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.

Mixtral 8x22B:

 Reasoning: (551/56) \* (8/28) = (551 \* 8) / (56 \* 28) = 4408 / 1568
The fraction 4408/1568 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 112.
Therefore, the simplified fraction is 4408/1568 = 4/14 = 2/7.
### Answer: 2/7

Expected answer: 551/196

Correct? No

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.

Mixtral 8x22B:

 Reasoning: (29/2) \* (19/14) = (29 \* 19) / (2 \* 14) = 551 / 28
The fraction 551/28 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 551/28.
### Answer: 551/28

Expected answer: 551/28

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: First, divide 26 by 12 to get 26/12 = <<26/12=2.1666666666666665>>2.1666666666666665.
Then, multiply 7 by 2.1666666666666665 to get 7 \* 2.1666666666666665 = <<7\*2.1666666666666665=15.166666666666666>>15.166666666666666.
The answer can be simplified to 15 and 1/6 or 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.

Mixtral 8x22B:

 Reasoning: The result of the previous problem was 288/187. Multiplying this by (27/18) gives:

(288/187) * (27/18) = (288 * 27) / (187 * 18) = 7776 / 3366

This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 6:

7776 / 3366 = (7776 / 6) / (3366 / 6) = 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.

Mixtral 8x22B:

 Reasoning: The expression can be simplified by canceling out common factors in the numerator and denominator.

((24 / 22) * (24 / 9)) = (12/11 * 24/9) = (12 * 24) / (11 * 9) = 288 / 99

### Answer: 288/99, which can be simplified to 32/11

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.

Mixtral 8x22B:

 Reasoning: (25/4) / (16/6) \* (19/6) = (25/4) \* (6/16) \* (19/6) = (25 \* 6 \* 19) / (4 \* 16 \* 6) = 2850 / 384.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4.
2850/384 = (2850/4) / (384/4) = 712.5 / 96.
To simplify further, we can divide both the numerator and the denominator by 96.
712.5 / 96 = (712.5/96) / (96/96) = 7.421875 / 1.
### Answer: 7.421875

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.

Mixtral 8x22B:

 Reasoning: 9 / (16/6) = 9 \* (6/16) = (9 \* 6) / 16 = 54 / 16.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.
54/16 = (54/2) / (16/2) = 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?

Mixtral 8x22B:

 Reasoning: From the previous question, we know that (3/7)*(26/6) = <<(3/7)*(26/6)=13/7>>13/7.
Now, multiply this result by 23/2: (13/7)*(23/2) = <<(13/7)*(23/2)=299/14>>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?

Mixtral 8x22B:

 Reasoning: Multiply the numerators and denominators separately: (7*26)/(7*6) = <<(7*26)/(7*6)=182/42>>182/42.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 14: 182/14 = <<182/14=13>>13 and 42/14 = <<42/14=3>>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.

Mixtral 8x22B:

 Reasoning: 4.76 * (11 / 18) = 4.76 * 0.6111111111111111 = <<4.76*0.6111111111111111=2.911111111111111>>2.911111111111111
### Answer: 2.911111111111111

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.

Mixtral 8x22B:

 Reasoning: (17 / 24) * (28 / 10) = (0.7083333333333333) * (2.8) = <<0.7083333333333333*2.8=1.9833333333333333>>1.9833333333333333
### Answer: 1.9833333333333333

Expected answer: 119/60

Correct? No

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.

Mixtral 8x22B:

 Reasoning: The result of ((18 / 19) * (19 / 6)) is 3.
Multiplying 3 by itself gives 3 * 3 = <<3*3=9>>9.
The result is a simplified fraction of 9/1, which can be written as 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.

Mixtral 8x22B:

 Reasoning: The expression can be simplified by canceling out the common factor of 19 in the numerator and denominator.
((9 / 19) * (19 / 6)) = (9 / 6) = <<9/6=1.5>>1.5
The result is a simplified fraction of 3/2, which can be written as 1.5.
### Answer: 1.5

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?

Mixtral 8x22B:

 Reasoning: The multiplication of the fraction 95/18 by itself is (95/18) \* (95/18) = (95 \* 95) / (18 \* 18) = 9025 / 324.
The fraction 9025 / 324 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
9025 / 1 = <<9025/1=9025>>9025 and 324 / 1 = <<324/1=324>>324.
So, the simplified fraction is 9025/324.
### 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?

Mixtral 8x22B:

 Reasoning: The multiplication of the fraction 10/12 by 20/6 is (10/12) \* (20/6) = (10 \* 20) / (12 \* 6) = 200 / 72.
The fraction 200 / 72 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
200 / 4 = <<200/4=50>>50 and 72 / 4 = <<72/4=18>>18.
So, the simplified fraction is 50/18.
### Answer: 50/18

Expected answer: 25/9

Correct? Yes

Problem: After calculating the total fractional representation of the cargo hauled in one day, suppose the ship needs to set aside 5/24 of this total fraction for an emergency supply run later in the week. What fraction of the overall cargo does this emergency supply run represent? To find this, calculate ((5 / 24) * your previous answer). Write your answer as a simplified fraction.

Mixtral 8x22B:

 Reasoning: The emergency supply run represents (5/24) \* (22/3) of the overall cargo.
To simplify this fraction, we can first simplify the numerator and the denominator separately.
The numerator is 5 \* 22 = <<5\*22=110>>110.
The denominator is 24 \* 3 = <<24\*3=72>>72.
Now we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 110 and 72 is 2.
So, the simplified fraction is (110/2) / (72/2) = <<110/2=55>>55 / <<72/2=36>>36 = <<55/36>>55/36.
### Answer: 55/36

Expected answer: 55/36

Correct? Yes

Problem: After recalculating the cargo hauled in one day with the new total of 29/21 representing the consumer goods, how does this change the overall cargo hauled in one day? If the cargo in the morning now represents 29/21 of its capacity, and the cargo in the afternoon still represents 22/4 of its capacity for industrial supplies, what is the new total fractional representation of these two types of cargo hauled in one day? Calculate ((29 / 21) * (22 / 4)). Write your answer as a simplified fraction.

