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CodeLlama 34B 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 34B: 

  (1 / 8) is less than (4 / 1) because 1/8 is equal to 0.125, while 4/1 is equal to 4.

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 34B: 

  To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 6. Then, we can convert both fractions to have a denominator of 6 and compare them.

(7 / 2) = (7 × 3) / 6 = 21 / 6
(10 / 6) = (10 × 2) / 6 = 20 / 6

Since 21 / 6 is greater than 20 / 6, the correct symbol to use is '>'.

Therefore, the correct answer is:

(7 / 2) > (10 / 6)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

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

So, (9 / 3) < (7 / 1).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (5 / 3) > (10 / 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 34B: 

  (3 / 2) < (9 / 10)

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (10 / 9) = (50 / 45)
(5 / 6) = (30 / 45)

Since (50 / 45) is greater than (30 / 45), we can say that (10 / 9) is greater than (5 / 6).

So, the correct answer is:

(10 / 9) > (5 / 6)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (10 / 9) > (5 / 10)

The first fraction is greater than the second fraction.

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (9 / 8) = (6 / 4)

Since both fractions are equal, we can write:

(9 / 8) = (6 / 4) = 3/2

Therefore, the two fractions are equal.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (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 to fill in the gap is <.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (2 / 1) = (12 / 5)
(6 / 5) = (12 / 5)

Therefore, (2 / 1) = (6 / 5) = (12 / 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 34B: 

  To compare the fractions 5/4 and 10/3, we need to find the least common multiple (LCM) of the denominators, which is 12. Then, we can convert both fractions to have a denominator of 12:

5/4 = 10/12
10/3 = 20/12

Now we can see that 10/3 is greater than 5/4, so the correct symbol to use is >.

Therefore, 10/3 > 5/4.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (7 / 5) = 1 4/5
(9 / 9) = 1

So, (7 / 5) is greater than (9 / 9).

Therefore, the correct answer is:

(7 / 5) > (9 / 9)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (3 / 7) is less than (5 / 8).

So, the correct answer is:

(3 / 7) < (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.

CodeLlama 34B: 

  (3 / 7) is less than (6 / 8).

So, the correct answer is:

(3 / 7) < (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 =.

CodeLlama 34B: 

  (3 / 1) _ (5 / 9)

To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 9.

Then, we can convert both fractions to have a denominator of 9:

(3 / 1) = (3 × 9) / 9 = 27 / 9
(5 / 9) = (5 × 9) / 9 = 45 / 9

Now we can compare the two fractions:

27 / 9 > 45 / 9

So, (3 / 1) is greater than (5 / 9).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

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

Since both fractions are equal to 1, we can write:

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

So, the values of the fractions are equal.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (7 / 6) = (9 / 6)

Both fractions are equal, so we insert "=" between them.

Expected answer: <

Correct? No

🔗 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 34B: 

  (2 / 7) < (2 / 9)

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 34B: 

  (9 / 4) = (7 / 1)

The two fractions are equal.

Expected answer: <

Correct? No

🔗 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 34B: 

  (4 / 8) > (2 / 1)

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.

CodeLlama 34B: 

  (9 / 9) = (8 / 9)

Therefore, the correct answer is:

(9 / 9) = (8 / 9)

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 34B: 

  (9 / 10) is greater than (3 / 10).

So, the correct answer is:

(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 34B: 

  (9 / 4) is greater than (3 / 10).

So, the correct answer is:

(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 34B: 

  (3 / 7) = 0.43
(5 / 3) = 1.67

Since 0.43 is less than 1.67, the first fraction is less than the second.

Therefore, the correct answer is:

(3 / 7) < (5 / 3)

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 34B: 

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

So, (6 / 5) > (7 / 10).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

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

Since 7 is greater than 6, the correct answer is:

(7 / 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)

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

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

The reason for this is that (8 / 9) is less than (3 / 4). To determine which symbol to use, you can simplify the fractions and compare the resulting values.

