InternLM-Math Base 20B on 5.NF.B.4
Common Core Standard 5.NF.B.4
This standard covers the following:
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Problem: Determine the product when you multiply the fraction 8/9 by the fraction 19/3. Please provide your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 8/9 × 19/3 = <<8/9*19/3=152/27>>152/27 ### Answer: 152/27
Expected answer: 152/27
Correct? Yes
Problem: After determining the product when multiplying the fraction 8/9 by the fraction 19/3, take your result and then multiply it by 2. What does this new calculation result in when written as a simplified fraction?
InternLM-Math Base 20B:
Reasoning: 152/27 × 2 = <<152/27*2=304/27>>304/27 ### Answer: 304/27
Expected answer: 304/27
Correct? Yes
Problem: Imagine you made an error in the original multiplication calculation where you incorrectly used 8/9 instead of the correct fraction 8/15. Can you correct this mistake and find the new product if you multiply 8/15 by 19/3? Please provide your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 8/15 × 19/3 = <<8/15*19/3=76/45>>76/45 ### Answer: 76/45
Expected answer: 152/45
Correct? No
Problem: Julian is cutting sections of rope for a project. Each section is 13/2 feet long. He is only able to use 5/7 of each section. How many feet are in the usable part of each section of rope? Calculate this by multiplying 13/2 by 5/7.
InternLM-Math Base 20B:
Reasoning: 13/2 * 5/7 = <<13/2*5/7=65/14>>65/14 ### Answer: 65/14
Expected answer: 65/14
Correct? Yes
Problem: Suppose Julian is considering replacing the rope sections with new ones. Each new section is 17/2 feet long and he is still able to use only 5/7 of each section. How many feet are in the usable part of each new section of rope? Calculate this by multiplying 17/2 by 5/7.
InternLM-Math Base 20B:
Reasoning: 17/2 * 5/7 = <<17/2*5/7=85/14>>85/14 ### Answer: 85/14
Expected answer: 85/14
Correct? Yes
Problem: What is the result when you multiply the whole number 12 by 1?
InternLM-Math Base 20B:
Reasoning: 12 × 1 = <<12*1=12>>12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: If you take the product of 12 and 1, and then multiply that result by the fraction 7/16, what would be the final result? Write your answer as a simplified fraction or a whole number, if possible.
InternLM-Math Base 20B:
Reasoning: 12 × 1 = <<12*1=12>>12 12 × 7/16 = <<12*7/16=21/4>>21/4 ### Answer: 21/4
Expected answer: 21/4
Correct? Yes
Problem: Previously, you found the result of multiplying 12 by 1. Now, let's change the scenario and replace the 12 with 11. What would be the result when you multiply the whole number 11 by 1?
InternLM-Math Base 20B:
Reasoning: 11 × 1 = <<11*1=11>>11 ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Find the answer of the given math problem: 14 / 15 * 12 / 4, performing the multiplication operation on fractions and whole numbers. Provide your answer as a simplified fraction or, if possible, as a whole number.
InternLM-Math Base 20B:
Reasoning: 14 / 15 * 12 / 4 = <<14/15*12/4=28/5>>28/5 ### Answer: 28/5
Expected answer: 14/5
Correct? No
Problem: Compute the value for the following expression: 15 * (5 / 17). Write your answer as a decimal rounded to the nearest hundredth.
InternLM-Math Base 20B:
Reasoning: 15 * (5 / 17) = <<15*5/17=0.88>>0.88 ### Answer: 0.88
Expected answer: 75/17
Correct? No
Problem: Find the result of the following calculation: 16 * (12 / 19)
InternLM-Math Base 20B:
Reasoning: 16 * (12 / 19) = <<16*12/19=96/19>>96/19 ### Answer: 96/19
Expected answer: 192/19
Correct? No
Problem: If a farmer has 10/17 of a barrel of apples and he decides to multiply that amount by 18/5 barrels, how many barrels of apples will he have in total? Calculate your answer keeping it as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: The farmer has 10/17 of a barrel of apples. The farmer has 10/17 × 18/5 = <<10/17*18/5=36/17>>36/17 barrels of apples in total. ### Answer: 36/17
Expected answer: 36/17
Correct? Yes
Problem: Given the farmer's new total of apples from the previous question, he decides to increase his total number of barrels by a factor of 7. Calculate the new total number of barrels of apples the farmer will have. Represent your answer as a simplified fraction where appropriate.
InternLM-Math Base 20B:
Reasoning: The farmer has 36/17 of a barrel of apples. The farmer has 36/17 × 7 = <<36/17*7=252/17>>252/17 barrels of apples in total. ### Answer: 252/17
Expected answer: 252/17
Correct? Yes
Problem: Suppose the farmer initially started with 10/17 of a barrel of apples but this time he decided to increase that amount by multiplying it with 19/5 barrels instead of 18/5. Calculate how many barrels of apples will he have now. Represent your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: The farmer has 10/17 of a barrel of apples. The farmer has 10/17 × 19/5 = <<10/17*19/5=38/17>>38/17 barrels of apples in total. ### Answer: 38/17
Expected answer: 38/17
Correct? Yes
Problem: Simplify the expression: (20 / 4) * (1 / 5). What is the result?
InternLM-Math Base 20B:
Reasoning: (20 / 4) * (1 / 5) = <<(20/4)*(1/5)=(5/1)*(1/5)=(5*1)/(1*5)=(5*1)/5=5/5=1>>1 ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After you have found the result of (20 / 4) * (1 / 5), multiply it by (16 / 3). What is the final result?
InternLM-Math Base 20B:
Reasoning: (20 / 4) * (1 / 5) * (16 / 3) = <<(20/4)*(1/5)*(16/3)=(5/1)*(1/5)*(16/3)=(5*1*16)/(1*5*3)=(5*16)/15=(5*16)/3=(80/3)>>80/3 ### Answer: 80/3
Expected answer: 16/3
Correct? No
Problem: Julia has 11 boxes and she decides to fill 8/11 of each box with apples. If each box can hold up to 1 bushel of apples, how many bushels of apples did she use in total?
InternLM-Math Base 20B:
Reasoning: Julia filled 8/11 of each box with apples. She filled 8/11 × 11 = <<8/11*11=8>>8 boxes with apples. She used 8 bushels of apples in total. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: In the continuation of the previous situation, Julia decided to sell 7/14, or half, of all the bushels of apples she had. How many bushels of apples did Julia sell?
InternLM-Math Base 20B:
Reasoning: Julia sold 7/14 of 8 = <<7/14*8=4>>4 bushels of apples. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: In continuation to the previous scenario, suppose Julia initially had 6 boxes instead of 11. How many bushels of apples would she have if she still fills 8/11 of each box with apples?
InternLM-Math Base 20B:
Reasoning: Julia filled 8/11 of each box with apples. She filled 8/11 × 6 = <<8/11*6=4.8>>4.8 boxes with apples. She used 4.8 bushels of apples in total. ### Answer: 4.8
Expected answer: 48/11
Correct? No
Problem: In a bakery, a baker uses 9/4 cups of sugar for a cake and 16/15 cups for a batch of cookies. If he needs the equal amount of sugar for the cake and the cookies, how much sugar in cups will he use in total? Calculate it by multiplying the two fractions.
InternLM-Math Base 20B:
Reasoning: 9/4 × 16/15 = <<9/4*16/15=32/5>>32/5. The baker will use 32/5 = <<32/5=6.4>>6.4 cups of sugar in total. ### Answer: 6.4
Expected answer: 12/5
Correct? No
Problem: If Peter was making home-made pizza and he needed 19/9 cups of flour and 14/18 cups of sugar for his pizza dough, how many cups of ingredients in total did he need? Multiply the amounts of flour and sugar together to find the total.
InternLM-Math Base 20B:
Reasoning: Peter needed 19/9 × 14/18 = <<19/9*14/18=1 1/9>>1 1/9 cups of ingredients in total. ### Answer: 1 1/9
Expected answer: 133/81
Correct? No
Problem: What is the result when you multiply the fractions 14/7 and 16/4?
InternLM-Math Base 20B:
Reasoning: 14/7 = <<14/7=2>>2 and 16/4 = <<16/4=4>>4. 2 × 4 = <<2*4=8>>8. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Continuing from our previous problem, instead of multiplying 14/7 and 16/4, let's consider we have 14/7 and 13/4. What is the result when you multiply these two fractions?
InternLM-Math Base 20B:
Reasoning: 14/7 = <<14/7=2>>2 and 13/4 = <<13/4=3.25>>3.25. 2 × 3.25 = <<2*3.25=6.5>>6.5. ### Answer: 6.5
Expected answer: 13/2
Correct? Yes
Problem: Calculate the result of (17 / 18) multiplied by (13 / 8). Write the answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (17 / 18) multiplied by (13 / 8) = <<(17/18)*(13/8)=(17*13)/(18*8)=(221)/(144)>>221/144 ### Answer: 221/144
Expected answer: 221/144
Correct? Yes
Problem: After calculating the result of (17 / 18) multiplied by (13 / 8), multiply the answer you got by itself. Write the final result as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (17 / 18) multiplied by (13 / 8) = <<(17/18)*(13/8)=(17*13)/(18*8)=(221)/(144)>>221/144 221/144 multiplied by 221/144 = <<(221/144)*(221/144)=(221*221)/(144*144)=(48641)/(20736)>>48641/20736 ### Answer: 48641/20736
Expected answer: 48841/20736
Correct? No
Problem: Evaluate the following expression: ((15 / 15) * 18) and write your answer.
InternLM-Math Base 20B:
Reasoning: ((15 / 15) * 18) = <<(15/15)*18=18>>18 ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: For this next question, let's slightly adjust our variables. Instead of doing (15 / 15) * 18 as in the previous problem, let's try (15 / 16) * 18. What's the result of this multiplication?
