🔗 Problem

Problem: Calculate the product of (29/2) and (19/28) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To find the product of (29/2) and (19/28), we multiply the numerators together and the denominators together.

    (29/2) * (19/28) = (29 * 19) / (2 * 28) = 551 / 56

    ### Answer: 551/56.

Expected answer: 551/56

Correct? Yes

🔗 Follow-up

Problem: After finding the product of (29/2) and (19/28), multiply your result by (8/28). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We already found the product of (29/2) and (19/28) to be 551/56. Now, we will multiply this result by (8/28).

    (551/56) * (8/28) = (551 * 8) / (56 * 28) = 4408 / 1568 = 275 / 98

    ### Answer: 275/98.

Expected answer: 551/196

Correct? No

🔗 Follow-up

Problem: After finding the product of (29/2) and (19/28), reconsider the calculation using (19/14) instead of (19/28). Recalculate the product of (29/2) and (19/14) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To find the product of (29/2) and (19/14), we multiply the numerators together and the denominators together.

    (29/2) * (19/14) = (29 * 19) / (2 * 14) = 551 / 28

    ### Answer: 551/28.

Expected answer: 551/28

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following problem: multiply 7 by the result of dividing 27 by 12. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we need to divide 27 by 12: 27 ÷ 12 = 2.25.

    Next, we multiply 7 by 2.25: 7 * 2.25 = 15.75.

    Therefore, the result is 15.75, which can be simplified to 63/4 as a fraction.

    ### Answer: 63/4.

Expected answer: 63/4

Correct? Yes

🔗 Follow-up

Problem: Let's reconsider the previous question. Instead of multiplying 7 by the result of dividing 27 by 12, calculate the result when you multiply 7 by the division of 26 by 12. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we need to divide 26 by 12: 26 ÷ 12 = 2.166666... (repeating).

    Next, we multiply 7 by 2.166666...: 7 * 2.166666... = 15.166666... (repeating).

    Therefore, the result is 15.166666..., which can be simplified to 455/30 as a fraction.

    ### Answer: 455/30.

Expected answer: 91/6

Correct? Yes

🔗 Problem

Problem: Susan has a recipe that calls for 30 parts of flour to 27 parts of water. If she decides to use 29 parts of flour instead, and she keeps the water proportion the same, how much water will she use? Calculate this using fraction multiplication: ((30 / 30) * (29 / 27)).

GPT-3.5 Turbo:

    Reasoning: To find out how much water Susan will use with 29 parts of flour, we can use the fraction multiplication ((30/30) * (29/27)).

    ((30/30) * (29/27)) = (29/27) = 29/27.

    Susan will use 29 parts of water.
    ### Answer: 29.

Expected answer: 29/27

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: ((24 / 22) * (24 / 17)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the parentheses: 24/22 = 12/11 and 24/17. Then, we multiply these fractions: (12/11) * (24/17) = (12*24) / (11*17) = 288 / 187. Therefore, the result is 288/187.
    ### Answer: 288/187.

Expected answer: 288/187

Correct? Yes

🔗 Follow-up

Problem: After finding the result of ((24 / 22) * (24 / 17)) in the previous problem, multiply the answer you found by (27 / 18). Write the result as a simplified fraction.

GPT-3.5 Turbo:

    First, we multiply the result from the previous problem, 288/187, by 27/18: (288/187) * (27/18) = (288*27) / (187*18) = 7776 / 3366. We simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6: 7776/3366 = 1296/561.
    ### Answer: 1296/561.

Expected answer: 432/187

Correct? Yes

🔗 Follow-up

Problem: Since the previous problem had you evaluating ((24 / 22) * (24 / 17)), consider this change: What if instead of multiplying (24 / 22) by (24 / 17), you multiplied it by (24 / 9)? Calculate the result of ((24 / 22) * (24 / 9)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the parentheses: 24/22 = 12/11 and 24/9 = 8/3. Then, we multiply these fractions: (12/11) * (8/3) = (12*8) / (11*3) = 96 / 33. We can simplify this fraction by dividing both the numerator and denominator by 3: 96/33 = 32/11. Therefore, the result is 32/11.
    ### Answer: 32/11.

Expected answer: 32/11

Correct? Yes

🔗 Problem

Problem: What is the result when you divide 25/4 by 16/6? Please write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To divide fractions, we multiply by the reciprocal of the divisor. So, 25/4 ÷ 16/6 = 25/4 * 6/16 = (25*6)/(4*16) = 150/64 = 75/32.

    ### Answer: 75/32.

Expected answer: 75/32

Correct? Yes

🔗 Follow-up

Problem: If the result of dividing 25/4 by 16/6 is multiplied by 19/6, what is the new result? Be sure to simplify your answer to lowest terms.

GPT-3.5 Turbo:

    Reasoning: We already found that 25/4 ÷ 16/6 = 75/32. Now, we multiply this result by 19/6: (75/32) * (19/6) = (75*19)/(32*6) = 1425/192 = 237/32.

    ### Answer: 237/32.

Expected answer: 475/64

Correct? No

🔗 Follow-up

Problem: Following up from the previous question, consider the new scenario where instead of dividing 25/4 we are now dividing 9 by 16/6. What is the answer to this problem? Please simplify your final answer.

GPT-3.5 Turbo:

    Reasoning: Dividing 9 by 16/6 is the same as multiplying 9 by the reciprocal of 16/6. So, 9 ÷ 16/6 = 9 * 6/16 = 54/16 = 27/8.

    ### Answer: 27/8.

Expected answer: 27/8

Correct? Yes

🔗 Problem

Problem: Determine the result of the following: Multiply the fraction 3/7 by the fraction 26/6 and express your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (3/7) * (26/6) = (3*26) / (7*6) = 78 / 42

    To simplify the fraction 78/42, we find the greatest common divisor of 78 and 42, which is 6. Dividing both the numerator and denominator by 6, we get:

    78 / 42 = 13 / 7

    ### Answer: 13/7.

Expected answer: 13/7

Correct? Yes

🔗 Follow-up

Problem: In the previous question, you found the result of (3 / 7) * (26 / 6). Now, take that result and multiply it by the fraction 23/2. What's the result of this calculation, expressed as a simplified fraction?

GPT-3.5 Turbo:

    Let's first find the result of (3/7) * (26/6) * (23/2):

    (13/7) * (23/2) = (13*23) / (7*2) = 299 / 14

    To simplify the fraction 299/14, we find the greatest common divisor of 299 and 14, which is 1. Therefore, the fraction is already in its simplest form.

    ### Answer: 299/14.

Expected answer: 299/14

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you multiplied the fraction 3/7 by the fraction 26/6. Now, let's change the fraction a bit. Instead of 3/7, use 7/7 (which is actually 1). Multiply this new fraction 7/7 by the same fraction 26/6. What is the result of this new calculation, expressed as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning: When we multiply any fraction by 1, the result is the same fraction.

    (7/7) * (26/6) = 26/6

    To simplify the fraction 26/6, we find the greatest common divisor of 26 and 6, which is 2. Dividing both the numerator and denominator by 2, we get:

    26 / 6 = 13 / 3

    ### Answer: 13/3.

Expected answer: 13/3

Correct? Yes

🔗 Problem

Problem: Calculate the result of the expression (17 / 10) * (28 / 10) and write your answer in decimal form.

GPT-3.5 Turbo:

    Reasoning: (17 / 10) * (28 / 10) = (1.7) * (2.8) = 4.76.
    ### Answer: 4.76

Expected answer: 119/25

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, you found the result of (17 / 10) * (28 / 10). Now, multiply that result by (11 / 18). What will the new result be? Write your answer in decimal form.

GPT-3.5 Turbo:

    Reasoning: Multiplying 4.76 by (11 / 18) gives 4.76 * (11 / 18) = 2.9244.
    ### Answer: 2.9244

Expected answer: 1309/450

Correct? No

🔗 Follow-up

Problem: In the previous problem, you were asked to calculate the result of (17 / 10) * (28 / 10). But consider this variation: calculate the result of the expression (17 / 24) * (28 / 10) instead. What would be the new result? Write your answer in decimal form.

GPT-3.5 Turbo:

    Reasoning: (17 / 24) * (28 / 10) = (0.708333...) * (2.8) = 1.983333...
    ### Answer: 1.983333...

Expected answer: 119/60

Correct? No

🔗 Problem

Problem: Determine the value of the given expression: ((29 / 14) * (23 / 6))

GPT-3.5 Turbo:

    Reasoning: ((29 / 14) * (23 / 6)) = (2.0714 * 3.8333) ≈ 7.9286
    ### Answer: 7.9286

Expected answer: 667/84

Correct? No

🔗 Problem

Problem: Calculate the answer for ((18 / 19) * (19 / 6)) and write the result as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{18}{19}\right) \times \left(\frac{19}{6}\right) = \frac{18 \times 19}{19 \times 6} = \frac{342}{114} = \frac{3}{1}
    \]

    ### Answer: \(\frac{3}{1}\)

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: After calculating the solution for ((18 / 19) * (19 / 6)), take the result and multiply it by itself. What do you get? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{3}{1}\right) \times \left(\frac{3}{1}\right) = \frac{3 \times 3}{1 \times 1} = \frac{9}{1} = 9
    \]

    ### Answer: \(\frac{9}{1}\)

Expected answer: 9

Correct? No

🔗 Follow-up

Problem: After you've calculated the solution for ((18 / 19) * (19 / 6)), now consider what would happen if the fraction was instead ((9 / 19) * (19 / 6)). What would be the result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{9}{19}\right) \times \left(\frac{19}{6}\right) = \frac{9 \times 19}{19 \times 6} = \frac{171}{114} = \frac{3}{2}
    \]

    ### Answer: \(\frac{3}{2}\)

Expected answer: 3/2

Correct? Yes

🔗 Problem

Problem: Calculate the result of the multiplication of the fraction 19/12 by 20/6. Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (19/12) * (20/6) = (19*20) / (12*6) = 380 / 72

    To simplify the fraction, we find the greatest common divisor (GCD) of 380 and 72, which is 4.

    380 / 72 = (380/4) / (72/4) = 95 / 18

    ### Answer: 95/18.

Expected answer: 95/18

Correct? Yes

🔗 Follow-up

Problem: Taking the answer from the previous problem (19/12 * 20/6), multiply this result with itself. What is the resulting fraction when simplified?

GPT-3.5 Turbo:

    Reasoning: We found in the previous problem that (19/12) * (20/6) = 95/18.

    To multiply this result by itself, we multiply the numerators together and the denominators together.

    (95/18) * (95/18) = (95*95) / (18*18) = 9025 / 324

    To simplify the fraction, we find the greatest common divisor (GCD) of 9025 and 324, which is 1.

    9025 / 324 = 9025 / 324

    ### Answer: 9025/324.

Expected answer: 9025/324

Correct? Yes

🔗 Follow-up

Problem: In the original problem, you multiplied the fractions 19/12 and 20/6. Now suppose you replace 19/12 with 10/12 and redo the calculation. What is the resulting fraction when it is simplified?

GPT-3.5 Turbo:

    Reasoning: If we replace 19/12 with 10/12 and redo the calculation, we have:

    (10/12) * (20/6) = (10*20) / (12*6) = 200 / 72

    To simplify the fraction, we find the greatest common divisor (GCD) of 200 and 72, which is 8.

    200 / 72 = (200/8) / (72/8) = 25 / 9

    ### Answer: 25/9.

Expected answer: 25/9

Correct? Yes

🔗 Problem

Problem: A cargo ship carries 28/21 of its capacity in the morning, and 22/4 of its capacity in the afternoon. If the cargo in the morning represents the load allocated to consumer goods and the cargo in the afternoon represents industrial supplies, what is the total fractional representation of these two types of cargo hauled in one day? Calculate ((28 / 21) * (22 / 4)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating the total fractional representation of the two types of cargo:
    (28/21) * (22/4) = (4/3) * (11/1) = 44/3 = 14 2/3.

    ### Answer: 14 2/3.

Expected answer: 22/3

Correct? No

🔗 Problem

Problem: Determine the result of the following mathematical expression: (16 / 4) / (24 / 21). Write your answer as a simplified fraction or decimal.

GPT-3.5 Turbo:

    Reasoning: First, we simplify the expression inside the parentheses: (16 / 4) / (24 / 21) = 4 / (24 / 21).
    Next, we simplify the division inside the parentheses: 24 / 21 = 8 / 7.
    Now, we substitute this back into the expression: 4 / (8 / 7) = 4 * (7 / 8) = 28 / 8 = 3.5.
    ### Answer: 3.5

Expected answer: 7/2

Correct? Yes

🔗 Follow-up

Problem: After you've calculated the result of the previous problem, which is (16 / 4) / (24 / 21), multiply your answer by (5 / 13). What is the final result in its simplified form?

GPT-3.5 Turbo:

    Let's first calculate the result of the expression (16 / 4) / (24 / 21), which we found to be 3.5 in the previous step.

    Now, we multiply 3.5 by (5 / 13):
    3.5 * (5 / 13) = 17.5 / 13 = 1.34615384615 (rounded to 11 decimal places).

    ### Answer: 1.34615384615

Expected answer: 35/26

Correct? No

🔗 Follow-up

Problem: Suppose you made a mistake when performing the previous calculation. Instead of (16 / 4) / (24 / 21), you should have calculated (16 / 4) / 3. What would the correct answer be if the original problem used this correct operation instead?

GPT-3.5 Turbo:

    Reasoning: The correct expression to evaluate is (16 / 4) / 3 = 4 / 3 = 1.33 (rounded to two decimal places).
    ### Answer: 1.33

Expected answer: 4/3

Correct? No

🔗 Problem

Problem: Calculate the product of the fractions 5/27 and 15/2. Write your answer in the simplest form.

GPT-3.5 Turbo:

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

    (5/27) * (15/2) = (5 * 15) / (27 * 2) = 75 / 54

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

    75 / 54 = 25 / 18

    ### Answer: 25/18.

Expected answer: 25/18

Correct? Yes

🔗 Follow-up

Problem: After finding the product of the fractions 5/27 and 15/2, take that result and multiply it by itself. What is the result when you write it in simplest form?

