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?

GPT-3.5 Turbo:

Reasoning: We already found that (8/9) * (19/3) = 152/27. Now, we need to multiply this result by 2.

(152/27) * 2 = 152/27 * 2/1 = (152 * 2) / (27 * 1) = 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.

GPT-3.5 Turbo:

Reasoning: The correct calculation should be:

(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.

GPT-3.5 Turbo:

To find the usable part of each new section of rope, we multiply 17/2 by 5/7:

(17/2) * (5/7) = (17*5) / (2*7) = 85/14 = 6 1/14 feet.

Therefore, the usable part of each new section of rope is 6 1/14 feet.
### Answer: 6 1/14 feet.

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.

GPT-3.5 Turbo:

Reasoning: First, we find the product of 12 and 1, which is 12. Then, we multiply 12 by 7/16.

12 * 7/16 = (12 * 7) / 16 = 84 / 16 = 21 / 4 = 5 1/4

### Answer: 5 1/4

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?

GPT-3.5 Turbo:

Reasoning: When you multiply any number by 1, the result is the number itself.
11 multiplied by 1 is equal to 11.
### 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.

GPT-3.5 Turbo:

Reasoning: We already found that 14 / 15 * 12 / 4 = 14 / 5.  
Now, we need to multiply this result by 12 / 14: (14 / 5) * (12 / 14) = (14*12) / (5*14) = 168 / 70.  
Next, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 14.  
This gives us 168 / 70 = 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.

GPT-3.5 Turbo:

Reasoning: If we have 5 parts instead of 15, the original fraction becomes 14 / 5.  
Now, we multiply the fractions: (14/5) * (12/4) = (14*12) / (5*4) = 168 / 20.  
Next, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4.  
This gives us 168 / 20 = 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.

GPT-3.5 Turbo:

Reasoning: To find the new total number of barrels, we multiply the previous total by the factor of 7:
(36/17) * 7 = 36 * 7 / 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.

GPT-3.5 Turbo:

Reasoning: To find the total amount of apples, we multiply the fraction of the barrel by the new multiplier:
(10/17) * (19/5) = (10*19) / (17*5) = 190 / 85 = 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?

GPT-3.5 Turbo:

First, we found that (20 / 4) * (1 / 5) = 1.  
Now, we will multiply 1 by (16 / 3):  
1 * (16 / 3) = 16 / 3 = 5.33 (rounded to two decimal places).  
### Answer: 5.33

Expected answer: 16/3

Correct? No

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?

GPT-3.5 Turbo:

Reasoning: Julia had 8 bushels of apples in total.
Julia decided to sell half of the bushels, which is 8 * 1/2 = <<8*1/2=4>>4 bushels of apples.
### Answer: 4 bushels.

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?

GPT-3.5 Turbo:

Reasoning: If Julia initially had 6 boxes, she would use 8/11 * 6 = <<8/11*6=48/11>>48/11 bushels of apples in total.
### Answer: 48/11 bushels.

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.

GPT-3.5 Turbo:

Reasoning: The new amount of sugar needed for the cake is 7/4 cups. The amount needed for the cookies remains 16/15 cups. Multiplying these two fractions gives us: (7/4) * (16/15) = (7*16)/(4*15) = 112/60 = 28/15 cups.
### Answer: 28/15 cups.

Expected answer: 28/15

Correct? Yes

Problem: In a new experiment, Peter decides to change his recipe slightly. Instead of using 19/9 cups of flour, he now uses 14/9 cups of flour but keeps the amount of sugar the same (14/18 cups). How would this affect the overall amount of ingredients used for his pizza dough? Multiply the new amount of flour and the original amount of sugar together to find the new total.

GPT-3.5 Turbo:

Reasoning: The new total amount of ingredients Peter needed is (14/9) * (14/18) = (14*14) / (9*18) = 196 / 162 = 98 / 81 cups.
### Answer: 98/81 cups.

Expected answer: 98/81

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?

GPT-3.5 Turbo:

Reasoning: First, simplify the fractions:
14/7 = 2
13/4 = 3.25
Now multiply the simplified fractions:
2 * 3.25 = 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.