InternLM-Math Base 20B:
Reasoning: (15 / 16) * 18 = <<(15/16)*18=13.125>>13.125 ### Answer: 13.125
Expected answer: 135/8
Correct? No
Problem: A group of 18 students is planning a pizza party. If each student will eat 17/20 of a pizza, how many pizzas should they order?
InternLM-Math Base 20B:
Reasoning: 18 × 17/20 = <<18*17/20=51/5>>51/5 pizzas. They should order 51/5 = <<51/5=10.2>>10.2 pizzas. ### Answer: 10.2
Expected answer: 153/10
Correct? No
Problem: Sophie picked 9 pounds of apples. She decided to make apple pies for a community gathering, and each pie requires about 1/14 of the total apples she picked. Sophie made 7 pies. How many pounds of apples did she use in total? Calculate it using the multiplication of fraction and a whole number, specifically ((9 / 14) * 7). Write your answer as a simplified fraction or a whole number.
InternLM-Math Base 20B:
Reasoning: Sophie used 9/14 * 7 = <<9/14*7=63/14>>63/14 pounds of apples in total. ### Answer: 63/14
Expected answer: 9/2
Correct? Yes
Problem: Sophie initially thought she had 9 pounds of apples, but upon rechecking, she found she actually had 18 pounds. Sophie still decided to make pies for the community gathering, with each pie requiring 1/14 of the total amount of apples. If Sophie still made 7 pies just like before, calculate how many pounds of apples she used this time. Solve the problem using the multiplication of the fraction and the whole number ((18 / 14) * 7). Write your answer as a simplified fraction or a whole number.
InternLM-Math Base 20B:
Reasoning: Sophie used 18/14 * 7 = <<18/14*7=126/14>>126/14 pounds of apples in total. ### Answer: 126/14
Expected answer: 9
Correct? No
Problem: John bought 2 boxes of cookies with 6/8 of a dozen cookies in each box. How many dozens of cookies did John buy in total?
InternLM-Math Base 20B:
Reasoning: John bought 2 boxes of cookies with 6/8 of a dozen cookies in each box. 6/8 = <<6/8=3/4>>3/4 of a dozen cookies. 2 boxes of cookies = 2 dozen cookies. 2 dozen cookies + 2 dozen cookies = 4 dozen cookies. 4 dozen cookies = <<4*12=48>>48 cookies. 48 cookies = <<48/12=4>>4 dozen cookies. ### Answer: 4
Expected answer: 3/2
Correct? No
Problem: Tom has a box that could potentially hold 6 gallons of paint. However, due to the design of the box, it can only be filled up to 16/17 of its capacity. How many gallons of paint can Tom actually store in the box?
InternLM-Math Base 20B:
Reasoning: 6*16/17 = <<6*16/17=3.94285714285714>>3.94285714285714 gallons of paint can be stored in the box. ### Answer: 3.94285714285714
Expected answer: 96/17
Correct? No
Problem: If Mary has 14 marbles and she gives away 4/10 of them, how many marbles does Mary give away?
InternLM-Math Base 20B:
Reasoning: Mary gives away 14*4/10 = <<14*4/10=5.6>>5.6 marbles. ### Answer: 5.6
Expected answer: 28/5
Correct? Yes
Problem: Using the previous scenario where Mary gave away 4/10 of her 14 marbles, what if she finds a box with that same amount of marbles she gave away, and decides to give away 4/9 of the marbles in the box. How many marbles does she give away now?
InternLM-Math Base 20B:
Reasoning: Mary gives away 4/9*14*4/10 = <<4/9*14*4/10=2.2>>2.2 marbles. ### Answer: 2.2
Expected answer: 112/45
Correct? No
Problem: Let's change the context of the previous problem: instead of Mary having 14 marbles, now she only has 12 marbles and she still decides to give away the same fraction, 4/10. How many marbles does she give away this time?
InternLM-Math Base 20B:
Reasoning: Mary gives away 12*4/10 = <<12*4/10=4.8>>4.8 marbles. ### Answer: 4.8
Expected answer: 24/5
Correct? Yes
Problem: Calculate the product of 19/6 and 4/4. Write the resulting answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 19/6 × 4/4 = <<19/6*4/4=19/6*1=19/6>>19/6. ### Answer: 19/6
Expected answer: 19/6
Correct? Yes
Problem: Use the answer you obtained from the previous word problem as a fraction, multiply it by itself, and write the resulting answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 19/6 × 19/6 = <<19/6*19/6=361/36>>361/36. ### Answer: 361/36
Expected answer: 361/36
Correct? Yes
Problem: In the previous word problem, use 19/6 and 9/4 instead of 19/6 and 4/4. Multiply these two fractions and write the resulting answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 19/6 × 9/4 = <<19/6*9/4=19*9/(6*4)=171/24>>171/24. ### Answer: 171/24
Expected answer: 57/8
Correct? Yes
Problem: What is the result when you divide 16 by 8 and then multiply the result by 10?
InternLM-Math Base 20B:
Reasoning: 16/8 = <<16/8=2>>2, 2*10 = <<2*10=20>>20. ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Using the result you obtained from the previous question, what is the outcome when you multiply it by 1/17?
InternLM-Math Base 20B:
Reasoning: 20*1/17 = <<20*1/17=1.18>>1.18 ### Answer: 1.18
Expected answer: 20/17
Correct? No
Problem: What would the result have been in the original problem if you had divided 16 by 10 instead of 8 before multiplying by 10?
InternLM-Math Base 20B:
Reasoning: 16/10 = <<16/10=1.6>>1.6, 1.6*10 = <<1.6*10=16>>16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: What is the product when 18 is multiplied by 1/11? Please provide your answer as a decimal or a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 18/11 = <<18/11=1.636363636363636>>1.636363636363636 ### Answer: 1.636363636363636
Expected answer: 18/11
Correct? No
Problem: Mary has a garden with apple trees. Each tree produces 3 bushels of apples, and she has 6 trees in total. However, due to pests, only half of her trees produce apples this year. How many bushels of apples does Mary harvest from her garden this year?
InternLM-Math Base 20B:
Reasoning: Mary has 3 trees that produce apples this year. Each tree produces 3 bushels of apples, so she harvests 3*3 = <<3*3=9>>9 bushels of apples. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Calculate the result of the following problem: (13 / 10) * (14 / 11). Please write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (13 / 10) * (14 / 11) = <<(13/10)*(14/11)=(13*14)/(10*11)=(182)/(110)=(91)/(55)>>91/55 ### Answer: 91/55
Expected answer: 91/55
Correct? Yes
Problem: Taking your answer from the previous problem, (13 / 10) * (14 / 11), calculate the square of that answer. Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (91/55)^2 = <<(91/55)^2=(91^2)/(55^2)=(8281)/(3025)>>8281/3025 ### Answer: 8281/3025
Expected answer: 8281/3025
Correct? Yes
Problem: Given the previous problem, now imagine that instead of multiplying by (14/11), we are multiplying by (14/4). What would be the result of (13 / 10) * (14 / 4)? Please give your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (13 / 10) * (14 / 4) = <<(13/10)*(14/4)=(13*14)/(10*4)=(182)/(40)=(91)/(20)>>91/20 ### Answer: 91/20
Expected answer: 91/20
Correct? Yes
Problem: James bought 20 very thin fabrics. Each piece of fabric has 2/19 meters of thread. How many meters of thread are there in total in 20 pieces of fabric? Calculate it by multiplying 2/19 by 20.
InternLM-Math Base 20B:
Reasoning: 2/19 * 20 = <<2/19*20=40/19>>40/19 There are 40/19 = <<40/19=2 1/19>>2 1/19 meters of thread in total in 20 pieces of fabric. ### Answer: 2 1/19
Expected answer: 40/19
Correct? No
Problem: What is the result of 1 times 16?
InternLM-Math Base 20B:
Reasoning: 1 times 16 = <<1*16=16>>16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: Taking the result you found from multiplying 1 times 16, what do you get if you then multiply that result by 2/11?
InternLM-Math Base 20B:
Reasoning: 16 times 2/11 = <<16*2/11=32/11>>32/11 ### Answer: 32/11
Expected answer: 32/11
Correct? Yes
Problem: If instead of 16, you were to multiply 1 by 11. What would the result be?
InternLM-Math Base 20B:
Reasoning: 1 times 11 = <<1*11=11>>11 ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Calculate the result of the following math problem: (18 / 12) * 6. Write your answer as a simplified fraction or a whole number.
InternLM-Math Base 20B:
Reasoning: (18 / 12) * 6 = <<(18/12)*6=3*6=18>>18 ### Answer: 18
Expected answer: 9
Correct? No
Problem: Here's a math problem about multiplying fractions and whole numbers: Johnny has 8 friends. He promised to give each of his friends 13/8 pounds of candy. How many pounds of candy will Johnny need in total?
InternLM-Math Base 20B:
Reasoning: Johnny will need 8 × 13/8 = <<8*13/8=13>>13 pounds of candy in total. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: Mathew was cutting up some square blocks for a craft project. Each block was 16/18th of a foot long. Mathew needed 16/7th of a foot long blocks for his project. If he uses all the blocks, how long in feet would the blocks be in total? Solve this by using multiplication of fractions.