GPT-3.5 Turbo:

    Let's first find the product of the fractions 5/27 and 15/2:

    (5/27) * (15/2) = 75 / 54 = 25 / 18

    Now, let's multiply this result by itself:

    (25/18) * (25/18) = (25 * 25) / (18 * 18) = 625 / 324

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

    625 / 324

    ### Answer: 625/324.

Expected answer: 625/324

Correct? Yes

🔗 Follow-up

Problem: After previously calculating the product of the fractions 5/27 and 15/2, what if the original number of the numerator in the first fraction was 24 instead of 5? Calculate the new product of the fractions 24/27 and 15/2 and write your answer in simplest form.

GPT-3.5 Turbo:

    Reasoning: If the numerator of the first fraction is changed to 24, the new calculation would be:

    (24/27) * (15/2) = (24 * 15) / (27 * 2) = 360 / 54

    To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 6.

    360 / 54 = 60 / 9 = 20 / 3 = 20 / 3 = 20/3

    ### Answer: 20/3.

Expected answer: 20/3

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following product of fractions: (15 / 13) * (19 / 7). Make sure to write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/13) * (19/7) = (15 * 19) / (13 * 7) = 285 / 91.

    ### Answer: 285/91.

Expected answer: 285/91

Correct? Yes

🔗 Follow-up

Problem: After finding the result of the product of fractions (15 / 13) * (19 / 7), multiply your result by another fraction (23/22). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Let's first multiply the result of the first multiplication by the fraction (23/22):

    (285/91) * (23/22) = (285 * 23) / (91 * 22) = 6555 / 2002.

    To simplify this fraction, we find the greatest common divisor (GCD) of 6555 and 2002, which is 1. Therefore, the fraction is already in its simplest form.

    ### Answer: 6555/2002.

Expected answer: 6555/2002

Correct? Yes

🔗 Follow-up

Problem: In the previous task, instead of calculating the product of fractions (15 / 13) * (19 / 7), now calculate the result of a slightly different operation: (15 / 29) * (19 / 7). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/29) * (19/7) = (15 * 19) / (29 * 7) = 285 / 203.

    To simplify the fraction 285/203, we can divide both the numerator and the denominator by their greatest common divisor, which is 1 in this case.

    ### Answer: 285/203.

Expected answer: 285/203

Correct? Yes

🔗 Problem

Problem: Calculate the product of the fractions 23/22 and 27/20. Express your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (23/22) * (27/20) = (23*27) / (22*20) = 621 / 440.

    ### Answer: 621/440.

Expected answer: 621/440

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: (12 / 25) * (20 / 4). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (12/25) * (20/4) = (12*20) / (25*4) = 240 / 100 = 24/10 = 12/5.

    ### Answer: 12/5.

Expected answer: 12/5

Correct? Yes

🔗 Follow-up

Problem: After finding the result of (12 / 25) * (20 / 4), now multiply this result by (17 / 17). Report your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (12/25) * (20/4) * (17/17) = (12*20*17) / (25*4*17) = 4080 / 1700 = 204 / 85.

    ### Answer: 204/85.

Expected answer: 12/5

Correct? Yes

🔗 Follow-up

Problem: After resolving the previous problem, let us consider a slightly different situation. Now, calculate the result of (10 / 25) * (20 / 4) instead of (12 / 25) * (20 / 4). What difference does this make to the result? Write your new answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (10/25) * (20/4) = (10*20) / (25*4) = 200 / 100 = 2.

    The difference in this case is that the numerator of the first fraction is different, resulting in a different final answer.

    ### Answer: 2.

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Calculate the following operation: multiply the fraction 14/10 by the fraction 30/5. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (14/10) * (30/5) = (14 * 30) / (10 * 5) = 420 / 50 = 42 / 5

    ### Answer: 42/5.

Expected answer: 42/5

Correct? Yes

🔗 Follow-up

Problem: After calculating the multiplication of 14/10 by 30/5, multiply that result by the fraction 13/15. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (42/5) * (13/15) = (42 * 13) / (5 * 15) = 546 / 75 = 182 / 25

    ### Answer: 182/25.

Expected answer: 182/25

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, suppose that instead of 14/10 we had 30/10. Now, the problem becomes: calculate the multiplication of 30/10 by 30/5. What would be the simplified fraction as an answer?

GPT-3.5 Turbo:

    Reasoning: We can simplify the fractions before multiplying to make the calculation easier.

    (30/10) * (30/5) = (3 * 30) / (10 * 5) = 90 / 50 = 9 / 5

    ### Answer: 9/5.

Expected answer: 18

Correct? No

🔗 Problem

Problem: A baker is preparing a large batch of cookies that requires 26 cups of sugar per each full batch. If he only has enough sugar to make a fraction of the batch, represented by 29/14 of a full batch, how many batches of cookies can the baker make? Calculate this as ((26 / 1) / (29 / 14)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating (26 / 1) / (29 / 14) gives us (26 / 1) * (14 / 29) = 26 * 14 / 29 = 364 / 29 = 364/29 =  12/1 = 12.
    ### Answer: 12.

Expected answer: 364/29

Correct? No

🔗 Problem

Problem: Evaluate the following expression: (27 / 10) * (9 / 4). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (27/10) * (9/4) = (27*9) / (10*4) = 243 / 40.
    ### Answer: 243/40.

Expected answer: 243/40

Correct? Yes

🔗 Follow-up

Problem: After solving for s in the previous problem, now calculate a new value o, where o = (9 / 13) * s. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Given that s = 243/40, we can calculate o as follows:
    o = (9/13) * (243/40) = (9*243) / (13*40) = 2187 / 520 = 729 / 173.
    ### Answer: 729/173.

Expected answer: 2187/520

Correct? No

🔗 Follow-up

Problem: After having calculated the previous problem where you multiplied (27 / 10) * (9 / 4), consider what would happen if instead of multiplying by (9 / 4), you multiplied by (9 / 11). Calculate the new value of s = ((27 / 10) * (9 / 11)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: s = (27/10) * (9/11) = (27*9) / (10*11) = 243 / 110.
    ### Answer: 243/110.

Expected answer: 243/110

Correct? Yes

🔗 Problem

Problem: Evaluate the expression ((24 / 11) * (27 / 26)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: ((24 / 11) * (27 / 26)) = (24 * 27) / (11 * 26) = 648 / 286 = 324 / 143.

    ### Answer: 324/143.

Expected answer: 324/143

Correct? Yes

🔗 Follow-up

Problem: You've just evaluated the expression ((24 / 11) * (27 / 26)) in the previous question. Now, go ahead and take the result from that previous operation and multiply it by (14 / 27). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we need to multiply the result from the previous operation, 324/143, by 14/27.

    (324/143) * (14/27) = (324 * 14) / (143 * 27) = 4536 / 3861 = 504 / 429 = 168 / 143.

    ### Answer: 168/143.

Expected answer: 168/143

Correct? Yes

🔗 Problem

Problem: Find the solution to the following multiplication problem: Multiply the fraction 26/9 by the fraction 17/13. Write your answer in simplest form.

GPT-3.5 Turbo:

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

    (26/9) * (17/13) = (26 * 17) / (9 * 13) = 442 / 117

    To simplify the fraction, we find the greatest common divisor of 442 and 117, which is 1.

    442 / 117 = 442 / 117

    ### Answer: 442/117.

Expected answer: 34/9

Correct? Yes

🔗 Follow-up

Problem: Having solved the previous problem, now multiply your answer by the fraction 24/30. What is the result in simplest form?

GPT-3.5 Turbo:

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

    (442/117) * (24/30) = (442 * 24) / (117 * 30) = 10608 / 3510

    To simplify the fraction, we find the greatest common divisor of 10608 and 3510, which is 234.

    10608 / 3510 = 44 / 15

    ### Answer: 44/15.

Expected answer: 136/45

Correct? No

🔗 Follow-up

Problem: If instead of multiplying the fraction 26/9 by the fraction 17/13, you multiplied 25/9 by 17/13, what would the result be in simplest form?

GPT-3.5 Turbo:

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

    (25/9) * (17/13) = (25 * 17) / (9 * 13) = 425 / 117

    To simplify the fraction, we find the greatest common divisor of 425 and 117, which is 1.

    425 / 117 = 425 / 117

    ### Answer: 425/117.

Expected answer: 425/117

Correct? Yes

🔗 Problem

Problem: Solve the following problem: What is the result of the expression (28 / 16) / (27 / 24)? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    (28 / 16) / (27 / 24) = (28 / 16) * (24 / 27) = (7/4) * (8/9) = 56/36 = 14/9.

    ### Answer: 14/9.

Expected answer: 14/9

Correct? Yes

🔗 Follow-up

Problem: After solving for the result of the original expression (28 / 16) / (27 / 24), now multiply this result by itself. What is the outcome? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    (14/9) * (14/9) = 196/81.

    ### Answer: 196/81.

Expected answer: 196/81

Correct? Yes

🔗 Problem

Problem: Calculate the expression ((15 / 3) * (19 / 26)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating the expression:
    ((15 / 3) * (19 / 26)) = (5 * 19) / (3 * 26) = 95 / 78.

    ### Answer: 95/78.

Expected answer: 95/26

Correct? No

🔗 Problem

Problem: The local bakery was making a special order for a customer. The recipe they are using requires 19/28, and they want to make exactly 30/4 of this recipe. How much of the ingredient will they require?

GPT-3.5 Turbo:

    To find out how much of the ingredient they will require, we need to multiply the fraction 19/28 by 30/4.

    (19/28) * (30/4) = (19*30) / (28*4) = 570 / 112 = 285 / 56.

    Therefore, the bakery will require 285/56 of the ingredient.
    ### Answer: 285/56.

Expected answer: 285/56

Correct? Yes

🔗 Follow-up

Problem: Continuing from the bakery scenario, suppose that the bakery has adjusted their special recipe, and instead of using 19/28, they now use 19/14 of the ingredient for a single cake. If a customer still wants to order 30/4 of this new recipe, how much of the ingredient will the bakery now require for this order?

GPT-3.5 Turbo:

    To find out how much of the ingredient the bakery will now require for this order, we need to multiply the fraction 19/14 by 30/4.

    (19/14) * (30/4) = (19*30) / (14*4) = 570 / 56 = 285 / 28.

    Therefore, the bakery will now require 285/28 of the ingredient for this order.
    ### Answer: 285/28.

Expected answer: 285/28

Correct? Yes

🔗 Problem

Problem: Determine the result of ((5 / 2) / (26 / 15)). Write the final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    ((5 / 2) / (26 / 15)) = (5 / 2) * (15 / 26) = (5 * 15) / (2 * 26) = 75 / 52.

    ### Answer: 75/52.

Expected answer: 75/52

Correct? Yes

🔗 Follow-up

Problem: After determining the result of ((5 / 2) / (26 / 15)) in the previous problem, take that result and multiply it by itself. What simplified fraction do you get?

GPT-3.5 Turbo:

    Reasoning:
    ((5 / 2) / (26 / 15)) = 75 / 52.
    (75 / 52) * (75 / 52) = (75 * 75) / (52 * 52) = 5625 / 2704.

    ### Answer: 5625/2704.

Expected answer: 5625/2704

Correct? Yes

🔗 Follow-up

Problem: After determining the result of ((5 / 2) / (26 / 15)) in the previous problem, consider a situation where there were initially 14 units instead of 5. What is the result when you divide 14 by (26 / 15)? Write the final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    When we divide 14 by (26 / 15), we can rewrite it as 14 * (15 / 26) = (14 * 15) / 26 = 210 / 26 = 105 / 13.

    ### Answer: 105/13.

Expected answer: 105/13

Correct? Yes

🔗 Problem

Problem: Calculate the result of the expression (9/3) * (27/28) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (9/3) * (27/28) = 3 * (27/28) = 81/28.

    ### Answer: 81/28.

Expected answer: 81/28

Correct? Yes

🔗 Follow-up

Problem: After you have calculated the result of the expression (9/3) * (27/28) from the previous problem, calculate the square of your answer. Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: The square of 81/28 is (81/28)^2 = (81^2)/(28^2) = 6561/784.

    ### Answer: 6561/784.

Expected answer: 6561/784

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you multiplied the fractions (9/3) * (27/28). Now consider the case where the second fraction has changed from (27/28) to (23/28). How does this change your answer? Recalculate using (9/3) * (23/28) and write your new answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (9/3) * (23/28) = 3 * (23/28) = 69/28.

    ### Answer: 69/28.

Expected answer: 69/28

Correct? Yes

🔗 Problem

Problem: Calculate the solution to the following equation and write your answer as a simplified fraction: ((15 / 13) * (24 / 24))

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{15}{13}\right) \times \left(\frac{24}{24}\right) = \frac{15 \times 24}{13 \times 24} = \frac{360}{312} = \frac{30}{26} = \frac{15}{13}
    \]

    ### Answer: \(\frac{15}{13}\)

Expected answer: 15/13

Correct? Yes

🔗 Follow-up

Problem: After calculating the solution to ((15 / 13) * (24 / 24)), multiply your answer with (22 / 7) and write that answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{15}{13}\right) \times \left(\frac{24}{24}\right) \times \left(\frac{22}{7}\right) = \frac{15 \times 24 \times 22}{13 \times 24 \times 7} = \frac{7920}{2184} = \frac{990}{273} = \frac{330}{91}
    \]

    ### Answer: \(\frac{330}{91}\)

Expected answer: 330/91

Correct? Yes

🔗 Follow-up

Problem: After calculating the solution to ((15 / 2) * (24 / 24)), consider what would happen if you originally had 15 halves instead of 15 thirteenths. Multiply this new fraction with 1 (represented by (24 / 24)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Given the new fraction \(\left(\frac{15}{2}\right) \times \left(\frac{24}{24}\right)\):
    \[
    \left(\frac{15}{2}\right) \times \left(\frac{24}{24}\right) = \frac{15 \times 24}{2 \times 24} = \frac{360}{48} = \frac{45}{6} = \frac{15}{2}
    \]

    Multiplying this new fraction by 1 (represented by \(\frac{24}{24}\)):
    \[
    \left(\frac{15}{2}\right) \times \left(\frac{24}{24}\right) = \frac{15}{2} \times 1 = \frac{15}{2}
    \]

    ### Answer: \(\frac{15}{2}\)

Expected answer: 15/2

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following multiplication of fractions operation: (9 / 7) * (25 / 30). Express your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (9/7) * (25/30) = (9 * 25) / (7 * 30) = 225 / 210 = 15 / 14

    ### Answer: 15/14.

Expected answer: 15/14

Correct? Yes

🔗 Follow-up

Problem: Using the answer you obtained from the previous problem, multiply it by 15/15. What simplified fraction do you get?

