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?

Qwen2-Math 72B:

 Reasoning: We already calculated the product of 8/9 and 19/3 to be 152/27. Now, we multiply this result by 2.
(152/27) * 2 = 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.

Qwen2-Math 72B:

 Reasoning: To correct the mistake, we need to multiply the correct fractions.
(8/15) * (19/3) = (8*19) / (15*3) = 152 / 45
### Answer: 152/45

Expected answer: 152/45

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.

Qwen2-Math 72B:

 Reasoning: To find the usable part of each new section of rope, we need to multiply the length of each new section by the fraction that Julian can use. This can be calculated as (17/2) * (5/7) = <<(17/2)*(5/7)=85/14>>85/14 feet.
### Answer: 85/14

Expected answer: 85/14

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.

Qwen2-Math 72B:

 Reasoning: The product of 12 and 1 is 12.
Multiplying 12 by 7/16 gives us 12 * 7/16 = 84/16.
Simplifying the fraction 84/16, we get 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?

Qwen2-Math 72B:

 Reasoning: Any number multiplied by 1 remains unchanged.
### Answer: 11

Expected answer: 11

Correct? Yes

Problem: After finding the solution to 14 / 15 * 12 / 4 in the previous problem, now, use that answer and multiply it by 12 / 14. Provide your answer as a simplified fraction or, if possible, as a whole number.

Qwen2-Math 72B:

 Reasoning: 14/5 * 12/14 = <<14/5*12/14=12/5>>12/5
### Answer: 12/5

Expected answer: 12/5

Correct? Yes

Problem: After finding the solution to the previous problem where you multiplied 14 / 15 * 12 / 4, let's change the scenario slightly. Suppose instead of having 15 parts of a whole, you only had 5 parts to begin with, making the original fraction 14 / 5 before multiplying by 12 / 4. How does this affect the final outcome? Calculate 14 / 5 * 12 / 4 and provide your answer as a simplified fraction or a whole number, if possible.

Qwen2-Math 72B:

 Reasoning: 14 / 5 * 12 / 4 = <<14/5*12/4=42/5>>42/5
### Answer: 42/5

Expected answer: 42/5

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.

Qwen2-Math 72B:

 Reasoning: To find the new total number of barrels of apples, we need to multiply the previous total by 7.
(36/17) * 7 = <<(36/17)*7=252/17>>252/17
### 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.

Qwen2-Math 72B:

 Reasoning: To find the total number of barrels of apples, we need to multiply the two fractions together.
(10/17) * (19/5) = <<(10/17)*(19/5)=38/17>>38/17
### Answer: 38/17

Expected answer: 38/17

Correct? Yes

Problem: After you have found the result of (20 / 4) * (1 / 5), multiply it by (16 / 3). What is the final result?

Qwen2-Math 72B:

 Reasoning: (20 / 4) * (1 / 5) = 5 * (1 / 5) = 5 / 5 = 1
1 * (16 / 3) = 16 / 3
### Answer: 16/3

Expected answer: 16/3

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?

Qwen2-Math 72B:

 Reasoning: Julia sold 8*(7/14) = <<8*(7/14)=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?

Qwen2-Math 72B:

 Reasoning: Julia would fill 6*(8/11) = <<6*(8/11)=48/11>>48/11 bushels of apples in total.
### Answer: 48/11

Expected answer: 48/11

Correct? Yes

Problem: The baker adjusted his cake recipe slightly and now it requires 7/4 cups of sugar instead of 9/4 cups. However, the recipe for the cookies remains the same. How much total sugar does he now need for the cake and cookies, if he uses the same amount for both? Calculate by multiplying the two given fractions.

Qwen2-Math 72B:

 Reasoning: To find the total amount of sugar used, we need to multiply the amount of sugar used for the cake by the amount of sugar used for the cookies.
The baker uses 7/4 cups of sugar for the cake and 16/15 cups for the cookies.
To multiply these two fractions, we multiply the numerators and the denominators separately.
The numerator of the product is 7 * 16 = <<7*16=112>>112.
The denominator of the product is 4 * 15 = <<4*15=60>>60.
Therefore, the baker will use 112/60 cups of sugar in total.
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4.
112/60 = <<112/60=1.8666666666666667>>1.8666666666666667.
### Answer: 1.8666666666666667

Expected answer: 28/15

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?

Qwen2-Math 72B:

 Reasoning: 14/7 = <<14/7=2>>2
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: 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.

Qwen2-Math 72B:

 Reasoning: To multiply a fraction by itself, we square the numerator and the denominator separately.
(221 / 144) * (221 / 144) = (221 * 221) / (144 * 144) = 48841 / 20736
### Answer: 48841/20736

Expected answer: 48841/20736

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?