GPT-3.5 Turbo:

Reasoning: To multiply a fraction by itself, we square both the numerator and the denominator.

(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?

GPT-3.5 Turbo:

To find the result of (15 / 16) * 18, we first calculate 15 / 16 which is 0.9375. Then, we multiply 0.9375 by 18 to get the final answer.

0.9375 * 18 = 16.875.

### Answer: 16.875

Expected answer: 135/8

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?

GPT-3.5 Turbo:

Reasoning: Each box has 6/8 = 3/4 dozen cookies.
If John buys 7 boxes, he would have 7 * 3/4 = 21/4 = 5.25 dozens of cookies.
### Answer: 5.25

Expected answer: 21/4

Correct? No

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.

GPT-3.5 Turbo:

Reasoning: We are multiplying 19/6 by itself.

(19/6) * (19/6) = (19 * 19) / (6 * 6) = 361 / 36

To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 1.

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.

GPT-3.5 Turbo:

Reasoning: To find the product of fractions, we multiply the numerators together and the denominators together. 

(19/6) * (9/4) = (19*9) / (6*4) = 171 / 24

To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3.

171 / 24 = 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?

GPT-3.5 Turbo:

We obtained the result 20 from the previous question.
Now, we multiply 20 by 1/17: 20 * 1/17 = 20/17 = 1.176470588235294.
### Answer: 1.176470588235294

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?

GPT-3.5 Turbo:

If we divide 16 by 10, we get 1.6. Then, multiplying by 10 gives us 1.6 * 10 = 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.

GPT-3.5 Turbo:

Reasoning: To find the product of 18/11 and 7, we multiply the two numbers:
18/11 * 7 = 18/11 * 7/1 = 126/11 = 11.4545454545 (rounded to 11 decimal places).
### Answer: 126/11 or 11.4545454545.

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.

GPT-3.5 Turbo:

Reasoning: To find the new product of 18 and 4/11, we multiply the two numbers:
18 * 4/11 = 72/11 = 6.54545454545 (rounded to 11 decimal places).
### Answer: 72/11 or 6.54545454545.

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.

GPT-3.5 Turbo:

Reasoning:
(91/55)^2 = (91^2) / (55^2) = 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.

GPT-3.5 Turbo:

Reasoning:
(13/10) * (14/4) = (13*14) / (10*4) = 182 / 40 = 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?

GPT-3.5 Turbo:

Reasoning: Multiplying 16 by 2/11 gives us 16 * 2/11 = 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?

GPT-3.5 Turbo:

Reasoning: 1 times 11 is equal to 1*11 = 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.

GPT-3.5 Turbo:

Given e = (18 / 12) * 6 = 9, we can now calculate e * 9/15.

e * 9/15 = 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.

GPT-3.5 Turbo:

Reasoning: (10 / 12) * 6 = 0.8333... * 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?

GPT-3.5 Turbo:

If each block is now 18/18 (a full foot) long, the total length of the blocks in feet would be:

(18/18) * (16/7) = (18*16) / (18*7) = 288 / 126 = 144 / 63 feet.

### Answer: 144/63 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?

GPT-3.5 Turbo:

Reasoning: Multiplying the result of 8/8 * 15, which is 15, by 19/18 gives 15 * 19/18 = 285/18 = 15.83 (rounded to two decimal places).
### Answer: 15.83

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?

GPT-3.5 Turbo:

Reasoning: Multiplying the fraction 8/7 by 15 gives (8/7) * 15 = 120/7.
### Answer: 120/7

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?

GPT-3.5 Turbo:

Reasoning: If you have 20/3 apples and then find some more apples doubling your current amount, you would have 20/3 * 2 = 40/3 apples.
### Answer: 40/3 apples.

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?

GPT-3.5 Turbo:

Reasoning: If the recipe requires 8 apples, two thirds of that amount is 8 * 2/3 = 16/3 apples.
Multiplying 8 apples by 4/6 gives 8 * 4/6 = 32/6 = 16/3 apples.
### Answer: 16/3 apples.

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.

GPT-3.5 Turbo:

Reasoning: To multiply two fractions, we multiply the numerators together and the denominators together. So, (33/2) * (14/13) = (33*14)/(2*13) = 462/26 = 231/13.
### Answer: 231/13

Expected answer: 231/13

Correct? Yes

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.

