MathCAMPS

🔗 Problem

Problem: Complete the following comparison between two fractions. (1 / 8) _ (4 / 1).

DeepSeek Math 7B Base:

 Reasoning: 1/8 is less than 1/2, and 4/1 is greater than 1/2.
Therefore, 1/8 is less than 4/1.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Using the same approach we used before, now think about the comparison between (6 / 8) and (4 / 1). Complete the comparison using the same symbols (<, >, =). (6 / 8) _ (4 / 1). This is similar to the previous problem but now you are comparing a different fraction with the same whole number.

DeepSeek Math 7B Base:

  Reasoning: 6/8 is less than 1/2, and 4/1 is greater than 1/2.
Therefore, 6/8 is less than 4/1.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Determine which symbol appropriately fills in the blank (either '<', '=', or '>') to accurately compare these two fractions: (7 / 2) _ (10 / 6)

DeepSeek Math 7B Base:

 Reasoning: 7/2 = <<7/2=3.5>>3.5 and 10/6 = <<10/6=1.6666666666666667>>1.6666666666666667.
Since 3.5 is greater than 1.6666666666666667, 7/2 is greater than 10/6.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Let's modify our previous problem slightly and continue the exercise. Fill in the blank with one of the following symbols: <, >, or =, to properly compare the two fractions. (6 / 2) _ (10 / 6)

DeepSeek Math 7B Base:

  Reasoning: 6/2 = <<6/2=3>>3 and 10/6 = <<10/6=1.6666666666666667>>1.6666666666666667.
Since 3 is greater than 1.6666666666666667, 6/2 is greater than 10/6.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Complete the following comparison by filling in the blank (<, >, or =): (6 / 8) _ (8 / 7)

DeepSeek Math 7B Base:

 (6 / 8) = (8 / 7)

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the values of the two fractions below by filling in the blank with <, >, or =. (9 / 3) _ (7 / 1)

DeepSeek Math 7B Base:

 9/3 = 3 and 7/1 = 7.
3 < 7.
(9 / 3) < (7 / 1)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the original problem where we compared the fractions (9 / 3) and (7 / 1). Now, instead of comparing it with (7 / 1), let's compare it with the fraction (1 / 1). Fill in the blank in the new problem: (9 / 3) _ (1 / 1) Use the symbols <, >, or = to make the correct comparison.

DeepSeek Math 7B Base:

  9/3 = 3 and 1/1 = 1.
3 > 1.
(9 / 3) > (1 / 1)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Fill in the blank with one of the following signs: <, >, or = (5 / 3) _ (10 / 5)

DeepSeek Math 7B Base:

 5/3 = 10/6, and 10/6 > 10/5.

### Answer: >

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the values of the two fractions by filling in the blank with <, >, or =. Here are the fractions: (3 / 2) _ (9 / 10)

DeepSeek Math 7B Base:

 Reasoning: 3/2 = <<3/2=1.5>>1.5 and 9/10 = <<9/10=0.9>>0.9.
1.5 is greater than 0.9, so 3/2 is greater than 9/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Let's consider a slight change to our previous fractions problem. This time, fill in the blank to compare these two fractions: (3 / 7) _ (9 / 10) Is the comparison the same or different than the comparison between 3 / 2 and 9 / 10? Think about the impact of decreasing the numerator of our first fraction on the comparison.

DeepSeek Math 7B Base:

  Reasoning: 3/7 = <<3/7=0.42857142857142855>>0.42857142857142855 and 9/10 = <<9/10=0.9>>0.9.
0.42857142857142855 is less than 0.9, so 3/7 is less than 9/10.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of these fractions by filling in the blank with <, >, or =. (10 / 9) _ (5 / 6)

DeepSeek Math 7B Base:

 Reasoning: 10/9 = <<10/9=1.1111111111111111>>1.1111111111111111
5/6 = <<5/6=0.8333333333333333>>0.8333333333333333
1.1111111111111111 > 0.8333333333333333

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now, consider the following fractions and fill in the blank with <, >, or =, to compare their values. (10 / 9) _ (5 / 5)

DeepSeek Math 7B Base:

  Reasoning: 10/9 = <<10/9=1.1111111111111111>>1.1111111111111111
5/5 = <<5/5=1>>1
1.1111111111111111 > 1

### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the two fractions and fill in the blank with <, >, or =. (10 / 9) _ (5 / 10)

DeepSeek Math 7B Base:

 Reasoning: 10/9 = <<10/9=1.1111111111111111>>1.1111111111111111
5/10 = <<5/10=0.5>>0.5
1.1111111111111111 > 0.5
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Using the same logic as the previous problem, fill in the blank with <, >, or =. However, now consider the case where the second fraction is changed to 5/3. So the question is: (10 / 9) _ (5 / 3)

DeepSeek Math 7B Base:

  Reasoning: 10/9 = <<10/9=1.1111111111111111>>1.1111111111111111
5/3 = <<5/3=1.6666666666666667>>1.6666666666666667
1.1111111111111111 < 1.6666666666666667
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions by completing the following statement with <, >, or =. (9 / 8) _ (6 / 4)

DeepSeek Math 7B Base:

 Reasoning: 9/8 = <<9/8=1.125>>1.125 and 6/4 = <<6/4=1.5>>1.5.
Since 1.125 < 1.5, 9/8 < 6/4.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Let's consider a modification to the previous problem. Now, compare the fractions in the following statement: (9 / 9) _ (6 / 4) What happens to the relational comparison when the numerator of first fraction changes from 9 to 9 (effectively making it 1), while the second fraction remains same? Fill in the blank with <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 9/9 = <<9/9=1>>1 and 6/4 = <<6/4=1.5>>1.5.
Since 1 < 1.5, 9/9 < 6/4.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions below by filling in the gap with the appropriate symbol (<,>,=). (10 / 3) _ (10 / 2)

DeepSeek Math 7B Base:

 Reasoning: 10/3 = <<10/3=3.3333333333333335>>3.3333333333333335
10/2 = <<10/2=5>>5
3.3333333333333335 < 5
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Let's revisit the previous comparison of fractions, but this time consider the change: (10 / 3) _ (10 / 10) Complete the comparison by filling in the blank with the appropriate symbol (<, >, or =). What happens to the comparison when the denominator of the second fraction is increased to 10?

DeepSeek Math 7B Base:

  Reasoning: 10/3 = <<10/3=3.3333333333333335>>3.3333333333333335
10/10 = <<10/10=1>>1
3.3333333333333335 > 1
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the two fractions by filling in the blank with <, >, or =. (2 / 1) _ (6 / 5)

DeepSeek Math 7B Base:

 2/1 = 2
6/5 = 1.2
2 > 1.2

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Compare the two fractions by filling in the blank with <, >, or =. In the last example, you were comparing the fractions 2 / 1 and 6 / 5. Now consider how the result might change when you compare these fractions: (2 / 2) _ (6 / 5)

DeepSeek Math 7B Base:

  2/2 = 1
6/5 = 1.2
1 < 1.2

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the fractions 5 / 4 and 10 / 3 by filling in the blank with one of the following symbols: <, >, or =.

