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.

Qwen2-Math 72B:

 Reasoning: First, divide 26 by 12 to get 26/12, which simplifies to 13/6.
Next, multiply 7 by 13/6 to get 91/6.
### Answer: 91/6

Expected answer: 91/6

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The result of the previous problem was 288/187. Multiply this by (27 / 18): (288/187) * (27/18) = <<(288*27)/(187*18)=7776/3366>>7776/3366.
Simplify the fraction: 7776/3366 = <<7776/3366=1296/561>>1296/561.
### Answer: 1296/561

Expected answer: 432/187

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, calculate the fractions: (24 / 22) = <<24/22=12/11>>12/11 and (24 / 9) = <<24/9=8/3>>8/3.
Then, multiply the fractions: (12/11) * (8/3) = <<(12*8)/(11*3)=96/33>>96/33.
### Answer: 96/33

Expected answer: 32/11

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, we need to find the result of dividing 25/4 by 16/6, which we already know is 75/32. Then, we multiply this result by 19/6. So, (75/32) * (19/6) = (75*19) / (32*6) = 1425 / 192. Simplifying this fraction, we get 475/64.
### Answer: 475/64

Expected answer: 475/64

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To divide 9 by 16/6, we multiply 9 by the reciprocal of 16/6, which is 6/16. So, 9 * (6/16) = 54/16. Simplifying this fraction, we get 27/8.
### Answer: 27/8

Expected answer: 27/8

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We already know that (3 / 7) * (26 / 6) = 13 / 7.
Now, we multiply this result by 23/2.
(13 / 7) * (23 / 2) = (13 * 23) / (7 * 2) = 299 / 14
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator, which is 1.
299 / 14 = (299 ÷ 1) / (14 ÷ 1) = 299 / 14
### Answer: 299/14

Expected answer: 299/14

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.
(7/7) * (26/6) = (7 * 26) / (7 * 6) = 182 / 42
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator, which is 14.
182 / 42 = (182 ÷ 14) / (42 ÷ 14) = 13 / 3
### Answer: 13/3

Expected answer: 13/3

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The result of (17 / 10) * (28 / 10) is 4.76.
Now, multiply 4.76 by (11 / 18): 4.76 * (11 / 18) = <<4.76*(11/18)=2.92>>2.92.
### Answer: 2.92

Expected answer: 1309/450

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: First, calculate the division: 17 / 24 = <<17/24=0.7083333333333334>>0.7083333333333334 and 28 / 10 = <<28/10=2.8>>2.8.
Then, multiply the results: 0.7083333333333334 * 2.8 = <<0.7083333333333334*2.8=1.9833333333333335>>1.9833333333333335.
### Answer: 1.9833333333333335

Expected answer: 119/60

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: ((18 / 19) * (19 / 6)) = (18 * 19) / (19 * 6) = 18 / 6 = 3 / 1 = 3
3 * 3 = 9
### Answer: 9

Expected answer: 9

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: ((9 / 19) * (19 / 6)) = (9 * 19) / (19 * 6) = 9 / 6 = 3 / 2
### Answer: 3/2

Expected answer: 3/2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The result from the previous problem is 95/18. To multiply this fraction by itself, we square both the numerator and the denominator.
(95/18) * (95/18) = (95 * 95) / (18 * 18) = 9025 / 324
This fraction is already in its simplest form.
### Answer: 9025/324

Expected answer: 9025/324

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
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 / 8 = 25
72 / 8 = 9
So, the simplified fraction is 25/9.
### Answer: 25/9

Expected answer: 25/9

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The result of the previous problem is 7/2. Multiplying this by (5 / 13) gives us (7/2) * (5 / 13) = 35 / 26.
### Answer: 35/26

Expected answer: 35/26

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (16 / 4) / 3 = 4 / 3
### Answer: 4/3

Expected answer: 4/3

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: We already calculated the product of the fractions 5/27 and 15/2 to be 25/18.
To multiply a fraction by itself, we square both the numerator and the denominator.
(25/18) * (25/18) = (25 * 25) / (18 * 18) = 625 / 324
To simplify the fraction, we find the greatest common divisor (GCD) of 625 and 324, which is 1.
625 / 324 = (625 / 1) / (324 / 1) = 625 / 324
### Answer: 625/324

Expected answer: 625/324

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(24/27) * (15/2) = (24 * 15) / (27 * 2) = 360 / 54
To simplify the fraction, we find the greatest common divisor (GCD) of 360 and 54, which is 18.
360 / 54 = (360 / 18) / (54 / 18) = 20 / 3
### Answer: 20/3

Expected answer: 20/3

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (285/91) * (23/22) = <<(285/91)*(23/22)=6555/1992>>6555/1992
### Answer: 6555/1992

Expected answer: 6555/2002

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: (15 / 29) * (19 / 7) = <<(15/29)*(19/7)=285/203>>285/203
### Answer: 285/203