Mixtral 8x22B:

 Reasoning: The new total fractional representation of the two types of cargo is (29/21) \* (22/4).
To simplify this fraction, we can first simplify the numerator and the denominator separately.
The numerator is 29 \* 22 = <<29\*22=638>>638.
The denominator is 21 \* 4 = <<21\*4=84>>84.
Now we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 638 and 84 is 2.
So, the simplified fraction is (638/2) / (84/2) = <<638/2=319>>319 / <<84/2=42>>42 = <<319/42>>319/42.
### Answer: 319/42

Expected answer: 319/42

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?

Mixtral 8x22B:

 Reasoning: From the previous problem, we know that the result is 7/2.
Now, we multiply this result by (5 / 13): (7/2) * (5/13) = (7 * 5) / (2 * 13) = <<(7*5)/(2*13)=35/26>>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?

Mixtral 8x22B:

 Reasoning: The numerator is 16 / 4 = <<16/4=4>>4.
The denominator is 3.
Now, we divide the numerator by the denominator: 4 / 3.
### Answer: 4/3 or 1.333...

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?

Mixtral 8x22B:

 Reasoning: The product of the fractions 5/27 and 15/2 is 25/18.
Multiplying this result by itself gives (25/18) \* (25/18) = (25 \* 25) / (18 \* 18) = 625 / 324.
The fraction 625/324 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
625/1 = 625 and 324/1 = 324, so the simplified form of the product is 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.

Mixtral 8x22B:

 Reasoning: The new product of the fractions 24/27 and 15/2 is (24/27) \* (15/2) = (24 \* 15) / (27 \* 2) = 360 / 54.
The fraction 360/54 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 18.
360/18 = 20 and 54/18 = 3, so the simplified form of the new product is 20/3.
### Answer: 20/3

Expected answer: 20/3

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.

Mixtral 8x22B:

 Reasoning: (12 / 25) * (20 / 4) = 2.4
Multiplying this result by (17 / 17) gives 2.4 * 1 = <<2.4*1=2.4>>2.4
The fraction 2.4 can be simplified to 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.

Mixtral 8x22B:

 Reasoning: (10 / 25) * (20 / 4) = (10 * 20) / (25 * 4) = 200 / 100 = <<200/100=2>>2
The fraction 2 can be simplified to 2/1.
### Answer: 2/1

The difference between the two results is that the first result is 12/5, while the second result is 2/1. The second result is a simpler fraction and is equivalent to the decimal number 2.0, while the first result is equivalent to the decimal number 2.4.

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.

Mixtral 8x22B:

 Reasoning: We have already calculated the multiplication of 14/10 by 30/5 as 42/5.

Now we need to multiply that result by the fraction 13/15.

(42/5) \* (13/15) = (42 \* 13) / (5 \* 15) = 546 / 75

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 546 and 75 is 3.

546 / 3 = 182
75 / 3 = 25

So the simplified fraction is 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?

Mixtral 8x22B:

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

(30/10) \* (30/5) = (30 \* 30) / (10 \* 5) = 900 / 50

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 900 and 50 is 50.

900 / 50 = 18
50 / 50 = 1

So the simplified fraction is 18/1.

### Answer: 18/1 or simply 18

Expected answer: 18

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.

Mixtral 8x22B:

 Reasoning: Since the value of s was not provided in the previous problem, I cannot calculate the value of o.
### Answer: Cannot be determined without the value of s.

Expected answer: 2187/520

Correct? No

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.

Mixtral 8x22B:

 Reasoning: (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.

Mixtral 8x22B:

 Reasoning: In the previous question, we found that the expression ((24 / 11) * (27 / 26)) simplifies to 324 / 143.
Now, we multiply this result by (14 / 27):
(324 / 143) * (14 / 27) = (324 * 14) / (143 * 27)
Next, we simplify the numerator and denominator:
(324 * 14) = 4536
(143 * 27) = 3861
Finally, we simplify the fraction:
4536 / 3861 = 1512 / 1287
### Answer: 1512/1287

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?

Mixtral 8x22B:

 Reasoning: To multiply two 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 can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 10608 and 3510 is 6.

Therefore, the simplest form of the fraction is (10608/6) / (3510/6) = 1768 / 585.

### Answer: 1768/585

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?

Mixtral 8x22B:

 Reasoning: To multiply two 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 can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 425 and 117 is 1.

Therefore, the simplest form of the fraction is 425/117.

### Answer: 425/117

Expected answer: 425/117

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.

Mixtral 8x22B:

 Reasoning: First, we simplify the fraction (14 / 24):
(14 / 24) = <<14/24=7/12>>7/12
Now, we multiply the result from the previous question by this fraction:
(95 / 26) * (7 / 12) = <<(95/26)*(7/12)=(95*7)/(26*12)=665/312>>665/312
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 13:
665 / 312 = <<665/13=51>>51 / <<312/13=24>>24
### Answer: 51/24

Expected answer: 665/312

Correct? No

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.

Mixtral 8x22B:

 Reasoning: First, we simplify the expression inside the parentheses:
(15 / 3) = <<15/3=5>>5
(27 / 26) = <<27/26=27/26>>27/26
Now, we multiply the two results:
5 * (27 / 26) = <<5*(27/26)=135/26>>135/26
### Answer: 135/26

Expected answer: 135/26

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.

