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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, the product of (29/2) and (19/28) is (29*19)/(2*28).
Calculating the numerator and denominator, we get (551/56).
So, the product of (29/2) and (19/28) is 551/56.
### Answer: 551/56

Expected answer: 551/56

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to divide 27 by 12.
27 � 12 = 2 R 3
So, 27 divided by 12 is equal to 2 with a remainder of 3.

Now, we need to multiply 7 by the result of dividing 27 by 12.
7 × 2 = 14

So, the result of the problem is 14.

However, the problem asks for the answer as a simplified fraction.
Since the division result is 2 with a remainder of 3, we can write it as a mixed number: 2 3/12.

Now, we need to multiply 7 by the mixed number 2 3/12.
7 × 2 = 14
7 × 3/12 = 21/12

So, the result of the problem as a simplified fraction is 14 + 21/12.

To add these fractions, we need a common denominator. The least common multiple of 12 and 12 is 12.

14 + 21/12 = 14 × 1/1 + 21/12 = 14/1 + 21/12 = 168/12 + 21/12 = 189/12

So, the result of the problem as a simplified fraction is 189/12.

Expected answer: 63/4

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To find out how much water Susan will use, we need to calculate the new ratio of flour to water. We can do this by multiplying the original ratio of flour to flour (30/30) by the new ratio of flour to water (29/27).

Calculation:
((30 / 30) * (29 / 27)) = (1 * (29 / 27)) = (29 / 27)

So, Susan will use 29/27 parts of water.

Expected answer: 29/27

Correct? Yes

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

DeepSeek 67B:

Reasoning:

First, we can simplify the fractions in the expression:

24 / 22 = 12 / 11
24 / 17 = 12 / 8.5

Now, we can rewrite the expression with the simplified fractions:

((12 / 11) * (12 / 8.5))

Next, we can multiply the numerators and denominators separately:

(12 * 12) / (11 * 8.5)

Now, we can simplify the numerator and denominator:

144 / 93.5

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 0.5:

144 / 0.5 = 288
93.5 / 0.5 = 187

So, the simplified fraction is 288 / 187.

### Answer: 288 / 187

Expected answer: 288/187

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, 25/4 divided by 16/6 is the same as 25/4 multiplied by 6/16.

25/4 * 6/16 = (25*6)/(4*16) = 150/64

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 8.

150/64 = (150/8)/(64/8) = 18.75

So, the result of dividing 25/4 by 16/6 is 18.75.

Expected answer: 75/32

Correct? No

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 3/7 * 26/6 = (3*26)/(7*6) = 78/42.
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 78 and 42 is 6.
So, 78/42 = (78/6)/(42/6) = 13/7.
The answer is: 13/7

Expected answer: 13/7

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out the common factors in the numerator and denominator.
(17 / 10) * (28 / 10) = (17 * 28) / (10 * 10) = 476 / 100
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2.
476 / 100 = (476 / 2) / (100 / 2) = 238 / 50
Finally, we can convert the fraction to decimal form by dividing the numerator by the denominator.
238 / 50 = 4.76
The result of the expression (17 / 10) * (28 / 10) is 4.76.
### Answer: 4.76

Expected answer: 119/25

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To solve the expression ((29 / 14) * (23 / 6)), we need to perform the division and multiplication operations step by step.

First, we perform the division operation:
29 / 14 = 2.0714285714285716

Next, we perform the division operation again:
23 / 6 = 3.8333333333333335

Finally, we perform the multiplication operation:
2.0714285714285716 * 3.8333333333333335 = 7.929203539823009

So, the value of the given expression ((29 / 14) * (23 / 6)) is 7.929203539823009.

### Answer: 7.929203539823009

Expected answer: 667/84

Correct? No

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out common factors in the numerator and denominator.

((18 / 19) * (19 / 6)) = (18 * 19) / (19 * 6) = 342 / 114

Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 342 and 114 is 42.

So, (342 / 114) = (342 / 42) / (114 / 42) = 8 / 3

Therefore, the simplified fraction is 8/3.

### Answer: 8/3

Expected answer: 3

Correct? No

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
19/12 * 20/6 = (19*20)/(12*6) = 380/72
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 380 and 72 is 4.
380/4 = 95
72/4 = 18
So, the simplified fraction is 95/18.
The answer is: 95/18

Expected answer: 95/18

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To find the total fractional representation of the two types of cargo hauled in one day, we need to multiply the fractions representing the cargo in the morning and the cargo in the afternoon.

The cargo in the morning is represented by the fraction 28/21, and the cargo in the afternoon is represented by the fraction 22/4.

To multiply these fractions, we multiply the numerators and the denominators separately:

(28/21) * (22/4) = (28 * 22) / (21 * 4) = 616 / 84

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

616 / 84 = (616 / 2) / (84 / 2) = 308 / 42

Finally, we simplify the fraction again by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

308 / 42 = (308 / 2) / (42 / 2) = 154 / 21

So, the total fractional representation of the two types of cargo hauled in one day is 154/21.