Expected answer: 285/203

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The result of (12 / 25) * (20 / 4) is 12 / 5.
Multiplying this result by (17 / 17) gives (12 / 5) * (17 / 17) = (12 * 17) / (5 * 17) = 204 / 85.
Simplifying the fraction, we get 204 / 85 = 24 / 10 = 12 / 5.
### Answer: 12/5

Expected answer: 12/5

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, simplify the fractions: (10 / 25) * (20 / 4) = (10 / 25) * (5 / 1).
Next, multiply the numerators and denominators: (10 * 5) / (25 * 1) = 50 / 25.
Finally, simplify the fraction: 50 / 25 = 2 / 1.
### Answer: 2/1

Expected answer: 2

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: We already calculated that 14/10 * 30/5 = 42/5.
Now, we multiply 42/5 by 13/15.
(42/5) * (13/15) = (42 * 13) / (5 * 15) = 546 / 75
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3.
546 / 75 = (546 / 3) / (75 / 3) = 182 / 25
### Answer: 182/25

Expected answer: 182/25

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: We follow the same steps as before.
30/10 * 30/5 = (30 * 30) / (10 * 5) = 900 / 50
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 50.
900 / 50 = (900 / 50) / (50 / 50) = 18 / 1
### Answer: 18/1

Expected answer: 18

Correct? Yes

Problem: After completing the cookie orders for the event, the baker considers a change in his recipe that will impact how much sugar he uses. Now, instead of 26 cups of sugar per batch, he only plans to use 16 cups of sugar in the recipe. If he still only has enough sugar on hand for 29/14 of a full batch, how many batches can he now prepare with the amount of sugar he has on hand? Calculate this as (16 / (29 / 14)). Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: To find out how many batches the baker can now prepare, we need to calculate (16 / (29 / 14)).
First, we simplify the expression inside the parentheses: (29 / 14) = 29/14.
Next, we divide 16 by 29/14: 16 / (29/14) = 16 * (14/29) = 224/29.
Therefore, the baker can now prepare 224/29 batches of cookies.
### Answer: 224/29

Expected answer: 224/29

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: o = (9 / 13) * (243 / 40) = (9 * 243) / (13 * 40) = 2187 / 520
### Answer: 2187/520

Expected answer: 2187/520

Correct? Yes

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.

Qwen2-Math 72B:

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

Expected answer: 243/110

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (324 / 143) * (14 / 27) = (324 * 14) / (143 * 27) = 4536 / 3861 = 168 / 143
### Answer: 168/143

Expected answer: 168/143

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We multiply the fraction 34/9 by the fraction 24/30.
34/9 * 24/30 = (34 * 24) / (9 * 30) = 816 / 270
To simplify the fraction, we find the greatest common divisor (GCD) of 816 and 270, which is 6.
816 / 270 = (816 / 6) / (270 / 6) = 136 / 45
### Answer: 136/45

Expected answer: 136/45

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators.
25/9 * 17/13 = (25 * 17) / (9 * 13) = 425 / 117
To simplify the fraction, we find the greatest common divisor (GCD) of 425 and 117, which is 1.
425 / 117 = (425 / 1) / (117 / 1) = 425 / 117
### Answer: 425/117

Expected answer: 425/117

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (14 / 9) * (14 / 9) = (14 * 14) / (9 * 9) = 196 / 81
### Answer: 196/81

Expected answer: 196/81

Correct? Yes

Problem: After you calculated ((15 / 3) * (19 / 26)), take that answer and multiply it by the fraction (14 / 24). Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (95/26) * (14 / 24) = <<95/26*14/24=1330/624>>1330/624
### Answer: 1330/624

Expected answer: 665/312

Correct? Yes

Problem: Let's consider a situation where instead of multiplying (15 / 3) by (19 / 26), you are now multiplying it by (27 / 26). What would be the result then? Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (15 / 3) = <<15/3=5>>5
(27 / 26) = <<27/26=27/26>>27/26
(5 * 27/26) = <<5*27/26=135/26>>135/26
### Answer: 135/26

Expected answer: 135/26

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To find the amount of the ingredient required for the new recipe, we need to multiply the amount required by the new recipe by the fraction of the recipe they want to make.
Amount required = (19/14) * (30/4)
Amount required = (19 * 30) / (14 * 4)
Amount required = 570 / 56
Amount required = 10.178571428571429
### Answer: 10.178571428571429

Expected answer: 285/28

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (75/52) * (75/52) = 5625/2704 = <<5625/2704=225/108.16=22500/10816=5625/2704>>5625/2704
### Answer: 5625/2704

Expected answer: 5625/2704

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To find the result of 14 divided by (26 / 15), we can multiply 14 by the reciprocal of (26 / 15), which is (15 / 26). This gives us (14 * 15) / 26 = 210 / 26 = <<210/26=105/13>>105/13.
### Answer: 105/13

Expected answer: 105/13

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (81/28)^2 = (81 * 81) / (28 * 28) = 6561 / 784
### Answer: 6561/784

Expected answer: 6561/784

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (9/3) * (23/28) = (9 * 23) / (3 * 28) = 207 / 84 = 69 / 28
### Answer: 69/28