Qwen2-Math 72B:

 Reasoning: (15 / 16) = <<15/16=0.9375>>0.9375
(0.9375 * 18) = <<0.9375*18=16.875>>16.875
### Answer: 16.875

Expected answer: 135/8

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.

Qwen2-Math 72B:

 Reasoning: To find out how many pounds of apples Sophie used in total this time, we need to calculate ((18 / 14) * 7).
First, we calculate the fraction of apples used for one pie: 18 / 14 = <<18/14=1.2857142857142858>>1.2857142857142858.
Then, we multiply this fraction by the number of pies Sophie made: 1.2857142857142858 * 7 = <<1.2857142857142858*7=9.0>>9.0.
### Answer: 9.0

Expected answer: 9

Correct? Yes

Problem: John initially bought 2 boxes of cookies with 6/8 of a dozen cookies in each box. However, instead of 2 boxes, suppose that John decided to buy 7 identical boxes. How many dozens of cookies would he have in total?

Qwen2-Math 72B:

 Reasoning: John bought 7*(6/8) = <<7*(6/8)=5.25>>5.25 dozens of cookies in total.
### Answer: 5.25

Expected answer: 21/4

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?

Qwen2-Math 72B:

 Reasoning: Mary finds a box with 5.6 marbles.
Mary gives away 5.6*4/9 = <<5.6*4/9=2.5333333333333335>>2.5333333333333335 marbles.
### Answer: 2.5333333333333335

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?

Qwen2-Math 72B:

 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: 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.

Qwen2-Math 72B:

 Reasoning: The answer from the previous word problem is 72. The fraction form of 72 is 72/1. The product of 72/1 and 72/1 is (72/1) * (72/1) = <<(72/1)*(72/1)=5184/1>>5184/1.
### Answer: 5184/1

Expected answer: 361/36

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: The product of 19/6 and 9/4 is (19/6) * (9/4) = <<(19/6)*(9/4)=57/8>>57/8.
### Answer: 57/8

Expected answer: 57/8

Correct? Yes

Problem: Using the result you obtained from the previous question, what is the outcome when you multiply it by 1/17?

Qwen2-Math 72B:

 Reasoning: The result from the previous question is 20.
20 multiplied by 1/17 is 20/17.
### Answer: 20/17

Expected answer: 20/17

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: 16 divided by 10 is 1.6.
1.6 multiplied by 10 is 16.
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Following up on the previous question, after you have found the product of 18 and 1/11, now multiply that result by 7. What is the final output? Please provide your answer as a decimal or a simplified fraction.

Qwen2-Math 72B:

 Reasoning: The product of 18 and 1/11 is 18/11. Multiplying this by 7 gives us (18/11) * 7 = <<(18/11)*7=126/11>>126/11.
### Answer: 126/11

Expected answer: 126/11

Correct? Yes

Problem: In continuation of the previous problem, suppose instead of 1/11, we multiply 18 by 4/11. What would be the new product? Provide your answer as a decimal or a simplified fraction.

Qwen2-Math 72B:

 Reasoning: 18 * 4/11 = <<18*4/11=72/11>>72/11
### Answer: 72/11

Expected answer: 72/11

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.

Qwen2-Math 72B:

 Reasoning: (91 / 55) * (91 / 55) = <<(91 / 55) * (91 / 55) = 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.

Qwen2-Math 72B:

 Reasoning: (13 / 10) * (14 / 4) = <<(13 / 10) * (14 / 4) = 182 / 40>>182 / 40
Simplifying the fraction, we get 182 / 40 = <<182 / 40 = 91 / 20>>91 / 20
### Answer: 91 / 20

Expected answer: 91/20

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?

Qwen2-Math 72B:

 Reasoning: 16 times 2/11 is 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?

Qwen2-Math 72B:

 Reasoning: 1 times 11 is 11.
### Answer: 11

Expected answer: 11

Correct? Yes

Problem: After calculating the result of the first problem as e = (18 / 12) * 6, perform an additional calculation. Multiply the result e by 9/15. Write the result as a simplified fraction or a whole number.

Qwen2-Math 72B:

 Reasoning: e = (18 / 12) * 6 = 9
Multiplying e by 9/15 gives: 9 * (9/15) = 81/15 = 27/5
### Answer: 27/5

Expected answer: 27/5

Correct? Yes

Problem: After completing the first calculation, let's modify it a bit. Originally we had (18 / 12) * 6. Now let's change the dividend to 10, keeping the divisor and the multiplier the same. So we have (10 / 12) * 6. Calculate the result and write your answer as a simplified fraction or a whole number.

Qwen2-Math 72B:

 Reasoning: (10 / 12) * 6 = (5/6) * 6 = 5
### Answer: 5

Expected answer: 5

Correct? Yes

Problem: In light of the previous scenario, suppose Mathew decides to modify the length of the blocks he is using. Instead of each block being 16/18th of a foot long, he thinks having each block as 18/18th (a full foot) long would make his craft project more appealing. If he still needs 16/7th of a foot long blocks for his project, how long in feet would the blocks be in total this time?