DeepSeek Math 7B Base:

 Reasoning: 5 / 4 = <<5/4=1.25>>1.25 and 10 / 3 = <<10/3=3.3333333333333335>>3.3333333333333335.
Since 1.25 < 3.3333333333333335, 5 / 4 <<5/4<10/3>> 10 / 3.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider now the fractions 5 / 4 and 8 / 3. Compare these two fractions by filling in the blank with one of the following symbols: <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 5 / 4 = <<5/4=1.25>>1.25 and 8 / 3 = <<8/3=2.6666666666666665>>2.6666666666666665.
Since 1.25 < 2.6666666666666665, 5 / 4 <<5/4<8/3>> 8 / 3.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of these two fractions by filling in the blank with <, > or =: (7 / 5) _ (9 / 9)

DeepSeek Math 7B Base:

 7/5 = <<7/5=1.4>>1.4
9/9 = <<9/9=1>>1
1.4 > 1
(7 / 5) > (9 / 9)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider this situation: Instead of dividing 7 by 5, you divided 7 by 10 to form a new fraction. How would this new fraction compare to the fraction 9 / 10? Fill in the blank using <, >, or =: (7 / 5) _ (9 / 10)

DeepSeek Math 7B Base:

  7/5 = <<7/5=1.4>>1.4
9/10 = <<9/10=0.9>>0.9
1.4 > 0.9
(7 / 5) > (9 / 10)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by filling in the blank with <, >, or =: (3 / 7) _ (5 / 8)

DeepSeek Math 7B Base:

 3/7 is less than 5/8.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous comparison, let's consider a similar one: Compare the value of the fractions (3 / 7) and (6 / 8) by filling in the blank with <, >, or =: (3 / 7) _ (6 / 8) This comparison would tell you how the situation would change if we considered 6 parts out of 8 instead of 5 parts out of 8 as on the previous case.

DeepSeek Math 7B Base:

  3/7 is less than 6/8.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Question: Compare these two fractions: (3 / 1) _ (5 / 9) Hint: Fill the blank with one of the following: <, >, or =.

DeepSeek Math 7B Base:

 Reasoning: 
(3 / 1) = 3
(5 / 9) = 0.5555555555555556
3 > 0.5555555555555556
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Question: In the previous question where we compared two fractions, we had (3 / 1) _ (5 / 9). Now, consider a change in the second number we are comparing. Instead of (5 / 9), we now have (5 / 5). Compare these two fractions: (3 / 1) _ (5 / 5) Hint: Fill the blank with one of the following: <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 
(3 / 1) = 3
(5 / 5) = 1
3 > 1
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions: (2 / 2) _ (6 / 6) Fill in the blank with <, >, or = .

DeepSeek Math 7B Base:

 Reasoning: 2/2 = 1 and 6/6 = 1.
Since 1 = 1, 2/2 = 6/6.
### Answer: =

Expected answer: =

Correct? Yes

🔗 Follow-up

Problem: Consider the change to the previous problem: instead of comparing (2 / 2) with (6 / 6), we now have (2 / 2) and (6 / 5). Now, fill in the blank with <, >, or = to compare these two fractions: (2 / 2) _ (6 / 5)

DeepSeek Math 7B Base:

  Reasoning: 2/2 = 1 and 6/5 = 1.2.
Since 1 < 1.2, 2/2 < 6/5.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by inserting "<", ">" or "=" between them. (7 / 6) _ (9 / 6)

DeepSeek Math 7B Base:

 7/6 is less than 9/6.
7/6 < 9/6

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now let's consider a slight change to the fractions. Please fill in the blank with <, >, or =: (7 / 9) _ (9 / 6) This is just like in our previous problem, but this time we're looking at 7/9 instead of 7/6.

DeepSeek Math 7B Base:

  7/9 is less than 9/6.
7/9 < 9/6

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank in the following question with <, >, or = : (2 / 7) _ (2 / 9) to express whether the first fraction is greater than, less than, or equal to the second fraction.

DeepSeek Math 7B Base:

 Reasoning: 

(2 / 7) = <<2/7=0.2857142857142857>>0.2857142857142857
(2 / 9) = <<2/9=0.2222222222222222>>0.2222222222222222

Since 0.2857142857142857 > 0.2222222222222222, 

(2 / 7) > (2 / 9)

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now let's consider a slight alteration to our previous question. Using the same comparison methods, compare the following fractions: (2 / 7) _ (2 / 4) As you did previously, fill in the blank with <, >, or = signs to correctly compare the two fractions. Does the outcome change if we adjust the denominator in our second fraction from a 9 to a 4?

DeepSeek Math 7B Base:

  Reasoning: 

(2 / 7) = <<2/7=0.2857142857142857>>0.2857142857142857
(2 / 4) = <<2/4=0.5>>0.5

Since 0.2857142857142857 < 0.5, 

(2 / 7) < (2 / 4)

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Determine the relation between the two following fractions by filling in the blank with <, >, or =: (9 / 4) _ (7 / 1)

DeepSeek Math 7B Base:

 9/4 = 2.25 and 7/1 = 7.
2.25 < 7, so 9/4 < 7/1.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider now a different set of fractions: (9 / 10) _ (7 / 1) Fill in the blank with <, >, or = to correctly compare these two fractions. How do these fractions compare to the previous fractions we worked with? Has our answer changed?

DeepSeek Math 7B Base:

  9/10 = 0.9 and 7/1 = 7.
0.9 < 7, so 9/10 < 7/1.

The fractions 9/10 and 7/1 are both less than 1, so they are less than the fractions 9/4 and 7/1.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank with one of the symbols <, >, or = to complete the comparison between the two fractions. (4 / 8) _ (2 / 1)

DeepSeek Math 7B Base:

 4/8 = 1/2
1/2 < 2/1
4/8 < 2/1

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the previous problem where we compared (4 / 8) with (2 / 1). Now, imagine we change the second fraction to (2 / 6) instead of (2 / 1). Fill in the blank with one of the symbols <, >, or = to complete this new comparison: (4 / 8) _ (2 / 6)

DeepSeek Math 7B Base:

  4/8 = 1/2
1/2 < 2/6
4/8 < 2/6

Expected answer: >

Correct? No

🔗 Problem

Problem: Fill in the blank with either <, >, or = in the following expression: (9 / 9) _ (8 / 9), to properly compare the two fractions.

DeepSeek Math 7B Base:

 Reasoning: 9/9 = 1, and 8/9 is less than 1.
Therefore, 9/9 is greater than 8/9.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous question, let's adjust the fractions slightly. Now consider: (9 / 2) _ (8 / 9) What symbol (<, >, =) would you use in the blank to accurately compare these two fractions?

DeepSeek Math 7B Base:

  Reasoning: 9/2 is greater than 1, and 8/9 is less than 1.
Therefore, 9/2 is greater than 8/9.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with <, >, or =. (9 / 10) _ (3 / 10)

DeepSeek Math 7B Base:

 9/10 is greater than 3/10.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the values of two different fractions instead of the ones in the previous problem. Fill in the blank with <, >, or = to compare the fractions: (9 / 4) _ (3 / 10)

DeepSeek Math 7B Base:

  9/4 is greater than 3/10.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Determine if the first fraction is less than, equal to, or greater than the second. Fill in the blank with one of the following: <, >, or =. (3 / 7) _ (5 / 3)

DeepSeek Math 7B Base:

 3/7 is less than 5/3.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the same fractions as in the previous problem, but with a change in the latter fraction. Determine if the first fraction is less than, equal to, or greater than the second. Fill in the blank with one of the following: <, >, or =. (3 / 7) _ (5 / 5)

DeepSeek Math 7B Base:

  3/7 is less than 5/5.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (6 / 5) _ (7 / 10)

DeepSeek Math 7B Base:

 Reasoning: 6/5 = <<6/5=1.2>>1.2 and 7/10 = <<7/10=0.7>>0.7.
Since 1.2 > 0.7, 6/5 > 7/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider a change in the fractions previously compared. Now, compare the values of the following fractions by filling in the blank <, >, or =. (1 / 5) _ (7 / 10)

DeepSeek Math 7B Base:

  Reasoning: 1/5 = <<1/5=0.2>>0.2 and 7/10 = <<7/10=0.7>>0.7.
Since 0.2 < 0.7, 1/5 < 7/10.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank in the following equation with one of these symbols: <, >, or =. (1 / 9) _ (1 / 4)

DeepSeek Math 7B Base:

 (1 / 9) = (1 / 4)

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the following fractions and fill in the blank with <, >, or =: (7 / 1) _ (6 / 1)

DeepSeek Math 7B Base:

 7/1 = 7
6/1 = 6
7/1 > 6/1

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Continue from the previous problem and now consider the fractions (9 / 1) and (6 / 1). Fill in the blank with <, >, or =: (9 / 1) _ (6 / 1)

DeepSeek Math 7B Base:

  9/1 = 9
6/1 = 6
9/1 > 6/1

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Please fill in the blank with <, >, or = to compare the following fractions. (5 / 4) _ (9 / 8)

DeepSeek Math 7B Base:

 5/4 = <<5/4=1.25>>1.25
9/8 = <<9/8=1.125>>1.125
1.25 > 1.125
5/4 > 9/8

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Please consider the following change to the previous problem and fill in the blank with <, >, or = to compare the fractions: If the value of the second fraction's denominator was 1 instead of 8, contrast the following fractions: (5 / 4) _ (9 / 1)

DeepSeek Math 7B Base:

  5/4 = <<5/4=1.25>>1.25
9/1 = <<9/1=9>>9
1.25 < 9
5/4 < 9/1

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Determine the correct symbol to place between the two fractions in the following expression. Fill in the blank with <, >, or =. (8 / 9) _ (3 / 4)

DeepSeek Math 7B Base:

 8/9 is less than 3/4.
8/9 < 3/4

Expected answer: >

Correct? No

🔗 Problem

Problem: Compare the following fractions by choosing the correct symbol (<, >, or =) to fill in the blank: (2 / 1) _ (4 / 9)

DeepSeek Math 7B Base:

 2/1 = 2
4/9 = 0.4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

Expected answer: >

Correct? No

🔗 Problem

Problem: Compare the following fractions by inserting either <, >, or = in the space provided: (9 / 9) _ (2 / 2)

DeepSeek Math 7B Base:

 (9 / 9) = (2 / 2)

Expected answer: =

Correct? Yes

🔗 Follow-up

Problem: Now consider the following fractions: (9 / 3) _ (2 / 2) Perform the same comparison operation as in the previous problem. Recall in the previous problem we compared the fractions (9 / 9) and (2 / 2). Consider what happens if we change the denominator of the first fraction from 9 to 3. Would this make the first fraction greater than, less than, or equal to the second fraction (2 / 2)? Fill in the blank with <, >, or =.

DeepSeek Math 7B Base:

  (9 / 3) > (2 / 2)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Determine the relationship between the following two fractions by filling the blank with <, >, or =: (6 / 1) _ (4 / 4)

DeepSeek Math 7B Base:

 6/1 = 6
4/4 = 1
6 > 1
6/1 > 4/4

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider this scenario: Determine the relationship between the following two fractions by filling the blank with <, >, or =: (6 / 1) _ (4 / 3) How does this result compare to the previous one?

DeepSeek Math 7B Base:

  6/1 = 6
4/3 = 1.3333333333333333
6 > 1.3333333333333333
6/1 > 4/3

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 9) _ (8 / 8)

DeepSeek Math 7B Base:

 Reasoning: 3/9 = 1/3 and 8/8 = 1.
1/3 < 1.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 9) _ (8 / 3) Reflect on the previous question and this question and see how changing the denominator in the second fraction affects the relation between the two fractions.

DeepSeek Math 7B Base:

  Reasoning: 3/9 = 1/3 and 8/3 = 2 2/3.
1/3 < 2 2/3.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (4 / 10) _ (1 / 2)

DeepSeek Math 7B Base:

 Reasoning: 4/10 = 40/100 and 1/2 = 50/100.
40/100 < 50/100, so 4/10 < 1/2.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider this change to the previous problem: (8 / 10) _ (1 / 2) Now, suppose instead of 4/10, we now have 8/10. How would this change the comparison? Fill in the blank with <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 8/10 = 80/100 and 1/2 = 50/100.
80/100 > 50/100, so 8/10 > 1/2.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the two fractions below by filling in the blank space with one of the following symbols: <, >, or =. (6 / 6) _ (6 / 3)

DeepSeek Math 7B Base:

 6/6 = 1 and 6/3 = 2.
1 < 2.
(6 / 6) < (6 / 3)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now consider a slight variation: (6 / 4) _ (6 / 3) Reassigning the values while maintaining the idea of comparison, frame the above expression into a question. Does the change in denominator affect the outcome as compared to the previous question, (6 / 6) _ (6 / 3)?

DeepSeek Math 7B Base:

 

(6 / 4) _ (6 / 3)

The change in denominator does not affect the outcome.

Expected answer: <

Correct? No

🔗 Problem

Problem: Determine which sign (<, >, or =) correctly fills the blank when comparing these two fractions: (2 / 3) _ (2 / 10)

DeepSeek Math 7B Base:

 2/3 is greater than 2/10.

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Following from the previous question, what would happen if we changed the first fraction from 2 / 3 to 10 / 3? Fill in the blank in the question with <, >, or = to compare the two fractions: (10 / 3) _ (2 / 10)

DeepSeek Math 7B Base:

  10/3 is greater than 2/10.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with either <, =, or >: (2 / 10) _ (6 / 4)

DeepSeek Math 7B Base:

 2/10 = 20/100
6/4 = 150/100
20/100 < 150/100
2/10 < 6/4

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now consider a slight change to the previous problem. Use the symbol <, =, or > to compare these two fractions: (6 / 10) _ (6 / 4) What happens if we increase the numerator of the first fraction from 2 to 6?

DeepSeek Math 7B Base:

  6/10 = 60/100
6/4 = 150/100
60/100 < 150/100
6/10 < 6/4

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions and indicate either <, >, or = to complete the equation. (5 / 10) _ (6 / 9)

DeepSeek Math 7B Base:

 Reasoning: 5/10 = 1/2 and 6/9 = 2/3.
1/2 < 2/3.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the change and answer this follow-up question: How does the comparison change when the value of the second fraction is slightly reduced? Fill in the blank with any of <, >, or =. (5 / 10) _ (4 / 9)

DeepSeek Math 7B Base:

  Reasoning: 5/10 = 1/2 and 4/9 = 2/3.
1/2 > 2/3.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the fractions by filling in the blank with <, >, or =. (2 / 9) _ (5 / 5)

DeepSeek Math 7B Base:

 Reasoning: 5/5 = 1, and 2/9 is less than 1.
Therefore, 2/9 is less than 5/5.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the follow-up question: Now let's change our fractional values. Instead of comparing 2/9 to a whole, as in the previous problem, let's compare it to 5/8. Fill in the blank with <, >, or =. (2 / 9) _ (5 / 8)

DeepSeek Math 7B Base:

  Reasoning: 5/8 is greater than 1, and 2/9 is less than 1.
Therefore, 2/9 is less than 5/8.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank with <, >, or = to correctly compare the two fractions: (1 / 9) _ (7 / 9)

DeepSeek Math 7B Base:

 1/9 is less than 7/9.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: For the follow-up question, consider now comparing the fractions again, but this time in this specific situation: (1 / 9) _ (7 / 7) Keep in mind the comparison you made in the previous question when 1/9 was compared with 7/9. How does the comparison change when the second fraction is in this new form, 7/7? Fill the blank with the correct symbol, <, > or =.