GPT-3.5 Turbo:

Reasoning: To multiply a fraction by a whole number, we can convert the whole number to a fraction by placing it over 1. So, 10 can be written as 10/1. Then, we multiply the numerators and denominators separately: (18*10)/(12*1) = 180/12 = 15.
### Answer: 15

Expected answer: 15

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.

GPT-3.5 Turbo:

Reasoning: The previous answer was 13/4 or 3.25. Squaring this number gives (13/4)^2 = (13^2)/(4^2) = 169/16 = 10.5625 as a decimal.
### Answer: 169/16 or 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.

GPT-3.5 Turbo:

Reasoning: To multiply 13 by 3/15, we can simplify the fraction first: 3/15 = 1/5. Then, we multiply 13 by 1/5 to get 13/5 or 2.6 as a decimal.
### Answer: 13/5 or 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.

GPT-3.5 Turbo:

Calculation: 8 * 1 = 8
8 * 2 = 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.

GPT-3.5 Turbo:

Calculation: 16 * 1 = 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?

GPT-3.5 Turbo:

Reasoning: We found that 9 * 9/17 = 81/17. Now, to multiply this result by 2, we multiply the numerator by 2: 81 * 2 = 162. The denominator remains the same.
So, 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?

GPT-3.5 Turbo:

Reasoning: To multiply 11 by the fraction 9/17, we multiply 11 by the numerator of the fraction and then divide by the denominator. So, 11 * 9/17 = 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?

GPT-3.5 Turbo:

Reasoning: Tom is donating 9/15 of the total boxes his friends received, which is 9/15 * 12 = <<9/15*12=7.2>>7.2 boxes. Since we cannot donate a fraction of a box, Tom will donate 7 boxes to the local school.
### Answer: 7

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?

GPT-3.5 Turbo:

Reasoning: Each friend will now receive 17/13 of a box. So, Tom's friends will receive a total of 13 * (17/13) = <<13*(17/13)=17>>17 boxes.
### 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.

GPT-3.5 Turbo:

Reasoning: The product of 16 and 1 is 16. Multiplying this by 3/8 gives 16 * 3/8 = 48/8 = 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?

GPT-3.5 Turbo:

Reasoning: The product of multiplying 16 and 1 by 3/8 is (16*1)*(3/8) = 16*(3/8) = 48/8 = <<16*(3/8)=48/8=6>>6.
The product of multiplying 15 and 1 is 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?

GPT-3.5 Turbo:

Reasoning: First, we found that 10 * 11/10 = 11. Now, we need to multiply 11 by 2/19. To do this, we multiply the numerators and denominators separately: 11 * 2 = 22 and 1 * 19 = 19. So, the final result is 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?

GPT-3.5 Turbo:

Reasoning: To multiply 10 by 11/17, we follow the same process as before. So, 10 * 11/17 = 10 * 11 / 17 = 110 / 17.
### Answer: 110/17

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.

GPT-3.5 Turbo:

Reasoning: First, we calculated 10 * 8/14 = 40/7. Now, we multiply this result by 9/6: (40/7) * (9/6) = (40*9)/(7*6) = 360/42 = 60/7 ≈ 8.57 (rounded to two decimal places).

### Answer: 60/7 ≈ 8.57

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.

GPT-3.5 Turbo:

Reasoning: The product of 18 and 8/14 is calculated as 18 * 8/14 = 144/14 = 72/7 ≈ 10.29 (rounded to two decimal places).

### Answer: 72/7 ≈ 10.29

Expected answer: 72/7

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?

GPT-3.5 Turbo:

Reasoning: We found that the result of multiplying twelve divided by twelve with the whole number sixteen is 16. To find the new result when this value is further multiplied by four divided by fourteen, we multiply 16 by 4/14.

Calculation: 16 * (4/14) = 16 * 2/7 = 32/7

### Answer: 32/7

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?

GPT-3.5 Turbo:

Reasoning: We already know that twelve divided by twelve equals 1. Multiplying 1 by 8 gives us the final result.