GPT-3.5 Turbo:

    Reasoning: To multiply a fraction by 15/15 is the same as multiplying by 1, which does not change the value of the fraction.

    (15/14) * (15/15) = 15/14

    ### Answer: 15/14.

Expected answer: 15/14

Correct? Yes

🔗 Follow-up

Problem: The previous problem involved calculating (9 / 7) * (25 / 30). Now calculate (9 / 7) * (25 / 21) which is similar but with a slight change in the second fraction. What simplified fraction do you get in this scenario?

GPT-3.5 Turbo:

    Reasoning:

    To multiply fractions, we multiply the numerators together and the denominators together separately.

    (9/7) * (25/21) = (9 * 25) / (7 * 21) = 225 / 147

    The fraction 225/147 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

    225 ÷ 3 = 75
    147 ÷ 3 = 49

    Therefore, 225/147 simplifies to 75/49.

    ### Answer: 75/49.

Expected answer: 75/49

Correct? Yes

🔗 Problem

Problem: Calculate the result of the problem ((9 / 8) / (20 / 18)). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    ((9 / 8) / (20 / 18)) = (9 / 8) * (18 / 20) = (9 * 18) / (8 * 20) = 162 / 160 = 81 / 80.

    ### Answer: 81/80.

Expected answer: 81/80

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, now calculate the result of multiplying your answer by the fraction (29 / 21). Write your final answer as a simplified fraction. In other words, calculate ((29 / 21) * ((9 / 8) / (20 / 18))).

GPT-3.5 Turbo:

    Reasoning:
    ((29 / 21) * ((9 / 8) / (20 / 18))) = (29 / 21) * (81 / 80) = (29 * 81) / (21 * 80) = 2349 / 1680 = 391 / 280.

    ### Answer: 391/280.

Expected answer: 783/560

Correct? No

🔗 Follow-up

Problem: In the previous scenario, instead of starting with a fraction of 9/8, let's say we started with a simpler fraction of 9 and divide it by the complex fraction 20/18. What would be the result? In other words, calculate (9 / (20 / 18)). Express your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    (9 / (20 / 18)) = 9 * (18 / 20) = 9 * 9 / 10 = 81 / 10.

    ### Answer: 81/10.

Expected answer: 81/10

Correct? Yes

🔗 Problem

Problem: What is the result of performing the operation (30 / 6) / (13 / 9)? Write your answer as a simplified number or fraction.

GPT-3.5 Turbo:

    Reasoning: (30 / 6) / (13 / 9) = 5 / (13 / 9) = 5 * (9 / 13) = 45 / 13.
    ### Answer: 45/13.

Expected answer: 45/13

Correct? Yes

🔗 Follow-up

Problem: Following the result of the previous question, calculate the new result if you multiply the answer you got by (14 / 4). What is your answer now?

GPT-3.5 Turbo:

    Reasoning: Multiplying 45/13 by 14/4 gives (45/13) * (14/4) = (45 * 14) / (13 * 4) = 630 / 52 = 315 / 26.
    ### Answer: 315/26.

Expected answer: 315/26

Correct? Yes

🔗 Problem

Problem: If you divide 30 by 18 and then multiply the result by the fraction 18/6, what is the result?

GPT-3.5 Turbo:

    First, we divide 30 by 18 to get 30/18 = 5/3.
    Then, we multiply 5/3 by 18/6 to get (5/3) * (18/6) = (5*18)/(3*6) = 90/18 = 5.
    ### Answer: 5.

Expected answer: 5

Correct? Yes

🔗 Follow-up

Problem: If you take the result from the previous problem (30 divided by 18, multiplied by 18/6) and multiply this by 8/20, what is the resulting value?

GPT-3.5 Turbo:

    We found in the previous problem that the result is 5. Now, we multiply 5 by 8/20 to get 5 * 8/20 = 40/20 = 2.
    ### Answer: 2.

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: If we adjust the original problem and now divide 30 by 4 and then multiply by the fraction 18/6, how does the result compares to our original calculation? What is the new value?

GPT-3.5 Turbo:

    First, we divide 30 by 4 to get 30/4 = 7.5.
    Then, we multiply 7.5 by 18/6 to get (7.5) * (18/6) = (7.5*18)/6 = 135/6 = 22.5.

    The new result is 22.5, which is greater than our original calculation of 5.
    ### Answer: 22.5.

Expected answer: 45/2

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem: ((20 / 2) * (2 / 18)) and write the answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the parentheses: (20/2) = 10 and (2/18) = 1/9.
    Then, we multiply 10 by 1/9 to get 10/9.
    ### Answer: 10/9.

Expected answer: 10/9

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of ((20 / 2) * (2 / 18)), now find the answer for ((27 / 4) * that result). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we found that ((20 / 2) * (2 / 18)) = 10/9.
    Now, we multiply 27/4 by 10/9 to get (27/4) * (10/9) = (27*10) / (4*9) = 270 / 36 = 15/2 = 7 1/2.
    ### Answer: 15/2.

Expected answer: 15/2

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of ((20 / 2) * (2 / 18)), reconsider your calculation, but this time using (15 / 18) instead of (2 / 18). Thus, find the answer for ((20 / 2) * (15 / 18)). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the parentheses: (20/2) = 10 and (15/18) = 5/6.
    Then, we multiply 10 by 5/6 to get 50/6, which simplifies to 25/3.
    ### Answer: 25/3.

Expected answer: 25/3

Correct? Yes

🔗 Problem

Problem: Solve the following problem and write your answer as a simplified fraction: ((11 / 9) * (29 / 6))

GPT-3.5 Turbo:

    To multiply fractions, we multiply the numerators together and the denominators together separately.

    (11/9) * (29/6) = (11 * 29) / (9 * 6) = 319 / 54

    ### Answer: 319/54

Expected answer: 319/54

Correct? Yes

🔗 Follow-up

Problem: After finding the result of ((11 / 9) * (29 / 6)), multiply your answer by the fraction (11 / 5). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    To multiply fractions, we multiply the numerators together and the denominators together separately.

    (319/54) * (11/5) = (319 * 11) / (54 * 5) = 3509 / 270

    To simplify the fraction 3509/270, we find the greatest common divisor (GCD) of 3509 and 270, which is 1. Therefore, the fraction is already in its simplest form.

    ### Answer: 3509/270

Expected answer: 3509/270

Correct? Yes

🔗 Follow-up

Problem: After finding the result of ((21 / 9) * (29 / 6)), consider what would have happened if the initial calculation involved (21 / 9) instead of (11 / 9). Calculate the new result and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Given the new calculation with (21/9) instead of (11/9):

    (21/9) * (29/6) = (21 * 29) / (9 * 6) = 609 / 54

    To simplify the fraction 609/54, we can divide both the numerator and denominator by their greatest common divisor, which is 9:

    609 ÷ 9 = 67
    54 ÷ 9 = 6

    Therefore, the simplified fraction is 67/6.

    ### Answer: 67/6

Expected answer: 203/18

Correct? No

🔗 Problem

Problem: Calculate the result for the following mathematical operation: (30 / 7) * (16 / 19). Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (30/7) * (16/19) = (30*16) / (7*19) = 480 / 133.
    ### Answer: 480/133.

Expected answer: 480/133

Correct? Yes

🔗 Follow-up

Problem: Let's proceed with the result found in the previous fraction multiplication task. Now, take that result and multiply it by 22/7. What is the new result? Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (480/133) * (22/7) = (480*22) / (133*7) = 10560 / 931.
    ### Answer: 10560/931.

Expected answer: 10560/931

Correct? Yes

🔗 Follow-up

Problem: Recall the earlier problem where we performed a fraction multiplication. If we consider a slight change and now multiply 21/7 (instead of 30/7) with 16/19, what would be the result? Remember to express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (21/7) * (16/19) = (3*16) / (1*19) = 48 / 19.
    ### Answer: 48/19.

Expected answer: 48/19

Correct? Yes

🔗 Problem

Problem: Calculate the product of 25/22 and 20/3 and write your 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.

    (25/22) * (20/3) = (25 * 20) / (22 * 3) = 500 / 66

    To simplify the fraction, we find the greatest common divisor of 500 and 66, which is 2.

    500 / 66 = (500 ÷ 2) / (66 ÷ 2) = 250 / 33

    ### Answer: 250/33.

Expected answer: 250/33

Correct? Yes

🔗 Follow-up

Problem: Following the previous calculation, take the product result of 25/22 and 20/3. Now multiply that result with 28/29 and write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Let's first multiply the fractions (25/22) and (20/3) that we found earlier:

    (25/22) * (20/3) = 500/66 = 250/33

    Now, let's multiply this result by 28/29:

    (250/33) * (28/29) = (250 * 28) / (33 * 29) = 7000 / 957

    This fraction is already simplified, so:

    ### Answer: 7000/957.

Expected answer: 7000/957

Correct? Yes

🔗 Follow-up

Problem: After reconsidering the calculation from the previous step, if we actually had 25/15 instead of 25/22. Recalculate the product with these new quantities. What is the product of 25/15 and 20/3? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (25/15) * (20/3) = (25 * 20) / (15 * 3) = 500 / 45

    To simplify the fraction, we find the greatest common divisor of 500 and 45, which is 5.

    500 / 45 = (500 ÷ 5) / (45 ÷ 5) = 100 / 9

    ### Answer: 100/9.

Expected answer: 100/9

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following problem and write your answer as a simplified fraction: ((29 / 2) / (23 / 19))

GPT-3.5 Turbo:

    Reasoning: To simplify the given expression, we first divide 29 by 2 to get 29/2. Then, we divide 23 by 19 to get 23/19. Finally, we divide 29/2 by 23/19, which is equivalent to multiplying by the reciprocal of the divisor. So, (29/2) / (23/19) = (29/2) * (19/23) = (29*19) / (2*23) = 551/46.

    ### Answer: 551/46.

Expected answer: 551/46

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of ((29 / 2) / (23 / 19)), multiply your answer by (29 / 18). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we multiply the result of ((29 / 2) / (23 / 19)), which is 551/46, by (29 / 18).

    (551/46) * (29/18) = (551*29) / (46*18) = 15979 / 828.

    ### Answer: 15979/828.

Expected answer: 15979/828

Correct? Yes

🔗 Problem

Problem: Calculate the solution for the following expression: (5 / 3) * (27 / 13) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Solution:
    (5/3) * (27/13) = (5*27) / (3*13) = 135 / 39 = 45 / 13.

    ### Answer: 45/13.

Expected answer: 45/13

Correct? Yes

🔗 Follow-up

Problem: After calculating the solution for the previous question ((5 / 3) * (27 / 13)), multiply the result you obtained by (8 / 14) and simplify the fraction that you get. What is your answer?

GPT-3.5 Turbo:

    First, we need to multiply (45/13) by (8/14):

    (45/13) * (8/14) = (45*8) / (13*14) = 360 / 182.

    To simplify the fraction 360/182, we find that both numbers are divisible by 2:

    360 ÷ 2 = 180
    182 ÷ 2 = 91

    Therefore, the simplified fraction is 180/91.

    ### Answer: 180/91.

Expected answer: 180/91

Correct? Yes

🔗 Follow-up

Problem: After considering the previous problem, there is a slight change. Instead of multiplying (5/3) by (27/13), let's make it a little easy and multiply (5/3) by (27/9). Calculate the new solution and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Solution:
    (5/3) * (27/9) = (5*27) / (3*9) = 135 / 27 = 5.

    ### Answer: 5.

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: Calculate the answer to the following problem: (29 / 29) * (1 / 1) and write your answer.

GPT-3.5 Turbo:

    Reasoning: (29 / 29) * (1 / 1) simplifies to 1 * 1 = 1.
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Now, use your answer from the last problem and multiply it by (27 / 27) to solve this follow-up problem. What is the result?

GPT-3.5 Turbo:

    Since the previous answer was 1, multiplying it by (27 / 27) gives 1 * 1 = 1.
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Now, let's change the problem a little bit. Instead of (29 / 29) * (1 / 1), let's use (29 / 6) * (1 / 1). What will the result be?

GPT-3.5 Turbo:

    Reasoning: (29 / 6) * (1 / 1) simplifies to 4.8333 * 1 = 4.8333 (rounded to four decimal places).
    ### Answer: 4.8333

Expected answer: 29/6

Correct? No

🔗 Problem

Problem: Calculate the product of the fractions 11/19 and 22/7. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (11/19) * (22/7) = (11 * 22) / (19 * 7) = 242 / 133

    ### Answer: 242/133.

Expected answer: 242/133

Correct? Yes

🔗 Follow-up

Problem: After you find the product of the fractions 11/19 and 22/7, multiply your answer by 25/4. What is the result as a simplified fraction?

GPT-3.5 Turbo:

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

    (242/133) * (25/4) = (242 * 25) / (133 * 4) = 6050 / 532

    ### Answer: 6050/532.

Expected answer: 3025/266

Correct? Yes

🔗 Follow-up

Problem: After you find the product of the fractions 11/19 and 25/7, suppose that we initially used 25/7 instead of 22/7. How does the result change? Write the new result as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: If we use 25/7 instead of 22/7, the calculation becomes:

    (11/19) * (25/7) = (11 * 25) / (19 * 7) = 275 / 133

    ### Answer: 275/133.

Expected answer: 275/133

Correct? Yes

🔗 Problem

Problem: What is the result of multiplying 21/30 by 19/5? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (21/30) * (19/5) = (21 * 19) / (30 * 5) = 399 / 150 = 133 / 50.