(8 / 9) = 0.888...
(3 / 4) = 0.75

Since 0.888... is less than 0.75, the correct symbol to use is <. Therefore, the expression (8 / 9) _ (3 / 4) can be written as (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)

CodeLlama 34B: 

  To compare the fractions, we need to find the least common multiple (LCM) of the denominators, which is 18. Then, we can convert both fractions to equivalent fractions with denominator 18.

(2 / 1) = (2 × 9) / 18 = 18 / 18 = 1

(4 / 9) = (4 × 1) / 18 = 4 / 18

Now we can compare the fractions:

1 > 4/18

So, (2 / 1) is greater than (4 / 9).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (9 / 9) = (2 / 2)

Both fractions are equal to 1.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (6 / 1) = (6 / 4)

Therefore, the relationship between the two fractions is =.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (3 / 9) = (24 / 27)
(8 / 8) = (8 / 8)

Since (24 / 27) is less than (8 / 8), the value of the first fraction is less than the value of the second fraction. Therefore, the correct answer is:

(3 / 9) < (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 34B: 

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

Since 0.4 < 0.5, the value of (4 / 10) is less than the value of (1 / 2). Therefore, the correct answer is:

(4 / 10) < (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 34B: 

  (6 / 6) = (6 / 3)

Both fractions are equal, so the correct symbol to fill in the blank space is "=".

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 30. Then, we can convert both fractions to equivalent fractions with denominator 30.

(2/3) = (40/60)
(2/10) = (40/120)

Now, we can compare the fractions:

(40/60) > (40/120)

Therefore, the correct sign is >.

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (2 / 10) = (6 / 4)

Both fractions are equal to 3/5.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  To compare the values of these fractions, we need to find the least common multiple (LCM) of the denominators, which is 18. Then, we can convert both fractions to equivalent fractions with a denominator of 18.

(5 / 10) = (5 × 9) / (10 × 9) = 45 / 90
(6 / 9) = (6 × 10) / (9 × 10) = 60 / 90

Now, we can compare the values of the fractions:

45 / 90 < 60 / 90

Therefore, (5 / 10) is less than (6 / 9).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (2 / 9) < (5 / 5)

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)

CodeLlama 34B: 

  (2 / 9) < (5 / 8)

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (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 34B: 

  (1 / 9) < (7 / 7)

In this case, the comparison changes because the second fraction, (7 / 7), is equal to 1. So, the comparison is now:

(1 / 9) < 1

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

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 34B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 42.

(2/7) = (42/42) x (2/7) = 6/42

(1/6) = (42/42) x (1/6) = 7/42

Now we can compare the two fractions:

6/42 < 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 34B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 90. Then, we can convert both fractions to equivalent fractions with a denominator of 90.

(9/9) = (9/9) x (90/90) = (81/90)
(9/10) = (9/10) x (90/90) = (81/90)

Now, we can compare the two fractions:

(81/90) = (81/90)

Therefore, the two fractions are equal.

Expected answer: >

Correct? No

🔗 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 34B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 4 and 2. The LCM of 4 and 2 is 8.

So, we can rewrite the fractions as:

(8 / 4) = (8 × 2) / 8 = 4 / 2 = 2

(5 / 2) = (5 × 2) / 8 = 10 / 8 = 1 2/8

Now we can see that the first fraction is greater than the second fraction, so the correct answer is:

(8 / 4) is greater than (5 / 2)

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 34B: 

  To compare the values of these fractions, we need to find the least common multiple (LCM) of the denominators, which is 20. Then, we can convert both fractions to equivalent fractions with a denominator of 20.

(5 / 2) = (5 × 20) / 20 = 100 / 20 = 5

(1 / 10) = (1 × 20) / 20 = 20 / 20 = 1

Now, we can compare the values of the fractions:

5 > 1

Therefore, the correct 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 34B: 

  (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)

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

  (6 / 3) > (10 / 2)

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (6 / 3) = (8 / 6)

Since both fractions are equal, we can fill in the blank with the symbol "=".