Calculation: 1 * 8 = 8

### 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.

GPT-3.5 Turbo:

To make 13 pies, Mrs. Parker will spend 13 * 14/12 = 182/12 hours.
Converting 182/12 to a mixed number, we get 15 2/12 hours, which simplifies to 15 1/6 hours.
### Answer: 15 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?

GPT-3.5 Turbo:

Reasoning: We already found that (18/11) * (17/8) = 153/44. Now, we need to multiply this result by (12/19).

(153/44) * (12/19) = (153 * 12) / (44 * 19) = 1836 / 836

The fraction 1836/836 simplifies to 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?

GPT-3.5 Turbo:

Reasoning: To evaluate the expression (10/11) * (17/8), we multiply the numerators together and the denominators together separately.

(10/11) * (17/8) = (10 * 17) / (11 * 8) = 170 / 88

The fraction 170/88 simplifies to 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?

GPT-3.5 Turbo:

Reasoning: You would be paying $2 * 7/10 = $<<2*7/10=1.4>>1.4 for the portion of banana you consume.
### 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?

GPT-3.5 Turbo:

Reasoning: The product of 1 and 8 is 8. When you multiply 8 by 9/8, you get 8*(9/8) = 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?

GPT-3.5 Turbo:

Reasoning: When you multiply 1 by 6, you get 1*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.

GPT-3.5 Turbo:

Reasoning: To triple the recipe, William needs to multiply the amount of sugar required by 3.
((9/17) * 3) = (9/17) * 3 = 27/17 ≈ 1.5882
William will need approximately 1.5882 cups of sugar this time.
### Answer: 1.5882

Expected answer: 27/17

Correct? No

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.

GPT-3.5 Turbo:

Reasoning: To multiply 18 by 5/14, we multiply the numerators and denominators separately: 18 * 5 = 90 and 1 * 14 = 14. So, the result is 90/14, which simplifies to 45/7.
### Answer: 45/7.

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))?

GPT-3.5 Turbo:

Calculating (7/13) * (15/8) gives (105/104).
Michael should use 105/104 times the amount of the new grape juice compared to the old undiluted recipe.
### Answer: 105/104.

Expected answer: 105/104

Correct? Yes

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).

GPT-3.5 Turbo:

Calculating (12/16) * (15/2) gives (3/4) * (15/2) = 45/8.
Michael should use 45/8 times the amount of the new grape juice compared to the old recipe.
### Answer: 45/8.

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?

GPT-3.5 Turbo:

Reasoning: If the smaller cake uses 6/18 of the original amount of flour, the amount of flour used for the smaller cake is 9 pounds * 6/18 = 9 * 1/3 = <<9*1/3=3>>3 pounds.
### Answer: 3 pounds.

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?

GPT-3.5 Turbo:

Reasoning: If the baker uses 1 cup of flour, the total weight of flour used is 1 cup * (19/19 pounds/cup) = 1 * 1 = <<1*1=1>>1 pound.
### Answer: 1 pound.

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?

GPT-3.5 Turbo:

To find out how much flour Julia's sister needs for the portion of the recipe she is making, we multiply the total amount of flour needed for the full recipe by the fraction representing the portion she is making:

12 * (9/13) = 108/13 = 8 4/13 cups of flour.

### Answer: 8 4/13 cups of flour.

Expected answer: 108/13

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.

GPT-3.5 Turbo:

First, we divide 16 by 5 to get 16/5 = 3.2. Then, we multiply 3.2 by the fraction 6/10 to get 3.2 * 6/10 = 19.2/10 = 1.92.
### Answer: 1.92

Expected answer: 48/25

Correct? No

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.

GPT-3.5 Turbo:

Reasoning: (247/187) * (247/187) = (247*247) / (187*187) = 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.

GPT-3.5 Turbo:

Reasoning: (19/8) * (13/17) = (19*13) / (8*17) = 247 / 136.

### Answer: 247/136.

Expected answer: 247/136

Correct? Yes

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

GPT-3.5 Turbo:

Reasoning: The previous answer is 7. When we multiply 7 by the fraction 5/5, we get 7 * 5/5 = 7 * 1 = 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?

GPT-3.5 Turbo:

Reasoning: When 1 is multiplied by 19, the result is 1*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?