DeepSeek Math 7B Base:

  1/9 is less than 7/7.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Analyze and compare the two fractions by determining whether (2 / 7) is either less than, greater than, or equal to (1 / 6). Use the symbols <, >, or =.

DeepSeek Math 7B Base:

 Reasoning: 2/7 = <<2/7=0.28571428571428571428571428571429>>0.28571428571428571428571428571429
1/6 = <<1/6=0.16666666666666666666666666666667>>0.16666666666666666666666666666667
Since 0.28571428571428571428571428571429 is greater than 0.16666666666666666666666666666667, 2/7 is greater than 1/6.
### Answer: 2/7 > 1/6

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following change to the previous problem: Use the fractions (2 / 10) and (1 / 6) instead of (2 / 7) and (1 / 6). Compare these two fractions by determining whether (2 / 10) is either less than, greater than, or equal to (1 / 6), filling in the blank with the symbols <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 2/10 = <<2/10=0.2>>0.2
1/6 = <<1/6=0.16666666666666666666666666666667>>0.16666666666666666666666666666667
Since 0.2 is greater than 0.16666666666666666666666666666667, 2/10 is greater than 1/6.
### Answer: 2/10 > 1/6

Expected answer: >

Correct? Yes

🔗 Problem

Problem: In the following expression, properly insert either <, >, or = in order to correctly compare the two fractions: (9 / 9) _ (9 / 10)

DeepSeek Math 7B Base:

 9/9 = 1, and 9/10 = 0.9.
1 > 0.9, so 9/9 > 9/10.

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following changes in the fractions: (9 / 9) _ (9 / 5) Based on the adjustments made, fill in the blank with <, >, or = to appropriately compare the values of the two fractions.

DeepSeek Math 7B Base:

  9/9 = 1, and 9/5 = 1.8.
1 < 1.8, so 9/9 < 9/5.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by determining if the first fraction is greater than, equal to, or less than the second fraction: (8 / 4) _ (5 / 2)

DeepSeek Math 7B Base:

 Reasoning: 8/4 = <<8/4=2>>2 and 5/2 = <<5/2=2.5>>2.5.
2 is less than 2.5.
### Answer: less than

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now consider a slight change to the values. Instead of the first fraction being (8 / 4), let's change it to (10 / 4). So, we have this comparison: (10 / 4) _ (5 / 2) Compare these two fractions as you did before by determining if the first fraction is greater than, equal to, or less than the second fraction.

DeepSeek Math 7B Base:

  Reasoning: 10/4 = <<10/4=2.5>>2.5 and 5/2 = <<5/2=2.5>>2.5.
2.5 is equal to 2.5.
### Answer: equal to

Expected answer: =

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by deciding which symbol (<, >, or =) to fill in the blank with: (5 / 2) _ (1 / 10)

DeepSeek Math 7B Base:

 5/2 = <<5/2=2.5>>2.5
1/10 = <<1/10=0.1>>0.1
2.5 > 0.1
(5 / 2) > (1 / 10)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Continuing from our previous comparison, now consider a new set of fractions. Compare the values of the following fractions by filling in the blank with <, >, or =. (5 / 2) _ (1 / 2) Now, think about what would happen if the first fraction was changed from (5 / 2) to (3 / 2). How would this change affect the comparison? Write down a similar comparison question replacing 5 with 3.

DeepSeek Math 7B Base:

  5/2 = <<5/2=2.5>>2.5
1/2 = <<1/2=0.5>>0.5
2.5 > 0.5
(5 / 2) > (1 / 2)

3/2 = <<3/2=1.5>>1.5
1/2 = <<1/2=0.5>>0.5
1.5 > 0.5
(3 / 2) > (1 / 2)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Fill in the blank with <, >, or = to compare the two fractions in the following question: (2 / 4) _ (9 / 2)

DeepSeek Math 7B Base:

 (2 / 4) = (1 / 2)
(1 / 2) < (9 / 2)
(2 / 4) < (9 / 2)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now suppose we change the fractions a bit in the previous problem. Fill in the blank with <, >, or = to compare the ratios in the following question: (2 / 4) _ (9 / 10)

DeepSeek Math 7B Base:

  (2 / 4) = (1 / 2)
(1 / 2) < (9 / 10)
(2 / 4) < (9 / 10)

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank in the following equation with either <, >, or = to show the comparison between the two fractions: (6 / 3) _ (10 / 2)

DeepSeek Math 7B Base:

 6/3 = <<6/3=2>>2
10/2 = <<10/2=5>>5
2 < 5
6/3 < 10/2

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now consider the fractions (6 / 8) and (10 / 2). Fill in the blank in the following equation with either <, >, or = to show the comparison between the two fractions: (6 / 8) _ (10 / 2)

DeepSeek Math 7B Base:

  6/8 = <<6/8=0.75>>0.75
10/2 = <<10/2=5>>5
0.75 < 5
6/8 < 10/2

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the given fractions by filling in the blank with the correct symbol (<, >, or =). (6 / 3) _ (8 / 6)

DeepSeek Math 7B Base:

 Reasoning: 6/3 = 2 and 8/6 = 1.3333333333333333.
2 > 1.3333333333333333.
(6 / 3) > (8 / 6)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the previous question where you compared the fractions (6 / 3) and (8 / 6). Now let's change the second fraction from (8 / 6) to (8 / 4). How would this affect the comparison? Fill in the blank with the correct symbol (<, >, or =). (6 / 3) _ (8 / 4)

DeepSeek Math 7B Base:

  Reasoning: 6/3 = 2 and 8/4 = 2.
2 = 2.
(6 / 3) = (8 / 4)

Expected answer: =

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 4) _ (6 / 5)

DeepSeek Math 7B Base:

 3/4 is less than 6/5.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 4) _ (6 / 9) Consider what happens if the second fraction changes, and 6 is divided by 9 instead of 5. How does this change affect the comparison between the two fractions?

DeepSeek Math 7B Base:

  3/4 is greater than 6/9.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the two fractions below by filling in the blank with <, >, or =: (1 / 1) _ (3 / 1)

DeepSeek Math 7B Base:

 1/1 = 1
3/1 = 3
1 < 3

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: After comparing (1 / 1) and (3 / 1), let's consider a new scenario. How would the comparison change if we replaced (3 / 1) with (3 / 7)? Fill in the blank with <, >, or = to compare the two fractions: (1 / 1) _ (3 / 7)

DeepSeek Math 7B Base:

  1/1 = 1
3/7 = 0.42857142857142855
1 > 0.42857142857142855

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with <, >, or =. (7 / 6) _ (4 / 5)

DeepSeek Math 7B Base:

 Reasoning: 7/6 = <<7/6=1.1666666666666667>>1.1666666666666667
4/5 = <<4/5=0.8>>0.8

Since 1.1666666666666667 > 0.8, 7/6 > 4/5.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the situation from the previous problem. Now, think about what would happen if the first fraction is 7 / 3 instead of 7 / 6. Fill in the blank to compare the two fractions: (7 / 3) _ (4 / 5)

DeepSeek Math 7B Base:

  Reasoning: 7/3 = <<7/3=2.3333333333333335>>2.3333333333333335
4/5 = <<4/5=0.8>>0.8

Since 2.3333333333333335 > 0.8, 7/3 > 4/5.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by filling the blank with <, >, or =. (6 / 4) _ (2 / 2)

DeepSeek Math 7B Base:

 Reasoning: 6/4 = 1.5 and 2/2 = 1.
1.5 > 1, so 6/4 > 2/2.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider a change in the problem. Compare the following two fractions by filling the blank with <, >, or =. (6 / 4) _ (2 / 10) In this scenario, suppose we replace the whole number in the denominator of the second fraction from 2 to 10. How does this change the comparison?