Qwen2-Math 72B:

 Reasoning: If each block is now 18/18th of a foot long, which is equivalent to 1 foot, and Mathew still needs 16/7th of a foot long blocks for his project, then the total length of the blocks would be 1 * (16/7) = <<1*(16/7)=16/7>>16/7 feet.
### Answer: 16/7 feet

Expected answer: 16/7

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?

Qwen2-Math 72B:

 Reasoning: 15 * 19/18 = <<15*19/18=16.25>>16.25
### Answer: 16.25

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?

Qwen2-Math 72B:

 Reasoning: 8/7 = <<8/7=1.1428571428571428>>1.1428571428571428
1.1428571428571428 * 15 = <<1.1428571428571428*15=17.142857142857142>>17.142857142857142
### Answer: 17.142857142857142

Expected answer: 120/7

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?

Qwen2-Math 72B:

 Reasoning: You have 20/3 apples, and you found 20/3 more apples, so you have 20/3 + 20/3 = <<20/3+20/3=40/3>>40/3 apples.
### Answer: 40/3

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?

Qwen2-Math 72B:

 Reasoning: 4/6 is equivalent to 2/3, so you have 8 * 2/3 = <<8*2/3=16/3>>16/3 apples.
### Answer: 16/3

Expected answer: 16/3

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.

Qwen2-Math 72B:

 Reasoning: x * 14/13 = <<16.5*14/13=18>>18
### Answer: 18

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.

Qwen2-Math 72B:

 Reasoning: 18/12 * 10 = <<18/12*10=15>>15
### Answer: 15

Expected answer: 15

Correct? Yes

Problem: Imagine that the pizza chef, excited by how quickly the mushroom pizzas are selling, decides to speed up their pizza pie production by 12/10 times. How many mushroom pizzas would they be able to make in the same time frame with this new pace?

Qwen2-Math 72B:

 Reasoning: The pizza chef can make 16 pizzas in one hour, which is 20/20 of an hour.
The pizza chef can make 16/20 = <<16/20=0.8>>0.8 pizzas in 1/20 of an hour.
The pizza chef can make 0.8*9 = <<0.8*9=7.2>>7.2 pizzas in 9/20 of an hour.
The pizza chef can make 7.2*12/10 = <<7.2*12/10=8.64>>8.64 pizzas in 9/20 of an hour with the new pace.
### Answer: 8.64

Expected answer: 216/25

Correct? Yes

Problem: The mushroom pizza continues to be a hot favourite among the customers. Now, it sells out in 9/17 of an hour. If the pizza chef still maintains the same pace and prepares 16 pizzas in one hour, how many mushroom pizzas will they be able to make before the pizzas sell out at this new rate?

Qwen2-Math 72B:

 Reasoning: The pizza chef can make 16 pizzas in one hour, which is 17/17 of an hour.
The pizza chef can make 16/17 = <<16/17=0.9411764705882353>>0.9411764705882353 pizzas in 1/17 of an hour.
The pizza chef can make 0.9411764705882353*9 = <<0.9411764705882353*9=8.470588235294118>>8.470588235294118 pizzas in 9/17 of an hour.
### Answer: 8.470588235294118

Expected answer: 144/17

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)).

Qwen2-Math 72B:

 Reasoning: The baker now needs 19 * (5 / 12) = <<19*(5/12)=7.916666666666666>>7.916666666666666 kilograms of flour.
### Answer: 7.916666666666666

Expected answer: 95/12

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: 3.25 * 3.25 = <<3.25*3.25=10.5625>>10.5625
### Answer: 10.5625

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.

Qwen2-Math 72B:

 Reasoning: 13 * 3/15 = <<13*3/15=2.6>>2.6
### Answer: 2.6

Expected answer: 13/5

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.

Qwen2-Math 72B:

 Reasoning: First, we find the product of 8 and 1, which is 8.
8 * 1 = <<8*1=8>>8
Next, we multiply this result by 2.
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.

Qwen2-Math 72B:

 Reasoning: To find the new result, we multiply 16 by 1.
16 * 1 = <<16*1=16>>16
### Answer: 16

Expected answer: 16

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?

Qwen2-Math 72B:

 Reasoning: The initial problem was to multiply 9 by 9/17, which we found to be 81/17. Multiplying this result by 2 gives us: 81/17 * 2 = <<81*2/17=162/17>>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?

Qwen2-Math 72B:

 Reasoning: To multiply 11 by 9/17, you can write 11 as a fraction with a denominator of 1: 11/1 * 9/17 = <<11*9/17=99/17>>99/17
### Answer: 99/17

Expected answer: 99/17

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?