Expected answer: 22/3

Correct? Yes

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

DeepSeek 67B:

First, we simplify the expression inside each set of parentheses:
(16 / 4) / (24 / 21) = 4 / (24 / 21)
Next, we simplify the expression by dividing the numerator by the denominator:
4 / (24 / 21) = 4 * (21 / 24)
Finally, we simplify the fraction:
4 * (21 / 24) = 4 * (7 / 8) = 28 / 8 = 7 / 2
The result is 7/2.
### Answer: 7/2

Expected answer: 7/2

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, the product of 5/27 and 15/2 is (5*15)/(27*2) = 75/54.
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 9.
So, 75/54 simplifies to 25/18.
The answer is: 25/18

Expected answer: 25/18

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, (15 / 13) * (19 / 7) = (15 * 19) / (13 * 7) = 285 / 91.
To simplify the fraction, we find the greatest common divisor (GCD) of 285 and 91.
The GCD of 285 and 91 is 1.
So, the simplified fraction is 285 / 91.
### Answer: 285 / 91

Expected answer: 285/91

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators together and the denominators together.
So, the product of 23/22 and 27/20 is (23*27)/(22*20).
Calculating the numerator and denominator, we get 621/440.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1.
So, the simplified fraction is 621/440.
### Answer: 621/440

Expected answer: 621/440

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To calculate the result of the given operation, we need to multiply the numerators and denominators separately.

(12 / 25) * (20 / 4) = (12 * 20) / (25 * 4)

Now, we can simplify the numerator and denominator separately.

Numerator: 12 * 20 = 240
Denominator: 25 * 4 = 100

So, the simplified fraction is 240 / 100.

To further simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).

GCD of 240 and 100 is 40.

240 / 40 = 6
100 / 40 = 2.5

So, the simplified fraction is 6 / 2.5.

### Answer: 6/2.5

Expected answer: 12/5

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
14/10 * 30/5 = (14*30)/(10*5) = 420/50
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 420 and 50 is 10.
So, 420/50 = (420/10)/(50/10) = 42/5
The simplified fraction is 42/5.
### Answer: 42/5

Expected answer: 42/5

Correct? Yes

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

DeepSeek 67B:

To find out how many batches of cookies the baker can make, we need to divide the total amount of sugar needed for one batch (26 cups) by the fraction of a batch that can be made (29/14).

So, we have:

(26 / 1) / (29 / 14)

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

(26 / 1) * (14 / 29)

Now, we can multiply the numerators and denominators separately:

(26 * 14) / (1 * 29)

364 / 29

The baker can make 364/29 batches of cookies.

Expected answer: 364/29

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To evaluate the expression, we need to perform the division and multiplication operations.

First, let's perform the division:
27 � 10 = 2 R 7
9 � 4 = 2 R 1

Now, let's perform the multiplication:
(2 R 7) * (2 R 1) = 4 R 14

So, the simplified fraction is 4 R 14, which can be written as 4 14/10.

### Answer: 4 14/10

Expected answer: 243/40

Correct? No

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

DeepSeek 67B:

Reasoning:

First, we need to simplify the expression by dividing the numerator and the denominator of each fraction by their greatest common divisor (GCD).

The GCD of 24 and 11 is 1, so the fraction 24/11 remains the same.

The GCD of 27 and 26 is 1, so the fraction 27/26 remains the same.

Now, we can multiply the two fractions:

(24/11) * (27/26) = (24 * 27) / (11 * 26) = 648 / 286

Next, we need to simplify the fraction 648/286 by dividing both the numerator and the denominator by their GCD.

The GCD of 648 and 286 is 14, so we can simplify the fraction as follows:

648 / 14 = 46
286 / 14 = 20

So, the simplified fraction is 46/20.

### Answer: 46/20

Expected answer: 324/143

Correct? No

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators together and the denominators together.
So, 26/9 * 17/13 = (26 * 17) / (9 * 13) = 442 / 117.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 442 and 117 is 1.
So, the simplified fraction is 442 / 117.
### Answer: 442/117

Expected answer: 34/9

Correct? Yes

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

DeepSeek 67B:

To solve the expression, we first need to simplify the fractions in the numerator and denominator.

Numerator: 28 / 16
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 28 and 16 is 4.
28 � 4 = 7
16 � 4 = 4
So, 28 / 16 simplifies to 7 / 4.

Denominator: 27 / 24
We can simplify this fraction by dividing both the numerator and denominator by their GCD. The GCD of 27 and 24 is 3.
27 � 3 = 9
24 � 3 = 8
So, 27 / 24 simplifies to 9 / 8.

Now, we can rewrite the expression as:
(7 / 4) / (9 / 8)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(7 / 4) * (8 / 9)

Now, we multiply the numerators and denominators:
(7 * 8) / (4 * 9)
56 / 36

Finally, we simplify the fraction by dividing both the numerator and denominator by their GCD. The GCD of 56 and 36 is 4.
56 � 4 = 14
36 � 4 = 9

So, the result of the expression is 14 / 9.

Expected answer: 14/9

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the expression by dividing 15 by 3 and 19 by 26.
15 / 3 = 5
19 / 26 = 19/26
Now, we can multiply the simplified fractions:
5 * (19/26) = 95/26
The expression ((15 / 3) * (19 / 26)) simplifies to 95/26.
### Answer: 95/26

Expected answer: 95/26

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To find out how much of the ingredient they will require, we need to multiply the amount of the recipe they want to make by the amount of the ingredient required for the whole recipe.