DeepSeek Math 7B Base:

  Reasoning: 6/4 = 1.5 and 2/10 = 0.2.
1.5 > 0.2, so 6/4 > 2/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with <, >, or =. (5 / 5) _ (9 / 10)

DeepSeek Math 7B Base:

 5/5 = 1, and 9/10 = 0.9.
1 > 0.9, so 5/5 > 9/10.

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider this follow-up to our previous fraction comparison question: Now, compare these fractions by filling in the blank with <, >, or =. (4 / 5) _ (9 / 10) Think of it like this: if you had 4 parts of a cake that was sliced into 5 equal pieces versus someone who had 9 parts of a cake that was sliced into 10 equal pieces, which one would have more cake?

DeepSeek Math 7B Base:

  4/5 = 0.8, and 9/10 = 0.9.
0.8 < 0.9, so 4/5 < 9/10.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank (1 / 5) _ (1 / 1) with <, >, or = to compare the two fractions.

DeepSeek Math 7B Base:

 Reasoning: 1/5 is less than 1/1.
(1 / 5) < (1 / 1)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now, let's consider a slight change in the problem. Fill in the blank (1 / 5) _ (2 / 1) with <, >, or = to compare the two fractions. This time, suppose you're comparing one fifth of your initially available sweets against two whole sweets someone offered you. Which is greater or are they equal?

DeepSeek Math 7B Base:

  Reasoning: 1/5 is less than 2/1.
(1 / 5) < (2 / 1)

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill the blank with either <, >, or = to compare the two fractions in the following equation: (7 / 1) _ (4 / 2)

DeepSeek Math 7B Base:

 7/1 = 7
4/2 = 2
7 > 2
7/1 > 4/2

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider if instead of dividing 4 by 2, we divided it by 7 in the previous question. Fill in the blank in the following equation with <, >, or = to compare the new fractions: (7 / 1) _ (4 / 7)

DeepSeek Math 7B Base:

  7/1 = 7
4/7 = 0.5714285714285714
7 > 0.5714285714285714
7/1 > 4/7

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by using <, >, or = to fill in the blank: (4 / 7) _ (9 / 4)

DeepSeek Math 7B Base:

 4/7 is less than 9/4.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the change in fraction comparison by filling in the blank with <, >, or =. Now, observe the relationship between the fractions (4 / 7) and (2 / 4). How does the comparison change from the previous problem with the fraction (9 / 4)?

DeepSeek Math 7B Base:

  4/7 is less than 9/4.

Expected answer: >

Correct? No

🔗 Problem

Problem: Fill in the blank in the question (5 / 9) _ (4 / 7) with <, >, or = to compare the two fractions.

DeepSeek Math 7B Base:

 5/9 is less than 4/7.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now, consider a slight change to the previous question: Compare the following fractions by filling in the blank with <, >, or =: (5 / 9) _ (4 / 10) What happens when we change the denominator of the second fraction from 7 to 10?

DeepSeek Math 7B Base:

  5/9 is greater than 4/10.

When the denominator of the second fraction is increased, the value of the fraction decreases.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions and fill in the blank with <, >, or =: (8 / 3) _ (7 / 3)

DeepSeek Math 7B Base:

 8/3 is greater than 7/3.
8/3 > 7/3

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, now consider what happens when the fraction changes. Using the same symbols, <, >, or =, compare the following fractions: (8 / 9) _ (7 / 3)

DeepSeek Math 7B Base:

  8/9 is less than 7/3.
8/9 < 7/3

Expected answer: <

Correct? Yes

🔗 Problem

Problem: In the equation: (5 / 1) _ (2 / 2), replace the underscore with one of the following signs: <, >, or = to compare the two fractions.

DeepSeek Math 7B Base:

 The two fractions are equal.

Expected answer: >

Correct? No

🔗 Problem

Problem: Compare the following fractions and fill in the blank with either <, >, or =: (5 / 8) _ (3 / 3)

DeepSeek Math 7B Base:

 5/8 is less than 3/3.
5/8 < 3/3

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: For a follow-up question: In our previous question, we compared (5 / 8) to (3 / 3), but what if the first fraction was a little different? Consider this scenario where you now have 5 fourths of a pizza instead of 5 eighths. Keeping the second fraction the same at (3 / 3), fill in the blank with <, >, or = to appropriately compare the fractions: (5 / 4) _ (3 / 3)

DeepSeek Math 7B Base:

 5/4 is greater than 3/3.
5/4 > 3/3

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Determine which symbol : <, >, or =, is appropriate to fill the blank in the following comparison: (5 / 8) _ (6 / 10)

DeepSeek Math 7B Base:

 5/8 = 50/80
6/10 = 48/80
50/80 > 48/80
5/8 > 6/10

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: In the same vein as the previous problem, consider a new comparison: (5 / 8) _ (6 / 5). Which symbol: <, >, or =, correctly complete the comparison? Keep in mind how your answer might change compared to the previous problem because of the different denominator in the second fraction.

DeepSeek Math 7B Base:

  5/8 = 25/40
6/5 = 48/40
25/40 < 48/40
5/8 < 6/5

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions by filling in the blank with <, >, or =: (5 / 10) _ (6 / 6)

DeepSeek Math 7B Base:

 5/10 = 1/2 and 6/6 = 1.
1/2 is less than 1, so 5/10 is less than 6/6.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now consider the change in fractions: (5 / 10) _ (6 / 1) Fill in the blank with <, >, or = to compare these two fractions. Suppose that out of 10 parts, you only have 5 parts, like the 5 apples from the previous problem. Compare this to a situation where you have 6 whole items, like the oranges. Which one has more parts or items?

DeepSeek Math 7B Base:

 5/10 is less than 6/1.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare these two fractions by filling in the blank with <, >, or =. (5 / 4) _ (2 / 4)

DeepSeek Math 7B Base:

 5/4 is greater than 2/4.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Considering the previous comparison between the fractions, what would be the result if we changed the fractions to: (5 / 4) _ (2 / 10) Fill in the blank with <, >, or = to make the comparison.

DeepSeek Math 7B Base:

  5/4 is greater than 2/10.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by using <, >, or = to fill in the blank: (6 / 10) _ (6 / 10)

DeepSeek Math 7B Base:

 6/10 = 6/10

Expected answer: =

Correct? Yes

🔗 Follow-up

Problem: Following the last problem, consider a change such that instead of having 6 tenths of a pizza, you now have 6 fifths of a pizza. Compare this with the previous scenario by using <, >, or = to fill in the blank: (6 / 5) _ (6 / 10)

DeepSeek Math 7B Base:

  6/5 > 6/10

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Please compare these two fractions and fill the blank with <, >, or =. (6 / 8) _ (2 / 9)

DeepSeek Math 7B Base:

 Reasoning: 6/8 = 6*9/8*9 = <<6*9/8*9=54/72>>54/72
2/9 = 2*8/9*8 = <<2*8/9*8=16/72>>16/72
54/72 > 16/72
6/8 > 2/9
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now, let's consider a slight change to the previous comparison. Instead of having a fraction of 6/8, let's change the numerator to 6 and denominator to 10. The new comparison now is: (6 / 10) _ (2 / 9) Please compare these two fractions and fill the blank with <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 6/10 = 6*9/10*9 = <<6*9/10*9=54/90>>54/90
2/9 = 2*10/9*10 = <<2*10/9*10=20/90>>20/90
54/90 > 20/90
6/10 > 2/9
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Fill in the blank with <, =, or > after comparing the fractions below: (2 / 10) _ (6 / 2)

DeepSeek Math 7B Base:

 2/10 = 1/5
6/2 = 3
1/5 < 3
(2 / 10) < (6 / 2)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Let's modify the previous problem slightly. Fill in the blank with <, =, or > after comparing the fractions: (2 / 10) _ (6 / 9)

DeepSeek Math 7B Base:

  2/10 = 1/5
6/9 = 2/3
1/5 < 2/3
(2 / 10) < (6 / 9)

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Determine which of the following fractions is greater by filling in the blank with <, >, or =. (2 / 7) _ (9 / 4)

DeepSeek Math 7B Base:

 2/7 is less than 9/4.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now suppose we change one of the fractions in the previous problem. Fill in the blank to compare the two fractions: (2 / 1) _ (9 / 4)

DeepSeek Math 7B Base:

  2/1 is greater than 9/4.