Mixtral 8x22B:

 Reasoning: The result of the previous expression was 81/28.
The square of 81/28 is (81/28)^2 = <<(81/28)^2=6561/784>>6561/784
The fraction 6561/784 is already in its simplest form.
### 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.

Mixtral 8x22B:

 Reasoning: (9/3) * (23/28) = 3 * (23/28) = <<3*(23/28)=69/28>>69/28
The fraction 69/28 is already in its simplest form.
### 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.

Mixtral 8x22B:

 Reasoning: From the previous question, we know that the solution to ((15/13) \* (24/24)) is 15/13.

Now, we need to multiply this fraction by (22/7).

So, the equation becomes (15/13) \* (22/7).

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

So, the equation becomes (15 \* 22) / (13 \* 7).

Now, we can simplify the fraction by canceling out any common factors. However, in this case, there are no common factors between the numerator and the denominator.

Therefore, the fraction remains as (15 \* 22) / (13 \* 7).

### Answer: (15 \* 22) / (13 \* 7)

Expected answer: 330/91

Correct? No

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.

Mixtral 8x22B:

 Reasoning: If you originally had 15 halves instead of 15 thirteenths, the equation would be ((15/2) \* (24/24)).

First, simplify the equation by canceling out the common factors. In this case, (24/24) simplifies to 1.

So, the equation becomes (15/2) \* 1 = 15/2.

Since 15 and 2 are not coprime (they have a common factor of 1), the fraction 15/2 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

Therefore, the simplified fraction is 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?

Mixtral 8x22B:

 Reasoning: Multiplying a fraction by 15/15 does not change its value, since 15/15 is equal to 1.
So, (15 / 14) * (15 / 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?

Mixtral 8x22B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(9 / 7) * (25 / 21) = (9 * 25) / (7 * 21) = 225 / 147
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 225 and 147 is 3.
225 / 3 = 75
147 / 3 = 49
So, the simplified fraction is 75 / 49.
### Answer: 75/49

Expected answer: 75/49

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?

Mixtral 8x22B:

 Reasoning: The result from the previous problem is 5.
Multiplying 5 by 8/20 is equal to 5 \* 2/5 = 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?

Mixtral 8x22B:

 Reasoning: 30 divided by 4 is equal to 7.5.
Multiplying 7.5 by 18/6 is equal to 7.5 \* 3 = 22.5.
The new value is 22.5, which is greater than the original value of 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.

Mixtral 8x22B:

 Reasoning: We already know that the result of ((20 / 2) * (2 / 18)) is 10/9.
Now, we need to find the result of ((27 / 4) * (10 / 9)).
First, we simplify the expression inside the parentheses:
(27 / 4) = 6.75
Now, we multiply the two results:
6.75 * (10 / 9) = 67.5 / 9
We can simplify this fraction by dividing both the numerator and the denominator by 9:
67.5 / 9 = 7.5
The answer is 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.

Mixtral 8x22B:

 Reasoning: First, we simplify the expression inside the parentheses:
(20 / 2) = 10
(15 / 18) = 5 / 6
Now, we multiply the two results:
10 * (5 / 6) = 50 / 6
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
50 / 6 = (50 / 2) / (6 / 2) = 25 / 3
The answer is 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.

Mixtral 8x22B:

 Reasoning: To solve this problem, we need to multiply the result of the previous problem by the fraction (11/5).
(319/54) * (11/5) = (319 * 11) / (54 * 5) = 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.

Mixtral 8x22B:

 Reasoning: If the initial calculation involved (21/9) instead of (11/9), the new result would be:
(21/9) * (29/6) = (21 * 29) / (9 * 6) = 609 / 54
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3:
609 / 54 = (609/3) / (54/3) = 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.

Mixtral 8x22B:

 Reasoning: (480 / 133) * (22 / 7) = (480 * 22) / (133 * 7) = 10560 / 931
The fraction 10560 / 931 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: (21 / 7) * (16 / 19) = (21 * 16) / (7 * 19) = 336 / 133
The fraction 336 / 133 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 336 / 133.
### Answer: 336 / 133

Expected answer: 48/19

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.

Mixtral 8x22B:

 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?

Mixtral 8x22B:

 Reasoning: (45 / 13) * (8 / 14) = (45 * 8) / (13 * 14) = 360 / 182
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
360 / 182 = (360 / 2) / (182 / 2) = 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.

Mixtral 8x22B:

 Reasoning: (5 / 3) * (27 / 9) = (5 * 27) / (3 * 9) = 135 / 27 = <<135/27=135/27>>135 / 27
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 27:
135 / 27 = (135 / 27) / (27 / 27) = 5 / 1
### Answer: 5/1 or simply 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?

Mixtral 8x22B:

 Reasoning: (27 / 27) * 1 = 1 * 1 = <<1*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?

Mixtral 8x22B:

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

Expected answer: 29/6

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.

Mixtral 8x22B:

 Reasoning: (133/50) \* (16/12) = (133 \* 16) / (50 \* 12) = 2128 / 600
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4.
2128 / 600 = (2128/4) / (600/4) = 532 / 150
### Answer: 532/150

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.

Mixtral 8x22B:

 Reasoning: (9/30) \* (19/5) = (9 \* 19) / (30 \* 5) = 171 / 150
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, 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.