InternLM-Math Base 20B:
Reasoning: Mathew needs 16/7th of a foot long blocks for his project. 16/18th of a foot long blocks are 16/18 x 7/16 = <<16/18 x 7/16=7/18>>7/18 of a foot long. Mathew needs 7/18 of a foot long blocks for his project. 7/18 of a foot long blocks are 7/18 x 16/7 = <<7/18 x 16/7=16/63>>16/63 of a foot long. Mathew needs 16/63 of a foot long blocks for his project. 16/63 of a foot long blocks are 16/63 x 18/16 = <<16/63 x 18/16=18/63>>18/63 of a foot long. Mathew needs 18/63 of a foot long blocks for his project. 18/63 of a foot long blocks are 18/63 x 7/18 = <<18/63 x 7/18=7/27>>7/27 of a foot long. Mathew needs 7/27 of a foot long blocks for his project. 7/27 of a foot long blocks are 7/27 x 16/7 = <<7/27 x 16/7=16/189>>16/189 of a foot long. Mathew needs 16/189 of a foot long blocks for his project. 16/189 of a foot long blocks are 16/189 x 18/16 = <<16/189 x 18/16=18/189>>18/189 of a foot long. Mathew needs 18/189 of a foot long blocks for his project. 18/189 of a foot long blocks are 18/189 x 7/18 = <<18/189 x 7/18=7/189>>7/189 of a foot long. Mathew needs 7/189 of a foot long blocks for his project. 7/189 of a foot long blocks are 7/189 x 16/7 = <<7/189 x 16/7=16/1323>>16/1323 of a foot long. Mathew needs 16/1323 of a foot long blocks for his project. 16/1323 of a foot long blocks are 16/1323 x 18/16 = <<16/1323 x 18/16=18/1323>>18/1323 of a foot long. Mathew needs 18/1323 of a foot long blocks for his project. 18/1323 of a foot long blocks are 18/1323 x 7/18 = <<18/1323 x 7/18=7/1323>>7/1323 of a foot long. Mathew needs 7/1323 of a foot long blocks for his project. 7/1323 of a foot long blocks are 7/1323 x 16/7 = <<7/1323 x 16/7=16/9246>>16/9246 of a foot long. Mathew needs 16/9246 of a foot long blocks for his project. 16/9246 of a foot long blocks are 16/9246 x 18/16 = <<16/9246 x 18/16=18/9246>>18/9246 of a foot long. Mathew needs 18/9246 of a foot long blocks for his project. 18/9246 of a foot long blocks are 18/9246 x 7/18 = <<18/9246 x 7/18=7/9246>>7/9246 of a foot long. Mathew needs 7/9246 of a foot long blocks for his project. 7/9246 of a foot long blocks are 7/9246 x 16/7 = <<7/9246 x 16/7=16/156692>>16/156692 of a foot long. Mathew needs 16/156692 of a foot long blocks for his project. 16/156692 of a foot long blocks are 16/156692 x 18/16 = <<16/156692 x 18/16=18/156692>>18/156692 of a foot long. Mathew needs 18/156692 of a foot long blocks for his project. 18/156692 of a foot long blocks are 18/156692 x 7/18 = <<18/156692 x 7/18=7/156692>>7/156692 of a foot long. Mathew needs
Expected answer: 128/63
Correct? No
Problem: What is the result when you multiply the fraction 8/8 by 15?
InternLM-Math Base 20B:
Reasoning: 8/8 = 1, so 8/8 × 15 = 1 × 15 = <<1*15=15>>15. ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: After you've calculated the result of 8/8 multiplied by 15, what do you get if you further multiple that result by 19/18?
InternLM-Math Base 20B:
Reasoning: 8/8 × 15 = 15, so 8/8 × 15 × 19/18 = 15 × 19/18 = <<15*19/18=19/2>>19/2. ### Answer: 19/2
Expected answer: 95/6
Correct? No
Problem: Suppose instead of having a fraction of 8/8 in the previous question, there was a fraction of 8/7. What would be the result when that fraction is multiplied by 15?
InternLM-Math Base 20B:
Reasoning: 8/7 × 15 = <<8/7*15=120/7>>120/7. ### Answer: 120/7
Expected answer: 120/7
Correct? Yes
Problem: A recipe for apple pie requires 10 apples. However, you only have two thirds of the amount needed. How many apples do you have if you multiply 10 apples by 4/6?
InternLM-Math Base 20B:
Reasoning: 10 apples x 4/6 = <<10*4/6=20/3>>20/3 apples. You have 20/3 = <<20/3=6 2/3>>6 2/3 apples. ### Answer: 6 2/3
Expected answer: 20/3
Correct? Yes
Problem: After calculating the amount of apples you have by multiplying 10 apples by two thirds, imagine you found some more apples in the backyard, doubling your current amount. How many apples would you have now?
InternLM-Math Base 20B:
Reasoning: 6 2/3 apples x 2 = <<6 2/3*2=13 1/3>>13 1/3 apples. You have 13 1/3 apples. ### Answer: 13 1/3
Expected answer: 40/3
Correct? Yes
Problem: You initially thought the recipe for apple pie required 10 apples, but upon re-reading it, you realize it actually only requires 8 apples. If you still have two thirds of the required amount, how many apples do you have now when you multiply 8 apples by 4/6?
InternLM-Math Base 20B:
Reasoning: 8 apples x 4/6 = <<8*4/6=16/3>>16/3 apples. You have 16/3 = <<16/3=5 1/3>>5 1/3 apples. ### Answer: 5 1/3
Expected answer: 16/3
Correct? Yes
Problem: What is the product when you multiply the fraction 18/12 by the whole number 11?
InternLM-Math Base 20B:
Reasoning: 18/12 = 3/2, so 18/12 × 11 = 3/2 × 11 = <<3/2*11=33/2>>33/2. ### Answer: 33/2
Expected answer: 33/2
Correct? Yes
Problem: You found that the product of 18/12 and 11 was 'x'. Now, multiply the result 'x' by the fraction 14/13. What is the new result? Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 18/12 × 11 = x, so 18/12 × 11 × 14/13 = x × 14/13 = <<x*14/13=33/2*14/13=77/4>>77/4. ### Answer: 77/4
Expected answer: 231/13
Correct? No
Problem: In the previous scenario, we calculated the product of the fraction 18/12 and the whole number 11. Now, consider what would happen if instead of multiplying by 11, we multiplied by 10. What would be the product of 18/12 and 10? Please write your answer as a simplified fraction or whole number as appropriate.
InternLM-Math Base 20B:
Reasoning: 18/12 = 3/2, so 18/12 × 10 = 3/2 × 10 = <<3/2*10=15>>15. ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: In a pizza shop, the mushroom pizza, which is very popular, usually sells out in just 9/20 of an hour. The pizza chef can make 16 pizzas in just one hour. How many mushroom pizzas can the chef make before they sell out?
InternLM-Math Base 20B:
Reasoning: The chef can make 16/9 = <<16/9=1.77777777777777777777777777777778>>1.77777777777777777777777777777778 pizzas in 9/20 of an hour. The chef can make 16/9 × 20 = <<16/9*20=35.5555555555555555555555555555556>>35.5555555555555555555555555555556 pizzas in 1 hour. The chef can make 16 × 20 = <<16*20=320>>320 pizzas in 9 hours. The chef can make 16 × 20 × 9/20 = <<16*20*9/20=144>>144 pizzas in 9/20 of an hour. The chef can make 16 × 20 × 9/20 × 20 = <<16*20*9/20*20=2880>>2880 pizzas in 1 hour. The chef can make 16 × 20 × 9/20 × 20 × 9 = <<16*20*9/20*20*9=25920>>25920 pizzas in 9 hours. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 = <<16*20*9/20*20*9*20=518400>>518400 pizzas in 1 day. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 = <<16*20*9/20*20*9*20*7=3628800>>3628800 pizzas in 1 week. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 = <<16*20*9/20*20*9*20*7*4=14515200>>14515200 pizzas in 1 month. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 × 12 = <<16*20*9/20*20*9*20*7*4*12=173036800>>173036800 pizzas in 1 year. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 × 12 × 100 = <<16*20*9/20*20*9*20*7*4*12*100=17303680000>>17303680000 pizzas in 100 years. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 × 12 × 100 × 1000 = <<16*20*9/20*20*9*20*7*4*12*100*1000=17303680000000>>17303680000000 pizzas in 1000 years. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 × 12 × 100 × 1000 × 10000 = <<16*20*9/20*20*9*20*7*4*12*100*1000*10000=17303680000000000>>17303680000000000 pizzas in 10000 years. The chef can make 16 × 20 × 9/20 × 20 × 9 × 20 × 7 × 4 × 12 × 100 × 1000 × 10000 × 100000 = <<16*20*9/20*20*9*20*7*4*12*100*1000*10000*100000=17303680000000000000>>17303680000000000000 pizzas in 100000 years. The chef can make 16 × 20 × 9/20 × 20
Expected answer: 36/5
Correct? No
Problem: A baker wants to bake enough cakes for a large party. Each cake requires 5/12 of a kilogram of flour. If the baker needs to bake 16 cakes, how many kilograms of flour will he need? Use the formula s = (16 * (5 / 12)) to calculate the answer.
InternLM-Math Base 20B:
Reasoning: The baker needs 16 * (5 / 12) = <<16*(5/12)=80/12=20/3>>20/3 kilograms of flour. ### Answer: 20/3
Expected answer: 20/3
Correct? Yes
Problem: The baker received a last-minute request to add an additional 3 cakes to his order, bringing the total up to 19 cakes. Each cake still requires 5/12 of a kilogram of flour. With this updated number of cakes, how much flour will he need now? Calculate this using the formula s = (19 * (5 / 12)).
InternLM-Math Base 20B:
Reasoning: The baker needs 19 * (5 / 12) = <<19*(5/12)=95/12=19/2>>19/2 kilograms of flour. ### Answer: 19/2
Expected answer: 95/12
Correct? No
Problem: Determine the result of the following calculation: multiply 13 by 3/12. Remember to write your answer as a fraction or a decimal number.