GPT-3.5 Turbo:

Reasoning: The product of 9 and 13/18 is 9 * 13/18 = 117/18 = 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?

GPT-3.5 Turbo:

Reasoning: The product of 1 and 4 is 1*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.

GPT-3.5 Turbo:

Reasoning: If we multiply the fraction 11/5 by itself, we get (11/5) * (11/5) = 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.

GPT-3.5 Turbo:

Reasoning: The product of the fractions (9/18) and (11/5) is (9/18) * (11/5) = (1/2) * (11/5) = 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.

GPT-3.5 Turbo:

Reasoning: We found that 4/5 * 15 = 12. Now, we need to multiply 12 by 3/15. To do this, we multiply the numerators and denominators separately: (12*3)/(5*1) = 36/5 = 7 1/5 in simplest form.
### Answer: 7 1/5.

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.

GPT-3.5 Turbo:

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, which is already in simplest form.
### Answer: 24/5.

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.

GPT-3.5 Turbo:

Reasoning: To square a fraction, we multiply the fraction by itself.

(95/48) * (95/48) = (95 * 95) / (48 * 48) = 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?

GPT-3.5 Turbo:

Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.

(20/12) * (19/12) = (20 * 19) / (12 * 12) = 380 / 144 = 95 / 36

### Answer: 95/36.

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.

GPT-3.5 Turbo:

Let's first calculate the result of 17/20 * 17/13:

f = 17/20 * 17/13 = 289/260.

Now, let's multiply f by 12/11:

f * 12/11 = (289/260) * (12/11) = (289 * 12) / (260 * 11) = 3468 / 2860.

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:

3468 / 2860 = 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.

GPT-3.5 Turbo:

Reasoning: If we have 16/20 instead of 17/20, the multiplication operation becomes:

(16/20) * (17/13) = (16 * 17) / (20 * 13) = 272 / 260.

To simplify the fraction 272/260, we can divide both the numerator and the denominator by their greatest common divisor, which is 4.

272/260 = 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?

GPT-3.5 Turbo:

To multiply 5 5/12 by 14/14, we first convert 5 5/12 to an improper fraction:

5 5/12 = (5 * 12 + 5) / 12 = 65/12

Now, we multiply this fraction by 14/14:

(65/12) * (14/14) = (65 * 14) / (12 * 14) = 910 / 168

910/168 can be simplified to 35/6 as a mixed number:

910 ÷ 168 = 5 with a remainder of 35, so the answer is 5 35/168 which simplifies to 5 5/24.

### Answer: 5 5/24.

Expected answer: 65/12

Correct? No

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?

GPT-3.5 Turbo:

To solve 5 * (13 / 10), we first divide 13 by 10:

13 / 10 = 1 and 3/10

Now, we multiply this result by 5:

5 * (1 + 3/10) = 5 + 15/10 = 5 + 1 1/2 = 6 1/2

When we use 13/10 instead of 13/12 in the problem, the result increases from 5 5/12 to 6 1/2.

### Answer: 6 1/2.

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?

GPT-3.5 Turbo:

Reasoning: If Jack ate 3/4 of the 17-piece chocolate bar, he ate 3/4 * 17 = <<3/4*17=12.75>>12.75 pieces. Since he can't eat a fraction of a piece, we round down to the nearest whole number. Therefore, Jack ate 12 pieces of the new chocolate bar.
### Answer: 12 pieces.

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?

GPT-3.5 Turbo:

To find the product of 17 and 13/18, we multiply 17 by 13/18:

17 * 13/18 = 17 * 13/18 = 221/18.

### Answer: 221/18.

Expected answer: 221/18

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.

GPT-3.5 Turbo:

Reasoning: Multiplying 19 by the fraction 6/10 gives 19 * 6/10 = 114/10 = 57/5 = 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.

GPT-3.5 Turbo:

Reasoning: Multiplying the fraction 15/15 by the whole number 20 gives (15/15) * 20 = 1 * 20 = 20.
### Answer: 20

Expected answer: 20

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?

GPT-3.5 Turbo:

Reasoning: When you divide 2 by 3, you get 2/3. Multiplying 2/3 by 3 gives you 2.
### Answer: 2

Expected answer: 2

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.