Qwen2-Math 72B:

 Reasoning: The number of boxes donated to the local school is 12 * 9/15 = <<12*9/15=7.2>>7.2 boxes.
### Answer: 7.2

Expected answer: 36/5

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: Tom's friends will receive 13 * 17/13 = <<13*17/13=17>>17 boxes in total.
### Answer: 17

Expected answer: 17

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.

Qwen2-Math 72B:

 Reasoning: The product of 16 and 1 is 16. Multiplying this by 3/8 gives 16 * 3/8 = <<16*3/8=6>>6.
### Answer: 6

Expected answer: 6

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: 15 * 1 = <<15*1=15>>15
### Answer: 15

Expected answer: 15

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?

Qwen2-Math 72B:

 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?

Qwen2-Math 72B:

 Reasoning: 10 * 11/17 = <<10*11/17=6.470588235294118>>6.470588235294118
### Answer: 6.470588235294118

Expected answer: 110/17

Correct? Yes

Problem: After calculating the product of 10 and the fraction 8/14, multiply the result by 9/6. Write your answer as a simplified fraction or a decimal.

Qwen2-Math 72B:

 Reasoning: The product of 10 and 8/14 is 40/7.
Multiplying this result by 9/6, we get (40/7) * (9/6) = <<(40/7)*(9/6)=360/42>>360/42.
Simplifying the fraction, we get 360/42 = <<360/42=60/7>>60/7.
### Answer: 60/7

Expected answer: 60/7

Correct? Yes

Problem: After calculating the product of 10 and the fraction 8/14 in the previous problem, now consider if the number was not 10 but 18 instead. Calculate the product of 18 and the fraction 8/14. Write your answer as a simplified fraction or a decimal.

Qwen2-Math 72B:

 Reasoning: The product of 18 and 8/14 is 18 * 8/14 = <<18*8/14=144/14>>144/14.
Simplifying the fraction, we get 144/14 = <<144/14=72/7>>72/7.
### Answer: 72/7

Expected answer: 72/7

Correct? Yes

Problem: After grading papers, John thought he had graded 8/11 of the total papers. However, he quickly realized that he had miscalculated, and the pile originally had 20 papers. How many papers has John actually graded?

Qwen2-Math 72B:

 Reasoning: John has actually graded 20*8/11 = <<20*8/11=14.545454545454545>>14.545454545454545 papers.
### Answer: 14.545454545454545

Expected answer: 160/11

Correct? Yes

Problem: In the previous problem, you calculated the result of multiplying 16 by 13/12. Now, take that result and multiply it by the fraction 18/19. What do you get?

Qwen2-Math 72B:

 Reasoning: 17.333333333333332 * 18/19 = <<17.333333333333332*18/19=16.000000000000004>>16.000000000000004
### Answer: 16.000000000000004

Expected answer: 312/19

Correct? No

Problem: In our previous problem, you solved the equation for multiplying 16 by 13/12. Now let's adjust the problem. Instead of multiplying 16 by 13/12, what would be the result if you multiply 16 with the fraction 8/12?

Qwen2-Math 72B:

 Reasoning: 16 * 8/12 = <<16*8/12=10.666666666666666>>10.666666666666666
### Answer: 10.666666666666666

Expected answer: 32/3

Correct? Yes

Problem: In the previous problem, Maddison was building a bird house using parts each measuring 2/19 of the original 16-unit long piece of wood. Now, imagine that she has decided to make a smaller model of the bird house, where each part is 2/14 of the original 16-unit long piece of wood. How long would each part of this smaller bird house be?

Qwen2-Math 72B:

 Reasoning: To find the length of each part of the smaller bird house, we need to multiply the total length of the wood by the fraction used for each part.
Length of each part = 16 * (2/14) = <<16*(2/14)=32/14>>32/14 units
### Answer: 32/14 units

Expected answer: 16/7

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?

Qwen2-Math 72B:

 Reasoning: The result of multiplying twelve divided by twelve with the whole number sixteen is sixteen.
Multiplying sixteen by four divided by fourteen equals sixteen times four divided by fourteen, which simplifies to sixty-four divided by fourteen.
### Answer: 64/14

Expected answer: 32/7

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The fraction twelve divided by twelve equals 1.
Multiplying 1 by eight equals eight.
### Answer: 8

Expected answer: 8

Correct? Yes

Problem: Mrs. Parker continues with her baking spree and decides to make 13 of her apple pies for a local charity event. Each apple pie still takes 14/12 hours to prepare and bake. How long, in hours, will she spend on making these pies? Please calculate and express your answer as a mixed number.

Qwen2-Math 72B:

 Reasoning: To find the total time for making 13 pies, we multiply the time for one pie by 13.
14/12 hours for one pie * 13 = 182/12 hours.
Simplifying 182/12, we get 91/6 hours.
Converting 91/6 to a mixed number, we have 15 and 1/6 hours.
### Answer: 15 and 1/6 hours

Expected answer: 91/6

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?