So, the correct answer is:

(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 34B: 

  (3 / 4) = (6 / 5)

Since both fractions are equal, we can fill in the blank with "=".

So, the correct answer is:

(3 / 4) = (6 / 5)

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (1 / 1) = (3 / 1)

Both fractions are equal, so the correct answer is "=".

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (7 / 6) = (14 / 10)
(4 / 5) = (8 / 10)

Since (14 / 10) is greater than (8 / 10), we can say that (7 / 6) is greater than (4 / 5).

Therefore, the correct answer is:

(7 / 6) > (4 / 5)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (6 / 4) = (3 / 1)
(2 / 2) = (1 / 1)

Since (3 / 1) is greater than (1 / 1), the correct answer is:

(6 / 4) > (2 / 2)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (5 / 5) = (9 / 10)

Since both fractions are equal, we can fill in the blank with "=".

So, the correct answer is:

(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 34B: 

  (1 / 5) is less than (1 / 1) because 5 is greater than 1.

So, the correct answer is <.

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 34B: 

  (1 / 5) is less than (2 / 1) because 5 is greater than 2.

So, the correct answer is <.

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 34B: 

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

So, we can rewrite the equation as:

(7 / 1) _ (4 / 2) = (7 \* 2) / (1 \* 2) _ (4 \* 2) / (2 \* 2) = 14 / 4 = 3.5

Therefore, the correct comparison is:

(7 / 1) _ (4 / 2) = 3.5

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (4 / 7) is less than (9 / 4) because 4/7 = 0.57 and 9/4 = 2.25, so the second fraction is greater.

Therefore, the correct answer is:

(4 / 7) < (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 34B: 

  (5 / 9) < (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?

CodeLlama 34B: 

  When we change the denominator of the second fraction from 7 to 10, the fraction becomes (4 / 10).

Now, we can compare the two fractions:

(5 / 9) < (4 / 10)

So, the fraction (5 / 9) is less than the fraction (4 / 10).

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (8 / 3) = 2.67
(7 / 3) = 2.33

Since 2.67 is greater than 2.33, 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 34B: 

  The equation is:

(5 / 1) _ (2 / 2)

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

So, the equation becomes:

(5 / 1) _ (2 / 2) = (10 / 2) _ (4 / 2) = 10 _ 4 = 40

Therefore, the correct sign to use is >, because 40 is greater than 10.

So, the final equation is:

(5 / 1) > (2 / 2)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (5 / 8) = (15 / 24)
(3 / 3) = (9 / 9)

Since (15 / 24) is less than (9 / 9), the correct answer is:

(5 / 8) < (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)

CodeLlama 34B: 

  To determine which symbol is appropriate to fill the blank in the comparison, we need to evaluate the two fractions and compare them.

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

Since 0.625 is greater than 0.6, the appropriate symbol to fill the blank is >.

Therefore, the correct comparison is:

(5 / 8) > (6 / 10)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (5 / 10) = (6 / 6)

Since both fractions are equal, we can fill in the blank with "=".

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (5 / 4) is greater than (2 / 4).

So, the correct answer is:

(5 / 4) > (2 / 4)

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.

CodeLlama 34B: 

  (5 / 4) is greater than (2 / 10).

So, the correct answer is:

(5 / 4) > (2 / 10)

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 34B: 

  (6 / 10) = (6 / 10)

Both fractions are equal to 0.6.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (6 / 8) is equal to (2 / 9).

Therefore, the blank is filled with "=".

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

  To compare fractions, we need to find the least common multiple (LCM) of the denominators, which is 28. Then, we can convert both fractions to equivalent fractions with denominator 28.

(2/7) = (2 x 14)/(7 x 14) = 28/98
(9/4) = (9 x 7)/(4 x 7) = 63/28

Now we can compare the fractions:

28/98 > 63/28

Therefore, (2/7) 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)

CodeLlama 34B: 

  (1 / 1) is equal to (2 / 10).