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the following fractions by filling in the blank with <, >, or =. (1 / 1) _ (2 / 10)

DeepSeek Math 7B Base:

 1/1 = 10/10
10/10 > 2/10
1/1 > 2/10

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the previous comparison between the fractions (1 / 1) and (2 / 10). Now let's change things a bit. Fill in the blank with <, >, or = to compare the following fractions: (10 / 1) _ (2 / 10)

DeepSeek Math 7B Base:

  10/1 = 100/10
100/10 > 2/10
10/1 > 2/10

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the results of the following fractions by filling the blank with <, >, or =. (8 / 2) _ (10 / 9)

DeepSeek Math 7B Base:

 8/2 = <<8/2=4>>4
10/9 = <<10/9=1.1111111111111111>>1.1111111111111111
4 > 1.1111111111111111
8/2 > 10/9

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Given the results you obtained from the previous question, let's alter the fractions slightly. Now, compare the following expressions: (8 / 2) _ (9 / 9) Fill in the blank with <, >, or = to indicate whether the first fraction is less than, greater than, or equal to the second fraction. What changes when the denominator of the second fraction is 9 instead of 10?

DeepSeek Math 7B Base:

  8/2 = <<8/2=4>>4
9/9 = <<9/9=1>>1
4 > 1
8/2 > 9/9

When the denominator of the second fraction is 9 instead of 10, the result is the same.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Determine the relationship between the fractions by filling in the blank in the following equation with either <, >, or =: (3 / 2) _ (9 / 8)

DeepSeek Math 7B Base:

 Reasoning: 

(3 / 2) = (3 * 4) / (2 * 4) = 12 / 8

(9 / 8) = (9 * 1) / (8 * 1) = 9 / 8

12 / 8 > 9 / 8

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Determine the relationship between the fractions by filling in the blank in the following equation with either <, >, or =: (3 / 2) _ (9 / 6) Consider what happens if the denominator of the second fraction was 6 instead of 8. How would that affect your answer?

DeepSeek Math 7B Base:

  Reasoning: 

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

(9 / 6) = (9 * 1) / (6 * 1) = 9 / 6

9 / 6 = 9 / 6

### Answer: =

Expected answer: =

Correct? Yes

🔗 Problem

Problem: Compare the following quantities by filling in the blank with <, >, or =: (4 / 6) _ (6 / 10)

DeepSeek Math 7B Base:

 (4 / 6) = (4 * 10) / (6 * 10) = 40 / 60
(6 / 10) = (6 * 6) / (10 * 6) = 36 / 60

Since 40 / 60 > 36 / 60, (4 / 6) > (6 / 10)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider a change to the previous problem as follows: (4 / 6) _ (6 / 5) Now, re-evaluate and compare the two fractions as before. Fill the blank with either <, >, or = sign.

DeepSeek Math 7B Base:

  (4 / 6) = (4 * 5) / (6 * 5) = 20 / 30
(6 / 5) = (6 * 6) / (5 * 6) = 36 / 30

Since 20 / 30 < 36 / 30, (4 / 6) < (6 / 5)

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Fill in the blank with the correct symbol to compare the following fractions: (8 / 10) _ (1 / 1)

DeepSeek Math 7B Base:

 8/10 is less than 1/1.
8/10 < 1/1

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Let's consider a slight change to our earlier comparison. What if instead of having 8 out of 10 parts, you now have 8 divided by 2 parts? Fill in the blank with the correct symbol to compare the following fractions: (8 / 2) _ (1 / 1)

DeepSeek Math 7B Base:

  8/2 is greater than 1/1.
8/2 > 1/1

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Using either <, >, or =, compare the following fractions by filling in the blank: (5 / 1) _ (5 / 8)

DeepSeek Math 7B Base:

 5/1 = 5
5/8 = 0.625
5/1 > 5/8

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Following up from the previous question, let's change the fractions and compare again. Using either <, >, or =, complete the new mathematical comparison below: (5 / 3) _ (5 / 8) Think of it this way, if the basket had initially 5/3 of the apples instead of 5 whole apples, and we still have 5/8 of the apples from the other basket. Would the first basket have more, less or the same number of apples than the second?

DeepSeek Math 7B Base:

  5/3 = 1.6666666666666667
5/8 = 0.625
5/3 > 5/8

Expected answer: >

Correct? Yes

🔗 Problem

Problem: What is the correct symbol to use in the following statement: (6 / 5) _ (9 / 6) Is it "<", ">", or "=" ? Fill in the blank with the correct symbol.

DeepSeek Math 7B Base:

 The correct symbol is ">" because 6/5 = <<6/5=1.2>>1.2 and 9/6 = <<9/6=1.5>>1.5.

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the following fractions by filling in the blank: (7 / 5) _ (1 / 10) You can use <, > or =.

DeepSeek Math 7B Base:

 Reasoning: 7/5 = <<7/5=1.4>>1.4, 1/10 = <<1/10=0.1>>0.1.
Since 1.4 > 0.1, 7/5 > 1/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Let's consider a variation of the previous problem. Now require the comparison of two different fractions: (1 / 5) _ (1 / 10) Use <, > or = to complete the comparison. This question asks you to think about what happens when we change the number of parts the whole is divided into.

DeepSeek Math 7B Base:

  Reasoning: 1/5 = <<1/5=0.2>>0.2, 1/10 = <<1/10=0.1>>0.1.
Since 0.2 > 0.1, 1/5 > 1/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the two fractions and fill in the blank with <, >, or =. (10 / 8) _ (10 / 1)

DeepSeek Math 7B Base:

 Reasoning: 10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
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10/8 = 10/8
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10/8 = 10/8
10/8 = 10/8
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10/8 = 10/8
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10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
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10/8 = 10/8
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10/8 = 10/8
10/8 = 10/8
10/8 = 10/8
10/8 =

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =: (3 / 2) _ (4 / 6)

DeepSeek Math 7B Base:

 Reasoning: 

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

(4 / 6) = (4 / 6)

9 / 6 > 4 / 6

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the change from the original problem. Now instead of having 3 halves, imagine it was changed to 3 ninths. Complete the comparison: (3 / 9) _ (4 / 6) Fill the blank with <, >, or =.