Expected answer: 69/28

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: ((15 / 13) * (24 / 24)) = <<(15/13)*(24/24)=15/13>>15/13
(15/13) * (22/7) = <<(15/13)*(22/7)=330/91>>330/91
### Answer: 330/91

Expected answer: 330/91

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: ((15 / 2) * (24 / 24)) = <<(15/2)*(24/24)=15/2>>15/2
### Answer: 15/2

Expected answer: 15/2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.
(15/14) * (15/15) = (15 * 15) / (14 * 15) = 225 / 210
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator.
GCD(225, 210) = 15
Dividing both the numerator and denominator by the GCD, we get:
225 / 210 = (225 / 15) / (210 / 15) = 15 / 14
### Answer: 15/14

Expected answer: 15/14

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.
(9 / 7) * (25 / 21) = (9 * 25) / (7 * 21) = 225 / 147
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator.
GCD(225, 147) = 3
Dividing both the numerator and denominator by the GCD, we get:
225 / 147 = (225 / 3) / (147 / 3) = 75 / 49
### Answer: 75/49

Expected answer: 75/49

Correct? Yes

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))).

Qwen2-Math 72B:

 Reasoning: ((29 / 21) * (81 / 80)) = (29 * 81) / (21 * 80) = 2349 / 1680 = 783 / 560
### Answer: 783/560

Expected answer: 783/560

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (9 / (20 / 18)) = (9 * (18 / 20)) = (9 * 18) / 20 = 162 / 20 = 81 / 10
### Answer: 81/10

Expected answer: 81/10

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: 5 * 8/20 = <<5*8/20=2>>2
### Answer: 2

Expected answer: 2

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: 30/4 = <<30/4=7.5>>7.5
7.5 * 18/6 = <<7.5*18/6=22.5>>22.5
### Answer: 22.5

Expected answer: 45/2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, calculate the division: 27 / 4 = <<27/4=6.75>>6.75.
Then, multiply the result by 10/9: 6.75 * 10/9 = <<6.75*10/9=7.5>>7.5.
### Answer: 7.5

Expected answer: 15/2

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, calculate the division: 20 / 2 = <<20/2=10>>10.
Then, multiply the result by 15: 10 * 15 = <<10*15=150>>150.
Next, divide the result by 18: 150 / 18 = <<150/18=25/3>>25/3.
### Answer: 25/3

Expected answer: 25/3

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: ((11 / 9) * (29 / 6)) = <<(11/9)*(29/6)=319/54>>319/54
((319 / 54) * (11 / 5)) = <<(319/54)*(11/5)=3509/270>>3509/270
### Answer: 3509/270

Expected answer: 3509/270

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: ((21 / 9) * (29 / 6)) = <<(21/9)*(29/6)=203/18>>203/18
### Answer: 203/18

Expected answer: 203/18

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We take the result from the previous task, which is 480/133, and multiply it by 22/7.
(480/133) * (22/7) = 10560/931.
### Answer: 10560/931

Expected answer: 10560/931

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, we calculate the division of 21 by 7, which gives us 21/7.
Next, we calculate the division of 16 by 19, which gives us 16/19.
Finally, we multiply the two fractions together: (21/7) * (16/19) = 336/133.
### Answer: 336/133

Expected answer: 48/19

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The product of 250/33 and 28/29 is (250/33) * (28/29) = <<(250/33) * (28/29) = 7000/957>>7000/957.
The simplified fraction of 7000/957 is 7000/957.
### Answer: 7000/957

Expected answer: 7000/957

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The product of 25/15 and 20/3 is (25/15) * (20/3) = <<(25/15) * (20/3) = 500/45>>500/45.
The simplified fraction of 500/45 is 100/9.
### Answer: 100/9

Expected answer: 100/9

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (551 / 46) * (29 / 18) = (551 * 29) / (46 * 18) = 15979 / 828
### Answer: 15979/828

Expected answer: 15979/828

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The solution for the previous question ((5 / 3) * (27 / 13)) is 45 / 13.
(45 / 13) * (8 / 14) = (45 * 8) / (13 * 14) = 360 / 182 = 180 / 91
### Answer: 180/91

Expected answer: 180/91

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (5 / 3) * (27 / 9) = (5 * 27) / (3 * 9) = 135 / 27 = 5
### Answer: 5

Expected answer: 5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: From the last problem, we have the answer 1. Now, multiplying this by (27 / 27) gives us 1 * 1 = 1.
### Answer: 1

Expected answer: 1

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (29 / 6) * (1 / 1) = 29 / 6 = 4.833333333333333
### Answer: 4.833333333333333

Expected answer: 29/6

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The product of the fractions is (242/133) * (25/4) = <<(242*25)/(133*4)=6050/532>>6050/532.
### Answer: 6050/532

Expected answer: 3025/266

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The new product is (11/19) * (25/7) = <<(11*25)/(19*7)=275/133>>275/133.
### Answer: 275/133

