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CodeLlama 13B on 4.NF.A.2

Common Core Standard 4.NF.A.2

This standard covers the following:

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions (1/8) and (4/1), we need to find the least common multiple (LCM) of the denominators. The LCM of 8 and 1 is 8, so we can rewrite the fractions as:

(1/8) = (1/8) x (8/8) = (8/64)
(4/1) = (4/1) x (8/8) = (32/64)

Now we can compare the fractions:

(8/64) < (32/64)

So, (1/8) is less than (4/1).

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)

CodeLlama 13B: 

  To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 6.

So, we can rewrite the fractions as:

(7 / 2) = (7 / 6)
(10 / 6) = (10 / 6)

Now, we can compare the two fractions:

(7 / 6) > (10 / 6)

Therefore, the symbol that appropriately fills in the blank is '>'.

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (6 / 8) < (8 / 7)

Explanation:

(6 / 8) = 0.75
(8 / 7) = 1.14

Since 0.75 is less than 1.14, we can say that (6 / 8) is less than (8 / 7).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (9 / 3) < (7 / 1)

Explanation:

(9 / 3) = 3
(7 / 1) = 7

Since 3 is less than 7, we can say that (9 / 3) is less than (7 / 1).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (5 / 3) < (10 / 5)

Explanation:

(5 / 3) = 1.67
(10 / 5) = 2

Therefore, (5 / 3) < (10 / 5)

Expected answer: <

Correct? Yes

🔗 Follow-up

Problem: Consider the following situation: Previously, you compared the values of the fractions (5 / 3) and (10 / 5). Now, imagine if the second fraction was changed to (7 / 5) instead. Based on this new situation, fill in the blank with one of the following signs: <, >, or = (5 / 3) _ (7 / 5)

CodeLlama 13B: 

  (5 / 3) < (7 / 5)

Explanation:

(5 / 3) = 1.67
(7 / 5) = 1.4

Therefore, (5 / 3) < (7 / 5)

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)

CodeLlama 13B: 

  The first fraction is 3/2 and the second fraction is 9/10.

To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 20.

So, we can rewrite the fractions as:

3/2 = 6/20
9/10 = 18/20

Now, we can compare the numerators:

6 > 18

Therefore, the first fraction is greater than the second fraction.

### Answer: (3/2) > (9/10)

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.

CodeLlama 13B: 

  The comparison between (3/7) and (9/10) is different than the comparison between 3/2 and 9/10.

When we compare (3/7) and (9/10), we find that the numerators are both less than the denominators, so we can compare the fractions directly. The fraction with the larger numerator is greater.

In this case, (3/7) < (9/10).

However, when we compare 3/2 and 9/10, we find that the denominators are different, so we need to find the least common multiple (LCM) of the denominators to compare the fractions. The LCM of 2 and 10 is 20, so we can rewrite the fractions as:

3/2 = 6/20
9/10 = 18/20

Now, we can compare the numerators:

6 > 18

Therefore, the fraction with the larger numerator is greater.

In this case, 3/2 > 9/10.

So, the comparison between (3/7) and (9/10) is different than the comparison between 3/2 and 9/10. The impact of decreasing the numerator of our first fraction on the comparison is that it makes the fraction less than the second fraction, whereas decreasing the denominator of our first fraction makes the fraction greater than the second fraction.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (10 / 9) < (5 / 6)

Explanation:

(10 / 9) = 1.1111...
(5 / 6) = 0.8333...

Since 1.1111... is greater than 0.8333..., we can say that (10 / 9) is greater than (5 / 6).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (10 / 9) < (5 / 10)

Explanation:

(10 / 9) = 1.1111...
(5 / 10) = 0.5555...