Therefore, the correct answer is =.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (8 / 2) = 4
(10 / 9) = 1.11...

So, (8 / 2) < (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 34B: 

  (3 / 2) > (9 / 8)

Explanation:

To compare fractions, we can use the following rule:

A/B > C/D if and only if AD > BC

In this case, we have:

3/2 > 9/8 if and only if 3/2 > 9/8

Which is true, so we can conclude that (3/2) > (9/8).

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?

CodeLlama 34B: 

  (3 / 2) < (9 / 6)

If the denominator of the second fraction was 6 instead of 8, the fraction would be (9 / 6), which is equal to (3 / 2). In this case, the relationship between the fractions would be =, since both fractions are equal.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (4 / 6) = 2/3
(6 / 10) = 3/5

Since 2/3 is less than 3/5, the correct answer is:

(4 / 6) < (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 34B: 

  The correct symbol to compare the following fractions is "is greater than".

(8 / 10) > (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 34B: 

  (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?

CodeLlama 34B: 

  (5 / 3) > (5 / 8)

If the first basket had 5/3 of the apples, it would have 5/3 x 3 = 5 apples.
If the second basket had 5/8 of the apples, it would have 5/8 x 3 = 3.75 apples.

Since 5 apples is greater than 3.75 apples, the first basket has more apples than the second basket.

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 34B: 

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

The statement is asking for the result of dividing 6 by 5 and then dividing the result by 9. The correct order of operations is to perform the division operations first, so the correct calculation is:

(6 / 5) = 1.2
(9 / 6) = 1.5

Therefore, the correct symbol to use in the statement is "=", which indicates that the two expressions are equal.

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (7 / 5) > (1 / 10)

Explanation:

To compare fractions, we need to find the least common multiple (LCM) of the denominators. In this case, the LCM of 5 and 10 is 50.

So, we can rewrite the fractions as:

(7 / 5) = (7 × 50 / 5 × 50) = 70/25
(1 / 10) = (1 × 50 / 10 × 50) = 5/50

Now we can compare the fractions:

70/25 > 5/50

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 34B: 

  (10 / 8) = (10 / 1)

Since both fractions are equal, we can fill in the blank with "=".

So, the correct answer is:

(10 / 8) = (10 / 1)

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (3 / 2) = 1.5
(4 / 6) = 0.67

So, (3 / 2) > (4 / 6).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (9 / 7) > (4 / 6)

To compare these fractions, we need to find the least common multiple (LCM) of the denominators, which is 42. Then, we can convert both fractions to equivalent fractions with denominator 42:

(9 / 7) = (9 × 6) / (7 × 6) = 54 / 42
(4 / 6) = (4 × 7) / (6 × 7) = 28 / 42

Now we can compare the fractions:

54 / 42 > 28 / 42

So, (9 / 7) is greater than (4 / 6).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (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.

CodeLlama 34B: 

  (7 / 7) = (8 / 8)

The fractions are equal.

Expected answer: =

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  To compare these two fractions, we need to find the least common multiple (LCM) of the denominators, which is 30. Then, we can convert both fractions to have a denominator of 30 and compare them.

(5 / 5) = (5 × 6) / 30 = 30 / 30 = 1

(4 / 6) = (4 × 5) / 30 = 20 / 30 = 2/3

So, (5 / 5) is greater than (4 / 6).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

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

So, (10 / 10) > (4 / 10).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (8 / 1) = 8
(4 / 9) = 0.44...

So, (8 / 1) > (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 34B: 

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

So, (9 / 3) > (4 / 8).

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  To compare fractions, we need to find the least common multiple (LCM) of the denominators, which is 42.

Then, we can convert both fractions to have a denominator of 42:

(10/7) = (10 \* 6) / (7 \* 6) = 60 / 42
(9/6) = (9 \* 7) / (6 \* 7) = 63 / 42

Now we can compare the fractions:

60/42 < 63/42

So, (10/7) < (9/6).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (10/8) < (3/1)

Explanation:

To compare fractions, we need to find the least common multiple (LCM) of the denominators. In this case, the LCM of 8 and 1 is 8.