Mixtral 8x22B:

 Reasoning: The result of the previous calculation was 253/120.
To find the result when you multiply this fraction by itself, you square the numerator and the denominator.
(253/120)^2 = (253^2)/(120^2) = 64009/14400
The fraction 64009/14400 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: To multiply two fractions, you multiply the numerators together and the denominators together.
(11/15) \* (26/8) = (11\*26)/(15\*8) = 286/120
The fraction 286/120 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
Therefore, the simplified fraction is 143/60.
### Answer: 143/60

Expected answer: 143/60

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (203 / 144) * (203 / 144) = (203 * 203) / (144 * 144) = 41209 / 20736
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 41209 and 20736 is 1.
So, 41209 / 20736 = (41209 / 1) / (20736 / 1) = 41209 / 20736
### Answer: 41209/20736

Expected answer: 41209/20736

Correct? Yes

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))?

Mixtral 8x22B:

 Reasoning: (29 / 5) * (21 / 27) = (29 * 21) / (5 * 27) = 609 / 135
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 609 and 135 is 3.
So, 609 / 135 = (609 / 3) / (135 / 3) = 203 / 45
### Answer: 203/45

Expected answer: 203/45

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.

Mixtral 8x22B:

 Reasoning: The result of (28 / 1) divided by (30 / 27) is 126/5.
126/5 \* 6/19 = <<126/5\*6/19=756/95>>756/95.
The fraction 756/95 is not in simplest form, so we need to simplify it.
The greatest common divisor of 756 and 95 is 1, so the fraction is already in simplest form.
### Answer: 756/95

Expected answer: 756/95

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (28 / 1) = 28 and 11 is a whole number.
28 divided by 11 = <<28/11=28/11>>28/11.
The result is already a simplified fraction.
### Answer: 28/11

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.

Mixtral 8x22B:

 Reasoning: The result of ((25 / 25) * (20 / 7)) is (20 / 7).
Multiplying this product by itself gives (20 / 7) * (20 / 7) = (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.

Mixtral 8x22B:

 Reasoning: (25 / 25) simplifies to 1, so the expression becomes (1 * (11 / 7)).
The result is (11 / 7), which cannot be simplified further.
### 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.

Mixtral 8x22B:

 Reasoning: To multiply a whole number with a fraction, we can write the whole number as a fraction with a denominator of 1.
30/1 \* 16/27 = (30\*16)/(1\*27) = 480/27
The fraction 480/27 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
480/27 = (480/3)/(27/3) = 160/9
### Answer: 160/9

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'.

Mixtral 8x22B:

 Reasoning: We previously calculated that 's' = 9.
Now, we multiply 's' by (21/17):
9 * (21/17) = <<9*21/17=189/17>>189/17
The result is already a simplified fraction, so the answer is 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'?

Mixtral 8x22B:

 Reasoning: First, we simplify the expression inside the parentheses.
(12 / 12) = <<12/12=1>>1
Now, we divide the results:
24 / 1 = <<24/1=24>>24
The result is already a simplified fraction, so the answer is 24.

The change from 27 items to 24 items affects the answer 's' by reducing it from 9 to 8. This is because (24 / 3) = <<24/3=8>>8, and the division by (12 / 12) = 1 does not change the result.
### Answer: 24

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.

Mixtral 8x22B:

 Reasoning: (435 / 32) * (18 / 18) = (435 * 18) / (32 * 18) = 435 / 32.
Since (18 / 18) = 1, the result remains the same.
### 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.

Mixtral 8x22B:

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

Expected answer: 195/32

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?

Mixtral 8x22B:

 Reasoning: We have already found that 7/1 divided by 15/9 equals 21/5.
Now we need to multiply 21/5 by 10/5.
21/5 * 10/5 = 210/25
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 5.
210/25 ÷ 5/5 = 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.

Mixtral 8x22B:

 Reasoning: To divide 20/1 by 15/9, we multiply 20/1 by the reciprocal of 15/9, which is 9/15.
20/1 * 9/15 = 180/15
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 15.
180/15 ÷ 15/15 = 12/1
### 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?

Mixtral 8x22B:

 Reasoning: (207/10) \* (1/16) = <<207/10\*1/16=207/160>>207/160
The result is 1.29375 when you multiply (207/10) by (1/16).
### Answer: 1.29375

Expected answer: 207/160

Correct? No

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?

Mixtral 8x22B:

 Reasoning: (23/10) \* (9/6) = <<23/10\*9/6=207/60>>207/60
The result is 3.45 when you multiply (23/10) by (9/6).
### Answer: 3.45

Expected answer: 69/20

Correct? No

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.

Mixtral 8x22B:

 Reasoning: (45/11) * (6/4) = (45 * 6) / (11 * 4) = 270 / 44 = <<270/44=135/22>>135/22
### Answer: 135/22

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.

Mixtral 8x22B:

 Reasoning: (18 / 1) * (10 / 11) = 18 * (10 / 11) = (18 * 10) / 11 = 180 / 11 = <<180/11=16 4/11>>16 4/11
### Answer: 16 4/11

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?

Mixtral 8x22B:

 Reasoning: The result from the previous problem is 184/23.
Multiplying this fraction by 30/21 gives us:
(184/23) \* (30/21) = (184 \* 30) / (23 \* 21) = <<184\*30=5520, 23\*21=483>>5520/483
The fraction 5520/483 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
5520/3 = <<5520/3=1840>>1840
483/3 = <<483/3=161>>161
So the simplified fraction is 1840/161.
### Answer: 1840/161

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?