    ### Answer: 133/50.

Expected answer: 133/50

Correct? Yes

🔗 Follow-up

Problem: If you further multiply the result you got from the last problem ((21/30) * (19/5)) by 16/12, what would be the final result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (133/50) * (16/12) = (133 * 16) / (50 * 12) = 2128 / 600 = 532 / 150 = 133 / 37.

    ### Answer: 133/37.

Expected answer: 266/75

Correct? No

🔗 Follow-up

Problem: If in the previous problem, instead of multiplying 21/30 by 19/5, you had to multiply 9/30 by 19/5, what would be the new result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:

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

    (9/30) * (19/5) = (9 * 19) / (30 * 5) = 171 / 150 = 57 / 50.

    ### Answer: 57/50.

Expected answer: 57/50

Correct? Yes

🔗 Problem

Problem: What is the result when you multiply the fraction 11/15 by the fraction 23/8? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (11/15) * (23/8) = (11*23)/(15*8) = 253/120.

    ### Answer: 253/120.

Expected answer: 253/120

Correct? Yes

🔗 Follow-up

Problem: Based on your previous calculation, what is the result when you multiply the answer you found for 11/15 * 23/8 by itself? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We found that (11/15) * (23/8) = 253/120. To find the result when we multiply this by itself, we square the fraction.

    (253/120) * (253/120) = (253*253)/(120*120) = 64009/14400.

    ### Answer: 64009/14400.

Expected answer: 64009/14400

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you multiplied the fractions 11/15 and 23/8. But what if instead, you multiply the fractions 11/15 and 26/8? What would be the result of this change? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (11/15) * (26/8) = (11*26)/(15*8) = 286/120.

    To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.

    286/120 = 143/60.

    ### Answer: 143/60.

Expected answer: 143/60

Correct? Yes

🔗 Problem

Problem: What is the result of (29 / 16) * (21 / 27)? Present your answer as a simplified fraction.

GPT-3.5 Turbo:

    We can simplify the given expression as follows:
    (29/16) * (21/27) = (29 * 21) / (16 * 27) = 609 / 432 = 203 / 144.

    ### Answer: 203/144.

Expected answer: 203/144

Correct? Yes

🔗 Follow-up

Problem: What is the result when the value from the previous problem ((29 / 16) * (21 / 27)) is multiplied by itself? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    To find the result when the value from the previous problem is multiplied by itself, we square the fraction (203/144):
    (203/144) * (203/144) = (203 * 203) / (144 * 144) = 41209 / 20736.

    ### Answer: 41209/20736.

Expected answer: 41209/20736

Correct? Yes

🔗 Follow-up

Problem: In the question before, we considered the multiplication of fractions (29 / 16) and (21 / 27). Now replace the fraction 16 in the denominator with 5. What is the result of this new operation? Present your answer as a simplified fraction. In other words, what is the output of ((29 / 5) * (21 / 27))?

GPT-3.5 Turbo:

    We can simplify the given expression as follows:
    ((29/5) * (21/27)) = (29 * 21) / (5 * 27) = 609 / 135 = 203 / 45.

    ### Answer: 203/45.

Expected answer: 203/45

Correct? Yes

🔗 Problem

Problem: What is the result when (28 / 1) is divided by (30 / 27)? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (28 / 1) divided by (30 / 27) is the same as (28 / 1) multiplied by (27 / 30).
    Calculating, we get (28 * 27) / (1 * 30) = 756 / 30 = 25/1 = 25.
    ### Answer: 25.

Expected answer: 126/5

Correct? No

🔗 Problem

Problem: What is the result when you multiply ((25 / 25) * (20 / 7))? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{25}{25}\right) \times \left(\frac{20}{7}\right) = \frac{25 \times 20}{25 \times 7} = \frac{500}{175} = \frac{100}{35} = \frac{20}{7}
    \]

    ### Answer: \(\frac{20}{7}\)

Expected answer: 20/7

Correct? Yes

🔗 Follow-up

Problem: After finding the result of ((25 / 25) * (20 / 7)), what is the result when you multiply this product by itself? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{20}{7}\right) \times \left(\frac{20}{7}\right) = \frac{20 \times 20}{7 \times 7} = \frac{400}{49}
    \]

    ### Answer: \(\frac{400}{49}\)

Expected answer: 400/49

Correct? Yes

🔗 Follow-up

Problem: After reevaluating the previous problem, if you found the result of ((25 / 25) * (11 / 7)) instead of ((25 / 25) * (20 / 7)), what would be the new result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{25}{25}\right) \times \left(\frac{11}{7}\right) = \frac{25 \times 11}{25 \times 7} = \frac{275}{175} = \frac{55}{35} = \frac{11}{7}
    \]

    ### Answer: \(\frac{11}{7}\)

Expected answer: 11/7

Correct? Yes

🔗 Problem

Problem: Calculate the following: multiply 5 (which is equivalent to the fraction 5/1) with the fraction 16/27. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To multiply a whole number by a fraction, we multiply the whole number by the numerator of the fraction and keep the denominator the same.

    5 * 16/27 = (5 * 16) / 27 = 80 / 27.

    ### Answer: 80/27.

Expected answer: 80/27

Correct? Yes

🔗 Follow-up

Problem: Suppose you initially started with 30 (instead of 5), which is equivalent to the fraction 30/1. You are then required to multiply this with the fraction 16/27. How does this change the result from the previous problem? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: When we multiply 30 by 16/27, we get:

    30 * 16/27 = (30 * 16) / 27 = 480 / 27.

    This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

    480 ÷ 3 = 160,
    27 ÷ 3 = 9.

    Therefore, the simplified fraction is 160/9.

    ### Answer: 160/9.

Expected answer: 160/9

Correct? Yes

🔗 Problem

Problem: Calculate the result of the expression ((27 / 3) / (12 / 12)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating the expression step by step:
    (27 / 3) = 9
    (12 / 12) = 1
    9 / 1 = 9

    Therefore, the result of the expression is 9 as a simplified fraction, which is 9/1.
    ### Answer: 9/1

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: You previously calculated the result of ((27 / 3) / (12 / 12)) and labeled that answer as 's'. Now, compute the result of multiplying your answer 's' by the fraction (21/17) and report the result as a simplified fraction. This new result will be labeled as 'b'.

GPT-3.5 Turbo:

    Given:
    s = 9
    Multiplying s by (21/17):
    s * (21/17) = 9 * (21/17) = 189/17

    Therefore, the result of multiplying s by (21/17) is 189/17.
    ### Answer: 189/17

Expected answer: 189/17

Correct? Yes

🔗 Follow-up

Problem: Earlier, you calculated the result of ((27 / 3) / (12 / 12)) and labeled that answer as 's'. Consider the same scenario, but this time, instead of having 27 items, you only have 24. Calculate the result of (24 / (12 / 12)) and report the answer as a simplified fraction. What effect does this change have on the answer 's'?

GPT-3.5 Turbo:

    Calculating the new expression step by step:
    (12 / 12) = 1
    24 / 1 = 24

    Therefore, the result of the new expression is 24 as a simplified fraction, which is 24/1.

    The change from 27 to 24 items in the expression ((27 / 3) / (12 / 12)) affects the final result as follows:
    s = 9
    new result = 24

    ### Answer: 24/1

Expected answer: 24

Correct? No

🔗 Problem

Problem: Calculate the result of the following operation: (15 / 16) * (29 / 2). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/16) * (29/2) = (15 * 29) / (16 * 2) = 435 / 32.

    ### Answer: 435/32.

Expected answer: 435/32

Correct? Yes

🔗 Follow-up

Problem: If the result from the previous problem is multiplied by (18/18), what is the new result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To multiply a fraction by (18/18) is the same as multiplying by 1, which does not change the value of the fraction.

    (435/32) * (18/18) = 435/32.

    ### Answer: 435/32.

Expected answer: 435/32

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, instead of multiplying (15/16) by (29/2), what would be the result if we multiply it by (13/2) instead? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/16) * (13/2) = (15 * 13) / (16 * 2) = 195 / 32.

    ### Answer: 195/32.

Expected answer: 195/32

Correct? Yes

🔗 Problem

Problem: Calculate the solution to this mathematical equation: ((6 / 2) / (13 / 9)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: First, we simplify the division inside the parentheses: 6 / 2 = 3 and 13 / 9 = 13/9. Then, we divide 3 by 13/9, which is the same as multiplying 3 by the reciprocal of 13/9, which is 9/13. So, 3 * 9/13 = 27/13.

    ### Answer: 27/13.

Expected answer: 27/13

Correct? Yes

🔗 Follow-up

Problem: Following your previous calculation, how would the result change if the first fraction was actually ((6 / 2) / 3) instead of ((6 / 2) / (13 / 9))? Calculate and write your answer as a simplfied fraction.

GPT-3.5 Turbo:

    Reasoning: If the first fraction is ((6 / 2) / 3), we simplify the division inside the parentheses first: 6 / 2 = 3. Then, we divide 3 by 3, which equals 1.

    ### Answer: 1.

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Calculate the answer to the following problem: divide seven wholes, which is the same as 7/1, by 15/9. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To divide by a fraction, we multiply by its reciprocal. So, 7/1 ÷ 15/9 is the same as 7/1 * 9/15 = 63/15 = 21/5.

    ### Answer: 21/5.

Expected answer: 21/5

Correct? Yes

🔗 Follow-up

Problem: Following up on the last question, once you have found the result of dividing seven wholes by 15/9, multiply your answer by the fraction 10/5. What do you get as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning: We already found that 7/1 ÷ 15/9 = 21/5. Now, multiplying by 10/5 gives us (21/5) * (10/5) = 210/25 = 42/5.

    ### Answer: 42/5.

Expected answer: 42/5

Correct? Yes

🔗 Follow-up

Problem: Previously, you evaluated the result of dividing seven wholes, or 7/1, by 15/9. Now, consider what would happen if instead of seven whole, there were twenty wholes, or 20/1. What would be the result if you divide twenty wholes by 15/9? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: Dividing 20/1 by 15/9 is the same as multiplying 20/1 by the reciprocal of 15/9, which is 9/15. This gives us 20/1 * 9/15 = 180/15 = 12.

    ### Answer: 12.

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: What is the result when you multiply (23/10) by (9/1)?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we simply multiply the numerators together and the denominators together. So, (23/10) * (9/1) = (23*9) / (10*1) = 207/10.

    ### Answer: 207/10.

Expected answer: 207/10

Correct? Yes

🔗 Follow-up

Problem: You have already calculated the result of (23/10) multiplied by (9/1). Now, multiply this result by (1/16). What is your answer?

GPT-3.5 Turbo:

    Reasoning: We already found that (23/10) * (9/1) = 207/10. Now, to multiply by (1/16), we multiply the numerators together and the denominators together: (207/10) * (1/16) = (207*1) / (10*16) = 207/160.

    ### Answer: 207/160.

Expected answer: 207/160

Correct? Yes

🔗 Follow-up

Problem: Previously, you computed the result of (23/10) multiplied by (9/1). Now, consider what would have happened if instead of (9/1), you had (9/6). Multiply (23/10) by this new fraction. What is your answer?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (23/10) * (9/6) = (23*9) / (10*6) = 207/60. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, 207/60 simplifies to 69/20.

    ### Answer: 69/20.

Expected answer: 69/20

Correct? Yes

🔗 Problem

Problem: What is ((18 / 4) * (10 / 11))? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    We can simplify the expression as follows:

    (18 / 4) * (10 / 11) = (9 / 2) * (10 / 11) = (9 * 10) / (2 * 11) = 90 / 22 = 45 / 11.

    ### Answer: 45/11.

Expected answer: 45/11

Correct? Yes

🔗 Follow-up

Problem: After calculating the value of ((18 / 4) * (10 / 11)), now multiply this result by the fraction (6 / 4). What is the final value? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we need to multiply the result of ((18 / 4) * (10 / 11)) by (6 / 4):

    ((45 / 11) * (6 / 4)) = (45 * 6) / (11 * 4) = 270 / 44 = 135 / 22.

    ### Answer: 135/22.

Expected answer: 135/22

Correct? Yes

🔗 Follow-up

Problem: After calculating the value of ((18 / 1) * (10 / 11)), consider what would happen if instead of dividing 18 by 4 in the initial step, you were to divide it by 1. Calculate the new result. What is the final answer? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, let's calculate ((18 / 1) * (10 / 11)):

    (18 / 1) * (10 / 11) = 18 * 10 / 1 * 11 = 180 / 11.

    ### Answer: 180/11.

Expected answer: 180/11

Correct? Yes

🔗 Problem

Problem: What is the numerical result when the fraction 24/23 is multiplied by the fraction 23/3?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (24/23) * (23/3) = (24*23)/(23*3) = 552/69 = 8.
    ### Answer: 8.

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, if the result is then multiplied by the fraction 30/21, what is the final numerical outcome?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (8) * (30/21) = (8*30)/(1*21) = 240/21 = 40/3 = 13.333333333333333.
    ### Answer: 13.333333333333333.

Expected answer: 80/7

Correct? No

🔗 Follow-up

Problem: Continuing from the previous problem, if we replace the original fraction of 23/3 with 18/3 and keep the 24/23 fraction the same, what now happens to the numerical result when we perform the multiplication?

GPT-3.5 Turbo:

    Reasoning: If we replace 23/3 with 18/3, the new multiplication becomes (24/23) * (18/3) = (24*18)/(23*3) = 432/69 = 6.
    ### Answer: 6.

Expected answer: 144/23

Correct? No

🔗 Problem

Problem: Determine the solution for the following division of fractions: (20 / 13) / (17 / 16) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    To divide fractions, we multiply by the reciprocal of the second fraction.

    (20 / 13) / (17 / 16) = (20 / 13) * (16 / 17) = (20 * 16) / (13 * 17) = 320 / 221.

    ### Answer: 320/221.

Expected answer: 320/221

Correct? Yes

🔗 Follow-up

Problem: After finding the solution for the division of fractions (20 / 13) / (17 / 16), now multiply that result by the fraction (20 / 26). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we multiply the result of the division of fractions by the fraction (20 / 26):

    (320 / 221) * (20 / 26) = (320 * 20) / (221 * 26) = 6400 / 5766.