InternLM-Math Base 20B:
Reasoning: 13 * 3/12 = <<13*3/12=13/4>>13/4 ### Answer: 13/4
Expected answer: 13/4
Correct? Yes
Problem: After calculating the result from the previous problem, take your answer and square it (multiply it by itself). Write your final answer as a fraction, decimal, or a whole number if possible.
InternLM-Math Base 20B:
Reasoning: 13/4 * 13/4 = <<13/4*13/4=169/16>>169/16 ### Answer: 169/16
Expected answer: 169/16
Correct? Yes
Problem: After previously calculating 13 multiplied by 3/12, now consider if instead we actually needed to multiply 13 by 3/15 instead of 3/12. What would be the result of this new calculation? Remember to write your answer as a fraction, decimal, or a whole number if possible.
InternLM-Math Base 20B:
Reasoning: 13 * 3/15 = <<13*3/15=13/5>>13/5 ### Answer: 13/5
Expected answer: 13/5
Correct? Yes
Problem: Find the product when 8 is multiplied by 1. Show your work and provide your answer.
InternLM-Math Base 20B:
Reasoning: 8 × 1 = <<8*1=8>>8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the product when 8 is multiplied by 1, take that result and multiply it by 2. What is the final result? Show your work process.
InternLM-Math Base 20B:
Reasoning: 8 × 1 = <<8*1=8>>8 8 × 2 = <<8*2=16>>16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: In the same situation as the previous question, consider that originally there were 16 units instead of 8. Multiply the 16 units by 1. What will the new result be? Show your calculations and the final figure.
InternLM-Math Base 20B:
Reasoning: 16 × 1 = <<16*1=16>>16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: What is the result when you multiply 9 by the fraction 9/17?
InternLM-Math Base 20B:
Reasoning: 9 × 9/17 = <<9*9/17=9^2/17=81/17>>9^2/17 = 81/17 ### Answer: 81/17
Expected answer: 81/17
Correct? Yes
Problem: After finding the answer to the initial problem of multiplying 9 by the fraction 9/17, what do you get if you then multiply that result by 2?
InternLM-Math Base 20B:
Reasoning: 9 × 9/17 × 2 = <<9*9/17*2=9^2/17*2=81/17*2=162/17>>9^2/17 × 2 = 81/17 × 2 = 162/17 ### Answer: 162/17
Expected answer: 162/17
Correct? Yes
Problem: After solving the previous scenario, let's consider a change. Instead of multiplying 9 by the fraction 9/17, we now multiply 11 by the fraction 9/17. What is the result now?
InternLM-Math Base 20B:
Reasoning: 11 × 9/17 = <<11*9/17=11*9/11/17=99/17>>11 × 9/17 = 11 × 9/11 × 17 = 99/17 ### Answer: 99/17
Expected answer: 99/17
Correct? Yes
Problem: Tom is planning to share his 13 boxes with his friends. He has decided each of them will get 12/13 of a box. How many boxes, in total, will Tom's friends receive?
InternLM-Math Base 20B:
Reasoning: Tom's friends will receive 13*12/13 = <<13*12/13=12>>12 boxes. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Tom has decided to donate some of the boxes to a local school after sharing with his friends. He is now giving away 9/15 of the total boxes his friends received. How many boxes are being donated to the local school?
InternLM-Math Base 20B:
Reasoning: Tom is donating 9/15 of 12 = <<9/15*12=6>>6 boxes to the local school. ### Answer: 6
Expected answer: 36/5
Correct? No
Problem: Tom originally wanted to divide 13 boxes among his friends with each of them getting 12/13 of a box. However, he changed his mind and decided to give each friend 17/13 of a box instead. How many boxes in total will his friends receive now?
InternLM-Math Base 20B:
Reasoning: Tom's friends will receive 13*17/13 = <<13*17/13=17>>17 boxes. ### Answer: 17
Expected answer: 17
Correct? Yes
Problem: What is the product of multiplying 16 and 1?
InternLM-Math Base 20B:
Reasoning: 16 × 1 = <<16*1=16>>16 ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: After finding the product of 16 and 1, what is the result when this product is multiplied by 3/8? Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 16 × 1 × 3/8 = <<16*1*3/8=3/2>>3/2 ### Answer: 3/2
Expected answer: 6
Correct? No
Problem: After finding the product of 16 and 1 and multiplying it by 3/8, consider a similar action with different numbers. What is the product of 15 and 1?
InternLM-Math Base 20B:
Reasoning: 15 × 1 = <<15*1=15>>15 ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: Multiply 10 by the fraction 11/10. What is the result?
InternLM-Math Base 20B:
Reasoning: 10 * 11/10 = <<10*11/10=11>>11 ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: After finding the result of 10 * 11/10, now multiply this result by 2/19. What is the final result when you write it as a simplified fraction?
InternLM-Math Base 20B:
Reasoning: 11 * 2/19 = <<11*2/19=22/19>>22/19 ### Answer: 22/19
Expected answer: 22/19
Correct? Yes
Problem: Now instead of 10 * 11/10, let's change the fraction to 11/17. Multiply 10 by 11/17. What is the new result?
InternLM-Math Base 20B:
Reasoning: 10 * 11/17 = <<10*11/17=110/17>>110/17 ### Answer: 110/17
Expected answer: 110/17
Correct? Yes
Problem: Calculate the product of 10 and the fraction 8/14. Write your answer as a simplified fraction or a decimal.
InternLM-Math Base 20B:
Reasoning: 10 × 8/14 = <<10*8/14=5/7>>5/7 ### Answer: 5/7
Expected answer: 40/7
Correct? No
Problem: John has a pile of 20 assignment papers to grade. However, he has only managed to grade 8/18 of the pile. How many papers has John graded?
InternLM-Math Base 20B:
Reasoning: John has graded 8/18 = <<8/18=4/9>>4/9 of the pile. John has graded 4/9 × 20 = <<4/9*20=8.89>>8.89 papers. ### Answer: 8.89
Expected answer: 80/9
Correct? No
Problem: Calculate the result of multiplying 16 by the fraction 13/12.
InternLM-Math Base 20B:
Reasoning: 16 × 13/12 = <<16*13/12=13/12*16=13*16/12=208/12=17 1/6>>17 1/6 ### Answer: 17 1/6
Expected answer: 52/3
Correct? No
Problem: Maddison is dividing a piece of wood to build a bird house. The piece of wood is initially 16 units long. If she uses 2/19 of the piece of wood for each part of the bird house, how long is each part?
InternLM-Math Base 20B:
Reasoning: 16/2 = <<16/2=8>>8 16/19 = <<16/19=0.8421052631578947>>0.8421052631578947 8*0.8421052631578947 = <<8*0.8421052631578947=6.737179487179487>>6.737179487179487 ### Answer: 6.737179487179487
Expected answer: 32/19
Correct? No
Problem: What is the result of multiplying the fraction twelve divided by twelve with the whole number sixteen?
InternLM-Math Base 20B:
Reasoning: 12/12 = <<12/12=1>>1, and 1 × 16 = <<1*16=16>>16. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: After finding the result of multiplying twelve divided by twelve with the whole number sixteen, what is the new result when that value is further multiplied by four divided by fourteen?
InternLM-Math Base 20B:
Reasoning: 12/12 = <<12/12=1>>1, and 1 × 16 = <<1*16=16>>16. ### Answer: 16
Expected answer: 32/7
Correct? No
Problem: After multiplying twelve divided by twelve with sixteen in the previous problem, let's consider a scenario where instead of sixteen, we have eight. What is the result of twelve divided by twelve multiplied by eight?
InternLM-Math Base 20B:
Reasoning: 12/12 = <<12/12=1>>1, and 1 × 8 = <<1*8=8>>8. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Albert plans to make miniature models for his project and needs certain amount of material. He knows that he needs 8/7th of a pound of clay per model and he wants to create 17/3rd models. Calculate amount of clay in pounds he will need. What is it when the fractions are multiplied?
InternLM-Math Base 20B:
Reasoning: Albert needs 8/7 × 17/3 = <<8/7*17/3=8*17/7*3=136/21>>136/21 pounds of clay. ### Answer: 136/21
Expected answer: 136/21
Correct? Yes
Problem: Mrs. Parker makes her famous apple pie using 14/12 hours for preparing and baking. If she decides to make 2 pies, how many total hours will she spend? Please calculate and express your answer as a mixed number.
InternLM-Math Base 20B:
Reasoning: Mrs. Parker spends 14/12 hours for preparing and baking one pie. She spends 2 × 14/12 = <<2*14/12=28/12=2 2/12>>2 2/12 hours for preparing and baking 2 pies. ### Answer: 2 2/12
Expected answer: 7/3
Correct? No
Problem: Evaluate the following expression and write your answer as a simplified fraction: (18/11) * (17/8)
InternLM-Math Base 20B:
Reasoning: (18/11) * (17/8) = <<(18/11)*(17/8)=(18*17)/(11*8)=(306)/(88)>>306/88 ### Answer: 306/88
Expected answer: 153/44
Correct? Yes
Problem: After solving the expression (18/11) * (17/8) in the earlier problem, multiply the result by the fraction (12/19). What is your answer as a simplified fraction?
InternLM-Math Base 20B:
Reasoning: (306/88) * (12/19) = <<(306/88)*(12/19)=(306*12)/(88*19)=(3708)/(1832)>>3708/1832 ### Answer: 3708/1832
Expected answer: 459/209
Correct? No
Problem: After previously solving (18/11) * (17/8), let's consider what would happen if we instead have a different fraction: (10/11). So, recalculate the expression, but this time use (10/11) * (17/8). What is your answer as a simplified fraction?