DeepSeek Math 7B Base:

  Reasoning: 

(3 / 9) = (3 / 3) / (9 / 3) = 1 / 3

(4 / 6) = (4 / 6)

1 / 3 < 4 / 6

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by filling in the blank with <, >, or =. (9 / 7) _ (4 / 6)

DeepSeek Math 7B Base:

 Reasoning: 9/7 = <<9/7=1.2857142857142858>>1.2857142857142858
4/6 = <<4/6=0.6666666666666666>>0.6666666666666666
1.2857142857142858 > 0.6666666666666666
9/7 > 4/6

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following scenario. What happens if we change the math problem (9 / 7) _ (4 / 6) to consider a different set of fractions? Fill in the blank with <, >, or = to compare these two new fractions. (7 / 7) _ (4 / 6)

DeepSeek Math 7B Base:

  Reasoning: 7/7 = <<7/7=1>>1
4/6 = <<4/6=0.6666666666666666>>0.6666666666666666
1 > 0.6666666666666666
7/7 > 4/6

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Fill in the blank in the following comparison with a <, >, or = sign. (8 / 7) _ (8 / 8)

DeepSeek Math 7B Base:

 8/7 is greater than 8/8.
8/7 > 8/8

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following change in fractions: (7 / 7) _ (8 / 8) Replace the earlier fractions with these new numbers. How do they compare now? Use the symbols <, >, or = to indicate your answer.

DeepSeek Math 7B Base:

  7/7 is equal to 8/8.
7/7 = 8/8

Expected answer: =

Correct? Yes

🔗 Problem

Problem: Fill in the blank with the correct symbol (<, >, =) to compare these two fractions: (5 / 5) _ (4 / 6)

DeepSeek Math 7B Base:

 5/5 = 1
4/6 = 2/3
1 > 2/3
5/5 > 4/6

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the two fractions from before: (5 / 5) and (4 / 6). Now, change the latter fraction's numerator to 2 instead of 4. Fill in the blank with the correct symbol (<, >, =) to compare these two fractions: (5 / 5) _ (2 / 6)

DeepSeek Math 7B Base:

  5/5 = 1
2/6 = 1/3
1 > 1/3
5/5 > 2/6

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions and use <, >, or = to fill the blank: (10 / 10) _ (4 / 10)

DeepSeek Math 7B Base:

 10/10 = 1
4/10 = 0.4
1 > 0.4
10/10 > 4/10

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following fractions and use <, >, or = to fill the blank: (10 / 10) _ (4 / 9) This is very similar to the last problem where we compared (10 / 10) to (4 / 10). What changes when the denominator of the second fraction is now 9 instead of 10?

DeepSeek Math 7B Base:

  10/10 = 1
4/9 = 0.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

Expected answer: >

Correct? No

🔗 Problem

Problem: Compare the following fractions and fill in the blank with <, >, or =. (8 / 1) _ (4 / 9)

DeepSeek Math 7B Base:

 Reasoning: 8/1 = 8 and 4/9 = 0.4444444444444444.
8/1 is greater than 4/9.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the values of the following fractions and fill in the blank with <, >, or =. How would your answer change if instead of 8 in the previous problem, we had 5? (5 / 1) _ (4 / 9)

DeepSeek Math 7B Base:

  Reasoning: 5/1 = 5 and 4/9 = 0.4444444444444444.
5/1 is greater than 4/9.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the two fractions below by choosing either <, >, or = to fill in the blank: (9 / 3) _ (4 / 8)

DeepSeek Math 7B Base:

 9/3 = <<9/3=3>>3
4/8 = <<4/8=0.5>>0.5
3 > 0.5
(9 / 3) > (4 / 8)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now reconsider the previous fractions, only this time they have slightly changed: Compare the values of the following fractions by completing the sentence with one of the following options: <, >, or = : (9 / 3) _ (4 / 2) Think of this like the previous situation, but instead of the second fraction having a numerator of 4 and a denominator of 8, it now has a numerator of 4 and denominator of 2. How does this change the comparison?

DeepSeek Math 7B Base:

  9/3 = <<9/3=3>>3
4/2 = <<4/2=2>>2
3 > 2
(9 / 3) > (4 / 2)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the fractions in the expression (10 / 7) _ (9 / 6). Fill in the blank with <, >, or =.

DeepSeek Math 7B Base:

 Reasoning: 10/7 = <<10/7=1.4285714285714285>>1.4285714285714285
9/6 = <<9/6=1.5>>1.5
1.4285714285714285 < 1.5
### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now, let's consider a change to the previous problem. Instead of comparing (10 / 7) and (9 / 6), compare the fractions (10 / 7) _ (9 / 3). Using the same method as before, fill in the blank with <, >, or =. Is this new ratio greater than, less than, or equal to the first one?

DeepSeek Math 7B Base:

  Reasoning: 10/7 = <<10/7=1.4285714285714285>>1.4285714285714285
9/3 = <<9/3=3>>3
1.4285714285714285 < 3
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following fractions, and complete the statement: (10 / 8) _ (3 / 1) Fill the blank space with <, >, or =.

DeepSeek Math 7B Base:

 10/8 is less than 3/1.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the following modification to our previous comparison: (10 / 7) _ (3 / 1) How does it affect the comparison? Place <, >, or = in the blank to make the statement true.

DeepSeek Math 7B Base:

 10/7 is less than 3/1.

### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Determine the relationship between the two fractions by filling in the blank with <, >, or =. The question is as follows: (3 / 2) _ (3 / 5)

DeepSeek Math 7B Base:

 The two fractions have the same numerator, so the fraction with the smaller denominator is the larger fraction.

(3 / 2) > (3 / 5)

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following scenario: You had 4 cups of blueberries and 2 cups of strawberries (4/2) and now have replaced the blueberries with 3 cups of raspberries. Keeping the strawberries still 5 cups, tell whether the new ratio of raspberries to strawberries (3/5) is more than, less than, or equal to the original ratio of blueberries to strawberries. Fill in the blank in the question (4 / 2) _ (3 / 5) with <, >, or =.

DeepSeek Math 7B Base:

 The two fractions have the same denominator, so the fraction with the larger numerator is the larger fraction.

(4 / 2) > (3 / 5)

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by filling in the blank with <, >, or =. (4 / 10) _ (2 / 2)

DeepSeek Math 7B Base:

 4/10 is less than 2/2.
4/10 < 2/2

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: After comparing (4 / 10) and (2 / 2), consider the scenario where instead of (2 / 2), the comparison fraction becomes (9 / 2). Now, compare these two fractions: (4 / 10) _ (9 / 2) Fill in the blank with either <, >, or =.

DeepSeek Math 7B Base:

  4/10 is less than 9/2.
4/10 < 9/2

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions and fill in the blank with <, >, or =: (6 / 7) _ (2 / 10)

DeepSeek Math 7B Base:

 Reasoning: 6/7 = <<6/7=0.8571428571428571>>0.8571428571428571
2/10 = <<2/10=0.2>>0.2
0.8571428571428571 > 0.2
6/7 > 2/10
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Following the previous question, now consider if the first fraction had been (5 / 7) instead. How would this change compare to the original (6 / 7)? Fill in the blank with <, >, or =: (5 / 7) _ (2 / 10)

DeepSeek Math 7B Base:

  Reasoning: 5/7 = <<5/7=0.7142857142857143>>0.7142857142857143
2/10 = <<2/10=0.2>>0.2
0.7142857142857143 > 0.2
5/7 > 2/10
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (9 / 7) _ (10 / 3)

DeepSeek Math 7B Base:

 9/7 = <<9/7=1.2857142857142858>>1.2857142857142858
10/3 = <<10/3=3.3333333333333335>>3.3333333333333335
1.2857142857142858 < 3.3333333333333335
9/7 < 10/3

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider a continuation of the previous comparison of fractions. Now, compare the following fractions by filling in the blank with <, >, or =. (9 / 7) _ (10 / 7) In other words, what would happen if the denominator of the second fraction was 7 instead of 3, keeping the ratio of 9 to 7 in the first fraction the same? How would this change affect the comparison?