The amount of the recipe they want to make is 30/4, and the amount of the ingredient required for the whole recipe is 19/28.

So, the amount of the ingredient they will require is (30/4) * (19/28).

To multiply these fractions, we need to multiply the numerators and denominators separately.

The numerator of the product is (30 * 19) = 570.
The denominator of the product is (4 * 28) = 112.

So, the amount of the ingredient they will require is 570/112.

To simplify this fraction, we need to find the greatest common divisor (GCD) of 570 and 112.

The GCD of 570 and 112 is 4.

Dividing both the numerator and denominator by 4, we get 570/4 = 142.5 and 112/4 = 28.

So, the amount of the ingredient they will require is 142.5/28.

To simplify this fraction further, we need to find the GCD of 142.5 and 28.

The GCD of 142.5 and 28 is 1.

So, the amount of the ingredient they will require is 142.5/28.

Therefore, the bakery will require 142.5/28 of the ingredient.

### Answer: 142.5/28

Expected answer: 285/56

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the expression inside the parentheses.

(5 / 2) = 2.5
(26 / 15) = 1.73333 (approximately)

Now, we can substitute these values back into the original expression.

((5 / 2) / (26 / 15)) = (2.5 / 1.73333)

To divide by a fraction, we can multiply by its reciprocal.

(2.5 / 1.73333) = 2.5 * (1 / 1.73333)

Now, we can multiply the numerators and denominators.

(2.5 * 1) / (1.73333 * 1) = 2.5 / 1.73333

Finally, we can simplify the fraction.

2.5 / 1.73333 = 1.45 (approximately)

So, the result of ((5 / 2) / (26 / 15)) is approximately 1.45.

Expected answer: 75/52

Correct? No

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

DeepSeek 67B:

Reasoning:
To calculate the result of the expression (9/3) * (27/28), we first simplify each fraction and then multiply them.

Simplifying the fractions:
9/3 = 3 (since 9 divided by 3 is 3)
27/28 remains the same as it is already in its simplest form.

Multiplying the fractions:
3 * (27/28) = 81/28

So, the result of the expression (9/3) * (27/28) is 81/28.

Expected answer: 81/28

Correct? Yes

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

DeepSeek 67B:

((15 / 13) * (24 / 24)) = (15 * 24) / (13 * 24) = 360 / 312 = 15 / 13

Expected answer: 15/13

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
(9 / 7) * (25 / 30) = (9 * 25) / (7 * 30) = 225 / 210
Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 225 and 210 is 15.
So, 225 / 15 = 15 and 210 / 15 = 14
Therefore, the simplified fraction is 15 / 14.
### Answer: 15 / 14

Expected answer: 15/14

Correct? Yes

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

DeepSeek 67B:

To solve the problem, we need to simplify the fractions and then perform the division.

First, let's simplify the fractions:

9 / 8 = 1.125
20 / 18 = 1.111 (approximately)

Now, let's perform the division:

1.125 / 1.111 = 1.013 (approximately)

To express this as a simplified fraction, we need to find the common denominator for 101 and 103 (the numerators and denominators of the decimal approximation). The common denominator is 1030.

So, 1.013 as a simplified fraction is 101/103.

Expected answer: 81/80

Correct? No

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the fractions in the expression.
The numerator of the first fraction is 30 and the denominator is 6, so the fraction is 30/6.
The numerator of the second fraction is 13 and the denominator is 9, so the fraction is 13/9.
Now, we can rewrite the expression as (30/6) / (13/9).
Next, we can simplify the fractions by dividing the numerator and denominator of each fraction by their greatest common divisor (GCD).
The GCD of 30 and 6 is 6, so we can simplify 30/6 to 5/1.
The GCD of 13 and 9 is 1, so we can simplify 13/9 to 13/9.
Now, we can rewrite the expression as (5/1) / (13/9).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 13/9 is 9/13.
So, we can rewrite the expression as (5/1) * (9/13).
Now, we can multiply the numerators and denominators of the fractions.
The numerator of the first fraction is 5 and the denominator is 1, so the fraction is 5/1.
The numerator of the second fraction is 9 and the denominator is 13, so the fraction is 9/13.
Multiplying the numerators gives us 5 * 9 = 45.
Multiplying the denominators gives us 1 * 13 = 13.
So, the expression simplifies to 45/13.
Therefore, the result of performing the operation (30 / 6) / (13 / 9) is 45/13.
The answer is: 45/13

Expected answer: 45/13

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we divide 30 by 18 to get 1.6666666666666667.
Then, we multiply this result by the fraction 18/6, which is equal to 3.
So, the final result is 1.6666666666666667 * 3 = 5.
### Answer: 5

Expected answer: 5

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we perform the division operation:
20 / 2 = 10
Then, we perform the division operation again:
2 / 18 = 1 / 9
Finally, we perform the multiplication operation:
10 * (1 / 9) = 10 / 9
So, the result of the problem is 10 / 9.

Expected answer: 10/9

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To solve the problem, we need to multiply the numerators and denominators of the fractions separately.