GPT-3.5 Turbo:

Reasoning: Each box contains 12 pieces, and each piece is split into 8 equal parts for tasting. So, each box contains 12/8 = 1.5 whole pieces.
Multiplying the number of boxes by the number of whole pieces in each box gives us 3 * 1.5 = 4.5 whole pieces of chocolate.
### Answer: 4.5.

Expected answer: 9/2

Correct? No

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.

GPT-3.5 Turbo:

Reasoning: To find out how much Emily plans on spending for the upcoming Tuesday, we need to decrease her spendings on Tuesday by 4 times less than what she had spent on Tuesday. This means we need to multiply the amount she spent on Tuesday, which is 20/19 of her weekly allowance, by 4: (20/19) * 4 = 80/19 of her weekly allowance.
### 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)

GPT-3.5 Turbo:

Reasoning: Emily now plans to spend 10/12 of her weekly allowance on Tuesday. She spends 14/7 times more than this new amount, which is equivalent to (10/12) * (14/7) = 20/12 of her weekly allowance.
### Answer: 20/12.

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?

GPT-3.5 Turbo:

To find the result of multiplying the product of 2 and 2 by 5/2, we first find the product of 2 and 2 which is 4. Then, we multiply 4 by 5/2:

4 * 5/2 = 4 * 5 / 2 = 20 / 2 = 10.

Therefore, the result of multiplying the product of 2 and 2 by 5/2 is 10.
### Answer: 10

Expected answer: 10

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?

GPT-3.5 Turbo:

Reasoning: With each box containing 6/5 dozen cookies, then 11 boxes will have 11 * 6/5 = 66/5 dozen cookies.
Converting 66/5 to a mixed number, we get 13 1/5 dozen cookies.
### Answer: 13 1/5.

Expected answer: 66/5

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.

GPT-3.5 Turbo:

First, we found that 6/18 * 3 = 1. Now, to find the square of 1, we simply multiply 1 by itself: 1 * 1 = 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.

GPT-3.5 Turbo:

Reasoning: To multiply the fraction 17/18 by the whole number 3, we multiply the numerator of the fraction by the whole number. So, (17/18) * 3 = (17*3)/18 = 51/18. Since 51 and 18 share a common factor of 3, we simplify the fraction by dividing both the numerator and denominator by 3 to get 17/6.

### Answer: 17/6.

Expected answer: 17/6

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?

GPT-3.5 Turbo:

Continuing from the previous step, we have found that 5 * (14 / 10) = 7. Now, we need to multiply this result by 5/6.

To multiply two fractions, we multiply the numerators together and the denominators together. So, (7 * 5) / (1 * 6) = 35 / 6.

Therefore, the final result is 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?

GPT-3.5 Turbo:

Reasoning: To calculate 5 * (14 / 13), we first multiply the numerators and denominators separately: 5 * 14 = 70 and 1 * 13 = 13. Then, we simplify the result: 70/13 cannot be simplified further, so the result is 70/13.
### Answer: 70/13

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.

GPT-3.5 Turbo:

To multiply 120/7 by 10/10, we multiply the numerators and denominators: (120/7) * (10/10) = (120*10) / (7*10) = 1200/70.

We can simplify this fraction by dividing both the numerator and denominator by 10: 1200/70 = 120/7 = 17 1/7.

Therefore, the result of multiplying 120/7 by 10/10 is 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.

GPT-3.5 Turbo:

First, let's find the result of multiplying 5/8 by 3:
(5/8) * 3 = (5*3) / 8 = 15/8.

Next, let's find the result of multiplying (20/10) by 6:
(20/10) * 6 = (20*6) / 10 = 120/10 = 12.

The result as a mixed number is 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.

GPT-3.5 Turbo:

Reasoning: When we have 8/8 instead of 8/19, we can simplify 8/8 to 1. So, the calculation becomes:
1 * 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?

GPT-3.5 Turbo:

Reasoning: We found that 8 multiplied by 1 is 8. Now, multiplying 8 by 3/2 gives us 8 * 3/2 = 24/2 = 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?