Since 1.1111... is greater than 0.5555..., we can say that (10 / 9) is greater than (5 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 8) < (6 / 4)

Explanation:

(9 / 8) = 1.125
(6 / 4) = 1.5

Since 1.125 is less than 1.5, we can say that (9 / 8) is less than (6 / 4).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (10 / 3) < (10 / 2)

Explanation:

(10 / 3) = 3.33
(10 / 2) = 5

Since 3.33 is less than 5, we can say that (10 / 3) is less than (10 / 2). Therefore, the correct symbol is "<".

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?

CodeLlama 13B: 

  (10 / 3) < (10 / 10)

Explanation:

(10 / 3) = 3.33
(10 / 10) = 1

Since 3.33 is less than 1, we can say that (10 / 3) is less than (10 / 10). Therefore, the correct symbol is "<".

When the denominator of the second fraction is increased to 10, the comparison changes to:

(10 / 3) = (10 / 10)

Explanation:

(10 / 3) = 3.33
(10 / 10) = 1

Since 3.33 is equal to 1, we can say that (10 / 3) is equal to (10 / 10). Therefore, the correct symbol is "=".

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (2 / 1) < (6 / 5)

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions 5/4 and 10/3, we need to find the least common multiple (LCM) of the denominators, which is 12.

5/4 = 12/4 = 3
10/3 = 12/3 = 4

Since 3 < 4, we can conclude that 5/4 is less than 10/3.

Therefore, the correct symbol to fill in the blank is <.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (7 / 5) < (9 / 9)

Explanation:

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

Since 1.4 is less than 1, we can say that (7 / 5) is less than (9 / 9).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (3 / 7) < (5 / 8)

Explanation:

(3 / 7) = 0.42857142857142857142857142857143
(5 / 8) = 0.625

Since 0.42857142857142857142857142857143 is less than 0.625, we can say that (3 / 7) is less than (5 / 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 =.

CodeLlama 13B: 

  Reasoning:

(3 / 1) = 3
(5 / 9) = 5/9

Comparing the two fractions:

3 > 5/9

Therefore, the correct answer is:

(3 / 1) > (5 / 9)
### Answer: (3 / 1) > (5 / 9)

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 =.

CodeLlama 13B: 

  Reasoning:

(3 / 1) = 3
(5 / 5) = 1

Comparing the two fractions:

3 > 1

Therefore, the correct answer is:

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

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (2 / 2) = (6 / 6)

Therefore, the fractions are equal.

### 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)

CodeLlama 13B: 

  (2 / 2) < (6 / 5)

Therefore, the fractions are not equal.

### Answer:

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (7 / 6) < (9 / 6)

Explanation:

(7 / 6) = 1 2/3
(9 / 6) = 1 5/6

Since 1 2/3 is less than 1 5/6, we can write (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.

CodeLlama 13B: 

  (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.

CodeLlama 13B: 

  The answer is:

(2 / 7) < (2 / 9)

Explanation:

The first fraction, (2 / 7), is less than the second fraction, (2 / 9), because the numerator of the first fraction is smaller than the numerator of the second fraction.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 4) < (7 / 1)

Explanation:

(9 / 4) = 2.25
(7 / 1) = 7

Since 2.25 is less than 7, we can say that (9 / 4) is less than (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)

CodeLlama 13B: 

  (4 / 8) < (2 / 1)

Explanation:

The fraction (4 / 8) is less than (2 / 1) because the numerator of (4 / 8) is smaller than the numerator of (2 / 1).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  To properly compare the two fractions, we need to use the same denominator. Therefore, we can rewrite the expression as:

(9 / 9) = (8 / 9)

Now we can see that the two fractions are equal.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 10) > (3 / 10)

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)

CodeLlama 13B: 

  (9 / 4) > (3 / 10)

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)

CodeLlama 13B: 

  To compare the two fractions, we need to find a common denominator. In this case, we can multiply both the numerator and denominator of the first fraction by 3 to get:

(3 / 7) x 3 = (9 / 21)

Now, we can compare the two fractions:

(9 / 21) < (5 / 3)

So, the first fraction is less than the second.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (6 / 5) < (7 / 10)

Explanation:

(6 / 5) = 1.2
(7 / 10) = 0.7

Since 1.2 is less than 0.7, we can say that (6 / 5) is less than (7 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  The correct answer is:

(1 / 9) < (1 / 4)

Explanation:

(1 / 9) is less than (1 / 4) because 9 is greater than 4.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (7 / 1) > (6 / 1)

Explanation:

(7 / 1) = 7
(6 / 1) = 6

7 > 6, so (7 / 1) is greater than (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)

CodeLlama 13B: 

  (9 / 1) > (6 / 1)

Explanation:

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

9 > 6, so (9 / 1) is greater than (6 / 1).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (5 / 4) < (9 / 8)

Expected answer: >

Correct? No

🔗 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)

CodeLlama 13B: 

  The correct symbol to place between the two fractions in the expression (8/9) _ (3/4) is <.

Explanation:

The expression (8/9) _ (3/4) can be simplified by multiplying the numerators and denominators of each fraction.

(8/9) = 8/9 = 0.8888888888888889
(3/4) = 3/4 = 0.75

Therefore, the expression (8/9) _ (3/4) can be simplified to 0.8888888888888889 _ 0.75 = 0.6666666666666667.

Therefore, the correct symbol to place between the two fractions in the expression (8/9) _ (3/4) is <.

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)

CodeLlama 13B: 

  The correct symbol to fill in the blank is <.

Explanation:

(2 / 1) = 2
(4 / 9) = 0.4444444444444444

Since 2 is greater than 0.4444444444444444, the correct symbol to fill in the blank is <.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 9) < (2 / 2)

Explanation:

(9 / 9) = 1, which is greater than (2 / 2) = 1. Therefore, (9 / 9) is greater than (2 / 2).

Expected answer: =

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  The relationship between the two fractions is:

(6 / 1) > (4 / 4)

Explanation:

The first fraction, (6 / 1), is greater than the second fraction, (4 / 4), because the numerator of the first fraction is greater than the numerator of the second fraction.

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (3 / 9) < (8 / 8)

Explanation:

(3 / 9) = 0.333...
(8 / 8) = 1

Since 0.333... is less than 1, we can say that (3 / 9) is less than (8 / 8).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (4 / 10) < (1 / 2)

Explanation:

(4 / 10) = 0.4
(1 / 2) = 0.5

Since 0.4 is less than 0.5, we can say that (4 / 10) is less than (1 / 2).

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)

CodeLlama 13B: 

  The first fraction is 6/6, which is equal to 1.
The second fraction is 6/3, which is equal to 2.

So, we can compare the two fractions by comparing their values:

1 < 2

Therefore, the first fraction is less than the second fraction.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 30.

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

Now, we can multiply both fractions by the LCM to get:

(2/3) x 30 = 60/30 = 2
(2/10) x 30 = 60/30 = 2

Therefore, (2/3) = (2/10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (2 / 10) < (6 / 4)

Explanation:

(2 / 10) = 0.2
(6 / 4) = 1.5

Since 0.2 is less than 1.5, we can say that (2 / 10) is less than (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)

CodeLlama 13B: 

  To compare the values of the fractions, we need to find the least common multiple (LCM) of the denominators, which is 90.

(5/10) = 1/18
(6/9) = 2/18

Now, we can multiply both fractions by the LCM to get:

(5/10) = 1/90
(6/9) = 2/90

Now, we can compare the values of the fractions:

1/90 < 2/90

Therefore, the correct equation is:

(5/10) < (6/9)

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (2 / 9) < (5 / 5)

Explanation:

(2 / 9) = 0.222...
(5 / 5) = 1

Since 0.222... is less than 1, we can say that (2 / 9) is less than (5 / 5).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (1 / 9) < (7 / 9)

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 =.

CodeLlama 13B: 

  In the previous question, we compared (1/9) and (7/9) and found that (1/9) < (7/9).

Now, let's compare (1/9) and (7/7).

(1/9) = (7/7)

So, in this situation, the comparison is equal ( = ).