Mixtral 8x22B:

 Reasoning: When we replace the fraction 23/3 with 18/3, the multiplication becomes:
(24/23) \* (18/3) = (24 \* 18) / (23 \* 3) = <<24\*18=432, 23\*3=69>>432/69
The fraction 432/69 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
432/3 = <<432/3=144>>144
69/3 = <<69/3=23>>23
So the simplified fraction is 144/23.
### Answer: 144/23

Expected answer: 144/23

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: We have already found that (20 / 13) / (17 / 16) = 320 / 221.
Now we need to multiply this result by (20 / 26).
Multiplying the numerators and denominators, we get:
(320 / 221) * (20 / 26) = (320 * 20) / (221 * 26)
Simplifying the numerator and denominator, we get:
(6400) / (5746)
The fraction 6400 / 5746 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 6400 and 5746 is 2.
Dividing both the numerator and denominator by 2, we get:
(6400 / 2) / (5746 / 2) = 3200 / 2873
The fraction 3200 / 2873 is already in simplest form.
### 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.

Mixtral 8x22B:

 Reasoning: (21 divided by 9) = 7/3
c = 4
(7/3 multiplied by 4) = 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.

Mixtral 8x22B:

 Reasoning: (5/15) multiplied by (4/1) = (5/15) \* (4/1) = (5 \* 4) / (15 \* 1) = 20/15
Simplifying the fraction: 20/15 = (20 divided by 5) / (15 divided by 5) = 4/3
### Answer: 4/3

Expected answer: 4/3

Correct? Yes

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?

Mixtral 8x22B:

 Reasoning: The result of the previous problem was 95/92. To find the new answer, we need to multiply this result by (28 / 4).

First, we can simplify the fraction (28 / 4) by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 28 and 4 is 4.

28 / 4 = 7
4 / 4 = 1

So the simplified fraction is 7/1, which is just 7.

Now we can multiply the result of the previous problem by 7:

(95/92) * 7 = 665/92

This fraction is already in its simplest form, so the new answer is 665/92.

### Answer: 665/92

Expected answer: 665/92

Correct? Yes

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?

Mixtral 8x22B:

 Reasoning: To simplify the new expression, we can first multiply the numerators and denominators separately:

(30 * 19) / (11 * 24) = 570 / 264

Next, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 570 and 264 is 6.

570 / 6 = 95
264 / 6 = 44

So the simplified fraction is 95/44.

### Answer: 95/44

Expected answer: 95/44

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.

Mixtral 8x22B:

 Reasoning: (4 / 7) * g = (4 / 7) * (184 / 13) = (4 * 184) / (7 * 13) = 736 / 91
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 1.
736 / 1 = 736
91 / 1 = 91
So, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: (2 / 26) * (16 / 1) = (2 * 16) / (26 * 1) = 32 / 26
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.
32 / 2 = 16
26 / 2 = 13
So, the simplified fraction is 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?

Mixtral 8x22B:

 Reasoning: The expression ((21 / 1) / (26 / 20)) simplifies to 210 / 13. Multiplying this by the fraction (21 / 29) gives us (210 / 13) \* (21 / 29). To simplify this expression, we can multiply the numerators and the denominators separately. This gives us (210 \* 21) / (13 \* 29).

### Answer: (210 \* 21) / (13 \* 29)

Expected answer: 4410/377

Correct? No

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?

Mixtral 8x22B:

 Reasoning: The expression can be simplified by first dividing 21 by 1, which is equal to 21. Then, divide 26 by 2, which is equal to 13. The expression can then be simplified to 21 / 13.

### Answer: 21/13

Expected answer: 21/2

Correct? No

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.

Mixtral 8x22B:

 Reasoning: To multiply two fractions, multiply the numerators and the denominators separately.
(20/19) \* (21/19) = (20 \* 21) / (19 \* 19) = <<20\*21=420>>420 / <<19\*19=361>>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.

Mixtral 8x22B:

 Reasoning: In the previous problem, we found that the result of the operation ((21 / 16) / (27 / 23)) is equal to 161/144.

To find the value of this new operation, we need to square the fraction:

(161/144)^2 = (161 * 161) / (144 * 144)

Now, we can simplify the numerator and the denominator by multiplying the numbers:

(161 * 161) = 25921
(144 * 144) = 20736

So, the expression becomes:

25921 / 20736

Now, we can simplify this fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 25921 and 20736 is 1.

Therefore, the simplified fraction is:

### 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.

Mixtral 8x22B:

 Reasoning: First, we need to simplify the expression by performing the division operation inside the parentheses.

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

Now, we can simplify the expression by multiplying the numbers:

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

Now, we can simplify this fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of (6 * 23) and 27 is 3.

So, we can simplify the fraction by dividing both the numerator and the denominator by 3:

((6 * 23) / 3) / (27 / 3) = (2 * 23) / 9

Therefore, the simplified fraction is:

### 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.

Mixtral 8x22B:

 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?

Mixtral 8x22B:

 Reasoning: (11 / 6) * (24 / 12) = (11 * 24) / (6 * 12) = 264 / 72 = <<264/72=11/3>>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?

Mixtral 8x22B:

 Reasoning: First, we simplify the expression from the previous problem:
(84 / 19) * (27 / 17)
Next, we multiply the numerators and the denominators:
(84 * 27) / (19 * 17)
Finally, we simplify the fraction:
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?

Mixtral 8x22B:

 Reasoning: First, we simplify the expression inside the parentheses:
(17 / 19) * (28 / 2) = (17 * 28) / (19 * 2)
Next, we simplify the numerator and the denominator:
(17 * 28) = 476
(19 * 2) = 38
Finally, we simplify the fraction:
476 / 38 = 12
### Answer: 12

Expected answer: 238/19

Correct? No

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.

Mixtral 8x22B:

 Reasoning: (24 / 5) * (15 / 10) = (24 * 15) / (5 * 10) = 360 / 50 = <<360/50=7.2>>7.2

Simplifying the fraction: 360 / 50 = (360 ÷ 10) / (50 ÷ 10) = 36 / 5

### Answer: 36/5 or 7.2

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.