InternLM-Math Base 20B:
Reasoning: (10/11) * (17/8) = <<(10/11)*(17/8)=(10*17)/(11*8)=(170)/(88)>>170/88 ### Answer: 170/88
Expected answer: 85/44
Correct? Yes
Problem: You are eating healthy and have decided to only eat half of an apple. Each apple costs $2. How much would you essentially be paying for half an apple?
InternLM-Math Base 20B:
Reasoning: You are paying $2 for 1 apple. You are eating half of an apple, so you are paying $2 for 1/2 of an apple. ### Answer: $2
Expected answer: 1
Correct? No
Problem: What is the product when you multiply 1 by 8?
InternLM-Math Base 20B:
Reasoning: 1*8 = <<1*8=8>>8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the product of 1 and 8, what is the value when you multiply this product with 9/8?
InternLM-Math Base 20B:
Reasoning: 8*9/8 = <<8*9/8=9>>9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: If instead of multiplying 1 by 8, we multiply 1 by 6, what would the new product be?
InternLM-Math Base 20B:
Reasoning: 1*6 = <<1*6=6>>6 ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: If a recipe calls for 5 cups of flour, but you are only using a scoop that is 14/16 the size of a cup, how many scoops do you need to have 5 whole cups of flour? Calculate it using the formula: p = 5 * (14 / 16)
InternLM-Math Base 20B:
Reasoning: p = 5 * (14 / 16) = <<5*(14/16)=5*(7/8)=35/8=4.375>>4.375 You need 4.375 scoops to have 5 whole cups of flour. ### Answer: 4.375
Expected answer: 35/8
Correct? Yes
Problem: Suppose you find that these scoops are still slightly too small for your baking needs, and you've decided to scale up the proportion of your scoop to 17/19 of a normal cup size. Using the result you got from the previous question, calculate how many scoops you would now need to make up for the missing quantity. Use the formula: k = ((17 / 19) * p) to compute this.
InternLM-Math Base 20B:
Reasoning: k = ((17 / 19) * p) = ((17 / 19) * 4.375) = <<(17/19)*4.375=(17/19)*35/8=17/19*4.4375=17/19*4+(17/19)*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375=17/19*4+17/19*0.4375
Expected answer: 595/152
Correct? No
Problem: Suppose you were operating under a misunderstanding and you actually need 15 cups of flour instead of 5. Recalculate how many scoops you need using the previous scoop size scaled to 14/16 of a normal cup. Use the formula: p = 15 * (14 / 16) to find the new number of scoops needed.
InternLM-Math Base 20B:
Reasoning: p = 15 * (14 / 16) = <<15*(14/16)=15*(7/8)=105/8=13.125>>13.125 You need 13.125 scoops to have 15 whole cups of flour. ### Answer: 13.125
Expected answer: 105/8
Correct? Yes
Problem: William has a recipe that requires 9/10 of a cup of sugar. However, he wants to triple the recipe. How many cups of sugar will William need? Follow the operation ((9 / 10) * 3) to answer the question.
InternLM-Math Base 20B:
Reasoning: William needs 9/10 * 3 = <<9/10*3=2.7>>2.7 cups of sugar. ### Answer: 2.7
Expected answer: 27/10
Correct? Yes
Problem: William decided to try a new recipe that only needed 9/17 of a cup of sugar for one batch. Just like the previous time, he wants to triple the recipe. How much sugar will he need this time? Use the operation in ((9 / 17) * 3) to answer the question.
InternLM-Math Base 20B:
Reasoning: William needs 9/17 * 3 = <<9/17*3=1.41>>1.41 cups of sugar. ### Answer: 1.41
Expected answer: 27/17
Correct? No
Problem: Compute the following operation: multiply 9 by 5/14. Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 9 × 5/14 = <<9*5/14=45/14>>45/14. 45/14 = <<45/14=3/2>>3/2. ### Answer: 3/2
Expected answer: 45/14
Correct? No
Problem: Michael wants to adjust a recipe that originally serves 16 servings to only serve 12 servings. He found a new vineyard that produces a type of grape juice that is 15/6 more concentrated than the one he originally uses. How much of the new grape juice should he use in comparison to the old recipe, if he calculates it as (12/16) * (15/6)?
InternLM-Math Base 20B:
Reasoning: (12/16) * (15/6) = <<(12/16) * (15/6) = (3/4) * (5/2) = (15/8)>>(15/8). Michael should use 15/8 of the new grape juice in comparison to the old recipe. ### Answer: (15/8)
Expected answer: 15/8
Correct? Yes
Problem: Now, let's say that Michael tasted the juice made with the adjusted recipe and found it too concentrated for his liking. He decides to dilute the juice by adding water, making the juice only 7/13 as concentrated as before. In comparison to the old undiluted recipe, how much of the new grape juice should he use now, if he calculates it as (7/13) * the previous fraction ((12/16) * (15/6))?
InternLM-Math Base 20B:
Reasoning: (7/13) * ((12/16) * (15/6)) = <<(7/13) * ((12/16) * (15/6)) = (7/13) * (15/8) = (35/104)>>(35/104). Michael should use 35/104 of the new grape juice in comparison to the old recipe. ### Answer: (35/104)
Expected answer: 105/104
Correct? No
Problem: Let's tweak the scenario again. This time, Michael found an even more concentrated grape juice. This new variant is 15/2 times as strong as the juice he originally used. Now, how much of this new juice should he use for 12 servings instead of 16, in comparison to the old recipe? So, he calculates it as (12/16) * (15/2).
InternLM-Math Base 20B:
Reasoning: (12/16) * (15/2) = <<(12/16) * (15/2) = (3/4) * (15/2) = (45/8)>>(45/8). Michael should use 45/8 of the new grape juice in comparison to the old recipe. ### Answer: (45/8)
Expected answer: 45/8
Correct? Yes
Problem: If a baker uses 9 cups of flour for a cake recipe and each cup of flour weighs 19/19 pounds, how many pounds of flour does the baker use for the cake?
InternLM-Math Base 20B:
Reasoning: 9 × 19/19 = <<9*19/19=9>>9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: If the baker decides to make a smaller cake that only uses 6/18 of the original amount of flour, how many pounds of flour would the baker use for the smaller cake?
InternLM-Math Base 20B:
Reasoning: 9 × 6/18 = <<9*6/18=3>>3 ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: If the baker decides to use just 1 cup of flour instead of 9 for the cake recipe, and each cup of flour still weighs 19/19 pounds, how many pounds of flour does the baker use now?
InternLM-Math Base 20B:
Reasoning: 1 × 19/19 = <<1*19/19=1>>1 ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: A baker needs 5 times the amount of sugar required in one recipe. If one recipe needs 9/4 cups of sugar, how much sugar does the baker need in cups? Do the multiplication and state your answer as a fraction in simplest form.
InternLM-Math Base 20B:
Reasoning: 5 * 9/4 = <<5*9/4=45/4>>45/4 The baker needs 45/4 = <<45/4=11 1/4>>11 1/4 cups of sugar. ### Answer: 11 1/4
Expected answer: 45/4
Correct? Yes
Problem: Julia is baking a cake that requires 12/8 cups of flour. However, she only needs to make 9/13 of the recipe. How much flour does she need for the portion of the recipe she is making?
InternLM-Math Base 20B:
Reasoning: Julia needs 12/8 × 9/13 = <<12/8*9/13=9/10>>9/10 cups of flour. ### Answer: 9/10
Expected answer: 27/26
Correct? No
Problem: Calculate the following expression: 9 * (20/11). Write the answer as a mixed number.
InternLM-Math Base 20B:
Reasoning: 9 * (20/11) = <<9*20/11=180/11>>180/11 180/11 = <<180/11=16 4/11>>16 4/11 ### Answer: 16 4/11
Expected answer: 180/11
Correct? Yes
Problem: After calculating the previous expression, which was 9 * (20/11), take your result and then multiply it by 4/5. What is the final result? Write your answer in the simplified form.
InternLM-Math Base 20B:
Reasoning: 9 * (20/11) = <<9*20/11=180/11>>180/11 180/11 = <<180/11=16 4/11>>16 4/11 16 4/11 * 4/5 = <<16 4/11 * 4/5=12 16/55>>12 16/55 ### Answer: 12 16/55
Expected answer: 144/11
Correct? No
Problem: In the previous problem, you calculated 9 * (20/11). But what if instead of multiplying by 20/11, you multiply by 7/11? Recalculate the expression now being 9 * (7/11). What is the new result? Write your answer in the simplified form.
InternLM-Math Base 20B:
Reasoning: 9 * (7/11) = <<9*7/11=63/11>>63/11 63/11 = <<63/11=5 8/11>>5 8/11 ### Answer: 5 8/11
Expected answer: 63/11
Correct? Yes
Problem: Solve the following problem: Divide 20 by 5 and then multiply the result by the fraction 6/10. Write down your answer.
InternLM-Math Base 20B:
Reasoning: 20/5 = <<20/5=4>>4, 4*6/10 = <<4*6/10=2.4>>2.4 ### Answer: 2.4
Expected answer: 12/5
Correct? Yes
Problem: After solving the previous problem, what if instead of dividing 20 by 5, you divided 16 by 5 and kept the rest of the problem the same, where the result is then multiplied by 6/10? Calculate this new problem and provide your answer.
InternLM-Math Base 20B:
Reasoning: 16/5 = <<16/5=3.2>>3.2, 3.2*6/10 = <<3.2*6/10=1.92>>1.92 ### Answer: 1.92
Expected answer: 48/25
Correct? Yes
Problem: In a school where there are 17 classrooms and each classroom has a bin for paper recycling, 5/14 of the total classrooms forgot to recycle their papers during a specific day. What fraction of the total classrooms didn't recycle their papers?