    To simplify this fraction, we find the greatest common divisor of 6400 and 5766, which is 34.

    6400 / 34 = 188 and 5766 / 34 = 169.

    Therefore, the simplified fraction is 188 / 169.

    ### Answer: 188/169.

Expected answer: 3200/2873

Correct? No

🔗 Problem

Problem: Calculate the result of the following problem: ((5 divided by 5) multiplied by (4 divided by 1))

GPT-3.5 Turbo:

    Reasoning: First, we solve the division inside the parentheses: 5 divided by 5 equals 1, and 4 divided by 1 equals 4. Then, we multiply the results: 1 multiplied by 4 equals 4.
    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Given that the result from the previous problem is c, calculate the result of the following formula: ((21 divided by 9) multiplied by c). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Given that c = 4, we can substitute c into the formula: ((21/9) * 4) = (7/3) * 4 = 28/3.

    ### Answer: 28/3.

Expected answer: 28/3

Correct? Yes

🔗 Follow-up

Problem: Assuming that in the previous problem, the initial amount of oranges was 5 but was changed to 5/15, how would this affect the outcome if it is multiplied by the same fraction (4/1)? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: If the initial amount of oranges was changed to 5/15, then the new amount is (5/15) * (4/1) = (5*4) / (15*1) = 20/15 = 4/3.
    ### Answer: 4/3

Expected answer: 4/3

Correct? Yes

🔗 Problem

Problem: Calculate the result for the following problem: ((30 / 23) * (19 / 24)). Write the answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To simplify the expression ((30 / 23) * (19 / 24)), we multiply the numerators together and the denominators together. This gives us (30 * 19) / (23 * 24) = 570 / 552. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6. This simplifies the fraction to 95 / 92.
    ### Answer: 95/92.

Expected answer: 95/92

Correct? Yes

🔗 Follow-up

Problem: After calculating the previous problem of ((30 / 23) * (19 / 24)) and getting the result, now proceed to multiply this result with (28 / 4). What is your new answer when written as a simplified fraction?

GPT-3.5 Turbo:

    First, we need to multiply the result of the previous problem, 95/92, with 28/4.

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

    (95/92) * (28/4) = (95 * 28) / (92 * 4) = 2660 / 368 = 665 / 92.

    Therefore, the new answer when written as a simplified fraction is 665/92.

    ### Answer: 665/92.

Expected answer: 665/92

Correct? Yes

🔗 Follow-up

Problem: After calculating the previous problem and getting a result, let's change the condition. Instead of (30 / 23) which you used last time, now use (30 / 11). Repeat the multiplication with (19 / 24). What is the new result when you write it as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning: When we calculate ((30 / 11) * (19 / 24)), we multiply the numerators together and the denominators together. This gives us (30 * 19) / (11 * 24) = 570 / 264. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6. This simplifies the fraction to 95 / 44.
    ### Answer: 95/44.

Expected answer: 95/44

Correct? Yes

🔗 Problem

Problem: Evaluate the expression (23 / 26) * (16 / 1) and express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (23/26) * (16/1) = (23*16) / (26*1) = 368 / 26 = 184 / 13.
    ### Answer: 184/13.

Expected answer: 184/13

Correct? Yes

🔗 Follow-up

Problem: Given that you previously calculated (23 / 26) * (16 / 1) as 'g', now find the value of (4 / 7) * g. Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: g = 184/13. Now, (4/7) * g = (4/7) * (184/13) = (4*184) / (7*13) = 736 / 91.
    ### Answer: 736/91.

Expected answer: 736/91

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated (23 / 26) * (16 / 1) as 'g'. Now assume that instead of 23/26, you had 2/26. How would that change the value of 'g'? Compute g as (2 / 26) * (16 / 1) and express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (2/26) * (16/1) = (2*16) / (26*1) = 32 / 26 = 16 / 13.
    ### Answer: 16/13.

Expected answer: 16/13

Correct? Yes

🔗 Problem

Problem: Compute the following fractional expression: ((21 / 1) / (26 / 20)), express your answer as a simplified fraction.

GPT-3.5 Turbo:

    To simplify the expression ((21 / 1) / (26 / 20)), we can first rewrite it as (21 / 1) * (20 / 26) since division by a fraction is the same as multiplication by its reciprocal.

    Now, we can multiply the fractions: (21 * 20) / (1 * 26) = 420 / 26.

    The fraction 420/26 simplifies to 210/13.

    ### Answer: 210/13.

Expected answer: 210/13

Correct? Yes

🔗 Follow-up

Problem: In continuation to the previous problem, let's assume that the value obtained from the expression ((21 / 1) / (26 / 20)) is multiplied by the fraction (21 / 29). What fraction will the result be?

GPT-3.5 Turbo:

    First, we need to find the value of the expression ((21 / 1) / (26 / 20)), which we found to be 210/13 in the previous step.

    Now, we need to multiply this value by the fraction (21 / 29):

    (210/13) * (21/29) = (210 * 21) / (13 * 29) = 4410 / 377.

    Therefore, the result of multiplying the expression ((21 / 1) / (26 / 20)) by the fraction (21 / 29) is 4410/377.

    ### Answer: 4410/377.

Expected answer: 4410/377

Correct? Yes

🔗 Follow-up

Problem: Let's revisit the previous problem. Let's assume now that the value obtained from the expression ((21 / 1) / 2). What will the result be now?

GPT-3.5 Turbo:

    To simplify the expression ((21 / 1) / 2), we can first simplify the division inside the parentheses: 21 / 1 = 21.

    Now, we have 21 / 2 = 10.5.

    ### Answer: 10.5.

Expected answer: 21/2

Correct? No

🔗 Problem

Problem: Calculate the following: multiply 24 over 19 by 21 over 19 without simplifying. Write your answer as a fraction.

GPT-3.5 Turbo:

    We have (24/19) * (21/19) = (24*21) / (19*19) = 504 / 361.

    ### Answer: 504/361.

Expected answer: 504/361

Correct? Yes

🔗 Follow-up

Problem: Considering the previous problem, let's make a small change to it. Instead of multiplying 24 over 19, let's multiply 20 over 19 by 21 over 19 but without simplifying. Write your answer as a fraction.

GPT-3.5 Turbo:

    We have (20/19) * (21/19) = (20*21) / (19*19) = 420 / 361.

    ### Answer: 420/361.

Expected answer: 420/361

Correct? Yes

🔗 Problem

Problem: Jim is baking a cake that calls for 12/2 cups of sugar and 17/14 cups of flour. If Jim needs to multiply the amount of sugar and flour he needs for a larger cake, how much sugar and flour does he need in total? Calculate ((12 / 2) * (17 / 14)) and express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating ((12 / 2) * (17 / 14)):
    (12 / 2) * (17 / 14) = 6 * 17 / 14 = 102 / 14 = 51 / 7

    ### Answer: 51/7.

Expected answer: 51/7

Correct? Yes

🔗 Follow-up

Problem: Jim realized he made a mistake while measuring components for his cake recipe. He actually needed to use 30/14 cups of flour instead of the 17/14 cups he previously used. Given that the amount of sugar remains the same at 12/2 cups, how much sugar and flour does he actually need? Calculate ((12 / 2) * (30 / 14)) and express your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating ((12 / 2) * (30 / 14)):
    (12 / 2) * (30 / 14) = 6 * 30 / 14 = 180 / 14 = 90 / 7

    ### Answer: 90/7.

Expected answer: 90/7

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: ((21 / 16) / (27 / 23)) and represent the answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To simplify the expression ((21 / 16) / (27 / 23)), we can rewrite it as (21 / 16) * (23 / 27) and then simplify the multiplication of fractions.

    (21 / 16) * (23 / 27) = (21 * 23) / (16 * 27) = 483 / 432

    The fraction 483/432 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.

    483 ÷ 3 = 161
    432 ÷ 3 = 144

    Therefore, the simplified fraction is 161/144.

    ### Answer: 161/144.

Expected answer: 161/144

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, if the result obtained from the operation ((21 / 16) / (27 / 23)) was squared, what would be the value of this new operation? Write the result as a simplified fraction.

GPT-3.5 Turbo:

    Let's first find the result of the operation ((21 / 16) / (27 / 23)), which we found to be 161/144.

    Now, to square this result, we simply square both the numerator and the denominator:

    (161/144)^2 = (161^2) / (144^2) = 25921 / 20736

    Therefore, the value of the new operation, after squaring the result of ((21 / 16) / (27 / 23)), is 25921/20736.

    ### Answer: 25921/20736.

Expected answer: 25921/20736

Correct? Yes

🔗 Follow-up

Problem: Given the previous problem where we multiplied and squared the result of ((21 / 16) / (27 / 23)), let's consider a new scenario. What would be the result if, instead of 21 / 16, we had 6? So, the new calculation would be (6 / (27 / 23)). Write the result as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: If we substitute 6 for 21/16 in the expression (6 / (27 / 23)), we get:

    6 / (27 / 23) = 6 * (23 / 27) = 6 * 23 / 27 = 138 / 27

    The fraction 138/27 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.

    138 ÷ 3 = 46
    27 ÷ 3 = 9

    Therefore, the simplified fraction is 46/9.

    ### Answer: 46/9.

Expected answer: 46/9

Correct? Yes

🔗 Problem

Problem: Calculate the answer to the following problem and write the answer as a simplified fraction: (11 / 20) * (24 / 12)

GPT-3.5 Turbo:

    Reasoning: To simplify the expression, we first multiply the numerators together and the denominators together. This gives us (11 * 24) / (20 * 12) = 264 / 240. To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 24. This gives us 11 / 10.

    ### Answer: 11/10.

Expected answer: 11/10

Correct? Yes

🔗 Follow-up

Problem: Continue the previous problem with this next step: Multiply your answer by (21 / 16) and write the result as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To multiply the fraction 11/10 by 21/16, we multiply the numerators together and the denominators together. This gives us (11 * 21) / (10 * 16) = 231 / 160. To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 1.

    ### Answer: 231/160.

Expected answer: 231/160

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated (11 / 20) * (24 / 12). Now, consider what would happen if you were to calculate (11 / 6) * (24 / 12) instead. What would be the result, expressed as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning: When calculating (11 / 6) * (24 / 12), we first multiply the numerators together and the denominators together. This gives us (11 * 24) / (6 * 12) = 264 / 72. To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 24. This gives us 11 / 3.

    ### Answer: 11/3.

Expected answer: 11/3

Correct? Yes

🔗 Problem

Problem: Calculate the answer to the following problem: ((6 / 19) * (28 / 2)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{6}{19}\right) \times \left(\frac{28}{2}\right) = \frac{6 \times 28}{19 \times 2} = \frac{168}{38} = \frac{84}{19}
    \]

    ### Answer: \(\frac{84}{19}\)

Expected answer: 84/19

Correct? Yes

🔗 Follow-up

Problem: After calculating the answer to ((6 / 19) * (28 / 2)), take that result and multiply it by (27 / 17). What is the final answer as a simplified fraction?

GPT-3.5 Turbo:

    Let's first calculate \(\left(\frac{6}{19} \times \frac{28}{2}\right)\):

    \[
    \left(\frac{6}{19} \times \frac{28}{2}\right) = \frac{84}{19}
    \]

    Now, let's multiply this result by \(\frac{27}{17}\):

    \[
    \left(\frac{84}{19} \times \frac{27}{17}\right) = \frac{84 \times 27}{19 \times 17} = \frac{2268}{323} = \frac{756}{107}
    \]

    ### Answer: \(\frac{756}{107}\)

Expected answer: 2268/323

Correct? No

🔗 Follow-up

Problem: Previously, you calculated the answer to ((6 / 19) * (28 / 2)). Now, consider if you had originally calculated ((17 / 19) * (28 / 2)) instead of ((6 / 19) * (28 / 2)). What would be the result of this calculation as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{17}{19}\right) \times \left(\frac{28}{2}\right) = \frac{17 \times 28}{19 \times 2} = \frac{476}{38} = \frac{238}{19}
    \]

    ### Answer: \(\frac{238}{19}\)

Expected answer: 238/19

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: (12 / 14) * (28 / 5). Simplify the resulting fraction to its lowest terms.

GPT-3.5 Turbo:

    First, we calculate the result of the operation:
    (12 / 14) * (28 / 5) = (6 / 7) * (28 / 5) = (6 * 28) / (7 * 5) = 168 / 35.

    To simplify the fraction 168/35 to its lowest terms, we find the greatest common divisor (GCD) of 168 and 35, which is 7. Dividing both the numerator and denominator by 7, we get:

    168 / 35 = 24 / 5.

    ### Answer: 24/5.

Expected answer: 24/5

Correct? Yes

🔗 Follow-up

Problem: You were given a fraction after calculating the result of (12 / 14) * (28 / 5) in a previous problem. Now multiply your result by 15/10. What new fraction do you get? Simplify your answer to the lowest terms.

GPT-3.5 Turbo:

    To multiply the fraction 24/5 by 15/10, we multiply the numerators and denominators:

    (24/5) * (15/10) = (24 * 15) / (5 * 10) = 360 / 50.

    To simplify the fraction 360/50 to its lowest terms, we find the greatest common divisor (GCD) of 360 and 50, which is 10. Dividing both the numerator and denominator by 10, we get:

    360 / 50 = 36 / 5.

    ### Answer: 36/5.

Expected answer: 36/5

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the result of (12 / 14) * (28 / 5) and then multiplied your result by 15/10. Now consider the situation where instead of 12/14, you have 3/14. What is the result when you multiply 3/14 by 28/5? Simplify your answer to the lowest terms.

GPT-3.5 Turbo:

    To find the result of multiplying 3/14 by 28/5, we perform the following calculation:

    (3/14) * (28/5) = (3 * 28) / (14 * 5) = 84 / 70.

    To simplify the fraction 84/70 to its lowest terms, we find the greatest common divisor (GCD) of 84 and 70, which is 14. Dividing both the numerator and denominator by 14, we get:

    84 / 70 = 6 / 5.