Numerator: 11 * 29 = 319
Denominator: 9 * 6 = 54

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

The fraction 319/54 cannot be simplified further as both the numerator and the denominator are prime numbers.

Answer: 319 / 54

Expected answer: 319/54

Correct? Yes

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

DeepSeek 67B:

To calculate the result of the given mathematical operation, we need to perform the division and multiplication operations in the given order.

First, we perform the division operation:
30 � 7 = 4.2857142857142855

Next, we perform the division operation:
16 � 19 = 0.8421052631578947

Finally, we perform the multiplication operation:
4.2857142857142855 * 0.8421052631578947 = 3.6000000000000005

So, the result of the given mathematical operation is 3.6.

Expected answer: 480/133

Correct? No

Problem: Calculate the product of 25/22 and 20/3 and write your answer as a simplified fraction.

DeepSeek 67B:

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

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

To simplify the fraction, we need to find the greatest common divisor (GCD) of 500 and 66.

The prime factors of 500 are 2, 5, 5, 2, 5, 5.
The prime factors of 66 are 2, 3, 3, 11.

The GCD of 500 and 66 is 2.

So, we can simplify the fraction by dividing both the numerator and the denominator by 2.

500/2 = 250
66/2 = 33

Therefore, the simplified fraction is 250/33.

### Answer: 250/33

Expected answer: 250/33

Correct? Yes

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

DeepSeek 67B:

To solve this problem, we need to simplify the expression ((29 / 2) / (23 / 19)).
First, we simplify the numerator and denominator separately:
(29 / 2) = 14.5
(23 / 19) = 1.2105263157894736
Now, we divide the numerator by the denominator:
14.5 / 1.2105263157894736 = 11.95474479095251
Therefore, the result of the expression is 11.95474479095251.
However, since the question asks for the answer as a simplified fraction, we need to convert the decimal to a fraction.
11.95474479095251 can be written as 1195474479095251 / 1000000000000000.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1.
Therefore, the simplified fraction is 1195474479095251 / 1000000000000000.
### Answer: 1195474479095251 / 1000000000000000

Expected answer: 551/46

Correct? No

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

DeepSeek 67B:

Reasoning:
To solve the expression, we need to multiply the numerators and denominators separately.

(5 / 3) * (27 / 13) = (5 * 27) / (3 * 13) = 135 / 39

Now, we need to simplify the fraction. The greatest common divisor (GCD) of 135 and 39 is 3.

135 / 3 = 45
39 / 3 = 13

So, the simplified fraction is 45 / 13.

### Answer: 45 / 13

Expected answer: 45/13

Correct? Yes

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

DeepSeek 67B:

The expression (29 / 29) * (1 / 1) simplifies to 1 * 1, which equals 1.

Expected answer: 1

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, the product of 11/19 and 22/7 is (11*22)/(19*7).
Calculating the numerator and denominator, we get 242/133.
To simplify the fraction, we find the greatest common divisor (GCD) of 242 and 133, which is 1.
Since the GCD is 1, the fraction is already in its simplest form.
Therefore, the product of 11/19 and 22/7 is 242/133.
### Answer: 242/133

Expected answer: 242/133

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 21/30 * 19/5 = (21*19)/(30*5) = 399/150.
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 1.
So, 399/150 cannot be simplified further.
### Answer: 399/150

Expected answer: 133/50

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 11/15 * 23/8 = (11*23)/(15*8) = 253/120.
The fraction 253/120 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
So, 253/120 cannot be simplified further.
### Answer: 253/120

Expected answer: 253/120

Correct? Yes

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

DeepSeek 67B:

To simplify the expression, we can cancel out common factors in the numerator and denominator.
The common factor in the numerator is 3, and the common factor in the denominator is 9.
So, we can simplify the expression as follows:
(29 / 16) * (21 / 27) = (29 * 3) / (16 * 9) = 87 / 144
Therefore, the result of the expression is 87/144.
### Answer: 87/144

Expected answer: 203/144

Correct? No

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

DeepSeek 67B:

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, (28 / 1) divided by (30 / 27) is the same as (28 / 1) multiplied by (27 / 30).
This simplifies to (28 * 27) / (1 * 30) = 756 / 30.
To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 2.
So, 756 / 30 simplifies to 378 / 15.
Therefore, the result is 378 / 15.
### Answer: 378/15

Expected answer: 126/5

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out common factors in the numerator and denominator.

((25 / 25) * (20 / 7)) = (1 * (20 / 7)) = (20 / 7)

So, the result is 20/7.
### Answer: 20/7

Expected answer: 20/7

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 5 * 16/27 = (5 * 16) / (1 * 27) = 80/27.
The fraction 80/27 is already in its simplest form.
### Answer: 80/27

Expected answer: 80/27

Correct? Yes

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

DeepSeek 67B:

First, we simplify the expression inside the parentheses:
27 / 3 = 9
12 / 12 = 1
Now, we substitute these values back into the original expression:
(9 / 1) = 9
So, the result of the expression is 9.

Expected answer: 9

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To calculate the result of the given operation, we need to multiply the numerators and denominators separately.