InternLM-Math Base 20B:
Reasoning: 5/14 of the total classrooms didn't recycle their papers. 5/14 = <<5/14=0.35714285714285714285714285714286>>0.35714285714285714285714285714286 of the total classrooms didn't recycle their papers. ### Answer: 0.35714285714285714285714285714286
Expected answer: 85/14
Correct? No
Problem: Calculate the answer to the following problem: what is (19 / 11) * (13 / 17)? Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (19 / 11) * (13 / 17) = <<19/11*13/17=1/2>>1/2 ### Answer: 1/2
Expected answer: 247/187
Correct? No
Problem: Samantha has a rope that is 9 feet long. She uses 3/11 of the rope to secure a tent. How long is the piece of rope that Samantha uses?
InternLM-Math Base 20B:
Reasoning: Samantha uses 9*3/11 = <<9*3/11=2.727272727272727>>2.727272727272727 feet of rope. ### Answer: 2.727272727272727
Expected answer: 27/11
Correct? No
Problem: What is the result of the multiplication when 1 is multiplied by 7?
InternLM-Math Base 20B:
Reasoning: 1*7 = <<1*7=7>>7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: What is the result when you multiply the previous answer (result of 1 multiplied by 7) by the fraction 5/5?
InternLM-Math Base 20B:
Reasoning: 7*5/5 = <<7*5/5=7>>7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: What would be the result of the multiplication if the original number was not 1 multiplied by 7, but rather 1 multiplied by 19?
InternLM-Math Base 20B:
Reasoning: 1*19 = <<1*19=19>>19 ### Answer: 19
Expected answer: 19
Correct? Yes
Problem: Find the product of the following calculation: 1 times 9.
InternLM-Math Base 20B:
Reasoning: 1 times 9 = <<1*9=9>>9 ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Take your answer from the previous problem which was the product of 1 and 9. Now multiply that result by the fraction 13/18. What is your new output?
InternLM-Math Base 20B:
Reasoning: 9 times 13/18 = <<9*13/18=13/2>>13/2 ### Answer: 13/2
Expected answer: 13/2
Correct? Yes
Problem: In the previous question, instead of multiplying 1 by 9, suppose you need to multiply 1 by 4. What would be the outcome in this case?
InternLM-Math Base 20B:
Reasoning: 1 times 4 = <<1*4=4>>4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Calculate the product of the fraction (18 / 18) and the fraction (11 / 5). Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (18 / 18) = 1, so the product is (11 / 5). ### Answer: 11/5
Expected answer: 11/5
Correct? Yes
Problem: Continuing from the previous problem where you calculated the product of (18 / 18) and (11 / 5), what would be the result if you multiplied this produced value by itself? Report your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (11 / 5) * (11 / 5) = (11 * 11) / (5 * 5) = 121 / 25. ### Answer: 121/25
Expected answer: 121/25
Correct? Yes
Problem: Let's modify the previous problem slightly. If instead of (18 / 18), you used (9 / 18), what would be the product of this fraction and (11 / 5)? Report your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: (9 / 18) = 1/2, so the product is (11 / 10). ### Answer: 11/10
Expected answer: 11/10
Correct? Yes
Problem: Calculate the answer for the following equation: (5 / 16) * 13. Please express your answer as a decimal.
InternLM-Math Base 20B:
Reasoning: (5 / 16) * 13 = <<5/16*13=39/16>>39/16 ### Answer: 39/16
Expected answer: 65/16
Correct? No
Problem: Find the result of the following calculation: Multiply the fraction 4/5 by the whole number 15. Write your answer in simplest form.
InternLM-Math Base 20B:
Reasoning: 4/5 × 15 = <<4/5*15=60/5=12>>12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: After finding the result of 4/5 multiplied by 15, multiply this result by the fraction 3/15. Write your answer in simplest form.
InternLM-Math Base 20B:
Reasoning: 12 × 3/15 = <<12*3/15=36/15=4/1=4>>4 ### Answer: 4
Expected answer: 12/5
Correct? No
Problem: Suppose that you have adjusted your previous calculation. Instead of multiplying 4/5 by 15, you now need to multiply 4/5 by 6. What is the result of that calculation? Please write your answer in the simplest form.
InternLM-Math Base 20B:
Reasoning: 4/5 × 6 = <<4/5*6=24/5=4 4/5>>4 4/5 ### Answer: 4 4/5
Expected answer: 24/5
Correct? Yes
Problem: What will be the result if you multiply the fraction 20/12 by the fraction 19/16?
InternLM-Math Base 20B:
Reasoning: 20/12 = <<20/12=5/3>>5/3 and 19/16 = <<19/16=19/16>>19/16. 5/3 × 19/16 = <<5/3*19/16=95/48>>95/48. ### Answer: 95/48
Expected answer: 95/48
Correct? Yes
Problem: In continuation from the previous problem, what will be the result if you square the obtained result? In other words, multiply the result of the previous operation with itself.
InternLM-Math Base 20B:
Reasoning: 95/48 = <<95/48=95/48>>95/48. (95/48)2 = <<(95/48)^2=9025/2304>>9025/2304. ### Answer: 9025/2304
Expected answer: 9025/2304
Correct? Yes
Problem: Instead of multiplying 20/12 by 19/16 as in the previous problem, what would be the result if you multiplied 20/12 by another fraction of similar value, namely 19/12?
InternLM-Math Base 20B:
Reasoning: 20/12 = <<20/12=5/3>>5/3 and 19/12 = <<19/12=19/12>>19/12. 5/3 × 19/12 = <<5/3*19/12=95/36>>95/36. ### Answer: 95/36
Expected answer: 95/36
Correct? Yes
Problem: Calculate the result of the following multiplication operation: 17/20 * 17/13. Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 17/20 * 17/13 = <<17/20 * 17/13 = 289/260>>289/260 ### Answer: 289/260
Expected answer: 289/260
Correct? Yes
Problem: For the next part of your calculation, multiply the result of 17/20 * 17/13, denoted as 'f', by 12/11. What is the result of this operation? Please write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: f * 12/11 = <<289/260 * 12/11 = 34/25>>34/25 ### Answer: 34/25
Expected answer: 867/715
Correct? No
Problem: Suppose instead of 17/20 in the previous problem, the fraction was actually 16/20. What would the result of the multiplication operation 16/20 * 17/13 be? Please write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 16/20 * 17/13 = <<16/20 * 17/13 = 16/13>>16/13 ### Answer: 16/13
Expected answer: 68/65
Correct? No
Problem: Solve the following problem: 5 * (13 / 12) and give your answer in the form of a mixed number or fraction where necessary.
InternLM-Math Base 20B:
Reasoning: 5 * (13 / 12) = <<5*13/12=65/12>>65/12 ### Answer: 65/12
Expected answer: 65/12
Correct? Yes
Problem: Continuing from our previous problem, now, multiply the answer you got by (14 / 14). What is your new result as a mixed number or fraction?
InternLM-Math Base 20B:
Reasoning: 65/12 * (14 / 14) = <<65/12*14/14=65/12>>65/12 ### Answer: 65/12
Expected answer: 65/12
Correct? Yes
Problem: Continuing from the first problem, suppose we used 5 * (13 / 10) instead of 5 * (13 / 12). Calculate the new problem and give your answer in the form of a mixed number or fraction where necessary. What happens to the result when we use 13 / 10 instead of 13 / 12 in the problem?
InternLM-Math Base 20B:
Reasoning: 5 * (13 / 10) = <<5*13/10=65/10>>65/10 ### Answer: 65/10
Expected answer: 13/2
Correct? Yes
Problem: Jack had a full bar of chocolate. If he ate 3/4 of it and each piece of the bar represented 1/4, how many pieces did he eat?
InternLM-Math Base 20B:
Reasoning: Jack ate 3/4 of 4 = <<3/4*4=3>>3 pieces of chocolate. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: Following the previous scenario, Jack found an even bigger bar of chocolate that had 17 pieces in total. If he ate the same amount (3/4) of this bar as he did with the previous one, how many pieces of the new chocolate bar did he eat?
InternLM-Math Base 20B:
Reasoning: Jack ate 3/4 of 17 = <<3/4*17=12.75>>12.75 pieces of chocolate. ### Answer: 12.75
Expected answer: 51/4
Correct? Yes
Problem: Calculate the product of 17 and 9/18 without simplifying the fraction. What is the result?
InternLM-Math Base 20B:
Reasoning: 17 × 9/18 = <<17*9/18=153/18>>153/18 ### Answer: 153/18
Expected answer: 17/2
Correct? Yes
Problem: Reconsider the previous problem, but this time replace 9/18 by 13/18. So, now calculate the product of 17 and 13/18 without simplifying the fraction. What is the result now?
InternLM-Math Base 20B:
Reasoning: 17 × 13/18 = <<17*13/18=221/18>>221/18 ### Answer: 221/18
Expected answer: 221/18
Correct? Yes
Problem: Calculate the result of multiplying the fraction 15/15 by the whole number 19. Leave your answer as a simplified fraction or whole number, as appropriate.
InternLM-Math Base 20B:
Reasoning: 15/15 = 1, so 15/15 × 19 = 1 × 19 = <<1*19=19>>19. ### Answer: 19
Expected answer: 19
Correct? Yes
Problem: Following your previous calculation, now multiply the result by the fraction 6/10. Write down the result as a simplified fraction or a whole number, as appropriate.
InternLM-Math Base 20B:
Reasoning: 19 × 6/10 = <<19*6/10=11.4>>11.4. ### Answer: 11.4
Expected answer: 57/5
Correct? Yes
Problem: Following your previous calculation, reconsider the problem assuming the whole number you previously used was 20 instead of 19. Calculate the result of multiplying the fraction 15/15 by this new whole number. Write down the result as a simplified fraction or a whole number, as appropriate.