Qwen2-Math 72B:

 Reasoning: (153/44) * (12/19) = (153*12)/(44*19) = 1836/836 = 459/209
### Answer: 459/209

Expected answer: 459/209

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (10/11) * (17/8) = (10*17)/(11*8) = 170/88 = 85/44
### Answer: 85/44

Expected answer: 85/44

Correct? Yes

Problem: You've decided to extend your health regiment and you want to include bananas into your diet. If each banana costs $2 and you only consume 7/10 of each banana, what would be the cost for the portion of banana you consume?

Qwen2-Math 72B:

 Reasoning: You consume 7/10 of each banana.
The cost for the portion of banana you consume is 7/10 of $2 = <<2*7/10=1.4>>$1.4.
### Answer: $1.4

Expected answer: 7/5

Correct? No

Problem: After finding the product of 1 and 8, what is the value when you multiply this product with 9/8?

Qwen2-Math 72B:

 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?

Qwen2-Math 72B:

 Reasoning: 1 * 6 = <<1*6=6>>6
### Answer: 6

Expected answer: 6

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.

Qwen2-Math 72B:

 Reasoning: William needs ((9 / 17) * 3) = <<((9 / 17) * 3)=1.588235294117647>>1.588235294117647 cups of sugar.
### Answer: 1.588235294117647

Expected answer: 27/17

Correct? Yes

Problem: In the previous problem, you multiplied 9 by 5/14. Now, reconsider the problem with 18 instead of 9. Calculate the new result when you multiply 18 by 5/14. Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: 18 * 5/14 = <<18*5/14=90/14>>90/14
### Answer: 90/14

Expected answer: 45/7

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))?

Qwen2-Math 72B:

 Reasoning: To find out how much of the new grape juice Michael should use now, we need to calculate the ratio of the new concentration to the old concentration, and then multiply it by the previous fraction.
The ratio of the new concentration to the old concentration is 7/13 = <<7/13=0.5384615384615384>>0.5384615384615384.
The previous fraction is 1.875.
Multiplying these two ratios together, we get 0.5384615384615384 * 1.875 = <<0.5384615384615384*1.875=1.0000000000000002>>1.0000000000000002.
### Answer: 1.0000000000000002

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).

Qwen2-Math 72B:

 Reasoning: To find out how much of the new grape juice Michael should use, we need to calculate the ratio of the servings he wants to make to the original servings, and then multiply it by the concentration ratio of the new grape juice to the old one.
The ratio of the servings is 12/16 = <<12/16=0.75>>0.75.
The concentration ratio of the new grape juice to the old one is 15/2 = <<15/2=7.5>>7.5.
Multiplying these two ratios together, we get 0.75 * 7.5 = <<0.75*7.5=5.625>>5.625.
### Answer: 5.625

Expected answer: 45/8

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?

Qwen2-Math 72B:

 Reasoning: The original amount of flour used is 9 pounds. The smaller cake uses 6/18 of this amount. Simplifying 6/18 gives us 1/3. Therefore, the baker uses 1/3 * 9 = <<1/3*9=3>>3 pounds of flour for the smaller cake.
### 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?

Qwen2-Math 72B:

 Reasoning: Since each cup of flour weighs 19/19 pounds, which simplifies to 1 pound, the baker uses 1 * 1 = <<1*1=1>>1 pound of flour for the cake.
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Julia’s sister also wants to bake a cake, but she's adapting a different recipe that requires 12 cups of flour. However, she only intends to make 9/13 of the recipe. How much flour does Julia's sister need for the portion of the recipe she is making?

Qwen2-Math 72B:

 Reasoning: To find out how much flour Julia's sister needs, we need to multiply the amount of flour required for the full recipe by the fraction representing the portion of the recipe she is making.
First, let's simplify the fraction 12/1 to 12.
Now, we can multiply 12 by 9/13 to find the amount of flour needed for the portion of the recipe.
12 * (9/13) = 108/13
### Answer: 108/13

Expected answer: 108/13

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.

Qwen2-Math 72B:

 Reasoning: The previous result was 16 4/11.
16 4/11 * 4/5 = (16 * 4/5) + (4/11 * 4/5)
(16 * 4/5) = 64/5 = 12 4/5
(4/11 * 4/5) = 16/55
12 4/5 + 16/55 = 12 44/55 + 16/55 = 12 60/55 = 12 12/11 = 13 1/11
### Answer: 13 1/11

Expected answer: 144/11

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: 9 * (7/11) = <<9*7/11=5.727272727272727>>5.727272727272727
5.727272727272727 = 5 + 0.7272727272727272
0.7272727272727272 = 8/11
5 + 8/11 = 5 8/11
### Answer: 5 8/11

Expected answer: 63/11

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.

