CodeLlama 7B 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: Complete the following comparison between two fractions. (1 / 8) _ (4 / 1).
CodeLlama 7B:
To compare the two fractions, we need to find their common denominator. The least common multiple of 8 and 1 is 8, so we can rewrite the fractions as: (1/8) = 1/8 (4/1) = 4/1 Now we can compare the two fractions: (1/8) = 1/8 = (4/1) So the two fractions are equal.
Expected answer: <
Correct? No
Problem: Determine which symbol appropriately fills in the blank (either '<', '=', or '>') to accurately compare these two fractions: (7 / 2) _ (10 / 6)
CodeLlama 7B:
To compare these two fractions, we need to convert them to the same denominator. Let's convert the second fraction to have a denominator of 12: (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7 / 2) _ (10 / 6) = (7
Expected answer: >
Correct? No
Problem: Complete the following comparison by filling in the blank (<, >, or =): (6 / 8) _ (8 / 7)
CodeLlama 7B:
(6 / 8) < (8 / 7)
Expected answer: <
Correct? Yes
Problem: Complete the following comparison by filling in the blank (<, >, or =). Consider what will happen if we are comparing the fraction 6/8 to the fraction 6/7 instead: (6 / 8) _ (6 / 7)
CodeLlama 7B:
(6 / 8) > (6 / 7)
Expected answer: <
Correct? No
Problem: Compare the values of the two fractions below by filling in the blank with <, >, or =. (9 / 3) _ (7 / 1)
CodeLlama 7B:
The two fractions are (9/3) and (7/1). To compare the values of these fractions, we need to compare their numerators and denominators. The numerators are 9 and 7, and the denominators are 3 and 1, respectively. Since 9 is greater than 7, we can say that (9/3) is greater than (7/1). Therefore, we can fill in the blank with <. So, the correct answer is: (9/3) < (7/1)
Expected answer: <
Correct? Yes
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.
CodeLlama 7B:
Sure! Let's compare the fractions (9/3) and (1/1) using the same method as before. To compare the values of these fractions, we need to compare their numerators and denominators. The numerators are 9 and 1, and the denominators are 3 and 1, respectively. Since 9 is greater than 1, we can say that (9/3) is greater than (1/1). Therefore, we can fill in the blank with >. So, the correct answer is: (9/3) > (1/1)
Expected answer: >
Correct? Yes
Problem: Fill in the blank with one of the following signs: <, >, or = (5 / 3) _ (10 / 5)
CodeLlama 7B:
(5 / 3) _ (10 / 5) = (5 / 3) * (10 / 5) = (5 / 3) * 2 = 10
Expected answer: <
Correct? No
Problem: Compare the values of the two fractions by filling in the blank with <, >, or =. Here are the fractions: (3 / 2) _ (9 / 10)
CodeLlama 7B:
The two fractions are (3/2) and (9/10). To compare the values of the two fractions, we need to compare their numerators and denominators. The numerators of the two fractions are 3 and 9, respectively. Since 3 is less than 9, we can say that (3/2) is less than (9/10). Therefore, the correct answer is: (3/2) < (9/10)
Expected answer: >
Correct? No
Problem: Compare the values of these fractions by filling in the blank with <, >, or =. (10 / 9) _ (5 / 6)
CodeLlama 7B:
(10 / 9) < (5 / 6) Explanation: (10 / 9) = 11/9 (5 / 6) = 5/6 Since 11/9 is greater than 5/6, we say that (10 / 9) is greater than (5 / 6). Therefore, we fill in the blank with <.
Expected answer: >
Correct? No
Problem: Compare the values of the two fractions and fill in the blank with <, >, or =. (10 / 9) _ (5 / 10)
CodeLlama 7B:
The values of the two fractions are: (10 / 9) = 1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
Expected answer: >
Correct? Yes
Problem: Compare the two fractions by completing the following statement with <, >, or =. (9 / 8) _ (6 / 4)
CodeLlama 7B:
(9 / 8) < (6 / 4) Explanation: (9 / 8) = 1 1/2 (6 / 4) = 3/2 So, (9 / 8) is less than (6 / 4).