(15 / 16) * (29 / 2) = (15 * 29) / (16 * 2)

Now, we can simplify the numerator and denominator separately.

Numerator: 15 * 29 = 435
Denominator: 16 * 2 = 32

So, the simplified fraction is 435 / 32.

### Answer: 435 / 32

Expected answer: 435/32

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the fractions in the parentheses:
6 / 2 = 3
13 / 9 = 1 4/9

Now, we can substitute these simplified fractions back into the original equation:
(3 / (1 4/9))

Next, we need to convert the mixed number back into an improper fraction:
1 4/9 = 13/9

Now, we can substitute this improper fraction back into the original equation:
(3 / (13/9))

Finally, we can divide the fractions:
(3 / (13/9)) = 3 * (9/13) = 27/13

So, the solution to the equation is 27/13.

Expected answer: 27/13

Correct? Yes

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

DeepSeek 67B:

To divide a fraction by a fraction, we multiply by the reciprocal of the second fraction.
So, we have \[\frac{7}{1} \div \frac{15}{9} = \frac{7}{1} \cdot \frac{9}{15}.\]
Simplifying, we get \[\frac{7}{1} \cdot \frac{9}{15} = \frac{7 \cdot 9}{1 \cdot 15} = \frac{63}{15}.\]
To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3.
So, \[\frac{63}{15} = \frac{63 \div 3}{15 \div 3} = \frac{21}{5}.\]
Therefore, the answer is \[\boxed{\frac{21}{5}}.\].
The answer is: \frac{21}{5}

Expected answer: 21/5

Correct? Yes

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

DeepSeek 67B:

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

Expected answer: 207/10

Correct? Yes

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

DeepSeek 67B:

Reasoning:

First, we need to perform the division operation: 18 / 4 = 4.5

Next, we need to multiply the result by the fraction 10 / 11: 4.5 * (10 / 11) = 45 / 11

So, the final answer is 45 / 11.

### Answer: 45 / 11

Expected answer: 45/11

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 24/23 * 23/3 = (24*23)/(23*3) = 552/69.
The answer is 552/69

Expected answer: 8

Correct? Yes

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

DeepSeek 67B:

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, (20 / 13) / (17 / 16) = (20 / 13) * (16 / 17).
To multiply fractions, we multiply the numerators and multiply the denominators.
So, (20 / 13) * (16 / 17) = (20 * 16) / (13 * 17).
Simplifying the numerator and denominator, we get (320) / (221).
Therefore, the solution is 320 / 221.
### Answer: 320 / 221

Expected answer: 320/221

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we perform the division operations:
5 divided by 5 = 1
4 divided by 1 = 4
Then, we perform the multiplication operation:
1 multiplied by 4 = 4
### Answer: 4

Expected answer: 4

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To solve the problem, we need to perform the division and multiplication operations.

First, we perform the division operation: 30 / 23 = 1 R 7. This means that 30 divided by 23 is 1 with a remainder of 7.

Next, we multiply the remainders: 7 * 19 = 133.

Finally, we divide the product by the divisor: 133 / 24 = 5 R 13. This means that 133 divided by 24 is 5 with a remainder of 13.

So, the simplified fraction for ((30 / 23) * (19 / 24)) is 5 R 13.

### Answer: 5 R 13

Expected answer: 95/92

Correct? No

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out common factors in the numerator and denominator.

(23 / 26) * (16 / 1) = (1 * 23) / (2 * 13) * (16 / 1)

Now, we can cancel out the common factor of 1 in the numerator and denominator of the first fraction:

(23 / 26) * (16 / 1) = (23 / 13) * (16 / 1)

Now, we can cancel out the common factor of 1 in the numerator and denominator of the second fraction:

(23 / 26) * (16 / 1) = (23 / 13) * (16 / 1) = (23 * 16) / (13 * 1)

Now, we can simplify the expression by multiplying the numerators and denominators:

(23 / 26) * (16 / 1) = (23 * 16) / (13 * 1) = 368 / 13

So, the simplified expression is 368 / 13.

### Answer: 368 / 13

Expected answer: 184/13

Correct? No

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by first simplifying the fractions in the numerator and denominator.

21 / 1 = 21
26 / 20 = 13 / 10

Now, we can rewrite the expression as:

(21 / (13 / 10))

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 13 / 10 is 10 / 13.

So, the expression becomes:

(21 * (10 / 13))

Now, we can multiply the numerators and denominators:

(21 * 10) / (13)

210 / 13

The fraction 210 / 13 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1.

So, the simplified fraction is:

210 / 13

Therefore, the answer is 210 / 13.

Expected answer: 210/13

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 24/19 * 21/19 = (24*21)/(19*19) = 504/361.
The answer is: \frac{504}{361}

Expected answer: 504/361

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To find the total amount of sugar and flour needed for the larger cake, we need to multiply the amount of sugar and flour by the same factor. Let's call this factor x.

The amount of sugar needed for the larger cake is (12/2) * x = 6x.
The amount of flour needed for the larger cake is (17/14) * x = (17/14)x.

To find the total amount of sugar and flour needed, we add the two amounts together:

Total amount = 6x + (17/14)x

To simplify the expression, we need to find a common denominator for 6 and 17/14. The common denominator is 14.