Mixtral 8x22B:

 Reasoning: (3 / 14) * (28 / 5) = (3 * 28) / (14 * 5) = 84 / 70 = <<84/70=1.2>>1.2

Simplifying the fraction: 84 / 70 = (84 ÷ 14) / (70 ÷ 14) = 6 / 5

### Answer: 6/5 or 1.2

Expected answer: 6/5

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (152 / 45) * (19 / 9) = (152 * 19) / (45 * 9) = 2888 / 405.
The fraction 2888 / 405 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 2888 / 405.
### Answer: 2888/405

Expected answer: 2888/405

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (19 / 7) * (8 / 15) = (19 * 8) / (7 * 15) = 152 / 105.
The fraction 152 / 105 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 152 / 105.
### Answer: 152/105

Expected answer: 152/105

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.

Mixtral 8x22B:

 Reasoning: From the previous question, we know that the result of ((15 / 3) * (7 / 25)) is 7/5.
Now, we multiply this result by (28 / 16):
(7/5) * (28 / 16) = (7 * 28) / (5 * 16) = <<(7*28)/(5*16)=196/80>>196/80
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8:
196 / 80 = (196 / 8) / (80 / 8) = <<(196/8)/(80/8)=24.5/10>>24.5/10
We can simplify this fraction further by dividing both the numerator and the denominator by 5:
24.5 / 10 = (24.5 / 5) / (10 / 5) = <<(24.5/5)/(10/5)=4.9/2>>4.9/2
We can simplify this fraction further by dividing both the numerator and the denominator by 2:
4.9 / 2 = (4.9 / 2) / (2 / 2) = <<(4.9/2)/(2/2)=2.45/1>>2.45/1
Since the denominator is 1, we can write the answer as a decimal:
2.45
### Answer: 2.45

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?

Mixtral 8x22B:

 Reasoning: First, we simplify the expression inside the parentheses:
(13 / 3) = <<13/3=13/3>>13/3
(7 / 25) = <<7/25>>7/25
Now, we multiply the results:
(13 / 3) * (7 / 25) = (13 * 7) / (3 * 25) = <<(13*7)/(3*25)=91/75>>91/75
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1:
91 / 75 = <<91/75>>91/75
### Answer: 91/75

The change in scenario affects the final result by changing the numerator of the fraction from 35 to 91, which results in a different fraction.

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.

Mixtral 8x22B:

 Reasoning: x = 20, so z = 20 * (19 / 15) = <<20*(19/15)=(20*19)/15=380/15=25.333333333333332>>380/15 = 25 1/3
### Answer: 25 1/3

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.

Mixtral 8x22B:

 Reasoning: We have the result from the previous calculation, which is 57/16.

Now, we multiply this result by the fraction (28/16):

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

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1596 and 256 is 8.

So, we divide both the numerator and the denominator by 8:

1596 / 8 = 199.5

256 / 8 = 32

Since we cannot have a fraction with a decimal in the numerator, we can express the result as a mixed number:

199 1/2 / 32

To simplify this mixed number, we can convert it to an improper fraction:

(199.5 * 32) / 32 = 6384 / 32

Now, we can simplify this fraction by dividing both the numerator and the denominator by their GCD, which is 32:

6384 / 32 = 199.5

32 / 32 = 1

So, the result of the expression is 199.5 / 1.

### Answer: 199.5 / 1 or simply 199.5

Expected answer: 399/64

Correct? No

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.

Mixtral 8x22B:

 Reasoning: First, we simplify the fractions inside the brackets.

27/18 simplifies to 3/2 because both 27 and 18 are divisible by 9.

19/17 cannot be simplified further.

Now, we multiply the simplified fractions:

(3/2) * (19/17) = (3 * 19) / (2 * 17) = 57 / 34

So, the result of the expression is 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.

Mixtral 8x22B:

 Reasoning: To find the result of multiplying 29/5 by 13/24, we first multiply the numerators together and the denominators together:

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

Next, we multiply this result by 25/11:

(377/120) \* (25/11) = (377\*25)/(120\*11) = 9425/1320

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 9425 and 1320 is 5, so we divide both numbers by 5:

9425/5 = 1885
1320/5 = 264

Therefore, the simplified fraction is 1885/264.

### Answer: 1885/264

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.

Mixtral 8x22B:

 Reasoning: To multiply two fractions, you multiply the numerators together and the denominators together.
(29/8) \* (13/24) = (29\*13)/(8\*24) = <<(29\*13)/(8\*24)=377/192>>377/192
### Answer: 377/192

Note: The fraction 377/192 is already in its simplest form, as 377 and 192 have no common factors other than 1.

Expected answer: 377/192

Correct? Yes

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

Mixtral 8x22B:

 Reasoning: First, we simplify the fractions: (20 / 27) = <<20/27>>20/27.
Then, we multiply the results: 22.5 * (20 / 27) = <<22.5*(20/27)=16.666666666666668>>16.666666666666668.
### Answer: 16.666666666666668

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?

Mixtral 8x22B:

 Reasoning: First, we simplify the fractions: (11 / 6) = <<11/6=1.8333333333333333>>1.8333333333333333 and (25 / 5) = <<25/5=5>>5.
Then, we multiply the results: 1.8333333333333333 * 5 = <<1.8333333333333333*5=9.166666666666666>>9.166666666666666.
### Answer: 9.166666666666666

Expected answer: 55/6

Correct? No

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.

Mixtral 8x22B:

 Reasoning: The expression (13 / 2) * e can be simplified by substituting the value of e and then multiplying the numerators and the denominators separately.
(13 / 2) * (13 / 6) = (13 * 13) / (2 * 6) = 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.