Expected answer: 275/133

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: We already found that (21/30) * (19/5) = 133/50.
Now, we multiply this result by 16/12.
(133/50) * (16/12) = (133 * 16) / (50 * 12) = 2128 / 600
To simplify the fraction, we find the greatest common divisor (GCD) of 2128 and 600, which is 8.
2128 / 600 = (2128 / 8) / (600 / 8) = 266 / 75
### Answer: 266/75

Expected answer: 266/75

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(9/30) * (19/5) = (9 * 19) / (30 * 5) = 171 / 150
To simplify the fraction, we find the greatest common divisor (GCD) of 171 and 150, which is 3.
171 / 150 = (171 / 3) / (150 / 3) = 57 / 50
### Answer: 57/50

Expected answer: 57/50

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators.
(253/120) * (253/120) = (253 * 253) / (120 * 120) = 64009 / 14400
### Answer: 64009/14400

Expected answer: 64009/14400

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators.
(11/15) * (26/8) = (11 * 26) / (15 * 8) = 286 / 120
### Answer: 286/120

Expected answer: 143/60

Correct? Yes

Problem: After finding the result of (28 / 1) divided by (30 / 27), what is the new result when this is multiplied by (6 / 19)? Write your final answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (28 / 1) / (30 / 27) = (28 * 27) / (1 * 30) = <<(28*27)/(1*30)=252/10=25.2>>25.2
25.2 * (6 / 19) = <<25.2*(6/19)=75.6/19=3.9736842105263157>>3.9736842105263157
### Answer: 3.9736842105263157

Expected answer: 756/95

Correct? No

Problem: Suppose instead of the original calculation, we now have to perform (28 / 1) divided by 11, how would the result change? Write your updated answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (28 / 1) / 11 = 28 / 11 = <<28/11=2.5454545454545454>>2.5454545454545454
### Answer: 2.5454545454545454

Expected answer: 28/11

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (20/7) * (20/7) = <<20/7*20/7=400/49>>400/49
### Answer: 400/49

Expected answer: 400/49

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (25 / 25) = <<25/25=1>>1
(11 / 7) = <<11/7=11/7>>11/7
(25 / 25) * (11 / 7) = 1 * (11 / 7) = <<1*11/7=11/7>>11/7
### Answer: 11/7

Expected answer: 11/7

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: 30/1 * 16/27 = <<(30*16)/(1*27)=480/27>>480/27
### Answer: 480/27

Expected answer: 160/9

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: First, multiply 's' by (21/17): 9 * (21/17) = 189/17.
### Answer: 189/17

Expected answer: 189/17

Correct? Yes

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'?

Qwen2-Math 72B:

 Reasoning: First, simplify the expression inside the parentheses: (12 / 12) = 1.
Then, divide 24 by 1: 24 / 1 = 24.
### Answer: 24
The change in the number of items from 27 to 24 results in a different answer, which is 24 instead of 9.

Expected answer: 24

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The result from the previous problem is 435 / 32. Multiplying this by (18/18) gives us (435 / 32) * (18/18) = <<(435 / 32) * (18/18) = 435 / 32>>435 / 32.
### Answer: 435 / 32

Expected answer: 435/32

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (15 / 16) * (13 / 2) = <<(15 / 16) * (13 / 2) = 195 / 32>>195 / 32
### Answer: 195 / 32

Expected answer: 195/32

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: ((6 / 2) / 3) = (6 / 2) * (1 / 3) = 6 / 6 = 1
### Answer: 1

Expected answer: 1

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We already found that 7/1 divided by 15/9 equals 21/5. Now, we need to multiply this result by 10/5.
21/5 * 10/5 = <<21*10/5*5=210/25>>210/25
Simplifying the fraction, we get:
210/25 = <<210/25=42/5>>42/5
### Answer: 42/5

Expected answer: 42/5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We follow the same process as before. The reciprocal of 15/9 is 9/15. So, we have:
20/1 * 9/15 = <<20*9/15=180/15>>180/15
Simplifying the fraction, we get:
180/15 = <<180/15=12>>12
### Answer: 12

Expected answer: 12

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: 20.7 * (1/16) = 20.7 / 16 = <<20.7/16=1.29375>>1.29375
### Answer: 1.29375

Expected answer: 207/160

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (23/10) * (9/6) = (23 * 9) / (10 * 6) = 207 / 60 = <<207/60=3.45>>3.45
### Answer: 3.45

Expected answer: 69/20

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (6 / 4) = <<6/4=1.5>>1.5
(4.090909090909091 * 1.5) = <<4.090909090909091*1.5=6.136363636363637>>6.136363636363637
### Answer: 6.136363636363637

Expected answer: 135/22

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (18 / 1) = <<18/1=18>>18
(10 / 11) = <<10/11=0.9090909090909091>>0.9090909090909091
(18 * 0.9090909090909091) = <<18*0.9090909090909091=16.363636363636363>>16.363636363636363
### Answer: 16.363636363636363

Expected answer: 180/11

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The multiplication of the result 8 by the fraction 30/21 is calculated as follows:
8 * (30/21) = (8 * 30) / 21 = 240 / 21 = <<240/21=11.428571428571429>>11.428571428571429
### Answer: 11.428571428571429