Total amount = (6 * 7/7)x + (17/14)x
Total amount = (42/7)x + (17/14)x
Total amount = (42 + 17)/14x
Total amount = 59/14x

So, the total amount of sugar and flour needed for the larger cake is 59/14 times the factor x.

### Answer: 59/14

Expected answer: 51/7

Correct? No

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the fractions in the numerator and denominator.

21 / 16 = 21/16 = 1.3125
27 / 23 = 27/23 = 1.1739

Now, we can perform the division operation:

(1.3125) / (1.1739) = 1.1158

To represent this as a simplified fraction, we need to find the common denominator for 11158 and 10000 (the number of decimal places). The common denominator is 10000.

11158 / 10000 = 1.1158

So, the simplified fraction is 11158/10000.

### Answer: 11158/10000

Expected answer: 161/144

Correct? No

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
(11 / 20) * (24 / 12) = (11 * 24) / (20 * 12) = 264 / 240

Simplifying the fraction:
264 / 240 = 132 / 120 = 66 / 60 = 33 / 30 = 11 / 10

Answer: 11 / 10

Expected answer: 11/10

Correct? Yes

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

DeepSeek 67B:

To solve this problem, we need to multiply the fractions ((6 / 19) * (28 / 2)).

First, let's simplify the fractions:
6 / 19 cannot be simplified further.
28 / 2 simplifies to 14.

Now, let's multiply the fractions:
(6 / 19) * (14 / 1) = 84 / 19

The simplified fraction is 84 / 19.

Expected answer: 84/19

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to perform the division operation: 12 / 14 = 0.8571428571428571.
Next, we multiply the resulting decimal by the second fraction: 0.8571428571428571 * (28 / 5) = 24.000000000000002.
Finally, we simplify the resulting fraction to its lowest terms: 24 / 1 = 24.
### Answer: 24

Expected answer: 24/5

Correct? No

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

DeepSeek 67B:

To calculate the result of the expression (19 / 3) * (8 / 15), we first need to simplify the fractions.

19 / 3 can be simplified to 6 1/3, and 8 / 15 can be simplified to 8/15.

Now, we can multiply the two fractions:

(6 1/3) * (8/15) = (6 * 8 + 1 * 8) / (3 * 15) = (48 + 8) / 45 = 56 / 45.

So, the result of the expression is 56/45.

Expected answer: 152/45

Correct? No

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

DeepSeek 67B:

Reasoning:
First, we need to perform the division operation:
15 / 3 = 5
Then, we multiply the result by the second fraction:
5 * (7 / 25) = 35 / 25
Finally, we simplify the fraction:
35 / 25 = 7 / 5

Answer: 7/5

Expected answer: 7/5

Correct? Yes

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

DeepSeek 67B:

Reasoning:
The equation can be simplified as follows:
(20 / 10) * (10 / 1) = 2 * 10 = 20
The answer is 20

Expected answer: 20

Correct? Yes

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

DeepSeek 67B:

Reasoning:

First, we need to simplify the fractions in the parentheses:

27/18 = 9/6 = 3/2
19/8 = 23/16

Now, we can multiply the fractions:

(3/2) * (23/16) = 69/32

So, the result is 69/32.

Expected answer: 57/16

Correct? No

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 29/5 * 13/24 = (29*13)/(5*24) = 377/120
The fraction 377/120 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 377 and 120 is 1.
So, 377/120 simplifies to 377/120.
### Answer: 377/120

Expected answer: 377/120

Correct? Yes

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

DeepSeek 67B:

To simplify the expression, we can simplify each fraction separately and then divide.
The first fraction, 29/17, can be simplified to 17/17, which is 1.
The second fraction, 27/22, can be simplified to 27/22.
Now, we can divide 1 by 27/22.
To divide by a fraction, we can multiply by its reciprocal.
So, we have 1 * 22/27.
This simplifies to 22/27.
Therefore, the value of the expression is 22/27.
The answer is: \frac{22}{27}

Expected answer: 638/459

Correct? No

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

DeepSeek 67B:

Reasoning:
First, we can simplify the fractions in the calculation:
(27 / 6) * (25 / 5) = (27/6) * (5/1)
Now, we can multiply the numerators and denominators separately:
(27 * 5) / (6 * 1) = 135 / 6
Finally, we can simplify the fraction:
135 / 6 = 22.5
So, the result of the calculation (27 / 6) * (25 / 5) is 22.5.
### Answer: 22.5

Expected answer: 45/2

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can multiply the numerators and denominators separately.
(13 * 1) / (1 * 6) = 13 / 6
The answer is: 13/6

Expected answer: 13/6

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 25/20 * 11/6 = (25*11)/(20*6) = 275/120.
To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 5.
So, 275/120 simplifies to (275/5)/(120/5) = 55/24.
### Answer: 55/24

Expected answer: 55/24

Correct? Yes

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

DeepSeek 67B:

To simplify the expression, we first need to simplify the fractions in the numerator and denominator.

The numerator is 7/2, which cannot be simplified further.

The denominator is 25/10, which can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5.

25/10 simplifies to 5/2.

Now we can rewrite the expression as (7/2) / (5/2).