InternLM-Math Base 20B:
Reasoning: 15/15 = 1, so 15/15 × 20 = 1 × 20 = <<1*20=20>>20. ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Mary has 16 apples. She shares 3/5 of them with her friends. How many apples does Mary share with her friends?
InternLM-Math Base 20B:
Reasoning: Mary shares 3/5 of 16 = <<3/5*16=24/5=4+4/5>>4 4/5 apples with her friends. ### Answer: 4 4/5
Expected answer: 48/5
Correct? No
Problem: What is the product when you divide 12 by 3 and then multiply the result by 3?
InternLM-Math Base 20B:
Reasoning: 12/3 = <<12/3=4>>4, and 4*3 = <<4*3=12>>12. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Reconsider the original problem, where 12 was divided by 3, and the result was multiplied by 3. Now, replace 12 with 2. What would be the product now?
InternLM-Math Base 20B:
Reasoning: 2/3 = <<2/3=0.6666666666666666>>0.6666666666666666, and 0.6666666666666666*3 = <<0.6666666666666666*3=2>>2. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: If each box of chocolates contains 12 pieces and each piece is split into 8 equal parts for tasting, how many whole pieces of chocolate are there if there are 6 boxes? Use the equation t = (6 * (12 / 8)) to calculate your answer.
InternLM-Math Base 20B:
Reasoning: t = (6 * (12 / 8)) = <<6*(12/8)=9>>9 There are 9 whole pieces of chocolate. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Let's consider a change in the previous problem. Instead of 6 boxes of chocolates, assume now that we only have 3 boxes. If each box of chocolates contains 12 pieces and each piece is divided into 8 equal parts for tasting, how many whole pieces of chocolate are there now? Use the equation t = 3 * (12 / 8) to calculate your answer.
InternLM-Math Base 20B:
Reasoning: t = 3 * (12 / 8) = <<3*(12/8)=4.5>>4.5 There are 4.5 whole pieces of chocolate. ### Answer: 4.5
Expected answer: 9/2
Correct? Yes
Problem: Emily uses 10/19th of her weekly allowance on Monday. On Tuesday, she spends an equivalent amount which is 14/7 times more compared to what she spent on Monday. How much of her weekly allowance did she spend on Tuesday? Calculate: (10 / 19) * (14 / 7)
InternLM-Math Base 20B:
Reasoning: Emily spent (10 / 19) * (14 / 7) = <<(10/19)*(14/7)=2/3>>2/3 of her weekly allowance on Tuesday. ### Answer: 2/3
Expected answer: 20/19
Correct? No
Problem: What is the product of 2 and 2?
InternLM-Math Base 20B:
Reasoning: 2*2 = <<2*2=4>>4 ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: After finding the product of 2 and 2, what would you get if you multiply that result by 5/2?
InternLM-Math Base 20B:
Reasoning: 2*2 = <<2*2=4>>4 4*5/2 = <<4*5/2=10>>10 ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: You have 11 boxes of cookies. Each box has 8/5 dozen cookies in it. How many dozens of cookies do you have in total?
InternLM-Math Base 20B:
Reasoning: 11 × 8/5 = <<11*8/5=88/5>>88/5 dozen cookies. ### Answer: 88/5
Expected answer: 88/5
Correct? Yes
Problem: Suppose that each box actually contained 6/5 dozen cookies instead of 8/5 dozen. With still 11 boxes of cookies, how many dozens of cookies do you have now?
InternLM-Math Base 20B:
Reasoning: 11 × 6/5 = <<11*6/5=66/5>>66/5 dozen cookies. ### Answer: 66/5
Expected answer: 66/5
Correct? Yes
Problem: Compute the result of the following operation: multiply the fraction 6/18 by the whole number 3. Write your answer in its simplest form.
InternLM-Math Base 20B:
Reasoning: 6/18 = 1/3. 1/3 × 3 = 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After finding the result of the operation 6/18 * 3, calculate the square of that result. Write your answer in the simplest form.
InternLM-Math Base 20B:
Reasoning: 6/18 = 1/3. 1/3 × 3 = 1. 1^2 = 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: After finding the result of the previous operation 6/18 * 3, consider a new situation where you multiply the fraction 17/18 by the whole number 3 instead. What is the result of this new operation? Write your answer in its simplest form.
InternLM-Math Base 20B:
Reasoning: 17/18 = 1 5/18. 1 5/18 × 3 = 3 15/18 = 3 5/6. ### Answer: 3 5/6
Expected answer: 17/6
Correct? No
Problem: Lucy had 18 candies which she evenly distributed into 8 bags, she then gave 5 bags to her friends. How many candies does she give away in total? Use the formula (18 / 8) * 5 to find the answer.
InternLM-Math Base 20B:
Reasoning: Lucy gave 18/8 = <<18/8=2.25>>2.25 candies to each of her friends. She gave 2.25 * 5 = <<2.25*5=11.25>>11.25 candies to her friends in total. ### Answer: 11.25
Expected answer: 45/4
Correct? Yes
Problem: If Lucy originally had 13 candies instead of 18, evenly distributed into 8 bags, and she then gave 5 bags to her friends, how many candies does she give away in total? Use the formula (13 / 8) * 5 to find the answer.
InternLM-Math Base 20B:
Reasoning: Lucy gave 13/8 = <<13/8=1.625>>1.625 candies to each of her friends. She gave 1.625 * 5 = <<1.625*5=8.125>>8.125 candies to her friends in total. ### Answer: 8.125
Expected answer: 65/8
Correct? Yes
Problem: Calculate the following multiplication of a whole number and a fraction. What is the result of 5 * (14 / 10)?
InternLM-Math Base 20B:
Reasoning: 5 * (14 / 10) = <<5*14/10=5*7/5=7>>7 ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After finding the result of 5 * (14 / 10), continue with the next step of the problem by multiplying this result by the fraction 5/6. What is the final result?
InternLM-Math Base 20B:
Reasoning: 5 * (14 / 10) * (5 / 6) = <<5*7/5*5/6=7*5/6=35/6>>35/6 ### Answer: 35/6
Expected answer: 35/6
Correct? Yes
Problem: After initially calculating the result of 5 * (14 / 10), consider a different scenario where you have to calculate 5 * (14 / 13) instead. What would the result be in this case?
InternLM-Math Base 20B:
Reasoning: 5 * (14 / 13) = <<5*14/13=5*14/13=140/13>>140/13 ### Answer: 140/13
Expected answer: 70/13
Correct? No
Problem: What is the result of multiplying 6 by the fraction (20/7)? Write your answer as a mixed number, if applicable.
InternLM-Math Base 20B:
Reasoning: 6*(20/7) = <<6*(20/7)=120/7=17 1/7>>17 1/7 ### Answer: 17 1/7
Expected answer: 120/7
Correct? Yes
Problem: After finding the result of multiplying 6 by the fraction (20/7), what would you get if you multiply this result by (10/10)? Write your answer as a mixed number, if applicable.
InternLM-Math Base 20B:
Reasoning: 6*(20/7)*(10/10) = <<6*(20/7)*(10/10)=120/7=17 1/7>>17 1/7 ### Answer: 17 1/7
Expected answer: 120/7
Correct? Yes
Problem: After finding the result of multiplying 5/8 by 3, what would be the result if instead of multiplying (20/7) by 6, you multiplied (20/10) by 6? Write your answer as a mixed number, if applicable.
InternLM-Math Base 20B:
Reasoning: 5/8*3 = <<5/8*3=15/8=1 7/8>>1 7/8 ### Answer: 1 7/8
Expected answer: 12
Correct? No
Problem: Calculate: What is the product of 8/19 times 6? Give your answer as a simplified fraction or a whole number, if possible.
InternLM-Math Base 20B:
Reasoning: 8/19 times 6 = <<8/19*6=8/19*6/1=48/19=2 6/19>>2 6/19 ### Answer: 2 6/19
Expected answer: 48/19
Correct? No
Problem: Calculate the answer to the following problem. What is the result of multiplying 8 by 1/1?
InternLM-Math Base 20B:
Reasoning: 8*1/1 = <<8*1/1=8>>8 ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: After finding the result of multiplying 8 by 1/1 in the previous problem, what is the result when we multiply that answer by 3/2?
InternLM-Math Base 20B:
Reasoning: 8*3/2 = <<8*3/2=12>>12 ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: After finding the result of multiplying 8 by 1/1 in the previous problem, what would be the result if you were originally working with 20 instead of 8? In other words, what would be the outcome of multiplying 20 by 1/1?
InternLM-Math Base 20B:
Reasoning: 20*1/1 = <<20*1/1=20>>20 ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Jack has a long sheet of paper that he wants to use for his art project. The sheet has a length of 5/15 meters. If Jack cuts 9 identical pieces from the sheet, what would be the total length of all the 9 pieces? Calculate the answer and write it as a fraction or a whole number.
InternLM-Math Base 20B:
Reasoning: The total length of the 9 pieces is 9 × 5/15 = <<9*5/15=3/5>>3/5 meters. ### Answer: 3/5
Expected answer: 3
Correct? No
Problem: Suppose the length of a book is 1 foot, and there are 13 books side by side on a shelf. How long is the shelf in feet? To find out, calculate the product of 1 and 13.
InternLM-Math Base 20B:
Reasoning: 1 × 13 = <<1*13=13>>13. The length of the shelf is 13 feet. ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: In the previous problem, the total length of the shelf was found to be 13 feet. Now, suppose that only 12/15 of that shelf is filled with books. What would be the length of the shelf that is filled with books? To find out, multiply the total length of the shelf by 12/15.
InternLM-Math Base 20B:
Reasoning: 13 × 12/15 = <<13*12/15=8.8>>8.8. The length of the shelf that is filled with books is 8.8 feet. ### Answer: 8.8
Expected answer: 52/5
Correct? No
Problem: Calculate the product when you multiply the fraction 6/5 by the whole number 1. Write your answer as a simplified fraction or whole number.