Mixtral 8x22B:

 Reasoning: The expression (11 / 1) * (1 / 6) can be simplified by multiplying the numerators and the denominators separately.
(11 * 1) / (1 * 6) = 11 / 6
### Answer: 11/6

If instead of having 13 of an item, you only had 11 of it, the result would be 11/6 instead of 13/6. The value of the expression would be smaller because the numerator is smaller.

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.

Mixtral 8x22B:

 Reasoning: (55/24) \* (20/26) = (55/12) \* (1/13) = (55/156)
### Answer: 55/156

Expected answer: 275/156

Correct? No

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.

Mixtral 8x22B:

 Reasoning: (25/17) \* (11/6) = (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.

Mixtral 8x22B:

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

Expected answer: 7/3

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.

Mixtral 8x22B:

 Reasoning: The answer to ((30 / 25) * (25 / 10)) is 3. Multiplying this by (5 / 9) gives:

3 * (5 / 9) = (3 * 5) / 9 = 15 / 9 = <<15/9=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.

Mixtral 8x22B:

 Reasoning: The product of the fractions 27/10 and 27/3 is (27/10) \* (27/3) = 27\*27 / 10\*3 = 729/30.
The product of the fractions 729/30 and 9/20 is (729/30) \* (9/20) = 729\*9 / 30\*20 = 6561/600.
The fraction 6561/600 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
6561/600 = (6561/9) / (600/9) = 729/66.6666666667.
### Answer: 729/66.6666666667

Expected answer: 2187/200

Correct? No

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.

Mixtral 8x22B:

 Reasoning: The product of the fractions 27/10 and 27/21 is (27/10) \* (27/21) = 27\*27 / 10\*21 = 729/210.
The fraction 729/210 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
729/210 = (729/3) / (210/3) = 243/70.
### Answer: 243/70

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.

Mixtral 8x22B:

 Reasoning: (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.

Mixtral 8x22B:

 Reasoning: The expression can be simplified by canceling out common factors.
(140 / 121) * (17 / 3) = (140 * 17) / (121 * 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.

Mixtral 8x22B:

 Reasoning: The original expression was ((20 / 22) * (14 / 11)) * (17/3).
The new expression is ((20 / 22) * (14 / 2)).
The difference is that the second fraction in the multiplication has changed from (14 / 11) to (14 / 2).
The new expression can be simplified as follows:
(20 / 22) * (14 / 2) = (10 / 11) * (7) = 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?

Mixtral 8x22B:

 Reasoning:
(75 / 32) * (29 / 23) = (75 * 29) / (32 * 23) = 2175 / 736

The additional operation represents scaling the original division or portion sharing scenario by a factor of 29/23.

### 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.

Mixtral 8x22B:

 Reasoning:
((25 / 8) * (29 / 4)) = (25 * 29) / (8 * 4) = 725 / 32

The result 725/32 can be interpreted as dividing 725 items into 32 equal portions.

In the real-world scenario, this change in the ratio would mean that the group is now receiving a larger portion of the items.

### Answer: 725/32

Expected answer: 725/32

Correct? Yes

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?

Mixtral 8x22B:

 Reasoning: (754/255) \* (21/9) = (754\*21)/(255\*9) = <<(754\*21)/(255\*9)=(15834/2295)>>15834/2295

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 15834 and 2295 is 3.

So, (15834/2295) / (3/3) = (15834/3) / (2295/3) = <<(15834/3)/(2295/3)=(5278/765)>>5278/765

### Answer: 5278/765

Expected answer: 5278/765

Correct? Yes

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)?

Mixtral 8x22B:

 Reasoning: (15/17) \* (26/15) = (15\*26)/(17\*15) = <<(15\*26)/(17\*15)=(26/17)>>26/17
### Answer: 26/17

Expected answer: 26/17

Correct? Yes

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?

Mixtral 8x22B:

 Reasoning: The expression can be simplified by first performing the division operations inside the parentheses.

(25 / 5) = 5
(19 / 8) = 19/8

Now, the expression becomes (5 * (19/8)).

5 * (19/8) = (5 * 19) / 8

5 * 19 = 95

Now, divide 95 by 8 to get the final answer.

95 / 8 = 11.875

The value of k is 11.875.

### Answer: 11.875

Expected answer: 95/8

Correct? No

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.

Mixtral 8x22B:

 Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.
(21 / 26) * (20 / 9) = (21 * 20) / (26 * 9) = 420 / 234
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 420 and 234 is 6.
420 / 6 = 70
234 / 6 = 39
So, the simplified fraction is 70 / 39.
Now, we multiply this result by the fraction (15 / 21).
(70 / 39) * (15 / 21) = (70 * 15) / (39 * 21) = 1050 / 819
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 1050 and 819 is 3.
1050 / 3 = 350
819 / 3 = 273
So, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: To multiply fractions, we multiply the numerators together and the denominators together.
(21 / 26) * (20 / 4) = (21 * 20) / (26 * 4) = 420 / 104
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 420 and 104 is 4.
420 / 4 = 105
104 / 4 = 26
So, the simplified fraction is 105 / 26.
### Answer: 105 / 26

Expected answer: 105/26

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: The previous problem found the product of ((17 / 13) \* (15 / 6)) to be 85/26.

Now, we need to multiply this fraction by (8 / 15).

(85 / 26) \* (8 / 15) = (85 \* 8) / (26 \* 15) = (680 / 390)

The fraction 680/390 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 10.

Therefore, the simplified fraction is 68/39.

### Answer: 68/39

Expected answer: 68/39

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.