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 =.

CodeLlama 13B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 7.

(2/7) = 2/7
(1/6) = 1/6

Now, we can multiply both fractions by the LCM to get:

(2/7) = 2/7 x 7 = 14/49
(1/6) = 1/6 x 7 = 7/42

Now, we can compare the two fractions:

14/49 < 7/42

Therefore, (2/7) is less than (1/6).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the two fractions, we need to find a common denominator. In this case, the least common multiple of 9 and 10 is 90.

So, we can rewrite the fractions as:

(9/9) = (9/90)
(9/10) = (9/90)

Now we can compare the two fractions:

(9/9) > (9/10)

Therefore, the correct symbol to use is ">".

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)

CodeLlama 13B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 4 and 2. The LCM is 4.

Now, we can rewrite the two fractions as:

(8/4) = (2/1)
(5/2) = (2 1/2)

Now, we can compare the two fractions:

(2/1) > (2 1/2)

Therefore, the first fraction is greater than the second fraction.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the values of the fractions, we need to find the least common multiple (LCM) of the denominators, which is 20.

(5/2) = 2 1/2
(1/10) = 1/10

Now, we can multiply both fractions by the LCM to get:

(5/2) = 2 1/2 x 20 = 40
(1/10) = 1/10 x 20 = 2

Now, we can compare the values of the fractions:

40 > 2

Therefore, the symbol to fill in the blank is >.

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)

CodeLlama 13B: 

  The two fractions are equal, so we can fill in the blank with =:

(2 / 4) = (9 / 2)

Expected answer: <

Correct? No

🔗 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)

CodeLlama 13B: 

  The equation is:

(6 / 3) < (10 / 2)

To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 6. Then, we can multiply both fractions by the LCM to get:

(6 / 3) = (60 / 18)
(10 / 2) = (20 / 10)

Now we can compare the two fractions:

(60 / 18) < (20 / 10)

So, the correct answer is:

(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)

CodeLlama 13B: 

  The equation is:

(6 / 8) < (10 / 2)

To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 8. Then, we can multiply both fractions by the LCM to get:

(6 / 8) = (36 / 48)
(10 / 2) = (20 / 16)

Now we can compare the two fractions:

(36 / 48) < (20 / 16)

So, the correct answer is:

(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)

CodeLlama 13B: 

  (6/3) < (8/6)

Explanation:

(6/3) = 2
(8/6) = 4

Since 2 < 4, we can say that (6/3) < (8/6).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (3 / 4) < (6 / 5)

Explanation:

(3 / 4) = 0.75
(6 / 5) = 1.2

Since 0.75 is less than 1.2, we can say that (3 / 4) is less than (6 / 5).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  The first fraction is 1/1 and the second fraction is 3/1.

To compare these fractions, we need to find the least common multiple (LCM) of the denominators, which is 1.

Now, we can compare the numerators:

1/1 = 1
3/1 = 3

So, the first fraction is less than the second fraction.

Therefore, the correct answer is:

(1 / 1) < (3 / 1)

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (7 / 6) < (4 / 5)

Explanation:

(7 / 6) = 1 2/3
(4 / 5) = 0 8/5

Since 1 2/3 is less than 0 8/5, we can say that (7 / 6) is less than (4 / 5).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (6 / 4) < (2 / 2)

Explanation:

(6 / 4) = 1.5
(2 / 2) = 1

1.5 is less than 1, so (6 / 4) is less than (2 / 2).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (5/5) < (9/10)

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (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?

CodeLlama 13B: 

  (1 / 5) < (2 / 1)

Explanation:

The fraction (1 / 5) represents one fifth of the sweets that were initially available.
The fraction (2 / 1) represents two whole sweets that were offered.

Since one fifth of the sweets is less than two whole sweets, we can write:

(1 / 5) < (2 / 1)

Therefore, the fractions are not equal, and the first fraction is less than the second fraction.