So, we can rewrite the fractions as:

(10/8) = (10/8) × (8/8) = 5/8
(3/1) = (3/1) × (1/1) = 3/1

Now we can compare the fractions:

5/8 < 3/1

Therefore, (10/8) is less than (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 34B: 

  (3 / 2) _ (3 / 5) = (3 × 5) / (2 × 3) = 15 / 6 = 5 / 2.

Therefore, the relationship between the two fractions is >.

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (4 / 10) = (2 / 2)

Since both fractions are equal, we can fill in the blank with "=".

So, the correct answer is:

(4 / 10) = (2 / 2)

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (6 / 7) is greater than (2 / 10) because 6/7 = 0.857 and 2/10 = 0.2.

Therefore, the correct answer is:

(6 / 7) > (2 / 10)

Expected answer: >

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  To compare the values of these fractions, we need to find the least common multiple (LCM) of the denominators, which is 21. Then, we can convert both fractions to have a denominator of 21 and compare them.

(9/7) = (9 x 3) / (7 x 3) = 27 / 21
(10/3) = (10 x 2) / (3 x 2) = 20 / 6

Now we can compare the fractions:

27 / 21 > 20 / 6

So (9/7) is greater than (10/3).

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (8 / 8) = (2 / 8)

Both fractions are equal, so the correct answer is =.

Expected answer: >

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (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?

CodeLlama 34B: 

  (4/9) < (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 34B: 

  (4 / 6) is less than (6 / 10) because 4/6 = 2/3 and 6/10 = 3/5, and 2/3 is less than 3/5.

Therefore, the correct symbol is <.

So, the comparison is:

(4 / 6) < (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 34B: 

  (9 / 6) = (9 × 8) / (6 × 8) = 72 / 48 = 1 1/2
(6 / 8) = (6 × 6) / (8 × 6) = 36 / 48 = 1/2

So, (9 / 6) > (6 / 8).

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)

CodeLlama 34B: 

  (2 / 6) = (8 / 7)

Since both fractions are equal, we can fill in the blank with the symbol "=".

So, the correct answer is:

(2 / 6) = (8 / 7)

Expected answer: <

Correct? No

🔗 Problem

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

CodeLlama 34B: 

  (9 / 6) = 1 1/2
(4 / 10) = 2/5

Since 1 1/2 is greater than 2/5, the correct answer is:

(9 / 6) > (4 / 10)

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)

CodeLlama 34B: 

  (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)

CodeLlama 34B: 

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

Since 2 is greater than 0.1, the correct answer is:

(8 / 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)

CodeLlama 34B: 

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

So, (6 / 3) < (8 / 2).

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  To compare the two fractions, we need to find the least common multiple (LCM) of the denominators, which is 6. Then, we can convert both fractions to equivalent fractions with denominator 6.

(4/6) = (4/6) x (6/6) = (24/36)
(6/3) = (6/3) x (3/3) = (18/9)

Now we can compare the two fractions:

(24/36) < (18/9)

Therefore, the correct answer is <.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  To compare the fractions 6/7 and 3/1 properly, we need to find the least common multiple (LCM) of the denominators, which is 7.

Then, we can convert both fractions to have a denominator of 7:

6/7 = 6/7 × 7/7 = 42/49
3/1 = 3/1 × 1/1 = 3/1

Now we can compare the fractions:

42/49 < 3/1

So, 6/7 is less than 3/1.

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

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

Since 0.6 < 0.9, the value of (6 / 10) is less than the value of (9 / 10). Therefore, the correct answer is:

(6 / 10) < (9 / 10)

Expected answer: <

Correct? Yes

🔗 Problem

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

CodeLlama 34B: 

  (6 / 8) is equal to (4 / 9).

Therefore, the correct answer is =.

Expected answer: >

Correct? No