    ### Answer: 6/5.

Expected answer: 6/5

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following expression: (19 / 3) * (8 / 15). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (19 / 3) * (8 / 15) = (19 * 8) / (3 * 15) = 152 / 45.

    ### Answer: 152/45.

Expected answer: 152/45

Correct? Yes

🔗 Follow-up

Problem: After you've calculated the result of (19 / 3) * (8 / 15), multiply your answer by (19 / 9). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression (19 / 3) * (8 / 15) which is 152/45. Then, we multiply this result by (19 / 9):

    (152/45) * (19/9) = (152 * 19) / (45 * 9) = 2888 / 405.

    ### Answer: 2888/405.

Expected answer: 2888/405

Correct? Yes

🔗 Follow-up

Problem: First, recalculate the previous problem using (19 / 7) instead of (19 / 3). So the new calculation is (19 / 7) * (8 / 15). What is the result? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (19 / 7) * (8 / 15) = (19 * 8) / (7 * 15) = 152 / 105.

    ### Answer: 152/105.

Expected answer: 152/105

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following expression: ((15 / 3) * (7 / 25)) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression:

    (15 / 3) * (7 / 25) = 5 * 7 / 3 * 25 = 35 / 75.

    Therefore, the result of the expression is 35/75, which can be simplified to 7/15.
    ### Answer: 7/15.

Expected answer: 7/5

Correct? No

🔗 Problem

Problem: Calculate the following equation: (20 / 10) * (10 / 1) and write your answer as a whole number.

GPT-3.5 Turbo:

    Calculating the given equation: (20 / 10) * (10 / 1) = 2 * 10 = 20.
    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, consider that you got an answer x from calculating (20 / 10) * (10 / 1). Now, evaluate z by multiplying your previous answer x with the fraction (19 / 15). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Given x = 20 from the previous calculation, we can evaluate z as follows:
    z = x * (19 / 15) = 20 * (19 / 15) = (20 * 19) / 15 = 380 / 15 = 76/3 = 25 1/3.
    ### Answer: 25 1/3.

Expected answer: 76/3

Correct? Yes

🔗 Problem

Problem: Calculate the result of the [(27 / 18) * (19 / 8)] and express your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the brackets:
    (27 / 18) * (19 / 8) = (3/2) * (19/8) = (3*19) / (2*8) = 57 / 16.

    Therefore, the result of [(27 / 18) * (19 / 8)] expressed as a simplified fraction is 57/16.
    ### Answer: 57/16.

Expected answer: 57/16

Correct? Yes

🔗 Follow-up

Problem: Now, multiplying the result from the previous calculation by the fraction (28 / 16), what do you get? Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    We have the fraction 57/16 from the previous calculation, and we need to multiply it by 28/16:

    (57/16) * (28/16) = (57*28) / (16*16) = 1596 / 256.

    Therefore, the result of multiplying (57/16) by (28/16) expressed as a simplified fraction is 1596/256.
    ### Answer: 1596/256.

Expected answer: 399/64

Correct? Yes

🔗 Follow-up

Problem: If we change the situation from the previous problem, and instead of the fraction (19 / 8), we now have (19 / 17), what will be the result of the calculation [(27 / 18) * (19 / 17)]? Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we simplify the expression inside the brackets:
    (27 / 18) * (19 / 17) = (3/2) * (19/17) = (3*19) / (2*17) = 57 / 34.

    Therefore, the result of [(27 / 18) * (19 / 17)] expressed as a simplified fraction is 57/34.
    ### Answer: 57/34.

Expected answer: 57/34

Correct? Yes

🔗 Problem

Problem: What is the result of the multiply operation when you multiply the fraction 29/5 by 13/24? Please write your response as a simplified fraction.

GPT-3.5 Turbo:

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

    (29/5) * (13/24) = (29 * 13) / (5 * 24) = 377 / 120.

    ### Answer: 377/120.

Expected answer: 377/120

Correct? Yes

🔗 Follow-up

Problem: After finding the result of multiplying 29/5 by 13/24, what is the result if you then multiply this answer by 25/11? Please write your answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we multiply 29/5 by 13/24:

    (29/5) * (13/24) = 377/120.

    Next, we multiply 377/120 by 25/11:

    (377/120) * (25/11) = (377 * 25) / (120 * 11) = 9425 / 1320 = 1895 / 264.

    ### Answer: 1895/264.

Expected answer: 1885/264

Correct? No

🔗 Follow-up

Problem: After recalculating the early problem, suppose we only had 29/8 instead of 29/5. In that case, what would be the result of multiplying the fraction 29/8 by 13/24? Please write your answer in its simplest form.

GPT-3.5 Turbo:

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

    (29/8) * (13/24) = (29 * 13) / (8 * 24) = 377 / 192.

    ### Answer: 377/192.

Expected answer: 377/192

Correct? Yes

🔗 Problem

Problem: Calculate the value of the expression ((29 / 17) / (27 / 22)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    ((29 / 17) / (27 / 22)) = (29 / 17) * (22 / 27) = (29 * 22) / (17 * 27) = 638 / 459 =  14 / 10 = 7 / 5.

    ### Answer: 7/5.

Expected answer: 638/459

Correct? No

🔗 Problem

Problem: What would be the result of the calculation (27 / 6) * (25 / 5)?

GPT-3.5 Turbo:

    Reasoning: First, we simplify the division inside the parentheses: 27/6 = 4.5 and 25/5 = 5. Then, we multiply these results: 4.5 * 5 = 22.5.
    ### Answer: 22.5

Expected answer: 45/2

Correct? Yes

🔗 Follow-up

Problem: If the result of (27 / 6) * (25 / 5) was multiplied by (20 / 27), what would be the outcome?

GPT-3.5 Turbo:

    Reasoning: We already know that (27 / 6) * (25 / 5) equals 22.5. Now, we multiply this result by (20 / 27): 22.5 * (20 / 27) = 16.6666666667 (rounded to 10 decimal places).
    ### Answer: 16.6666666667

Expected answer: 50/3

Correct? No

🔗 Follow-up

Problem: If instead of the initial calculation with (27 / 6), we used (11 / 6) and repeated the multiplication with (25 / 5), what would the new result be?

GPT-3.5 Turbo:

    Reasoning: First, we simplify the division inside the parentheses: 11/6. Then, we multiply this result by 25/5.

    11/6 = 1.83 (rounded to two decimal places)
    1.83 * 5 = 9.15

    ### Answer: 9.15

Expected answer: 55/6

Correct? No

🔗 Problem

Problem: Calculate and write your answer as a simplified fraction for the following expression: (13 / 1) * (1 / 6).

GPT-3.5 Turbo:

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

    (13/1) * (1/6) = (13*1) / (1*6) = 13 / 6.

    ### Answer: 13/6.

Expected answer: 13/6

Correct? Yes

🔗 Follow-up

Problem: Calculate the value of the following, given that e = 13/6: (13 / 2) * e. Write your final answer as a simplified fraction. This is a follow-up question to a previous problem.

GPT-3.5 Turbo:

    Reasoning: We are given that e = 13/6.

    Now, we substitute e = 13/6 into the expression (13/2) * e:

    (13/2) * (13/6) = (13*13) / (2*6) = 169 / 12.

    ### Answer: 169/12.

Expected answer: 169/12

Correct? Yes

🔗 Follow-up

Problem: Calculate the value of the following, given the modification to the previous problem: (11 / 1) * (1 / 6). What happens to the result if instead of having 13 of an item as in the previous problem, you only had 11 of it now? Write your new final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: Following the same steps as before,

    (11/1) * (1/6) = (11*1) / (1*6) = 11 / 6.

    If we change the value from 13 to 11, the result changes accordingly.

    ### Answer: 11/6.

Expected answer: 11/6

Correct? Yes

🔗 Problem

Problem: What is the product when you multiply 25/20 and 11/6? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (25/20) * (11/6) = (25 * 11) / (20 * 6) = 275 / 120 = 55 / 24

    ### Answer: 55/24.

Expected answer: 55/24

Correct? Yes

🔗 Follow-up

Problem: After finding the product of 25/20 and 11/6, now multiply that result by the fraction 20/26. What do you get? Remember to write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (55/24) * (20/26) = (55 * 20) / (24 * 26) = 1100 / 624 = 25 / 14

    ### Answer: 25/14.

Expected answer: 275/156

Correct? No

🔗 Follow-up

Problem: After calculating the product of 25/20 and 11/6 and multiplying that result by 20/26, now consider what would happen if you initially multiplied 25/17 instead of 25/20 by 11/6. What new result do you get? Please write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Let's first calculate the product of (25/20) * (11/6) * (20/26):

    (25/20) * (11/6) * (20/26) = (25 * 11 * 20) / (20 * 6 * 26) = 5500 / 3120 = 275 / 156

    Now, let's calculate the product of (25/17) * (11/6):

    (25/17) * (11/6) = (25 * 11) / (17 * 6) = 275 / 102

    ### Answer: 275/102.

Expected answer: 275/102

Correct? Yes

🔗 Problem

Problem: Determine the value of (7 / 2) / (25 / 10). Please provide your answer as a simplified fraction.

GPT-3.5 Turbo:

    We simplify the expression as follows:
    (7 / 2) / (25 / 10) = (7 / 2) * (10 / 25) = (7 * 10) / (2 * 25) = 70 / 50 = 7 / 5.

    ### Answer: 7/5.

Expected answer: 7/5

Correct? Yes

🔗 Follow-up

Problem: After determining the value of ((7 / 2) / (25 / 10)), now calculate the result when this value is multiplied by (5 / 3). Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    We have the value of ((7 / 2) / (25 / 10)) as 7/5. Now, we multiply this value by 5/3:
    (7/5) * (5/3) = (7*5) / (5*3) = 35 / 15 = 7 / 3.

    ### Answer: 7/3.

Expected answer: 7/3

Correct? Yes

🔗 Problem

Problem: Calculate the multiplication of two fractions: Multiply 15/16 by 29/27. Give your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/16) * (29/27) = (15 * 29) / (16 * 27) = 435 / 432.

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

    435 / 432 = 145 / 144.

    ### Answer: 145/144.

Expected answer: 145/144

Correct? Yes

🔗 Follow-up

Problem: After calculating the multiplication of the fractions 15/16 by 29/27, multiply that answer by the fraction 27/4. What is the result as a simplified fraction?

GPT-3.5 Turbo:

    Let's first multiply the fractions 15/16 by 29/27:

    (15/16) * (29/27) = 435/432.

    Now, let's multiply this result by 27/4:

    (435/432) * (27/4) = (435 * 27) / (432 * 4) = 11745 / 1728.

    To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 9:

    11745 / 1728 = 1305 / 192.

    ### Answer: 1305/192.

Expected answer: 435/64

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the multiplication of the fractions 15/16 and 29/27. Now, let's imagine that you initially had a fraction with 15 as the numerator and 10 as the denominator instead of 15/16. How would the result differ if you multiply 15/10 by 29/27? Give your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: If we have the fraction 15/10, we can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 5.

    15/10 simplifies to 3/2.

    Now, we can multiply 3/2 by 29/27.

    (3/2) * (29/27) = (3 * 29) / (2 * 27) = 87 / 54.

    To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 9.

    87 / 54 = 29 / 18.

    ### Answer: 29/18.

Expected answer: 29/18

Correct? Yes

🔗 Problem

Problem: Evaluate the following expression to find the answer: ((30 / 25) * (25 / 10)). Simplify your answer.

GPT-3.5 Turbo:

    First, we simplify the expression inside the parentheses: 30 / 25 = 1.2 and 25 / 10 = 2.5.
    Then, we multiply these two results: 1.2 * 2.5 = 3.
    ### Answer: 3.

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: After calculating the answer to ((30 / 25) * (25 / 10)), multiply your answer by (5 / 9). What is the result? Be sure to simplify your final answer.

GPT-3.5 Turbo:

    First, we multiply the previous answer by 5/9: 3 * 5/9 = 15/9 = 5/3.
    ### Answer: 5/3.

Expected answer: 5/3

Correct? Yes

🔗 Problem

Problem: Calculate the product of the fractions 27/10 and 27/3. Write your answer in simplest form.

GPT-3.5 Turbo:

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

    (27/10) * (27/3) = (27 * 27) / (10 * 3) = 729 / 30 = 243 / 10.

    ### Answer: 243/10.

Expected answer: 243/10

Correct? Yes

🔗 Follow-up

Problem: First, calculate the product of the fractions 27/10 and 27/3. Then, multiply the result by 9/20. Write your answer in simplest form.

GPT-3.5 Turbo:

    First, we calculate the product of the fractions 27/10 and 27/3:

    (27/10) * (27/3) = (27 * 27) / (10 * 3) = 729 / 30 = 243 / 10.

    Next, we multiply the result by 9/20:

    (243/10) * (9/20) = (243 * 9) / (10 * 20) = 2187 / 200.

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

    2187 / 200 = 729 / 67.

    ### Answer: 729/67.

Expected answer: 2187/200

Correct? No

🔗 Follow-up

Problem: First, calculate the product of the fractions 27/10 and 27/21, instead of 27/3 as we had in the previous question. Write your answer in simplest form.

GPT-3.5 Turbo:

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

    (27/10) * (27/21) = (27 * 27) / (10 * 21) = 729 / 210.

    To simplify this fraction, we find the greatest common divisor (GCD) of 729 and 210, which is 3. Dividing both the numerator and denominator by 3, we get:

    729 / 210 = 243 / 70.

    ### Answer: 243/70.

Expected answer: 243/70

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: (10 / 8) * (30 / 26). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    We can simplify the expression as follows:
    (10/8) * (30/26) = (5/4) * (15/13) = (5*15) / (4*13) = 75 / 52.

    ### Answer: 75/52.

Expected answer: 75/52

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of the following operation: (10 / 8) * (30 / 26), find the square of your answer by multiplying it with itself. Write the final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we found that (10/8) * (30/26) = 75/52. Now, we need to find the square of 75/52:
    (75/52) * (75/52) = (75 * 75) / (52 * 52) = 5625 / 2704.