Expected answer: <
Correct? Yes
Problem: Compare the two fractions below by filling in the gap with the appropriate symbol (<,>,=). (10 / 3) _ (10 / 2)
CodeLlama 7B:
(10 / 3) < (10 / 2)
Expected answer: <
Correct? Yes
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 7B:
(10 / 3) _ (10 / 10) The comparison is: (10 / 3) < (10 / 10) When the denominator of the second fraction is increased to 10, the comparison becomes: (10 / 3) < (10 / 10) This comparison is true, because (10 / 3) is less than (10 / 10).
Expected answer: >
Correct? No
Problem: Compare the two fractions by filling in the blank with <, >, or =. (2 / 1) _ (6 / 5)
CodeLlama 7B:
(2 / 1) < (6 / 5)
Expected answer: >
Correct? No
Problem: Compare the fractions 5 / 4 and 10 / 3 by filling in the blank with one of the following symbols: <, >, or =.
CodeLlama 7B:
The fractions 5/4 and 10/3 can be compared using the following symbols: * < if 5/4 is less than 10/3 * > if 5/4 is greater than 10/3 * = if 5/4 is equal to 10/3 To compare these fractions, we can convert them to decimals by multiplying both the numerator and denominator by the same number, in this case, 10. 5/4 = 5/4 x 10 = 50/40 10/3 = 10/3 x 10 = 100/30 Now we can compare the decimals: 50/40 < 100/30 Therefore, 5/4 is less than 10/3.
Expected answer: <
Correct? Yes
Problem: Compare the values of these two fractions by filling in the blank with <, > or =: (7 / 5) _ (9 / 9)
CodeLlama 7B:
(7/5) < (9/9)
Expected answer: >
Correct? No
Problem: Compare the following two fractions by filling in the blank with <, >, or =: (3 / 7) _ (5 / 8)
CodeLlama 7B:
(3 / 7) < (5 / 8)
Expected answer: <
Correct? Yes
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 7B:
(3 / 7) < (6 / 8)
Expected answer: <
Correct? Yes
Problem: Question: Compare these two fractions: (3 / 1) _ (5 / 9) Hint: Fill the blank with one of the following: <, >, or =.
CodeLlama 7B:
The two fractions are: (3 / 1) = (5 / 9) Comparing the numerators, we see that 3 = 5, so the fractions are equal. Therefore, the correct answer is: (3 / 1) = (5 / 9) = <<=>>
Expected answer: >
Correct? No
Problem: Compare the values of the following fractions: (2 / 2) _ (6 / 6) Fill in the blank with <, >, or = .
CodeLlama 7B:
The values of the fractions are: (2 / 2) = 1 (6 / 6) = 1 Therefore, the comparison is: 1 = 1 So, the fractions are equal. The symbol used to represent this equality is: =
Expected answer: =
Correct? Yes
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 7B:
The values of the fractions are: (2 / 2) = 1 (6 / 5) = 1.2 Therefore, the comparison is: 1 < 1.2 So, the fraction (2 / 2) is less than the fraction (6 / 5). The symbol used to represent this inequality is:
Expected answer: <
Correct? Yes
Problem: Compare the following fractions by inserting "<", ">" or "=" between them. (7 / 6) _ (9 / 6)
CodeLlama 7B:
(7/6) < (9/6) Explanation: The first fraction is less than the second fraction because 7/6 is less than 9/6.
Expected answer: <
Correct? Yes
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 7B:
The correct answer is <. (2 / 7) < (2 / 9) because 2/7 is less than 2/9.
Expected answer: >
Correct? No
Problem: Determine the relation between the two following fractions by filling in the blank with <, >, or =: (9 / 4) _ (7 / 1)
CodeLlama 7B:
The relation between the two fractions is: (9 / 4) = (7 / 1) This is because the numerator of the first fraction is 9, which is equal to the numerator of the second fraction, and the denominator of the first fraction is 4, which is equal to the denominator of the second fraction. Therefore, the two fractions are equal.
Expected answer: <
Correct? No
Problem: Fill in the blank with one of the symbols <, >, or = to complete the comparison between the two fractions. (4 / 8) _ (2 / 1)
CodeLlama 7B:
(4 / 8) < (2 / 1) The fraction (4 / 8) is less than the fraction (2 / 1).
Expected answer: <
Correct? Yes
Problem: Fill in the blank with either <, >, or = in the following expression: (9 / 9) _ (8 / 9), to properly compare the two fractions.