Expected answer: 80/7

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The multiplication of the fractions 24/23 and 18/3 is calculated as follows:
(24/23) * (18/3) = (24 * 18) / (23 * 3) = 432 / 69 = <<432/69=6.26>>6.26
### Answer: 6.26

Expected answer: 144/23

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators.
(320 / 221) * (20 / 26) = (320 * 20) / (221 * 26) = 6400 / 5746
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator.
GCD(6400, 5746) = 2
Dividing both the numerator and the denominator by the GCD, we get:
6400 / 5746 = (6400 / 2) / (5746 / 2) = 3200 / 2873
### Answer: 3200/2873

Expected answer: 3200/2873

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (21 divided by 9) = <<21/9=7/3>>7/3
(7/3 multiplied by 4) = <<(7/3)*4=28/3>>28/3
### Answer: 28/3

Expected answer: 28/3

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (5/15) = <<5/15=1/3>>1/3
(1/3 multiplied by 4/1) = <<1/3*4/1=4/3>>4/3
### Answer: 4/3

Expected answer: 4/3

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We know that g = 184/13. Now, multiply g by (4 / 7): (184/13) * (4 / 7) = 736 / 91.
### Answer: 736/91

Expected answer: 736/91

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, simplify the expression by multiplying the numerators and denominators: (2 * 16) / (26 * 1) = 32 / 26.
Next, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 32 / 26 = 16 / 13.
### Answer: 16/13

Expected answer: 16/13

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: The value obtained from the expression ((21 / 1) / (26 / 20)) is 210 / 13.
Multiplying this value by the fraction (21 / 29) gives (210 / 13) * (21 / 29) = <<(210*21)/(13*29)=4410/377>>4410 / 377.
### Answer: 4410/377

Expected answer: 4410/377

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: ((21 / 1) / 2) = 21 / 2 = <<21/2=10.5>>10.5
### Answer: 10.5

Expected answer: 21/2

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: 20/19 * 21/19 = <<(20*21)/(19*19)=420/361>>420/361
### Answer: 420/361

Expected answer: 420/361

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The result of the previous operation was 161 / 144. Squaring this fraction means multiplying it by itself: (161 / 144) * (161 / 144) = 25921 / 20736.
Now, simplify the fraction 25921 / 20736 by dividing both the numerator and the denominator by their greatest common divisor, which is 1: 25921 / 1 = 25921, 20736 / 1 = 20736.
So, the simplified fraction is 25921 / 20736.
### Answer: 25921 / 20736

Expected answer: 25921/20736

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, calculate the division of the two fractions: (6 / (27 / 23)) = (6 * 23) / 27 = 138 / 27.
Now, simplify the fraction 138 / 27 by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 138 / 3 = 46, 27 / 3 = 9.
So, the simplified fraction is 46 / 9.
### Answer: 46 / 9

Expected answer: 46/9

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (11 / 10) * (21 / 16) = (11 * 21) / (10 * 16) = 231 / 160
### Answer: 231/160

Expected answer: 231/160

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (11 / 6) * (24 / 12) = (11 * 24) / (6 * 12) = 264 / 72 = 11 / 3
### Answer: 11/3

Expected answer: 11/3

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (84/19) * (27/17) = <<(84/19) * (27/17) = 2268/323>>2268/323
### Answer: 2268/323

Expected answer: 2268/323

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: ((17 / 19) * (28 / 2)) = <<((17 / 19) * (28 / 2)) = 238/19>>238/19
### Answer: 238/19

Expected answer: 238/19

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: Multiply the fraction from the previous problem (4.8) by 15/10: 4.8 * (15/10) = 7.2.
Simplify the resulting fraction: 7.2 = 72/10 = 36/5.
### Answer: 36/5

Expected answer: 36/5

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, simplify the fractions: (3 / 14) = (3 / 14) and (28 / 5) = (28 / 5).
Next, multiply the simplified fractions: (3 / 14) * (28 / 5) = (3 * 28) / (14 * 5) = 84 / 70.
Finally, simplify the resulting fraction: 84 / 70 = 1.2.
### Answer: 1.2

Expected answer: 6/5

Correct? Yes

Problem: After finding the result of ((15 / 3) * (7 / 25)), take that result and multiply it by (28 / 16). Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: First, calculate the division: 15 / 3 = <<15/3=5>>5.
Then, calculate the multiplication: 5 * (7 / 25) = <<5*(7/25)=7/5>>7/5.
Next, calculate the multiplication: (7/5) * (28 / 16) = <<(7/5)*(28/16)=49/20>>49/20.
### Answer: 49/20

Expected answer: 49/20

Correct? Yes

Problem: Given the result of the previous problem, let's consider a new scenario. Suppose instead of (15 / 3), we have (13 / 3). Now, multiply (13 / 3) * (7 / 25) and write your answer as a simplified fraction. How does this change in scenario affect the final result?