Mixtral 8x22B:

 Reasoning: (25 / 18) * (17 / 6) = 425/108.
Multiplying this by (23 / 17) gives (425 * 23) / (108 * 17) = <<425*23=9775>>9775 / <<108*17=1836>>1836.
The fraction 9775/1836 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: (25 / 18) * (14 / 6) = (25 * 14) / (18 * 6) = <<25*14=350>>350 / <<18*6=108>>108.
The fraction 350/108 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
Therefore, the simplified fraction is 175/54.
### Answer: 175/54

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.

Mixtral 8x22B:

 Reasoning: The result of multiplying 9/1 by 2/17 is t = 18/17.
Multiplying t by itself is (18/17)*(18/17) = (18*18)/(17*17) = <<(18*18)/(17*17)=324/289>>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.

Mixtral 8x22B:

 Reasoning: Multiplying 12 by 2/17 is the same as multiplying 12/1 by 2/17.
The result is (12*2)/17 = <<(12*2)/17=24/17>>24/17.
### Answer: 24/17

Expected answer: 24/17

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (513 / 196) \* (17 / 23) = (513 \* 17) / (196 \* 23) = 8721 / 4508

### Answer: 8721/4508

Expected answer: 8721/4508

Correct? Yes

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.

Mixtral 8x22B:

 Reasoning: (15 / 14) \* (19 / 14) = (15 \* 19) / (14 \* 14) = 285 / 196

### Answer: 285/196

Expected answer: 285/196

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.

Mixtral 8x22B:

 Reasoning: (16 / 15) * (30 / 24) = (16 * 30) / (15 * 24) = 480 / 360 = 4 / 3
### Answer: 4/3

Expected answer: 4/3

Correct? Yes

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.

Mixtral 8x22B:

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

Mixtral 8x22B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(16 / 7) * (23 / 20) = (16 * 23) / (7 * 20) = 368 / 140
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 368 and 140 is 8.
368 / 8 = 46 and 140 / 8 = 17.5
Since we cannot have a fraction with a decimal in the denominator, we can multiply both the numerator and the denominator by 2 to get rid of the decimal.
46 * 2 = 92 and 17.5 * 2 = 35
So, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: To multiply fractions, we multiply the numerators and the denominators separately.
(8 / 3) * (11 / 21) = (8 * 11) / (3 * 21) = 88 / 63
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 88 and 63 is 1.
88 / 1 = 88 and 63 / 1 = 63
So, the simplified fraction is 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.

Mixtral 8x22B:

 Reasoning: The value of r is 56/33.
Multiply r by 9/4: (56/33) * (9/4) = (56 * 9) / (33 * 4) = <<(56*9)/(33*4)=1512/132>>1512/132.
Simplify the fraction: 1512/132 = <<1512/132=11/1>>11.
### Answer: 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.

Mixtral 8x22B:

 Reasoning: The new expression is 13 / (22/16) = 13 * (16/22) = <<13*(16/22)=104/22>>104/22.
Simplify the fraction 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.

Mixtral 8x22B:

 Reasoning: From the previous problem, we know that a = 13/11.
Now, we need to find (a * a), which is (13/11) * (13/11).
(13/11) * (13/11) = (13 * 13) / (11 * 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.

Mixtral 8x22B:

 Reasoning: (16 / 12) * (26 / 22) = (4/3) * (26 / 22) = (4 * 26) / (3 * 22) = 104 / 66
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
104 / 66 = (104 ÷ 2) / (66 ÷ 2) = 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?

Mixtral 8x22B:

 Reasoning: The result of the previous operation is 17/14. Multiplying this by 21/25 gives:
(17/14) * (21/25) = (17 * 21) / (14 * 25) = 357 / 350
### Answer: 357/350

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?

Mixtral 8x22B:

 Reasoning: The operation can be simplified by canceling out the common factor of 5 in the numerator and denominator.
(17 / 5) * (5 / 12) = 17 * (1 / 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.

Mixtral 8x22B:

 Reasoning: (16 / 6) \* (29 / 10) = (16 \* 29) / (6 \* 10) = <<(16 \* 29)/(6 \* 10)=464/60>>464 / 60
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 464 and 60 is 4.
So, 464 / 60 = (464 / 4) / (60 / 4) = <<(464 / 4)/(60 / 4)=116/15>>116 / 15
### Answer: 116/15

Expected answer: 116/15

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.

Mixtral 8x22B:

 Reasoning: Jeremy's result from the previous problem was 45/4.
To multiply this result with the fraction (22/14), we multiply the numerators and the denominators separately.
(45/4) \* (22/14) = (45 \* 22) / (4 \* 14) = 990 / 56
To simplify the fraction, we can divide both the numerator and the 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?

Mixtral 8x22B:

 Reasoning: To multiply two fractions, we multiply the numerators and the denominators separately.
(15/12) \* (27/5) = (15 \* 27) / (12 \* 5) = 405 / 60
To simplify the fraction, we can divide both the numerator and the 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?

Mixtral 8x22B:

 Reasoning: The previous answer was 1, so we need to multiply 1 by 27/15.
1 \* (27 / 15) = 27 / 15
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.
27 / 3 = 9 and 15 / 3 = 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)?

Mixtral 8x22B:

 Reasoning: (7 / 7) = 1 and (16 / 12) = 4/3
So, (7 / 7) \* (16 / 12) = 1 \* (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.

Mixtral 8x22B:

 Reasoning: First, simplify the fractions inside the parentheses.
22/6 = <<22/6=11/3>>11/3
16/24 = <<16/24=2/3>>2/3
Now, multiply the simplified fractions.
(11/3) * (2/3) = <<(11/3)*(2/3)=22/9>>22/9
### Answer: 22/9

Expected answer: 22/9

Correct? Yes