    ### Answer: 5625/2704.

Expected answer: 5625/2704

Correct? Yes

🔗 Problem

Problem: Evaluate the following expression: ((20 / 22) * (14 / 11)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    \[
    \left(\frac{20}{22}\right) \times \left(\frac{14}{11}\right) = \frac{20 \times 14}{22 \times 11} = \frac{280}{242} = \frac{140}{121}
    \]

    ### Answer: \(\frac{140}{121}\)

Expected answer: 140/121

Correct? Yes

🔗 Follow-up

Problem: After evaluating the expression ((20 / 22) * (14 / 11)), multiply your result by (17/3). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning:
    First, we evaluate \(\left(\frac{20}{22} \times \frac{14}{11}\right) = \frac{140}{121}\).
    Then, we multiply this result by \(\frac{17}{3}\):
    \[
    \frac{140}{121} \times \frac{17}{3} = \frac{140 \times 17}{121 \times 3} = \frac{2380}{363}
    \]

    ### Answer: \(\frac{2380}{363}\)

Expected answer: 2380/363

Correct? Yes

🔗 Follow-up

Problem: Previously, you evaluated ((20 / 22) * (14 / 11)) and multiplied the result by (17/3). Now consider changing the second fraction in the initial multiplication to (14 / 2). Now how does the expression ((20 / 22) * (14 / 2)) differ from the original? Evaluate the new expression and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    The original expression was \(\left(\frac{20}{22}\right) \times \left(\frac{14}{11}\right)\), which we found to be \(\frac{140}{121}\).

    Now, the new expression is \(\left(\frac{20}{22}\right) \times \left(\frac{14}{2}\right) = \frac{20 \times 14}{22 \times 2} = \frac{280}{44} = \frac{70}{11}\).

    The new expression \(\left(\frac{20}{22}\right) \times \left(\frac{14}{2}\right)\) differs from the original expression \(\left(\frac{20}{22}\right) \times \left(\frac{14}{11}\right)\) by the second fraction used in the multiplication.

    ### Answer: \(\frac{70}{11}\)

Expected answer: 70/11

Correct? Yes

🔗 Problem

Problem: Evaluate the following operation: ((25 / 8) * (3 / 4)) and write your answer as a simplified fraction. Does the result signify some form of division amongst a group or sharing something in portions?

GPT-3.5 Turbo:

    First, we simplify the multiplication of fractions: (25/8) * (3/4) = (25*3) / (8*4) = 75 / 32.

    The result 75/32 does not signify division amongst a group or sharing something in portions. It is simply a fraction resulting from the multiplication of two fractions.

    ### Answer: 75/32.

Expected answer: 75/32

Correct? Yes

🔗 Follow-up

Problem: After finding the result of ((25 / 8) * (3 / 4)), now take your answer and multiply it by the fraction (29 / 23). Write this new result as a simplified fraction. What would this additional operation represent in terms of the original division or portion sharing scenario?

GPT-3.5 Turbo:

    First, we multiply the result from the previous operation (75/32) by (29/23):

    (75/32) * (29/23) = (75*29) / (32*23) = 2175 / 736.

    This additional operation represents a further multiplication of the previous result by the fraction (29/23). In terms of the original division or portion sharing scenario, this could represent an additional sharing or division of the existing portions.

    ### Answer: 2175/736.

Expected answer: 2175/736

Correct? Yes

🔗 Follow-up

Problem: After solving the previous problem, now evaluate the new expression ((25 / 8) * (29 / 4)). This means we have changed the second fraction from (3 / 4) to (29 / 4). Under the previous scenario where the fractions referred to sharing or dividing amongst a group, consider what would happen if the proportions you multiplied with were changed to this new ratio. Write the result of ((25 / 8) * (29 / 4)) as a simplified fraction and reflect on the impact of this change in the real-world scenario.

GPT-3.5 Turbo:

    First, we simplify the multiplication of fractions: (25/8) * (29/4) = (25*29) / (8*4) = 725 / 32.

    The result 725/32 does not signify division amongst a group or sharing something in portions. It is simply a fraction resulting from the multiplication of two fractions.

    In a real-world scenario where fractions represent sharing or dividing amongst a group, changing the proportions being multiplied can significantly impact the outcome. In this case, changing the second fraction from 3/4 to 29/4 led to a different result, highlighting the importance of understanding the fractions being used in such scenarios.

    ### Answer: 725/32.

Expected answer: 725/32

Correct? Yes

🔗 Problem

Problem: Calculate the value of the following expression as a decimal: (29 / 1) * (8 / 15).

GPT-3.5 Turbo:

    Reasoning: (29 / 1) * (8 / 15) = 29 * 8 / 1 * 15 = 232 / 15 = 15.4666666667 (rounded to 10 decimal places).
    ### Answer: 15.4666666667

Expected answer: 232/15

Correct? No

🔗 Problem

Problem: What is the result when you multiply (29/17) by (26/15)?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (29/17) * (26/15) = (29*26) / (17*15) = 754 / 255.

    ### Answer: 754/255.

Expected answer: 754/255

Correct? Yes

🔗 Follow-up

Problem: Using the previous result ((29/17) * (26/15)), multiply this answer by (21/9). What is the result when you simplify the final fraction?

GPT-3.5 Turbo:

    Reasoning: We already have the result of (29/17) * (26/15) as 754/255. Now, we need to multiply this by 21/9.

    (754/255) * (21/9) = (754*21) / (255*9) = 15834 / 2295 = 686 / 99.

    To simplify the final fraction, we divide both the numerator and denominator by their greatest common divisor, which is 11.

    686 / 99 = 62 / 9.

    ### Answer: 62/9.

Expected answer: 5278/765

Correct? No

🔗 Follow-up

Problem: If the original fraction were (15/17) instead of (29/17), what would be the result when you multiply (15/17) by (26/15)?

GPT-3.5 Turbo:

    Reasoning: If the original fraction were (15/17) instead of (29/17), then (15/17) * (26/15) = (15*26) / (17*15) = 390 / 255.

    ### Answer: 390/255.

Expected answer: 26/17

Correct? Yes

🔗 Problem

Problem: Calculate the value of the expression ((25 / 5) * (16 / 8)) and provide your answer as a simplified fraction.

GPT-3.5 Turbo:

    Calculating the expression step by step:
    (25 / 5) * (16 / 8) = 5 * 2 = 10
    Therefore, the value of the expression is 10 as a simplified fraction.
    ### Answer: 10.

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we used the numbers 25 and 5, and 16 and 8 in our calculations. Now consider a slight change where we keep the '25 and '5', but instead of '16 and 8', we use '19 and 8'. Recalculate the value of k using this new information: ((25 / 5) * (19 / 8)). What is the value of k in this scenario?

GPT-3.5 Turbo:

    Calculating the expression with the new numbers:
    ((25 / 5) * (19 / 8)) = (5 * 19) / 8 = 95 / 8
    Therefore, the value of the expression is 95/8.
    ### Answer: 95/8.

Expected answer: 95/8

Correct? Yes

🔗 Problem

Problem: What is the result when you multiply (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (23/4) * (10/12) = (23*10) / (4*12) = 230 / 48 = 115 / 24.

    ### Answer: 115/24.

Expected answer: 115/24

Correct? Yes

🔗 Follow-up

Problem: What would be the result if you changed the previous problem by multiplying (28 / 4) by (10 / 12) instead of (23 / 4) by (10 / 12)? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (28/4) * (10/12) = (28*10) / (4*12) = 280 / 48 = 35 / 6.

    ### Answer: 35/6.

Expected answer: 35/6

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form.

GPT-3.5 Turbo:

    To multiply fractions, we multiply the numerators together and the denominators together separately.

    (21/26) * (20/9) = (21 * 20) / (26 * 9) = 420 / 234

    To simplify the fraction, we find the greatest common divisor of 420 and 234, which is 6.

    420 / 234 = (420 / 6) / (234 / 6) = 70 / 39

    ### Answer: 70/39.

Expected answer: 70/39

Correct? Yes

🔗 Follow-up

Problem: Calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 9). Write your answer in simplest form. Then, take that result and multiply it by the fraction (15 / 21). Write the final answer in simplest form.

GPT-3.5 Turbo:

    First, we multiply the fractions (21/26) * (20/9):

    (21/26) * (20/9) = (21 * 20) / (26 * 9) = 420 / 234 = 70 / 39

    Next, we multiply the result by the fraction (15/21):

    (70/39) * (15/21) = (70 * 15) / (39 * 21) = 1050 / 819

    To simplify the fraction, we find the greatest common divisor of 1050 and 819, which is 3.

    1050 / 819 = (1050 / 3) / (819 / 3) = 350 / 273

    ### Answer: 350/273.

Expected answer: 50/39

Correct? Yes

🔗 Follow-up

Problem: Recalculate the previous problem, but this time change the second fraction in the initial multiplication to (20 / 4) instead of (20 / 9). So, your new problem would be to calculate the result of the following multiplication of fractions: (21 / 26) * (20 / 4). Write your answer in simplest form.

GPT-3.5 Turbo:

    To multiply fractions, we multiply the numerators together and the denominators together separately.

    (21/26) * (20/4) = (21 * 20) / (26 * 4) = 420 / 104

    To simplify the fraction, we find the greatest common divisor of 420 and 104, which is 4.

    420 / 104 = (420 / 4) / (104 / 4) = 105 / 26

    ### Answer: 105/26.

Expected answer: 105/26

Correct? Yes

🔗 Problem

Problem: Calculate the following expression: ((17 / 13) * (15 / 6)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: ((17 / 13) * (15 / 6)) = (17 * 15) / (13 * 6) = 255 / 78 = 85 / 26.
    ### Answer: 85/26.

Expected answer: 85/26

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you calculated the product of ((17 / 13) * (15 / 6)) and found it as a simplified fraction. Now, use that answer and further multiply it by (8 / 15). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We already found ((17 / 13) * (15 / 6)) = 85 / 26. Now, we need to multiply this by (8 / 15):

    (85 / 26) * (8 / 15) = (85 * 8) / (26 * 15) = 680 / 390 = 34 / 19.

    ### Answer: 34/19.

Expected answer: 68/39

Correct? No

🔗 Problem

Problem: Calculate the result of the following equation: (25 / 18) * (17 / 6). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To simplify the given expression, we multiply the numerators together and the denominators together.

    (25/18) * (17/6) = (25 * 17) / (18 * 6) = 425 / 108.

    ### Answer: 425/108.

Expected answer: 425/108

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of the initial problem: (25 / 18) * (17 / 6), proceed to multiply your answer by the fraction (23 / 17). Write your final answer as a simplified fraction.

GPT-3.5 Turbo:

    First, we multiply the result of the initial problem by the fraction (23/17):

    (425/108) * (23/17) = (425 * 23) / (108 * 17) = 9775 / 1836.

    To simplify this fraction, we find the greatest common divisor (GCD) of 9775 and 1836, which is 61.

    9775 / 61 = 160, and 1836 / 61 = 30.

    Therefore, the simplified fraction is 160 / 30.

    ### Answer: 160/30.

Expected answer: 575/108

Correct? No

🔗 Follow-up

Problem: After initially calculating the result of the problem: (25 / 18) * (17 / 6), let's consider a change. Assume that instead of 17 portions in the second fraction, you only had 14 portions to begin with. Recalculate the product: (25 / 18) * (14 / 6). Write your updated answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We can calculate the new result by multiplying the numerators and denominators of the fractions.

    (25/18) * (14/6) = (25 * 14) / (18 * 6) = 350 / 108.

    To simplify the fraction 350/108, we can divide both the numerator and denominator by their greatest common divisor, which is 2.

    350 ÷ 2 = 175, and 108 ÷ 2 = 54.

    Therefore, the simplified fraction is 175/54.

    ### Answer: 175/54.

Expected answer: 175/54

Correct? Yes

🔗 Problem

Problem: Calculate the result of multiplying 9 (which is a fraction equivalent to 9/1) by 2/17. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    \(9 \times \frac{2}{17} = \frac{9 \times 2}{1 \times 17} = \frac{18}{17}\).

    ### Answer: \(\frac{18}{17}\)

Expected answer: 18/17

Correct? Yes

🔗 Follow-up

Problem: After solving the earlier problem, you found a result by multiplying the fraction 9/1 by 2/17. Let's denote this result as t. Now, find what happens when you multiply the result with itself (t * t). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We found that \(t = \frac{18}{17}\). To find \(t \times t\), we multiply the numerators and denominators separately.

    \(t \times t = \frac{18}{17} \times \frac{18}{17} = \frac{18 \times 18}{17 \times 17} = \frac{324}{289}\).

    ### Answer: \(\frac{324}{289}\)

Expected answer: 324/289

Correct? Yes

🔗 Follow-up

Problem: In the earlier problem, you multiplied the fraction 9/1 by 2/17. Now, we consider a similar scenario, but with a change: Instead of starting with 9 (or 9/1), you now start with 12 (or 12/1). Calculate the result of multiplying 12 by the fraction 2/17. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    \(12 \times \frac{2}{17} = \frac{12 \times 2}{1 \times 17} = \frac{24}{17}\).

    ### Answer: \(\frac{24}{17}\)

Expected answer: 24/17

Correct? Yes

🔗 Problem

Problem: Calculate the result of the multiplication: (27 / 14) * (19 / 14). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (27/14) * (19/14) = (27 * 19) / (14 * 14) = 513 / 196.

    ### Answer: 513/196.

Expected answer: 513/196

Correct? Yes

🔗 Follow-up

Problem: Having found the value of z from the previous problem ((27 / 14) * (19 / 14)), now multiply your answer by the fraction 17/23. Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We already found that z = 513/196. Now, we need to multiply z by 17/23.

    z * (17/23) = (513/196) * (17/23) = (513 * 17) / (196 * 23) = 8721 / 4508.

    ### Answer: 8721/4508.

Expected answer: 8721/4508

Correct? Yes

🔗 Follow-up

Problem: Previously, you calculated the result of the multiplication (27 / 14) * (19 / 14). Now, what if instead of 27, we had a value of 15? So calculate the new result for the multiplication problem (15 / 14) * (19 / 14). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: Using the same method as before, we multiply the numerators together and the denominators together. So, (15/14) * (19/14) = (15 * 19) / (14 * 14) = 285 / 196.