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)

CodeLlama 13B: 

  To compare the two fractions in the equation (7 / 1) _ (4 / 2), we need to find the least common multiple (LCM) of the denominators.

The LCM of 1 and 2 is 2.

So, we can rewrite the equation as:

(7 / 2) _ (4 / 2)

Now, we can compare the two fractions by multiplying the numerators and denominators:

(7 × 2) / (4 × 2) = (14 / 4)

Therefore, the equation is equal to (14 / 4).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (4 / 7) < (9 / 4)

Explanation:

(4 / 7) = 0.5714285714285714
(9 / 4) = 2.25

Since 0.5714285714285714 is less than 2.25, we can say that (4 / 7) is less than (9 / 4).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  To compare the two fractions, we can use the following steps:

1. Multiply the first fraction by the reciprocal of the second fraction: (5/9) x (7/4) = (35/36)
2. Multiply the second fraction by the reciprocal of the first fraction: (4/7) x (9/5) = (32/35)
3. Compare the two results: (35/36) > (32/35)

Therefore, the first fraction is greater than the second fraction.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (8 / 3) = (7 / 3)

Explanation:

8 / 3 = 2.67
7 / 3 = 2.33

Since 2.67 is greater than 2.33, we can say that (8 / 3) is greater than (7 / 3).

Therefore, the correct answer is:

(8 / 3) > (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.

CodeLlama 13B: 

  To compare the two fractions, we can use the greater than or equal to sign (>=).

(5 / 1) >= (2 / 2)

This is because the first fraction is greater than the second fraction.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 3 is 24.

So, we can rewrite the fractions as:

(5/8) = (5/24)
(3/3) = (3/24)

Now we can compare the fractions:

(5/24) < (3/24)

Therefore, the correct answer is <.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  The correct symbol to fill the blank is <.

Explanation:

(5 / 8) = 0.625
(6 / 10) = 0.6

Therefore, (5 / 8) < (6 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (5/10) < (6/6)

Explanation:

(5/10) is less than (6/6) because the numerator of (5/10) is smaller than the numerator of (6/6).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (5 / 4) > (2 / 4)

Explanation:

(5 / 4) = 1 3/4
(2 / 4) = 1/2

Since 1 3/4 is greater than 1/2, we can say that (5 / 4) is greater than (2 / 4).

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)

CodeLlama 13B: 

  (6 / 10) = (6 / 10)

The two fractions are equal.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (6 / 8) < (2 / 9)

Explanation:

(6 / 8) = 0.75
(2 / 9) = 0.2222...

Since 0.75 is less than 0.2222..., we can say that (6 / 8) is less than (2 / 9).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (2 / 10) < (6 / 2)

Explanation:

(2 / 10) = 0.2
(6 / 2) = 3

Since 0.2 is less than 3, we can say that (2 / 10) is less than (6 / 2).

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)

CodeLlama 13B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 28.

(2/7) = 2/7 x 28/28 = 14/28
(9/4) = 9/4 x 28/4 = 22/28

Now, we can compare the two fractions:

14/28 < 22/28

Therefore, (2/7) is less than (9/4).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (1 / 1) < (2 / 10)

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (8 / 2) < (10 / 9)

Explanation:

(8 / 2) = 4
(10 / 9) = 1.111...

Since 4 is less than 1.111..., we can say that (8 / 2) is less than (10 / 9).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (3/2) < (9/8)

Explanation:

(3/2) = 1.5 and (9/8) = 1.125.

Since 1.5 is less than 1.125, we can say that (3/2) is less than (9/8).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (4 / 6) < (6 / 10)

Explanation:

(4 / 6) = 0.67
(6 / 10) = 0.6

Therefore, (4 / 6) is less than (6 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions (8/10) and (1/1), we need to find a common denominator. The least common multiple of 10 and 1 is 10, so we can rewrite the fractions as:

(8/10) = (8/10) x (10/10) = (80/100)
(1/1) = (1/1) x (10/10) = (10/100)

Now we can compare the fractions:

(80/100) > (10/100)

Therefore, (8/10) is greater than (1/1).