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

So, (7/2) / (5/2) becomes (7/2) * (2/5).

Multiplying the numerators and denominators, we get (7*2) / (2*5) = 14/10.

Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2.

14/10 simplifies to 7/5.

Therefore, the value of (7/2) / (25/10) is 7/5.

### Answer: 7/5

Expected answer: 7/5

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply two fractions, we multiply the numerators together and the denominators together.
So, 15/16 * 29/27 = (15 * 29) / (16 * 27) = 435/432.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 435 and 432 is 9, so we divide both numbers by 9 to get the simplified fraction: 435/9 = 48.
### Answer: 48

Expected answer: 145/144

Correct? No

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

DeepSeek 67B:

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

30 / 25 = 1.2
25 / 10 = 2.5

Now, we can multiply the simplified values:

1.2 * 2.5 = 3

So, the answer is 3.

Expected answer: 3

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, the product of 27/10 and 27/3 is (27*27)/(10*3) = 729/30.
To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 9.
So, 729/30 simplifies to 81/3.
The answer is: 81

Expected answer: 243/10

Correct? No

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

DeepSeek 67B:

Reasoning:
First, we need to perform the division operations:
10 / 8 = 1.25
30 / 26 = 1.1538461538461537 (approximately)

Next, we multiply the results:
1.25 * 1.1538461538461537 = 1.4423076923076923

To express this as a simplified fraction, we can multiply the numerator and denominator by 100 to get rid of the decimal:
1.4423076923076923 * 100 = 144.23076923076923

Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 144 and 100 is 4:
144 / 4 = 36
100 / 4 = 25

So, the simplified fraction is 36/25.

Answer: 36/25

Expected answer: 75/52

Correct? No

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

DeepSeek 67B:

Reasoning:
To evaluate the expression, we need to perform the division and multiplication operations.

First, we perform the division: 20 / 22 = 10 / 11.

Next, we multiply the resulting fractions: (10 / 11) * (14 / 11) = 140 / 121.

So, the simplified fraction is 140 / 121.

### Answer: 140 / 121

Expected answer: 140/121

Correct? Yes

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

DeepSeek 67B:

The given operation is ((25 / 8) * (3 / 4)).

First, we perform the division: 25 / 8 = 3.125.

Then, we multiply the result by the fraction: 3.125 * (3 / 4) = 2.34375.

The result is a decimal, not a fraction. However, if we want to express it as a fraction, we can write it as 234375 / 100000.

The result does not signify any form of division amongst a group or sharing something in portions. It is simply the result of the given mathematical operation.

Expected answer: 75/32

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To calculate the value of the expression, we need to perform the multiplication operation.

First, we can simplify the fractions:
29 / 1 = 29
8 / 15 = 0.5333 (rounded to four decimal places)

Now, we can multiply the two numbers:
29 * 0.5333 = 15.4 (rounded to one decimal place)

So, the value of the expression is approximately 15.4.

Expected answer: 232/15

Correct? No

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

DeepSeek 67B:

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

Expected answer: 754/255

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we simplify the fractions in the expression:
25 / 5 = 5
16 / 8 = 2
Now, we substitute the simplified fractions back into the expression:
(5 * 2) = 10
So, the value of the expression ((25 / 5) * (16 / 8)) is 10.
### Answer: 10

Expected answer: 10

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
(23 / 4) * (10 / 12) = (23 * 10) / (4 * 12) = 230 / 48
To simplify the fraction, we find the greatest common divisor (GCD) of 230 and 48, which is 2.
230 / 2 = 115
48 / 2 = 24
So, the simplified fraction is 115 / 24.
### Answer: 115 / 24

Expected answer: 115/24

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
(21 / 26) * (20 / 9) = (21 * 20) / (26 * 9) = 420 / 234
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 420 and 234 is 6.
So, 420 / 6 = 70 and 234 / 6 = 39.
Therefore, the simplified fraction is 70 / 39.
### Answer: 70 / 39

Expected answer: 70/39

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we need to simplify the expression by dividing the numerator and denominator of each fraction separately.

17 / 13 = 1 R 4
15 / 6 = 2 R 3

So, the expression becomes ((4 / 13) * (3 / 2)).

Now, we can multiply the numerators and denominators separately.

Numerator: 4 * 3 = 12
Denominator: 13 * 2 = 26

So, the simplified fraction is 12 / 26.

To further simplify the fraction, we need to find the greatest common divisor (GCD) of 12 and 26.

The factors of 12 are: 1, 2, 3, 4, 6, and 12.
The factors of 26 are: 1, 2, 13, and 26.

The GCD of 12 and 26 is 2.

Now, we can divide both the numerator and denominator by the GCD.

Numerator: 12 / 2 = 6
Denominator: 26 / 2 = 13

So, the simplified fraction is 6 / 13.

Answer: 6 / 13

Expected answer: 85/26

Correct? No

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

DeepSeek 67B:

Reasoning:
To calculate the result of the given equation, we can multiply the numerators and denominators separately.

Numerator: 25 * 17 = 425
Denominator: 18 * 6 = 108

So, the result of the equation is 425/108.

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

GCD of 425 and 108 is 1.