Qwen2-Math 72B:

 Reasoning: First, calculate the new division: 13 / 3 = <<13/3=13/3>>13/3.
Then, calculate the multiplication: (13/3) * (7 / 25) = <<(13/3)*(7/25)=91/75>>91/75.
### Answer: 91/75

Expected answer: 91/75

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: z = x * (19 / 15) = 20 * (19 / 15) = (20 * 19) / 15 = 380 / 15 = 76 / 3
### Answer: 76 / 3

Expected answer: 76/3

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: We multiply the fraction 57/16 by the fraction 28/16. To do this, we multiply the numerators together and the denominators together, which gives us (57 * 28) / (16 * 16) = 1596/256.
We simplify the fraction 1596/256 by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This gives us 399/64.
### Answer: 399/64

Expected answer: 399/64

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, we simplify the fraction 27/18 by dividing both the numerator and the denominator by their greatest common divisor, which is 9. This gives us 3/2.
Next, we multiply the simplified fraction 3/2 by the fraction 19/17. To do this, we multiply the numerators together and the denominators together, which gives us (3 * 19) / (2 * 17) = 57/34.
### Answer: 57/34

Expected answer: 57/34

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
377/120 * 25/11 = (377 * 25) / (120 * 11) = 9425 / 1320
### Answer: 9425/1320

Expected answer: 1885/264

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
29/8 * 13/24 = (29 * 13) / (8 * 24) = 377 / 192
### Answer: 377/192

Expected answer: 377/192

Correct? Yes

Problem: After finding the value of the expression ((29 / 17) / (27 / 22)), now calculate the result of that value when it is multiplied by (27 / 2). Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (638 / 459) * (27 / 2) = (638 * 27) / (459 * 2) = 17226 / 918 = 19 / 1
### Answer: 19/1

Expected answer: 319/17

Correct? No

Problem: After finding the value of the expression ((29 / 17) / (27 / 22)), consider how the result would change if instead of 29/17, we had 4/1. Calculate the value of this new expression, 4 / (27 / 22). Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: 4 / (27 / 22) = 4 * (22 / 27) = 88 / 27
### Answer: 88/27

Expected answer: 88/27

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (27 / 6) * (25 / 5) = 22.5
(20 / 27) = <<20/27=0.7407407407407407>>0.7407407407407407
(27 / 6) * (25 / 5) * (20 / 27) = 22.5 * 0.7407407407407407 = <<22.5*0.7407407407407407=16.666666666666664>>16.666666666666664
### Answer: 16.666666666666664

Expected answer: 50/3

Correct? No

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?

Qwen2-Math 72B:

 Reasoning: (11 / 6) = <<11/6=1.8333333333333333>>1.8333333333333333
(25 / 5) = <<25/5=5>>5
(11 / 6) * (25 / 5) = 1.8333333333333333 * 5 = <<1.8333333333333333*5=9.166666666666666>>9.166666666666666
### Answer: 9.166666666666666

Expected answer: 55/6

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (13 / 2) * (13 / 6) = <<(13/2)*(13/6)=169/12>>169/12
### Answer: 169/12

Expected answer: 169/12

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (11 / 1) * (1 / 6) = <<(11/1)*(1/6)=11/6>>11/6
### Answer: 11/6

Expected answer: 11/6

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, we find the product of 25/20 and 11/6, which we already know is 55/24.
Now, we multiply 55/24 by 20/26.
(55/24) * (20/26) = (55 * 20) / (24 * 26) = 1100 / 624
To simplify the fraction, we find the greatest common divisor (GCD) of 1100 and 624, which is 4.
1100 / 624 = (1100 / 4) / (624 / 4) = 275 / 156
### Answer: 275/156

Expected answer: 275/156

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, let's calculate the product of 25/17 and 11/6.
(25/17) * (11/6) = (25 * 11) / (17 * 6) = 275 / 102
To simplify the fraction, we find the greatest common divisor (GCD) of 275 and 102, which is 1.
275 / 102 = (275 / 1) / (102 / 1) = 275 / 102
### Answer: 275/102

Expected answer: 275/102

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (7 / 5) * (5 / 3) = (7 * 5) / (5 * 3) = 35 / 15 = 7 / 3
### Answer: 7/3

Expected answer: 7/3

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: Multiply the numerators: 145 * 27 = <<145*27=3915>>3915
Multiply the denominators: 144 * 4 = <<144*4=576>>576
The product is 3915/576. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 3915/3 = <<3915/3=1305>>1305, 576/3 = <<576/3=192>>192
### Answer: 1305/192

Expected answer: 435/64

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: Multiply the numerators: 15 * 29 = <<15*29=435>>435
Multiply the denominators: 10 * 27 = <<10*27=270>>270
The product is 435/270. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15: 435/15 = <<435/15=29>>29, 270/15 = <<270/15=18>>18
### Answer: 29/18

Expected answer: 29/18

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: ((30 / 25) * (25 / 10)) = <<(30/25)*(25/10)=3>>3
(3 * (5 / 9)) = <<3*(5/9)=5/3>>5/3
### Answer: 5/3