CodeLlama 7B:
The correct comparison is: (9 / 9) > (8 / 9) Explanation: The first fraction is 9/9, which is equal to 1. The second fraction is 8/9, which is less than 1. Therefore, the correct comparison is (9/9) > (8/9).
Expected answer: >
Correct? Yes
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?
CodeLlama 7B:
The correct comparison is: (9 / 2) < (8 / 9) Explanation: The first fraction is 9/2, which is less than 8/9.
Expected answer: >
Correct? No
Problem: Compare the following fractions by filling in the blank with <, >, or =. (9 / 10) _ (3 / 10)
CodeLlama 7B:
(9 / 10) < (3 / 10)
Expected answer: >
Correct? No
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 7B:
The first fraction is less than the second. (3 / 7) = (5 / 3) 3/7 = 5/3 3 = 5 7 = 3 So, the first fraction is less than the second.
Expected answer: <
Correct? Yes
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (6 / 5) _ (7 / 10)
CodeLlama 7B:
(6 / 5) < (7 / 10)
Expected answer: >
Correct? No
Problem: Fill in the blank in the following equation with one of these symbols: <, >, or =. (1 / 9) _ (1 / 4)
CodeLlama 7B:
The correct symbol to fill in the blank with is <. (1 / 9) < (1 / 4) This is because the left side of the equation is less than the right side.
Expected answer: <
Correct? Yes
Problem: Compare the following fractions and fill in the blank with <, >, or =: (7 / 1) _ (6 / 1)
CodeLlama 7B:
(7 / 1) < (6 / 1)
Expected answer: >
Correct? No
Problem: Please fill in the blank with <, >, or = to compare the following fractions. (5 / 4) _ (9 / 8)
CodeLlama 7B:
To compare the following fractions, we need to compare their common denominators. (5 / 4) = (9 / 8) The common denominator is 8, so we can compare the numerators: 5 = 9 Therefore, the fractions are equal. ### Answer: =
Expected answer: >
Correct? No
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 7B:
The correct symbol to place between the two fractions in the expression (8 / 9) _ (3 / 4) is <. The expression (8 / 9) _ (3 / 4) can be simplified as follows: (8 / 9) _ (3 / 4) = (8 / 9) \* (3 / 4) = (8 \* 3) / (9 \* 4) = 24 / 36 = 1 / 2 Therefore, the correct answer is 1/2.
Expected answer: >
Correct? No
Problem: Compare the following fractions by choosing the correct symbol (<, >, or =) to fill in the blank: (2 / 1) _ (4 / 9)
CodeLlama 7B:
The correct symbol to fill in the blank is <. (2/1) < (4/9) Explanation: (2/1) = 2 (4/9) = 4/9 Since 2 is less than 4/9, the correct symbol to use is <.
Expected answer: >
Correct? No
Problem: Compare the following fractions by inserting either <, >, or = in the space provided: (9 / 9) _ (2 / 2)
CodeLlama 7B:
(9 / 9) = (2 / 2)
Expected answer: =
Correct? Yes
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 =.
CodeLlama 7B:
(9 / 3) < (2 / 2)
Expected answer: >
Correct? No
Problem: Determine the relationship between the following two fractions by filling the blank with <, >, or =: (6 / 1) _ (4 / 4)
CodeLlama 7B:
The relationship between the two fractions is: (6 / 1) = (4 / 4) This is because the numerator of the first fraction is 6, and the numerator of the second fraction is 4. The denominator of both fractions is 4, so the fractions are equal.
Expected answer: >
Correct? No
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 9) _ (8 / 8)
CodeLlama 7B:
The values of the fractions can be compared by dividing the numerators by the denominators. (3 / 9) = 3/9 (8 / 8) = 8/8 Comparing the values, we see that (3 / 9) is less than (8 / 8), so we fill in the blank with <. Therefore, the correct answer is: (3 / 9) < (8 / 8)
Expected answer: <
Correct? Yes
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (4 / 10) _ (1 / 2)
CodeLlama 7B:
(4 / 10) < (1 / 2)
Expected answer: <
Correct? Yes
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 =.