So, the simplified fraction is 425/108.

### Answer: 425/108

Expected answer: 425/108

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, 9/1 * 2/17 = (9*2)/(1*17) = 18/17.
The fraction 18/17 is already in its simplest form.
### Answer: 18/17

Expected answer: 18/17

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can simplify the given expression by canceling out the common factors in the numerator and denominator.

(27 / 14) * (19 / 14) = (27 * 19) / (14 * 14)

Now, we can simplify the numerator and denominator separately.

Numerator: 27 * 19 = 513
Denominator: 14 * 14 = 196

So, the simplified fraction is 513 / 196.

### Answer: 513 / 196

Expected answer: 513/196

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out common factors in the numerator and denominator.

(16 / 5) * (5 / 15) = (16 * 5) / (5 * 5 * 3) = 80 / 75

So, the simplified fraction is 80/75.
### Answer: 80/75

Expected answer: 16/15

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
(8 / 3) * (18 / 21) = (8 * 18) / (3 * 21) = 144 / 63.
To simplify the fraction, we find the greatest common divisor (GCD) of 144 and 63, which is 9.
144 / 9 = 16 and 63 / 9 = 7.
So, the simplified fraction is 16 / 7.
### Answer: 16 / 7

Expected answer: 16/7

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To evaluate the expression, we first need to simplify the fractions.

14 / 6 = 7 / 3
22 / 16 = 11 / 8

Now, we can substitute these simplified fractions back into the expression:

((7 / 3) / (11 / 8))

Next, we need to divide the fractions. To do this, we multiply the first fraction by the reciprocal of the second fraction:

(7 / 3) * (8 / 11)

Now, we can multiply the numerators and denominators:

(7 * 8) / (3 * 11) = 56 / 33

So, the simplified fraction is 56 / 33.

Expected answer: 56/33

Correct? Yes

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

DeepSeek 67B:

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

Expected answer: 200/39

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To solve the problem, we need to multiply the numerators and denominators separately.

Numerator: 16 * 26 = 416
Denominator: 16 * 22 = 352

So, the simplified fraction is 416 / 352.

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

The GCD of 416 and 352 is 16.

Divide both the numerator and the denominator by the GCD:

Numerator: 416 / 16 = 26
Denominator: 352 / 16 = 22

So, the simplified fraction is 26 / 22.

### Answer: 26 / 22

Expected answer: 13/11

Correct? Yes

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

DeepSeek 67B:

Reasoning:
We can simplify the expression by canceling out common factors in the numerator and denominator.

(17 / 5) * (5 / 14) = (17 * 5) / (5 * 14) = 85 / 70

Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

The GCD of 85 and 70 is 5.

85 / 5 = 17
70 / 5 = 14

So, the simplified fraction is 17 / 14.

### Answer: 17/14

Expected answer: 17/14

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, you multiply the numerators together and the denominators together.
So, (16 / 6) * (29 / 27) = (16 * 29) / (6 * 27) = 464 / 162.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 464 and 162 is 2, so we divide both numbers by 2 to get 232 / 81.
Therefore, the simplified fraction is 232 / 81.
### Answer: 232 / 81

Expected answer: 232/81

Correct? Yes

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

DeepSeek 67B:

Reasoning:
The car consumes 16/10 gallons of petrol every mile.
The route is 13/17 of a mile long.
To find out how many gallons of petrol the car will have consumed when you finish the drive, we need to multiply the consumption per mile by the length of the route.
So, the car will have consumed (16/10) * (13/17) = 208/170 gallons of petrol when you finish the drive.
### Answer: 208/170

Expected answer: 104/85

Correct? Yes

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

DeepSeek 67B:

To solve this problem, we need to divide the numerators and divide the denominators.
(29 / 10) / (18 / 16) = (29 * 16) / (10 * 18) = 464 / 180
To simplify the fraction, we need to find the greatest common divisor (GCD) of 464 and 180.
The GCD of 464 and 180 is 4, so we divide both the numerator and the denominator by 4.
464 / 4 = 116
180 / 4 = 45
Therefore, (29 / 10) / (18 / 16) = 116 / 45
The answer is: 116/45

Expected answer: 116/45

Correct? Yes

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

DeepSeek 67B:

Reasoning:
To multiply fractions, we multiply the numerators and multiply the denominators.
So, (15/12) * (27/3) = (15 * 27) / (12 * 3) = 405/36.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 405 and 36 is 9.
So, 405/36 = (405/9) / (36/9) = 45/4.
The simplified fraction is 45/4.
### Answer: 45/4

Expected answer: 45/4

Correct? Yes

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

DeepSeek 67B:

Reasoning:
The expression (7 / 7) * (12 / 12) can be simplified by canceling out the common factors in the numerator and denominator.

(7 / 7) * (12 / 12) = 1 * 1 = 1

So, the answer to the math problem is 1.

Expected answer: 1

Correct? Yes

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

DeepSeek 67B:

Reasoning:
First, we simplify the fractions:
28/6 = 14/3
16/24 = 2/3

Now, we perform the multiplication:
(14/3) * (2/3) = 28/9

So, the result is 28/9.

Expected answer: 28/9

Correct? Yes