Expected answer: 5/3

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The product of the fractions 27/10 and 27/3 is (27/10) * (27/3) = <<(27/10) * (27/3) = 243/10>>243/10.
Multiplying this result by 9/20 gives (243/10) * (9/20) = <<(243/10) * (9/20) = 2187/200>>2187/200.
### Answer: 2187/200

Expected answer: 2187/200

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The product of the fractions is (27/10) * (27/21) = <<(27/10) * (27/21) = 729/210>>729/210.
### Answer: 729/210

Expected answer: 243/70

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The result of the previous operation is 75/52.
To find the square of this fraction, multiply it by itself: (75/52) * (75/52) = (75 * 75) / (52 * 52) = 5625 / 2704.
### Answer: 5625/2704

Expected answer: 5625/2704

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: ((20 / 22) * (14 / 11)) = ((10 / 11) * (14 / 11)) = (140 / 121)
(140 / 121) * (17/3) = (2380 / 363)
### Answer: 2380/363

Expected answer: 2380/363

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: The new expression ((20 / 22) * (14 / 2)) differs from the original because the second fraction has been changed to (14 / 2). This means that the numerator of the second fraction is now larger, which will result in a larger product when multiplied by the first fraction.
((20 / 22) * (14 / 2)) = ((10 / 11) * (14 / 2)) = (140 / 22) = (70 / 11)
### Answer: 70/11

Expected answer: 70/11

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (75/32) * (29/23) = <<(75/32)*(29/23)=2175/736>>2175/736
### Answer: 2175/736

Expected answer: 2175/736

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: ((25 / 8) * (29 / 4)) = <<(25/8)*(29/4)=725/32>>725/32
### Answer: 725/32

In the real-world scenario, if the proportions you multiplied with were changed from (3 / 4) to (29 / 4), it would mean that each person or group is now receiving a larger portion or share. This could be interpreted as an increase in the amount of resources or items being shared among the group.

Expected answer: 725/32

Correct? Yes

Problem: After you have calculated the value of (29 / 1) * (8 / 15), use that result to multiply by 4/7. What is the final decimal result?

Qwen2-Math 72B:

 Reasoning: (29 / 1) * (8 / 15) = 232 / 15 = 15.466666666666666
(232 / 15) * (4 / 7) = 928 / 105 = <<928/105=8.838095238095238>>8.838095238095238
### Answer: 8.838095238095238

Expected answer: 928/105

Correct? Yes

Problem: Suppose we change the number of parts in the fraction from the previous question. Instead of (29 / 1) * (8 / 15), suppose we have (29 / 1) * (11 / 15). Again, calculate the value of the new expression as a decimal. What would be the resulting decimal?

Qwen2-Math 72B:

 Reasoning: (29 / 1) * (11 / 15) = 29 * 11 / 15 = 319 / 15 = <<319/15=21.266666666666668>>21.266666666666668
### Answer: 21.266666666666668

Expected answer: 319/15

Correct? No

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?

Qwen2-Math 72B:

 Reasoning: First, simplify the expression inside the parentheses: (25 / 5) = 5 and (19 / 8) = 19/8.
Next, multiply the simplified fractions: 5 * (19/8) = 95/8.
### Answer: 95/8

Expected answer: 95/8

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (28 / 4) * (10 / 12) = <<(28 / 4) * (10 / 12) = 280 / 48>>280 / 48
280 / 48 = <<280 / 48 = 35 / 6>>35 / 6
### Answer: 35 / 6

Expected answer: 35/6

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(21 / 26) * (20 / 9) = (21 * 20) / (26 * 9) = 420 / 234
To simplify the fraction, we find the greatest common divisor (GCD) of 420 and 234, which is 6.
420 / 234 = (420 / 6) / (234 / 6) = 70 / 39
Now, 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 (GCD) of 1050 and 819, which is 3.
1050 / 819 = (1050 / 3) / (819 / 3) = 350 / 273
### Answer: 350 / 273

Expected answer: 50/39

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(21 / 26) * (20 / 4) = (21 * 20) / (26 * 4) = 420 / 104
To simplify the fraction, we find the greatest common divisor (GCD) 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: 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.

Qwen2-Math 72B:

 Reasoning: (425 / 108) * (23 / 17) = (425 * 23) / (108 * 17) = 9775 / 1836
### Answer: 9775/1836

Expected answer: 575/108

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (25 / 18) * (14 / 6) = (25 * 14) / (18 * 6) = 350 / 108
### Answer: 350/108

Expected answer: 175/54

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: We already know that t = 18/17.
To find t * t, we multiply the numerators and the denominators separately.
t * t = (18/17) * (18/17) = (18*18)/(17*17) = 324/289
### Answer: 324/289

Expected answer: 324/289

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
12/1 * 2/17 = (12*2)/(1*17) = 24/17
### Answer: 24/17

Expected answer: 24/17

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (16/15) * (30/24) = <<(16/15)*(30/24)=2>>2
### Answer: 2

Expected answer: 4/3

Correct? No

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

Qwen2-Math 72B:

 Reasoning: (16 / 5) * (5 / 7) = <<(16/5)*(5/7)=16/7>>16/7
### Answer: 16/7

Expected answer: 16/7

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, recall the result from the previous problem: 16 / 7.
Next, multiply this result by the new fraction: (16 / 7) * (23 / 20).
Simplify the fractions: (16 / 7) * (23 / 20) = (16 / 7) * (23 / 20).
Multiply the numerators and denominators: (16 * 23) / (7 * 20) = 368 / 140.
Finally, simplify the fraction: 368 / 140 = 92 / 35.
### Answer: 92/35

Expected answer: 92/35

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: First, simplify the fractions: (8 / 3) * (11 / 21) = (8 / 3) * (11 / 21).
Next, multiply the numerators and denominators: (8 * 11) / (3 * 21) = 88 / 63.
Finally, simplify the fraction: 88 / 63 = 88 / 63.
### Answer: 88/63

Expected answer: 88/63

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (56/33) * (9/4) = <<(56/33)*(9/4)=14/11>>14/11
### Answer: 14/11

Expected answer: 42/11

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: The new expression is 13 / (22 / 16). We can simplify this by multiplying the numerator by the reciprocal of the denominator: 13 * (16 / 22) = <<13*(16/22)=104/22>>104/22. This can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 104/22 = <<104/22=52/11>>52/11.
### Answer: 52/11

Expected answer: 104/11

Correct? No

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.

Qwen2-Math 72B:

 Reasoning: a = 13 / 11
(a * a) = (13 / 11) * (13 / 11) = 169 / 121
### Answer: 169 / 121

Expected answer: 169/121

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (16 / 12) * (26 / 22) = (4 / 3) * (26 / 22) = (4 * 26) / (3 * 22) = 104 / 66 = 52 / 33
### Answer: 52 / 33

Expected answer: 52/33

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (17 / 14) * (21 / 25) = <<(17/14)*(21/25)=51/50>>51/50
### Answer: 51/50

Expected answer: 51/50

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: (17 / 5) * (5 / 12) = <<(17/5)*(5/12)=17/12>>17/12
### Answer: 17/12

Expected answer: 17/12

Correct? Yes

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.

Qwen2-Math 72B:

 Reasoning: (16 / 6) * (29 / 10) = <<(16 / 6) * (29 / 10) = 464 / 60>>464 / 60
464 / 60 = <<464 / 60 = 116 / 15>>116 / 15
### Answer: 116 / 15

Expected answer: 116/15

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The car consumes 16/10 gallons of petrol every mile, so for a route that is 13/7 miles long, the car will consume (16/10) * (13/7) = <<(16/10) * (13/7) = 208/70>>208/70 gallons of petrol.
### Answer: 208/70

Expected answer: 104/35

Correct? Yes

Problem: Suppose you took the result of the previous problem ((29 / 10) / (18 / 16)) and then you further multiplied this result by (8 / 17). Calculate this new result and express your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: The result of the previous problem is 116 / 45. Multiplying this by (8 / 17) gives (116 / 45) * (8 / 17) = (116 * 8) / (45 * 17) = 928 / 765.
### Answer: 928 / 765

Expected answer: 928/765

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: To solve this problem, we need to multiply the two fractions together. We can do this by multiplying the numerators and denominators separately.
(45/4) * (22/14) = (45 * 22) / (4 * 14) = 990 / 56
Now, we need to simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2.
990 / 56 = (990 / 2) / (56 / 2) = 495 / 28
### Answer: 495/28

Expected answer: 495/28

Correct? Yes

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?

Qwen2-Math 72B:

 Reasoning: To solve this problem, we need to multiply the two fractions together. We can do this by multiplying the numerators and denominators separately.
(15/12) * (27/5) = (15 * 27) / (12 * 5) = 405 / 60
Now, we need to simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15.
405 / 60 = (405 / 15) / (60 / 15) = 27 / 4
### Answer: 27/4

Expected answer: 27/4

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: The previous answer was 1.
Multiplying 1 by 27/15 gives us 27/15.
To simplify 27/15, we divide both the numerator and the denominator by their greatest common divisor, which is 3.
27 ÷ 3 = <<27/3=9>>9
15 ÷ 3 = <<15/3=5>>5
So, 27/15 simplifies to 9/5.
### Answer: 9/5

Expected answer: 9/5

Correct? Yes

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

Qwen2-Math 72B:

 Reasoning: (7 / 7) = <<7/7=1>>1
(16 / 12) = <<16/12=4/3>>4/3
(7 / 7) * (16 / 12) = 1 * 4/3 = <<1*4/3=4/3>>4/3
### Answer: 4/3

Expected answer: 4/3

Correct? Yes

Problem: Suppose you reevaluate the previous problem but use 22 instead of 28 when you perform the multiplication ((22 / 6) * (16 / 24)). What would be the result this time? Write your answer as a simplified fraction.

Qwen2-Math 72B:

 Reasoning: (22 / 6) = <<22/6=11/3>>11/3
(16 / 24) = <<16/24=2/3>>2/3
(11/3) * (2/3) = <<(11/3)*(2/3)=22/9>>22/9
### Answer: 22/9

Expected answer: 22/9

Correct? Yes