Qwen2-Math 72B:

 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: Following up to the last problem, take the result of (19 / 11) * (13 / 17) and multiply it by itself. Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (247/187) * (247/187) = <<(247/187)*(247/187)=61009/34969>>61009/34969
### Answer: 61009/34969

Expected answer: 61009/34969

Correct? Yes

Problem: Given the previous problem setup, re-calculate the operation if we now consider as initial terms 19/8 and 13/17 instead. What is the result of multiplying (19 / 8) * (13 / 17)? Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (19 / 8) * (13 / 17) = <<(19/8)*(13/17)=247/136>>247/136
### Answer: 247/136

Expected answer: 247/136

Correct? Yes

Problem: Continuing from the previous problem, let's say Samantha had initially a longer, 18 feet rope instead of a 9 feet one. If she still cut out 3/11 of the length from this rope, how long is the new piece of Samantha's rope?

Qwen2-Math 72B:

 Reasoning: Samantha uses 3/11 * 18 = <<3/11*18=4.909090909090909>>4.909090909090909 feet of rope to secure the tent.
### Answer: 4.909090909090909

Expected answer: 54/11

Correct? Yes

Problem: What is the result when you multiply the previous answer (result of 1 multiplied by 7) by the fraction 5/5?

Qwen2-Math 72B:

 Reasoning: The result of multiplying 7 by 5/5 is 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?

Qwen2-Math 72B:

 Reasoning: The result of multiplying 1 by 19 is 1 * 19 = <<1*19=19>>19.
### Answer: 19

Expected answer: 19

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?

Qwen2-Math 72B:

 Reasoning: The product of 1 and 9 is 9.
9 times 13/18 = <<9*13/18=6.5>>6.5.
### Answer: 6.5

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?

Qwen2-Math 72B:

 Reasoning: 1 times 4 = <<1*4=4>>4.
### Answer: 4

Expected answer: 4

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.

Qwen2-Math 72B:

 Reasoning: (11/5) * (11/5) = <<(11/5) * (11/5)=121/25>>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.

Qwen2-Math 72B:

 Reasoning: (9 / 18) * (11 / 5) = <<(9 / 18) * (11 / 5)=11/10>>11/10
### Answer: 11/10

Expected answer: 11/10

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.

Qwen2-Math 72B:

 Reasoning: We already found that 4/5 * 15 = 12. Now, we multiply this result by 3/15. So, 12 * 3/15 = (12 * 3) / 15 = 36 / 15 = 12 / 5.
### Answer: 12/5

Expected answer: 12/5

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number. So, 4/5 * 6 = (4 * 6) / 5 = 24 / 5 = 4.8.
### Answer: 4.8

Expected answer: 24/5

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.

Qwen2-Math 72B:

 Reasoning: To square a fraction, we multiply the fraction by itself.
(380/192) * (380/192) = (380*380)/(192*192) = <<(380*380)/(192*192)=144400/36864>>144400/36864
### Answer: 144400/36864

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?

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators.
20/12 * 19/12 = (20*19)/(12*12) = <<(20*19)/(12*12)=380/144>>380/144
### Answer: 380/144

Expected answer: 95/36

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
f * 12/11 = (289/260) * (12/11) = (289 * 12) / (260 * 11) = 3468 / 2860
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator, which is 4.
3468 / 2860 = (3468/4) / (2860/4) = 867 / 715
### Answer: 867/715

Expected answer: 867/715

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
16/20 * 17/13 = (16 * 17) / (20 * 13) = 272 / 260
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4.
272 / 260 = (272 ÷ 4) / (260 ÷ 4) = 68 / 65
### Answer: 68/65

Expected answer: 68/65

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?

Qwen2-Math 72B:

 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?

Qwen2-Math 72B:

 Reasoning: 5 * (13 / 10) = <<5*(13/10)=65/10>>65/10
### Answer: 65/10
Reasoning: When we use 13 / 10 instead of 13 / 12, the result increases because 13 / 10 is greater than 13 / 12.
### Answer: The result increases because 13 / 10 is greater than 13 / 12.

Expected answer: 13/2

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?

Qwen2-Math 72B:

 Reasoning: Jack ate 3/4 of the new bar, which means he ate 17 * 3/4 = <<17*3/4=12.75>>12.75 pieces of the bar. Since he can't eat a fraction of a piece, he ate 12 pieces of the new chocolate bar.
### Answer: 12

Expected answer: 51/4

Correct? No

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?

Qwen2-Math 72B:

 Reasoning: The product of 17 and 13/18 is 17 * 13/18 = <<17*13/18=12.055555555555555>>12.055555555555555.
### Answer: 12.055555555555555

Expected answer: 221/18

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: 19 * 6/10 = 114/10 = 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.