DeepSeek Math 7B Base:

  9/7 = <<9/7=1.2857142857142858>>1.2857142857142858
10/7 = <<10/7=1.4285714285714286>>1.4285714285714286
1.2857142857142858 < 1.4285714285714286
9/7 < 10/7

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following two fractions by filling in the blank with <, >, or =. (8 / 8) _ (2 / 8)

DeepSeek Math 7B Base:

 Reasoning: 8/8 = 1 and 2/8 = 1/4. Since 1 is greater than 1/4, 8/8 is greater than 2/8.

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following fractions: (8 / 10) _ (2 / 8) How does the comparison of these two fractions change from the previous problem where you compared 8 / 8 and 2 / 8? Fill in the blank with <, >, or = to express your answer.

DeepSeek Math 7B Base:

  Reasoning: 8/10 is less than 1 and 2/8 is less than 1. Since 8/10 is less than 1 and 2/8 is less than 1, 8/10 is less than 2/8.

### Answer: <

Expected answer: >

Correct? No

🔗 Problem

Problem: Evaluate the following expression by comparing the two fractions using <, >, or =: (4 / 3) _ (1 / 8)

DeepSeek Math 7B Base:

 4/3 = <<4/3=1.3333333333333333>>1.3333333333333333
1/8 = <<1/8=0.125>>0.125
1.3333333333333333 > 0.125
4/3 > 1/8

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Consider the following problem: (4 / 9) _ (1 / 8) In the previous scenario, we compared the differences between 4/3 and 1/8. Now, let's change the first fraction from 4/3 to 4/9. Fill in the blank by comparing the fractions using <, >, or =. Would the relationship between the fractions be the same, or it would be different?

DeepSeek Math 7B Base:

  4/9 = <<4/9=0.4444444444444444>>0.4444444444444444
1/8 = <<1/8=0.125>>0.125
0.4444444444444444 > 0.125
4/9 > 1/8

The relationship between the fractions would be the same.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by completing the sentence with the appropriate symbol (<, >, or =): (4 / 6) _ (6 / 10)

DeepSeek Math 7B Base:

 Reasoning: 4/6 = <<4/6=2/3>>2/3 and 6/10 = <<6/10=3/5>>3/5.
Since 2/3 <<2/3>3/5, 4/6>>3/5, we have 4/6 <<4/6>6/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider this scenario: There are some large birds in a grove: 4 of every 6 are hawks, while the rest are falcons. In comparison, at another location 6 out of every 1 bird is a raven. Compare the ratios of hawks to total birds and of ravens to total birds. Fill in replacing _ with the correct sign (either <, >, or =). (4 / 6) _ (6 / 1)

DeepSeek Math 7B Base:

  Reasoning: 4/6 = <<4/6=2/3>>2/3 and 6/1 = <<6/1=6>>6.
Since 2/3 <<2/3>6, 4/6>>6, we have 4/6 <<4/6>6/1.
### Answer: <

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions by filling the blank using <, >, or =. Here's the question: (9 / 6) _ (6 / 8)

DeepSeek Math 7B Base:

 9/6 = 1.5
6/8 = 0.75
1.5 > 0.75

### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Considering the same comparison concept as the previous problem, but this time let's change the fractions. Still filling the blank with <, >, or =, answer this question: (9/6) _ (4/8) Think about how this change, reducing the number in the numerator of the second fraction, affects the comparison between the two fractions.

DeepSeek Math 7B Base:

  9/6 = 1.5
4/8 = 0.5
1.5 > 0.5

### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with one of the following symbols: <, >, or =. (2 / 6) _ (8 / 7)

DeepSeek Math 7B Base:

 2/6 is less than 8/7.

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now think about a slightly different situation: Compare the two fractions below by filling the blank with <, >, or =. (2 / 7) _ (8 / 7) This time, instead of 2 out of 6 parts of a pizza, suppose you only got 2 out of 7 parts while the rest was still 8 out of 7. What would be the comparison between the two fractions then?

DeepSeek Math 7B Base:

  2/7 is less than 8/7.

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the following fractions by filling in the blank with <, >, or =. (9 / 6) _ (4 / 10)

DeepSeek Math 7B Base:

 Reasoning: 9/6 = 1.5 and 4/10 = 0.4.
1.5 is greater than 0.4, so 9/6 is greater than 4/10.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider the new scenario. Instead of comparing the fractions (9 / 6) and (4 / 10), we want to compare (9 / 6) and (4 / 6). Fill in the blank with <, >, or = to compare these two fractions.

DeepSeek Math 7B Base:

  Reasoning: 9/6 = 1.5 and 4/6 = 0.6666666666666666.
1.5 is greater than 0.6666666666666666, so 9/6 is greater than 4/6.
### Answer: >

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Fill in the blank in the following question with <, >, or = to correctly indicate which fraction is greater in value: (6 / 8) _ (5 / 1)

DeepSeek Math 7B Base:

 (6 / 8) = (5 / 1)

Expected answer: <

Correct? No

🔗 Problem

Problem: Compare these two fractions by filling in the blank with <, >, or =. (8 / 4) _ (1 / 10)

DeepSeek Math 7B Base:

 8/4 = <<8/4=2>>2, 1/10 = <<1/10=0.1>>0.1, 2 > 0.1, so 8/4 > 1/10.

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: Now consider the comparison, (2 / 4) _ (1 / 10). How does this comparison change if we replace the fraction 8 / 4 from the previous problem with 2 / 4? Fill in the blank with <, >, or =.

DeepSeek Math 7B Base:

  2/4 = <<2/4=0.5>>0.5, 1/10 = <<1/10=0.1>>0.1, 0.5 > 0.1, so 2/4 > 1/10.

Expected answer: >

Correct? Yes

🔗 Problem

Problem: Compare the values of the following expressions by filling in the blank with <, >, or =. (6 / 3) _ (8 / 2)

DeepSeek Math 7B Base:

 (6 / 3) = (8 / 2)

Expected answer: <

Correct? No

🔗 Problem

Problem: Please compare the following two fractions and fill the blank with one of the symbols: <, >, or =: (4 / 6) _ (6 / 3)

DeepSeek Math 7B Base:

 (4 / 6) = (6 / 3)

Expected answer: <

Correct? No

🔗 Problem

Problem: Fill in the blank with <, >, or = to compare the fractions 6 / 7 and 3 / 1 properly.

DeepSeek Math 7B Base:

 6 / 7 <<6/7=6/7>> 3 / 1

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now let's change up the fractions a little. Let's consider 6 / 7 and 9 / 1 this time. Fill in the blank with <, >, or = to correctly compare these two fractions.

DeepSeek Math 7B Base:

  6 / 7 <<6/7<9/1>> 9 / 1

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (6 / 10) _ (9 / 10)

DeepSeek Math 7B Base:

 6/10 is less than 9/10.
6/10 < 9/10

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Now, consider if the fraction had been different. Compare the following fractions: (1 / 10) _ (9 / 10) How would your answer change from the previous question where you compared (6 / 10) and (9 / 10)?

DeepSeek Math 7B Base:

  1/10 is less than 9/10.
1/10 < 9/10

Expected answer: <

Correct? Yes

🔗 Problem

Problem: Compare the two fractions by filling in the blank with <, >, or =. (6 / 8) _ (4 / 9)

DeepSeek Math 7B Base:

 6/8 = 6/8
4/9 = 4/9
6/8 > 4/9

Expected answer: >

Correct? Yes

🔗 Follow-up

Problem: As a follow-up to the previous question, now consider these two fractions. Fill in the blank with <, > or = to compare the values. (6 / 8) _ (4 / 4)

DeepSeek Math 7B Base:

  6/8 = 6/8
4/4 = 1
6/8 < 4/4

Expected answer: <

Correct? Yes