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (5/1) > (5/8)

Explanation:

(5/1) = 5
(5/8) = 0.625

Since 5 is greater than 0.625, (5/1) is greater than (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.

CodeLlama 13B: 

  The correct symbol to use in the statement (6 / 5) _ (9 / 6) is "=".

The statement (6 / 5) _ (9 / 6) is an equality, so the correct symbol to use is "=".

The symbol "<" is used to indicate that the expression on the left is less than the expression on the right, while the symbol ">" is used to indicate that the expression on the left is greater than the expression on the right.

Therefore, the correct statement is:

(6 / 5) _ (9 / 6) =

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  The fraction (7/5) is greater than (1/10).

Explanation:

(7/5) = 1.4
(1/10) = 0.1

Therefore, (7/5) is greater than (1/10).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (10/8) < (10/1)

Explanation:

(10/8) = 1.25
(10/1) = 10

Since 1.25 is less than 10, we can say that (10/8) is less than (10/1).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (3/2) < (4/6)

Explanation:

(3/2) = 1.5
(4/6) = 0.666...

Since 1.5 is less than 0.666..., we can say that (3/2) is less than (4/6).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 7) < (4 / 6)

Explanation:

(9 / 7) = 1.33
(4 / 6) = 0.67

Since 1.33 is less than 0.67, we can say that (9 / 7) is less than (4 / 6).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (8 / 7) < (8 / 8)

Explanation:

(8 / 7) = 1.1428571428571428
(8 / 8) = 1

Therefore, (8 / 7) is less than (8 / 8).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  The correct symbol to compare these two fractions is ">".

(5 / 5) > (4 / 6)

Explanation:

The first fraction, (5 / 5), is equal to 1, while the second fraction, (4 / 6), is equal to 2/3. Since 1 is greater than 2/3, the correct symbol to use is ">".

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)

CodeLlama 13B: 

  The correct symbol to compare these two fractions is "<".

(5 / 5) < (2 / 6)

Explanation:

The first fraction, (5 / 5), is equal to 1, while the second fraction, (2 / 6), is equal to 1/3. Since 1 is less than 1/3, the correct symbol to use is "<".

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (10/10) > (4/10)

Explanation:

(10/10) is equal to 1, while (4/10) is equal to 0.4. Since 1 is greater than 0.4, we can say that (10/10) is greater than (4/10).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (8 / 1) > (4 / 9)

Explanation:

* 8 is greater than 4.
* 1 is greater than 9.

Therefore, (8 / 1) is greater than (4 / 9).

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)

CodeLlama 13B: 

  (9 / 3) < (4 / 8)

Explanation:

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

Since 3 is less than 0.5, we can say that (9 / 3) is less than (4 / 8).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions in the expression (10/7) _ (9/6), we need to find the least common multiple (LCM) of the denominators, which is 42.

(10/7) = 10/42
(9/6) = 9/42

Now, we can compare the fractions by multiplying both numerators by the LCM:

(10/7) _ (9/6) = (10 \* 42)/(7 \* 42) _ (9 \* 42)/(6 \* 42)
= (420)/(28 \* 42) _ (36)/(6 \* 42)
= (420)/(28) _ (36)/(6)

Since (420)/(28) > (36)/(6), we can say that (10/7) > (9/6).

Therefore, the correct answer is:

(10/7) _ (9/6) = >

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (10 / 8) < (3 / 1)

Explanation:

(10 / 8) = 1.25
(3 / 1) = 3

Since 1.25 is less than 3, we can write:

(10 / 8) < (3 / 1)

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.