GPT-3.5 Turbo:

Reasoning: Similar to the previous problem, multiplying any number by 1 does not change the value of the number. Therefore, 20 multiplied by 1 is equal to 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.

GPT-3.5 Turbo:

Reasoning: To find the length of the shelf that is filled with books, we multiply 13 (total length of the shelf) by 12/15.

Calculation: 13 * 12/15 = 13 * 4/5 = 52/5 = 10.4

### 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.

GPT-3.5 Turbo:

Reasoning: To multiply a fraction by itself, we multiply the numerators and denominators separately. So, (6/5) * (6/5) = (6*6)/(5*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.

GPT-3.5 Turbo:

Reasoning: \( \frac{5}{5} = 1 \), so \( 1 \times \frac{6}{6} = \frac{6}{6} = 1 \).

### Answer: \(\frac{6}{6} = 1\)

Expected answer: 1

Correct? No

Problem: Continuing from the initial problem: Suppose this time, all 10 out of 10 students participated in the school project, each of them preparing 8 models. Calculate how many total models were prepared for the science fair now, by multiplying the new fraction of students participating (10/10) with the number of models each student made (8).

GPT-3.5 Turbo:

Reasoning: Since all 10 out of 10 students participated, the fraction of students participating is 10/10. Each participating student prepared 8 models. So, the total number of models prepared is (10/10) * 8 = 1 * 8 = 8.
### Answer: 8

Expected answer: 8

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.

GPT-3.5 Turbo:

To multiply 18/4 by 3/3, we first simplify the fractions:
18/4 = 9/2.

Now, we multiply 9/2 by 3/3:
(9/2) * (3/3) = (9*3) / (2*3) = 27 / 6 = 9/2.

### Answer: 9/2.

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?

GPT-3.5 Turbo:

Reasoning: The result of multiplying thirteen by the ratio of two to two is 13.
The fraction eight fourteenths is 8/14.
Multiplying 13 by 8/14 gives 13 * 8/14 = 104/14 = 52/7.
### Answer: 52/7

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.

GPT-3.5 Turbo:

Reasoning: We can simplify the expression by multiplying the numerators and denominators together.

20/6 * 6/4 = (20*6)/(6*4) = 120/24 = 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.

GPT-3.5 Turbo:

For the first part:
2 * 6 = 12 times Bear brought the ball back in 6 minutes.

For the second part:
(19/14) * (2 * 6) = (19/14) * 12 = 228/14 = 114/7 times Bear would bring back the ball in 6 minutes at the increased speed.

### 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.

GPT-3.5 Turbo:

Reasoning: The product of 3 and 6 is calculated as 3 * 6 = 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'?

GPT-3.5 Turbo:

Calculating (1.4) * (7 / 2):
(1.4) * (7 / 2) = 1.4 * 3.5 = 4.9
### Answer: 4.9

Expected answer: 49/10

Correct? No

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?

GPT-3.5 Turbo:

Recalculating with the new fraction (2/12) * 14:
(2/12) * 14 = (1/6) * 14 = 14/6 = 7/3 = 2.333333...
### Answer: 7/3 or 2.333333...

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?

GPT-3.5 Turbo:

Reasoning: To find the final result, we multiply 45/7 by 9/7. This gives us (45/7) * (9/7) = 405/49.
### Answer: 405/49.

Expected answer: 405/49

Correct? Yes

Problem: If instead of 18, we had 17 wholes, what would be the result of multiplying 5/14 of a whole by 17?

GPT-3.5 Turbo:

Reasoning: To find the result, we multiply 5/14 of a whole by 17. This gives us (5/14) * 17 = 85/14.
### Answer: 85/14.

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?

GPT-3.5 Turbo:

Reasoning: To multiply a fraction by another fraction, we multiply the numerators together and the denominators together.

(55/8) * (1/5) = (55 * 1) / (8 * 5) = 55 / 40 = 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?

GPT-3.5 Turbo:

Reasoning: To multiply a fraction by an integer, we simply multiply the numerator of the fraction by the integer and keep the denominator the same.

(11/8) * 9 = (11 * 9) / 8 = 99 / 8.

### Answer: 99/8.

Expected answer: 99/8

Correct? Yes