    ### Answer: 285/196.

Expected answer: 285/196

Correct? Yes

🔗 Problem

Problem: Calculate the result for the expression: (16 / 5) * (5 / 15) and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (16 / 5) * (5 / 15) = (16 * 5) / (5 * 15) = 80 / 75 = 16 / 15.

    ### Answer: 16/15.

Expected answer: 16/15

Correct? Yes

🔗 Follow-up

Problem: After finding the solution to the previous problem, which was (16 / 5) * (5 / 15), multiply your answer with the fraction (30 / 24) and again write your result as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (16 / 5) * (5 / 15) * (30 / 24) = (16 / 5) * (5 / 15) * (30 / 24) = (16 * 5 * 30) / (5 * 15 * 24) = 240 / 180 = 4 / 3.

    ### Answer: 4/3.

Expected answer: 4/3

Correct? Yes

🔗 Follow-up

Problem: The previous problem involved calculating an expression (16 / 5) * (5 / 15). But what if the situation changed slightly and instead of (16 / 5) * (5 / 15), you now have to calculate (16 / 5) * (5 / 7). What would the result be now? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: (16 / 5) * (5 / 7) = (16 * 5) / (5 * 7) = 80 / 35 = 16 / 7.

    ### Answer: 16/7.

Expected answer: 16/7

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following fraction multiplication: (8 / 3) * (18 / 21). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (8/3) * (18/21) = (8 * 18) / (3 * 21) = 144 / 63

    To simplify the fraction, we find the greatest common divisor of 144 and 63, which is 9.

    144 / 63 = 144 ÷ 9 / 63 ÷ 9 = 16 / 7

    ### Answer: 16/7.

Expected answer: 16/7

Correct? Yes

🔗 Follow-up

Problem: As a follow-up to the previous problem, suppose the result you obtained from the multiplication (8 / 3) * (18 / 21) is then multiplied by the fraction (23 / 20). Calculate the new result and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Let's first multiply the result of the previous multiplication by the fraction (23/20).

    (16/7) * (23/20) = (16 * 23) / (7 * 20) = 368 / 140

    To simplify the fraction, we find the greatest common divisor of 368 and 140, which is 4.

    368 / 140 = 368 ÷ 4 / 140 ÷ 4 = 92 / 35

    ### Answer: 92/35.

Expected answer: 92/35

Correct? Yes

🔗 Follow-up

Problem: Previously, you calculated the result of the multiplication (8 / 3) * (18 / 21). Now, let's consider a slightly different scenario. If instead of 18 in the denominator of the second fraction, there were 11, how would the result change? Recalculate the multiplication (8 / 3) * (11 / 21). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: We will calculate the new multiplication with the updated denominator in the second fraction.

    (8/3) * (11/21) = (8 * 11) / (3 * 21) = 88 / 63

    To simplify the fraction, we find the greatest common divisor of 88 and 63, which is 1.

    88 / 63 = 88 / 63

    ### Answer: 88/63.

Expected answer: 88/63

Correct? Yes

🔗 Problem

Problem: Evaluate the following expression and write the answer as a simplified fraction: ((14 / 6) / (22 / 16))

GPT-3.5 Turbo:

    To simplify the expression ((14 / 6) / (22 / 16)), we first simplify the fractions inside the parentheses:
    14 / 6 = 7 / 3
    22 / 16 = 11 / 8

    Now, we divide the two simplified fractions:
    (7 / 3) / (11 / 8) = (7 / 3) * (8 / 11) = 56 / 33

    ### Answer: 56/33.

Expected answer: 56/33

Correct? Yes

🔗 Follow-up

Problem: Based on the previous problem, you found the value of r by evaluating the fraction ((14 / 6) / (22 / 16)). For this problem, multiply the result you obtained previously by 9/4 and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    We found the value of r to be 56/33 in the previous problem. Now, we need to multiply this result by 9/4:

    (56/33) * (9/4) = (56 * 9) / (33 * 4) = 504 / 132 = 42 / 11

    ### Answer: 42/11.

Expected answer: 42/11

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we evaluated the expression (14 / 6) / (22 / 16). Now, suppose we changed the 14/6 to 13. How would this change the result? Evaluate the new expression, 13 / (22 / 16), and write your answer as a simplified fraction.

GPT-3.5 Turbo:

    To evaluate the new expression 13 / (22 / 16), we first simplify the fraction inside the parentheses:
    22 / 16 = 11 / 8

    Now, we divide 13 by 11/8:
    13 / (11 / 8) = 13 * (8 / 11) = 104 / 11 = 104/11

    ### Answer: 104/11.

Expected answer: 104/11

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following fraction multiplication: (16 / 3) * (25 / 26)

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (16/3) * (25/26) = (16 * 25) / (3 * 26) = 400 / 78 = 200 / 39.

    ### Answer: 200/39.

Expected answer: 200/39

Correct? Yes

🔗 Follow-up

Problem: Given the same situation as the previous problem, imagine that you started with (10 / 3) instead of (16 / 3). Multiply (10 / 3) with (25 / 26). What fraction do you end up with in this situation?

GPT-3.5 Turbo:

    Reasoning: To multiply fractions, we multiply the numerators together and the denominators together. So, (10/3) * (25/26) = (10 * 25) / (3 * 26) = 250 / 78 = 125 / 39.

    ### Answer: 125/39.

Expected answer: 125/39

Correct? Yes

🔗 Problem

Problem: Solve the following problem, writing the answer as a simplified fraction: (16 / 16) * (26 / 22)

GPT-3.5 Turbo:

    We can simplify the fractions first:
    (16/16) = 1
    (26/22) = (13/11)

    Now, we multiply the simplified fractions:
    1 * (13/11) = 13/11

    ### Answer: 13/11.

Expected answer: 13/11

Correct? Yes

🔗 Follow-up

Problem: Now, consider what happens when you square the result of the previous problem. Solve for (a * a), where 'a' is the answer to the previous problem: (16 / 16) * (26 / 22). Write the answer as a simplified fraction.

GPT-3.5 Turbo:

    Given that 'a' is 13/11, we need to find (a * a) = (13/11) * (13/11).

    Multiplying the fractions, we get:
    (13/11) * (13/11) = (13 * 13) / (11 * 11) = 169 / 121

    ### Answer: 169/121.

Expected answer: 169/121

Correct? Yes

🔗 Follow-up

Problem: Now, modify the previous problem by changing the numerator of the first fraction. Instead of following the first procedure using (16 / 16), consider what would happen if we used (16 / 12) instead. Solve (16 / 12) * (26 / 22) and write the result as a simplified fraction.

GPT-3.5 Turbo:

    We can simplify the fractions first:
    (16/12) = (4/3)
    (26/22) = (13/11)

    Now, we multiply the simplified fractions:
    (4/3) * (13/11) = (4*13) / (3*11) = 52/33

    ### Answer: 52/33.

Expected answer: 52/33

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following operation: (17 / 5) * (5 / 14). Write your answer as a simplest form fraction.

GPT-3.5 Turbo:

    Reasoning: (17/5) * (5/14) = (17*5) / (5*14) = 85 / 70 = 17 / 14.
    ### Answer: 17/14.

Expected answer: 17/14

Correct? Yes

🔗 Follow-up

Problem: After calculating the result of the previous operation: (17 / 5) * (5 / 14), now take that result and multiply it by the fraction 21 / 25. What is your final answer, written as a simplified fraction?

GPT-3.5 Turbo:

    Reasoning: (17/5) * (5/14) * (21/25) = (17*5*21) / (5*14*25) = 1785 / 1750 = 357 / 350.
    ### Answer: 357/350.

Expected answer: 51/50

Correct? Yes

🔗 Follow-up

Problem: After performing the prior operation: (17 / 5) * (5 / 14), consider what would happen if instead of multiplying the value by 5 / 14, we multiplied it by 5 / 12. What would be the result, written as a simplified fraction, in this case?

GPT-3.5 Turbo:

    Reasoning: (17/5) * (5/12) = (17*5) / (5*12) = 85 / 60 = 17 / 12.
    ### Answer: 17/12.

Expected answer: 17/12

Correct? Yes

🔗 Problem

Problem: What is the fraction you get when you multiply (16 / 6) with (29 / 27)? Write your answer in simplest form.

GPT-3.5 Turbo:

    First, we multiply the fractions:
    (16/6) * (29/27) = (16*29) / (6*27) = 464 / 162.

    To simplify the fraction, we find the greatest common divisor of 464 and 162, which is 2. Dividing both the numerator and denominator by 2, we get:
    464 / 162 = 232 / 81.

    ### Answer: 232/81.

Expected answer: 232/81

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, you multiplied (16 / 6) with (29 / 27). Now, let's consider if the fraction you multiplied by was (29 / 10) instead. What fraction would you get if you multiply (16 / 6) with (29 / 10)? Write your answer in simplest form.

GPT-3.5 Turbo:

    First, we multiply the fractions:
    (16/6) * (29/10) = (16*29) / (6*10) = 464 / 60.

    To simplify the fraction, we find the greatest common divisor of 464 and 60, which is 4. Dividing both the numerator and denominator by 4, we get:
    464 / 60 = 116 / 15.

    ### Answer: 116/15.

Expected answer: 116/15

Correct? Yes

🔗 Problem

Problem: If a car consumes 16/10 gallons of petrol every mile and you have to drive a route that is 13/17 of a mile long, how many gallons of petrol will the car have consumed when you finish the drive? Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    To find out how many gallons of petrol the car will consume for the entire drive, we need to multiply the consumption rate per mile by the length of the route.

    Consumption rate per mile: 16/10 gallons
    Length of the route: 13/17 miles

    Total consumption = (16/10) * (13/17) = (16*13)/(10*17) = 208/170 = 104/85

    Therefore, the car will consume 104/85 gallons of petrol when you finish the drive.
    ### Answer: 104/85.

Expected answer: 104/85

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, you drove a route that was 13/17 miles long. This time, suppose that you have to drive a route that is slightly longer, at 13/7 miles long. If your car still consumes 16/10 gallons of petrol every mile, calculate how many gallons of petrol will the car have consumed when you finish this drive? Express your answer as a simplified fraction.

GPT-3.5 Turbo:

    To find out how many gallons of petrol the car will consume for the longer drive, we need to multiply the consumption rate per mile by the length of the longer route.

    Consumption rate per mile: 16/10 gallons
    Length of the longer route: 13/7 miles

    Total consumption = (16/10) * (13/7) = (16*13)/(10*7) = 208/70 = 104/35

    Therefore, the car will consume 104/35 gallons of petrol when you finish the longer drive.
    ### Answer: 104/35.

Expected answer: 104/35

Correct? Yes

🔗 Problem

Problem: Calculate the result of the following problem and express your answer as a simplified fraction: (29 / 10) / (18 / 16)

GPT-3.5 Turbo:

    Reasoning: To divide fractions, we multiply by the reciprocal of the divisor. So, (29/10) / (18/16) = (29/10) * (16/18) = (29*16) / (10*18) = 464 / 180 = 58 / 22 = 29 / 11.

    ### Answer: 29/11.

Expected answer: 116/45

Correct? No

🔗 Problem

Problem: Jeremy is trying to solve a complex fraction problem. He needs to find out the result of multiplying (15/12) by (27/3). Can you help Jeremy solve this problem? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (15/12) * (27/3) = (15 * 27) / (12 * 3) = 405 / 36 = 45 / 4.

    ### Answer: 45/4.

Expected answer: 45/4

Correct? Yes

🔗 Follow-up

Problem: Following up on Jeremy's previous question, he now faces another complex problem. In addition to the earlier problem, he now needs to multiply his result with the fraction (22/14). Can you help Jeremy solve this problem? Write your answer as a simplified fraction.

GPT-3.5 Turbo:

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

    (45/4) * (22/14) = (45 * 22) / (4 * 14) = 990 / 56 = 495 / 28 = 99 / 7.

    ### Answer: 99/7.

Expected answer: 495/28

Correct? No

🔗 Follow-up

Problem: Jeremy realized he made a mistake in his calculations. Instead of multiplying the fraction (15/12) by (27/3) as previously thought, he actually needs to multiply it by (27/5). What is the resulting simplified fraction, now that Jeremy has corrected his mistake?

GPT-3.5 Turbo:

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

    (15/12) * (27/5) = (15 * 27) / (12 * 5) = 405 / 60 = 27 / 4.

    ### Answer: 27/4.

Expected answer: 27/4

Correct? Yes

🔗 Problem

Problem: Calculate the answer to the following math problem: (7 / 7) * (12 / 12)

GPT-3.5 Turbo:

    Reasoning: (7 / 7) * (12 / 12) simplifies to 1 * 1 = 1.
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Given your previous answer, now multiply it by the fraction 27/15. What is the resulting value when simplified?

GPT-3.5 Turbo:

    Reasoning: Multiplying 1 by 27/15 gives 27/15 = 9/5 when simplified.
    ### Answer: 9/5

Expected answer: 9/5

Correct? Yes

🔗 Follow-up

Problem: In your previous calculation where you multiplied (7 / 7) * (12 / 12), what if instead of 12 in the denominator of the second fraction you have 16? What would be the result of the expression (7 / 7) * (16 / 12)?

GPT-3.5 Turbo:

    Reasoning: (7 / 7) * (16 / 12) simplifies to 1 * (16 / 12) = 16 / 12 = 4 / 3.
    ### Answer: 4/3

Expected answer: 4/3

Correct? Yes

🔗 Problem

Problem: Find the result of ((28 / 6) * (16 / 24)). Write your answer as a simplified fraction.

GPT-3.5 Turbo:

    Reasoning: First, we simplify the division inside the parentheses: 28 / 6 = 4.666... ≈ 4.67 and 16 / 24 = 0.666... ≈ 0.67. Then, we multiply these results: 4.67 * 0.67 = 3.1289... ≈ 3.13. This can be simplified to 313/100.

    ### Answer: 313/100.

Expected answer: 28/9

Correct? No