CodeLlama 13B: 

  (10 / 7) < (3 / 1)

Explanation:

(10 / 7) = 1.43
(3 / 1) = 3

Since 1.43 is less than 3, we can write:

(10 / 7) < (3 / 1)

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)

CodeLlama 13B: 

  The relationship between the two fractions is:

(3 / 2) < (3 / 5)

Explanation:

(3 / 2) = 1.5
(3 / 5) = 0.6

Since 1.5 is less than 0.6, we can say that (3 / 2) is less than (3 / 5).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (4 / 10) < (2 / 2)

Explanation:

(4 / 10) = 0.4
(2 / 2) = 1

Since 0.4 is less than 1, we can say that (4 / 10) is less than (2 / 2).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (6 / 7) < (2 / 10)

Explanation:

(6 / 7) = 0.86
(2 / 10) = 0.2

Since 0.86 is less than 0.2, we can say that (6 / 7) is less than (2 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 7) < (10 / 3)

Explanation:

(9 / 7) = 1.333...
(10 / 3) = 3.333...

Since 1.333... is less than 3.333..., we can say that (9 / 7) is less than (10 / 3).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (8 / 8) > (2 / 8)

Explanation:

(8 / 8) = 1, which is greater than (2 / 8) = 0.5.

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.

CodeLlama 13B: 

  (8 / 10) < (2 / 8)

Explanation:

(8 / 10) = 0.8, which is less than (2 / 8) = 0.25.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 24. Then, we can multiply both fractions by the LCM to get:

(4/3) = 4/24 = 1/6
(1/8) = 1/24 = 1/6

Since both fractions are equal, we can say that (4/3) _ (1/8) = =.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (4 / 6) < (6 / 10)

Explanation:

The fraction (4 / 6) is less than (6 / 10) because the numerator of (4 / 6) is smaller than the numerator of (6 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (9 / 6) < (6 / 8)

Explanation:

(9 / 6) = 1.5
(6 / 8) = 0.75

Since 1.5 is less than 0.75, we can say that (9 / 6) is less than (6 / 8).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (2/6) < (8/7)

Explanation:

(2/6) = 1/3
(8/7) = 8/7

Since 1/3 is less than 8/7, we can write:

(2/6) < (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?

CodeLlama 13B: 

  (2/7) < (8/7)

Explanation:

(2/7) = 2/7
(8/7) = 8/7

Since 2/7 is less than 8/7, we can write:

(2/7) < (8/7)

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (9 / 6) < (4 / 10)

Explanation:

(9 / 6) = 1.5
(4 / 10) = 0.4

1.5 is less than 0.4, so (9 / 6) is less than (4 / 10).

Expected answer: >

Correct? No

🔗 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)

CodeLlama 13B: 

  (6 / 8) > (5 / 1)

Explanation:

(6 / 8) = 0.75
(5 / 1) = 5

Since 0.75 is greater than 5, we can conclude that (6 / 8) is greater than (5 / 1).

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (8 / 4) < (1 / 10)

Explanation:

(8 / 4) = 2
(1 / 10) = 0.1

2 < 0.1, so (8 / 4) is less than (1 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (6 / 3) = (8 / 2)

The expressions are equal because the numerators and denominators are equal.

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)

CodeLlama 13B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 6.

(4/6) = 2/3
(6/3) = 2

Now, we can compare the two fractions:

2/3 < 2

Therefore, the symbol that should be used is "<".

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  To compare the fractions 6/7 and 3/1, we can use the following steps:

1. Multiply both fractions by their least common multiple (LCM), which is 21 in this case.
2. Now we have 6/7 = 12/21 and 3/1 = 6/21.
3. Compare the numerators: 12 > 6, so 6/7 > 3/1.

Therefore, we can say that 6/7 > 3/1.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 13B: 

  (6 / 10) < (9 / 10)

Explanation:

(6 / 10) = 0.6
(9 / 10) = 0.9

Since 0.6 is less than 0.9, we can say that (6 / 10) is less than (9 / 10).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 13B: 

  (6 / 8) < (4 / 9)

Explanation:

(6 / 8) = 3/4
(4 / 9) = 4/9

Since 3/4 is less than 4/9, we can fill in the blank with "<".

Expected answer: >

Correct? No