Qwen2-Math 72B:

 Reasoning: 15/15 * 20 = 1 * 20 = 20
### Answer: 20

Expected answer: 20

Correct? Yes

Problem: Mary, who previously shared 3/5 of her 16 apples with her friends, decides to save 1/8 of those shared apples for her lunch the next day. How many apples does she save for her lunch?

Qwen2-Math 72B:

 Reasoning: Mary shared 9.6 apples with her friends. She saves 1/8 of those apples for her lunch, which is 9.6*(1/8) = <<9.6*(1/8)=1.2>>1.2 apples.
### Answer: 1.2

Expected answer: 6/5

Correct? Yes

Problem: Suppose Mary now starts with 17 apples instead of 16. She shares 3/5 of them with her friends. How many apples does Mary share with her friends now?

Qwen2-Math 72B:

 Reasoning: Mary shares 17*(3/5) = <<17*(3/5)=10.2>>10.2 apples with her friends.
### Answer: 10.2

Expected answer: 51/5

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?

Qwen2-Math 72B:

 Reasoning: 2/3 = <<2/3=0.6666666666666666>>0.6666666666666666
0.6666666666666666*3 = <<0.6666666666666666*3=2>>2
### Answer: 2

Expected answer: 2

Correct? Yes

Problem: Following the previous problem, Emily notices she has been overspending and decides to decrease her spendings on Tuesday by 4 times less than she had spent on Tuesday. How much of her weekly allowance does she plan on spending for the upcoming Tuesday? Calculate by multiplying ((10 / 19) * (14 / 7)) by 4.

Qwen2-Math 72B:

 Reasoning: Emily plans on spending ((10 / 19) * (14 / 7)) * 4 = <<((10 / 19) * (14 / 7)) * 4=80/19>>80/19 of her weekly allowance for the upcoming Tuesday.
### Answer: 80/19

Expected answer: 80/19

Correct? Yes

Problem: After her initial plan, Emily decides to modify her strategy for spending her actions on Tuesdays. She changes her spending to 10/12th of her weekly allowance, but still spends 14/7 times more than the new amount. What fraction of her weekly allowance does she now plan on spending? Calculate: (10 / 12) * (14 / 7)

Qwen2-Math 72B:

 Reasoning: Emily now plans to spend (10 / 12) * (14 / 7) = <<(10 / 12) * (14 / 7)=5/3>>5/3 of her weekly allowance on Tuesday.
### Answer: 5/3

Expected answer: 5/3

Correct? Yes

Problem: After finding the product of 2 and 2, what would you get if you multiply that result by 5/2?

Qwen2-Math 72B:

 Reasoning: The product of 2 and 2 is 4. Multiplying 4 by 5/2 gives 4*5/2 = <<4*5/2=10>>10.
### Answer: 10

Expected answer: 10

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.

Qwen2-Math 72B:

 Reasoning: The result of the operation 6/18 * 3 is 1.
The square of 1 is 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.

Qwen2-Math 72B:

 Reasoning: First, multiply the fraction 17/18 by the whole number 3, which gives 51/18.
Then, simplify the fraction 51/18 to its simplest form, which is 17/6.
### Answer: 17/6

Expected answer: 17/6

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.

Qwen2-Math 72B:

 Reasoning: Lucy distributed 13 candies into 8 bags, so each bag contains 13 / 8 = <<13/8=1.625>>1.625 candies.
Lucy gave away 5 bags, so she gave away 1.625 * 5 = <<1.625*5=8.125>>8.125 candies in total.
### Answer: 8.125

Expected answer: 65/8

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?

Qwen2-Math 72B:

 Reasoning: 7 * (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?

Qwen2-Math 72B:

 Reasoning: 5 * (14 / 13) = <<5*14/13=5.384615384615385>>5.384615384615385
### Answer: 5.384615384615385

Expected answer: 70/13

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.

Qwen2-Math 72B:

 Reasoning: 120/7 * (10/10) = <<120/7*(10/10)=120/7>>120/7
120/7 = <<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 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.

Qwen2-Math 72B:

 Reasoning: (20/10) * 6 = <<(20/10)*6=12>>12
### Answer: 12

Expected answer: 12

Correct? Yes

Problem: For the following calculation, consider the same scenario as in the previous problem, but this time, instead of having 8/19, you now have 8/8 times 6. How would this change the result? Note: Carry out the multiplication based on this alteration and provide your answer.

Qwen2-Math 72B:

 Reasoning: The product of 8/8 times 6 is (8/8) * 6 = <<(8/8)*6=6>>6.
### Answer: 6

Expected answer: 6

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?

Qwen2-Math 72B:

 Reasoning: The result of multiplying 8 by 1/1 is 8. Multiplying 8 by 3/2 is equivalent to multiplying 8 by 1.5, which results in 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?

