * 18) / (3 * 21) = <<8*18=144>>144 / <<3*21=63>>63 = <<144/63=2.3076923076923077>>2.3076923076923077 ### Answer: 2.3076923076923077
Expected answer: 16/7
Correct? No
Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))
LLemma 34B:
Reasoning: ((14 / 6) / (22 / 16)) = ((14 / 6) * (16 / 22)) = (14 * 16 / 6 * 22) = (14 * 2 / 6 * 11) = (28 / 66) = (2 / 3) ### Answer: 2/3
Expected answer: 56/33
Correct? No
Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)
LLemma 34B:
Reasoning: (16 / 3) * (25 / 26) = (16 * 25) / (3 * 26) = <<16*25=400>>400 / <<3*26=78>>78 = <<400/78=5.128205128205128>>5.128205128205128 ### Answer: 5.128205128205128
Expected answer: 200/39
Correct? No
Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)
LLemma 34B:
Reasoning: (16 / 16) * (26 / 22) = <<16/16*26/22=13/11>>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 34B:
Reasoning: (16 / 16) * (26 / 22) = <<16/16*26/22=13/11>>13/11 (13/11) * (13/11) = <<13/11*13/11=169/121>>169/121 ### Answer: 169/121
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 34B:
Reasoning: (16 / 12) * (26 / 22) = <<16/12*26/22=13/6>>13/6 ### Answer: 13/6
Expected answer: 52/33
Correct? No
Problem: Calculate the result of the following operation: (17 / 5) * (5 / 14). Write your answer as a simplest form fraction.
LLemma 34B:
Reasoning: (17 / 5) * (5 / 14) = <<(17/5)*(5/14)=(17/14)>>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 34B:
Reasoning: (17 / 5) * (5 / 14) = <<(17/5)*(5/14)=(17/14)>>17/14 (17 / 14) * (21 / 25) = <<(17/14)*(21/25)=(17*21)/(14*25)>>17*21/14*25 17*21/14*25 = <<17*21/14*25=(17*21)/(14*25)=(17*3)/(14*5)>>17*3/14*5 17*3/14*5 = <<17*3/14*5=(17*3)/(14*5)=(17*3)/(7*5)>>17*3/7*5 17*3/7*5 = <<17*3/7*5=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(17*3)/(7*5)=(1
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 34B:
Reasoning: (17 / 5) * (5 / 12) = <<(17/5)*(5/12)=(17/12)>>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 34B:
Reasoning: (16 / 6) * (29 / 27) = <<16/6*29/27=16/9>>16/9 ### Answer: 16/9
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.
LLemma 34B:
Reasoning: The car will consume 16/10 * 13/17 = <<16/10*13/17=16/10*13/17=16*13/10*17=208/170>>208/170 gallons of petrol. ### 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.
LLemma 34B:
Reasoning: The car will consume 16/10 * 13/7 = <<16/10*13/7=16/10*13/7=16*13/10*7=208/70>>208/70 gallons of petrol. ### 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)
LLemma 34B:
Reasoning: (29 / 10) / (18 / 16) = (29 / 10) * (16 / 18) = (29 * 16) / (10 * 18) = <<29*16=464>>464 / <<10*18=180>>180 = <<464/180=2.5555555555555554>>2.5555555555555554 ### Answer: 2.5555555555555554
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 34B:
Reasoning: (15/12) * (27/3) = (15*27)/(12*3) = <<15*27=405>>405/36 = <<405/36=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 34B:
Reasoning: (15/12) * (27/3) * (22/14) = (15*27*22)/(12*3*14) = <<15*27*22=13860>>13860/126 = <<13860/126=110.5>>110.5 ### Answer: 110.5
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 34B:
Reasoning: (15/12) * (27/5) = (15*27)/(12*5) = <<15*27=405>>405/60 = <<405/60=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 34B:
Reasoning: (7 / 7) * (12 / 12) = <<(7/7)*(12/12)=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?
LLemma 34B:
Reasoning: 1 * (27 / 15) = <<1*(27/15)=(27/15)>>(27 / 15) ### Answer: (27 / 15)
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 34B:
Reasoning: (7 / 7) * (16 / 12) = <<(7/7)*(16/12)=1.3333333333333333>>1.3333333333333333 ### Answer: 1.3333333333333333
Expected answer: 4/3
Correct? Yes
Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: ((28 / 6) * (16 / 24)) = (<<28/6=4.666666666666667>>4 * (<<16/24=0.666666666666667>>0.666666666666667)) = (<<4*0.666666666666667=2.666666666666667>>2.666666666666667) ### Answer: 2.666666666666667
Expected answer: 28/9
Correct? No