InternLM-Math Base 20B:
Reasoning: 6/5 × 1 = <<6/5*1=6/5>>6/5 ### Answer: 6/5
Expected answer: 6/5
Correct? Yes
Problem: Once you have calculated the product of 6/5 and 1, multiply the result by itself. Write your answer as a simplified fraction or whole number.
InternLM-Math Base 20B:
Reasoning: 6/5 × 1 × 6/5 = <<6/5*1*6/5=36/25>>36/25 ### Answer: 36/25
Expected answer: 36/25
Correct? Yes
Problem: Solve the following problem: Recognize that 5/5 is the same as 1, then multiply that result by 17/6. Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 5/5 = <<5/5=1>>1, so 5/5 * 17/6 = 1 * 17/6 = <<1*17/6=17/6>>17/6. ### Answer: 17/6
Expected answer: 17/6
Correct? Yes
Problem: In the previous problem, we multiplied 5/5 with 17/6. This time, let's consider that instead of 17/6, we want to multiply 5/5 by 6/6. What would be the result of this multiplication? Write down your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 5/5 = <<5/5=1>>1, so 5/5 * 6/6 = 1 * 6/6 = <<1*6/6=6/6>>6/6. ### Answer: 6/6
Expected answer: 1
Correct? Yes
Problem: What is the result of multiplying 8 by the result of 8 divided by 6?
InternLM-Math Base 20B:
Reasoning: 8/6 = <<8/6=1.333...>>1.333... 8*1.333... = <<8*1.333...=10.666...>>10.666... ### Answer: 10.666...
Expected answer: 32/3
Correct? No
Problem: Susan bought 9 apples. She used 15/16 of those apples to make a big apple pie for her family. What fraction of the total apples did Susan use?
InternLM-Math Base 20B:
Reasoning: Susan used 9 × 15/16 = <<9*15/16=13.875>>13.875 apples to make the pie. Susan used 13.875/9 = <<13.875/9=1.5416666666666667>>1.5416666666666667 of the total apples to make the pie. ### Answer: 1.5416666666666667
Expected answer: 135/16
Correct? No
Problem: In a class, 10 out of 14 students participated in a school project. Each of those students prepared 8 models for the science fair. Calculate the total number of models prepared for the science fair by multiplying the fraction of students who participated (10/14) with the number of models each student made (8).
InternLM-Math Base 20B:
Reasoning: 10/14 = <<10/14=5/7>>5/7 of the students participated in the project. Each student made 8 models. So, the total number of models is 5/7 × 8 = <<5/7*8=40/7=5.71>>40/7 = 5.71. ### Answer: 5.71
Expected answer: 40/7
Correct? No
Problem: What is the product of the fraction 3/3 and the mixed number 13/4? Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 3/3 = 1, and 13/4 = 3 1/4. 1 × 3 1/4 = 3 1/4 3 1/4 = 13/4 ### Answer: 13/4
Expected answer: 13/4
Correct? Yes
Problem: Given the original question, but now let's consider a change in quantity. Instead of multiplying 13/4 with 3/3. Now assume you're multiplying 18/4 by 3/3. What would be the product of these numbers now? Write your answer as a simplified fraction.
InternLM-Math Base 20B:
Reasoning: 18/4 = 4 2/4, and 3/3 = 1. 1 × 4 2/4 = 4 2/4 4 2/4 = 18/4 ### Answer: 18/4
Expected answer: 9/2
Correct? Yes
Problem: Calculate the result of multiplying thirteen by the ratio of two to two.
InternLM-Math Base 20B:
Reasoning: 13 * (2/2) = <<13*2/2=13*1=13>>13 ### Answer: 13
Expected answer: 13
Correct? Yes
Problem: After finding the result of multiplying thirteen by the ratio of two to two, now calculate the result of multiplying this outcome by the fraction eight fourteenths. What is the final result?
InternLM-Math Base 20B:
Reasoning: 13 * (2/2) = <<13*2/2=13*1=13>>13 13 * (8/14) = <<13*8/14=13*4/7=52/7>>52/7 ### Answer: 52/7
Expected answer: 52/7
Correct? Yes
Problem: Calculate the value of the expression 17/6 * 6/4. Write your answer in the simplest form.
InternLM-Math Base 20B:
Reasoning: 17/6 * 6/4 = <<17/6*6/4=17/4=4 1/4>>4 1/4 ### Answer: 4 1/4
Expected answer: 17/4
Correct? Yes
Problem: Recalculate the previous problem, however, instead of using 17/6, use 20/6. The new problem should be 20/6 * 6/4. Find the result and write it in its simplest form.
InternLM-Math Base 20B:
Reasoning: 20/6 * 6/4 = <<20/6*6/4=20/4=5>>5 ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: Find the product of 2 and 6.
InternLM-Math Base 20B:
2 × 6 = <<2*6=12>>12
Expected answer: 12
Correct? Yes
Problem: Your pet dog, Bear, can chase and bring back the ball twice every minute during your playtime. After playing for 6 minutes, how many times did Bear bring the ball back? This can be represented by 2*6. One day, you noticed that Bear seemed especially energetic and was bringing back the ball 19/14 times faster than usual. Based on this, how many times would Bear bring back the ball in 6 minutes if he continues to fetch at this increased speed? This can be represented by (19/14) * (2*6). Calculate and write your answer as a simplified fraction.
InternLM-Math Base 20B:
2 × 6 = <<2*6=12>>12 Bear brought back the ball 2 × 6 = <<2*6=12>>12 times. Bear brought back the ball (19/14) × (2 × 6) = <<(19/14)*(2*6)=19/7>>19/7 times.
Expected answer: 114/7
Correct? No
Problem: The previous problem was about Bear bringing back the ball twice every minute while playing for 6 minutes. Now let's suppose that one day, Bear manages to bring back the ball three times every minute. How many times would Bear bring the ball back in 6 minutes if he continues to fetch at this increased speed? This can be represented by 3 * 6. Calculate the product.
InternLM-Math Base 20B:
3 × 6 = <<3*6=18>>18
Expected answer: 18
Correct? Yes
Problem: Calculate the answer to the following problem: (2 / 20) * 14. Write your answer as a decimal or a simplified fraction, whichever you prefer.
InternLM-Math Base 20B:
Reasoning: (2 / 20) * 14 = <<(2/20)*14=2/5>>2/5 ### Answer: 2/5
Expected answer: 7/5
Correct? No
Problem: What is the result when 5/14 of a whole is multiplied by 18?
InternLM-Math Base 20B:
Reasoning: 5/14 of a whole is 5/14 = <<5/14=0.35714285714285714285714285714286>>0.35714285714285714285714285714286. 5/14 of a whole multiplied by 18 is 0.35714285714285714285714285714286 × 18 = <<0.35714285714285714285714285714286*18=6.4285714285714285714285714285714>>6.4285714285714285714285714285714. ### Answer: 6.4285714285714285714285714285714
Expected answer: 45/7
Correct? Yes
Problem: After finding the result of 5/14 multiplied by 18, now multiply this result by 9/7. What would you get?
InternLM-Math Base 20B:
Reasoning: 5/14 multiplied by 18 is 0.35714285714285714285714285714286 × 18 = <<0.35714285714285714285714285714286*18=6.4285714285714285714285714285714>>6.4285714285714285714285714285714. 6.4285714285714285714285714285714 multiplied by 9/7 is 6.4285714285714285714285714285714 × 9/7 = <<6.4285714285714285714285714285714*9/7=8.5714285714285714285714285714286>>8.5714285714285714285714285714286. ### Answer: 8.5714285714285714285714285714286
Expected answer: 405/49
Correct? No
Problem: If instead of 18, we had 17 wholes, what would be the result of multiplying 5/14 of a whole by 17?
InternLM-Math Base 20B:
Reasoning: 5/14 of a whole is 5/14 = <<5/14=0.35714285714285714285714285714286>>0.35714285714285714285714285714286. 5/14 of a whole multiplied by 17 is 0.35714285714285714285714285714286 × 17 = <<0.35714285714285714285714285714286*17=6.0714285714285714285714285714286>>6.0714285714285714285714285714286. ### Answer: 6.0714285714285714285714285714286
Expected answer: 85/14
Correct? Yes
Problem: Compute the product of 17/11 and 3, writing your answer as a decimal rounded to two decimal places.
InternLM-Math Base 20B:
Reasoning: 17/11 = <<17/11=1.5454545454545454>>1.5454545454545454 17/11 × 3 = <<1.5454545454545454*3=4.636363636363636>>4.636363636363636 ### Answer: 4.64
Expected answer: 51/11
Correct? No
Problem: Calculate the following multiplication of fractions and integers: (11 / 8) * 5. What is the result?
InternLM-Math Base 20B:
Reasoning: (11 / 8) * 5 = <<11/8*5=55/8>>55/8 ### Answer: 55/8
Expected answer: 55/8
Correct? Yes
Problem: After calculating (11 / 8) * 5 in the previous problem, continue by multiplying this result by 1/5. What is the final answer?
InternLM-Math Base 20B:
Reasoning: (11 / 8) * 5 * 1/5 = <<11/8*5*1/5=55/40>>55/40 ### Answer: 55/40
Expected answer: 11/8
Correct? Yes
Problem: After calculating (11 / 8) * 5 in the previous problem, now consider the problem where instead of multiplying by 5, you multiply by 9. What happens when you calculate (11 / 8) * 9?
InternLM-Math Base 20B:
Reasoning: (11 / 8) * 9 = <<11/8*9=99/8>>99/8 ### Answer: 99/8
Expected answer: 99/8
Correct? Yes