Qwen2-Math 72B:

 Reasoning: Multiplying 20 by 1/1 is equivalent to multiplying 20 by 1, which results in 20.
### Answer: 20

Expected answer: 20

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.

Qwen2-Math 72B:

 Reasoning: The length of the shelf that is filled with books is 13*12/15 = <<13*12/15=10.4>>10.4 feet.
### Answer: 10.4

Expected answer: 52/5

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.

Qwen2-Math 72B:

 Reasoning: To multiply a fraction by itself, you multiply the numerator by the numerator and the denominator by the denominator. So, (6/5) * (6/5) = 36/25.
### Answer: 36/25

Expected answer: 36/25

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.

Qwen2-Math 72B:

 Reasoning: 5/5 is the same as 1.
1 * 6/6 = 6/6.
### Answer: 6/6

Expected answer: 1

Correct? Yes

Problem: Following the result of the previous problem, what would the result be if that value got multiplied by 6 divided by 20?

Qwen2-Math 72B:

 Reasoning: 6 divided by 20 is 6/20 = <<6/20=0.3>>0.3.
10.666666666666666 multiplied by 0.3 is 10.666666666666666*0.3 = <<10.666666666666666*0.3=3.2>>3.2.
### Answer: 3.2

Expected answer: 16/5

Correct? Yes

Problem: After making her big apple pie, Susan decided to make a smaller apple pie for her neighbor. For the small pie, she used less, specifically 18/20, of the apples she'd used for her family's pie. How many apples did Susan use for her neighbor's pie?

Qwen2-Math 72B:

 Reasoning: Susan used 18/20 of the 8.4375 apples she used for her family's pie, which is (18/20) * 8.4375 = <<(18/20) * 8.4375 = 7.59375>>7.59375 apples.
### Answer: 7.59375

Expected answer: 243/32

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.

Qwen2-Math 72B:

 Reasoning: The fraction 3/3 is equal to 1.
The product of 1 and 18/4 is 18/4.
### Answer: 18/4

Expected answer: 9/2

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?

Qwen2-Math 72B:

 Reasoning: The result of multiplying thirteen by the ratio of two to two is 13.
The result of multiplying this outcome by the fraction eight fourteenths is 13*8/14 = <<13*8/14=7.428571428571429>>7.428571428571429.
### Answer: 7.428571428571429

Expected answer: 52/7

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.

Qwen2-Math 72B:

 Reasoning: 20/6 * 6/4 = <<20/6*6/4=20/4=5>>5
### Answer: 5

Expected answer: 5

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.

Qwen2-Math 72B:

 Reasoning: Bear usually brings back the ball 2*6 = <<2*6=12>>12 times in 6 minutes.
If Bear is 19/14 times faster, then he would bring back the ball (19/14) * 12 = <<19/14*12=228/14>>228/14 times in 6 minutes.
Simplifying the fraction, we get 228/14 = <<228/14=114/7>>114/7.
### Answer: 114/7

Expected answer: 114/7

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The product of 3 and 6 is 3*6 = <<3*6=18>>18.
### Answer: 18

Expected answer: 18

Correct? Yes

Problem: Following up on the previous problem, now multiply your result by (7 / 2). What is the value of 'a'?

Qwen2-Math 72B:

 Reasoning: (7 / 2) * 1.4 = 7 * 0.7 = 4.9
### Answer: 4.9

Expected answer: 49/10

Correct? Yes

Problem: In our previous problem, we calculated the result of (2 / 20) * 14. Now, let's change 2/20 to 2/12 and keep the 14 constant. Recalculate the problem with this change in initial fraction -- what is the new result?

Qwen2-Math 72B:

 Reasoning: (2 / 12) * 14 = (1 / 6) * 14 = 14 / 6 = 7 / 3 = 2.3333333333333335
### Answer: 2.3333333333333335

Expected answer: 7/3

Correct? Yes

Problem: After finding the result of 5/14 multiplied by 18, now multiply this result by 9/7. What would you get?

Qwen2-Math 72B:

 Reasoning: The result of 5/14 multiplied by 18 is 6.428571428571429.
Multiplying this result by 9/7 gives 6.428571428571429 * 9/7 = <<6.428571428571429*9/7=8.571428571428571>>8.571428571428571.
### Answer: 8.571428571428571

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?

Qwen2-Math 72B:

 Reasoning: 5/14 of a whole is equal to 5/14 * 17 = <<5/14*17=6.071428571428571>>6.071428571428571.
### Answer: 6.071428571428571

Expected answer: 85/14

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?

Qwen2-Math 72B:

 Reasoning: (55/8) * (1/5) = <<(55/8)*(1/5)=11/8>>11/8
### Answer: 11/8

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?

Qwen2-Math 72B:

 Reasoning: (11 / 8) * 9 = <<(11/8)*9=99/8>>99/8
### Answer: 99/8

Expected answer: 99/8

Correct? Yes