CodeLlama 7B:
(8 / 10) > (1 / 2)
Expected answer: >
Correct? Yes
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 7B:
The two fractions are: (6 / 6) = (6 / 3) The symbol to fill in the blank space with is "=".
Expected answer: <
Correct? No
Problem: Determine which sign (<, >, or =) correctly fills the blank when comparing these two fractions: (2 / 3) _ (2 / 10)
CodeLlama 7B:
To compare these two fractions, we need to find the least common multiple (LCM) of the denominators. The LCM of 3 and 10 is 30. So, we can convert the fractions to equivalent fractions with a denominator of 30: (2/3) = 2/30 = 1/15 (2/10) = 2/30 = 1/15 Now we can compare the two fractions: (1/15) = (1/15) Therefore, the sign that correctly fills the blank is =.
Expected answer: >
Correct? No
Problem: Compare the following fractions by filling in the blank with either <, =, or >: (2 / 10) _ (6 / 4)
CodeLlama 7B:
(2 / 10) < (6 / 4)
Expected answer: <
Correct? Yes
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?
CodeLlama 7B:
(6 / 10) < (6 / 4) If we increase the numerator of the first fraction from 2 to 6, the fraction becomes (6 / 10) > (6 / 4).
Expected answer: <
Correct? Yes
Problem: Compare the values of the following fractions and indicate either <, >, or = to complete the equation. (5 / 10) _ (6 / 9)
CodeLlama 7B:
To compare the values of the fractions, we need to compare the numerators and denominators. (5 / 10) = (6 / 9) 5/10 = 6/9 5 = 6 So, the fractions are equal. Therefore, we write: (5 / 10) = (6 / 9) ### Answer: =
Expected answer: <
Correct? No
Problem: Compare the fractions by filling in the blank with <, >, or =. (2 / 9) _ (5 / 5)
CodeLlama 7B:
(2/9) < (5/5)
Expected answer: <
Correct? Yes
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 7B:
(2/9) < (5/8)
Expected answer: <
Correct? Yes
Problem: Fill in the blank with <, >, or = to correctly compare the two fractions: (1 / 9) _ (7 / 9)
CodeLlama 7B:
To compare the two fractions, we need to compare their denominators. (1 / 9) = (7 / 9) Since 9 is greater than 7, the first fraction is less than the second fraction. Therefore, the correct comparison is: (1 / 9) < (7 / 9)
Expected answer: <
Correct? Yes
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 7B:
To compare the two fractions, we need to determine whether (2/7) is less than, greater than, or equal to (1/6). First, we can simplify the fractions by multiplying both numerator and denominator by the least common multiple of 7 and 6, which is 21. (2/7) = 2/7 = 2/21 = 1/10 (1/6) = 1/6 = 1/21 = 1/10 Since both fractions are equal, we can conclude that (2/7) is neither less than, greater than, nor equal to (1/6). Therefore, we write: (2/7) = (1/6) = 1/10 Therefore, the comparison between the two fractions is: (2/7) = (1/6) = 1/10 So, the answer is: ### Answer: 1/10
Expected answer: >
Correct? No
Problem: In the following expression, properly insert either <, >, or = in order to correctly compare the two fractions: (9 / 9) _ (9 / 10)
CodeLlama 7B:
To compare the two fractions, we need to compare the numerators and denominators. (9 / 9) = (9 / 10) Therefore, the correct comparison is: (9 / 9) > (9 / 10)
Expected answer: >
Correct? Yes
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 7B:
To compare the two fractions, we need to compare the numerators and denominators. (8/4) = 2 (5/2) = 2.5 Since 2 is less than 2.5, the first fraction is less than the second fraction. Therefore, the first fraction is less than the second fraction. ### Answer: The first fraction is less than the second fraction.
Expected answer: <
Correct? Yes
Problem: Compare the values of the following fractions by deciding which symbol (<, >, or =) to fill in the blank with: (5 / 2) _ (1 / 10)
CodeLlama 7B:
To compare the values of the fractions, we need to compare their denominators and numerators. The fraction (5/2) has a denominator of 2 and a numerator of 5. The fraction (1/10) has a denominator of 10 and a numerator of 1. Since the denominator of (5/2) is less than the denominator of (1/10), we can fill in the blank with <. Therefore, the correct answer is: (5/2) < (1/10)
Expected answer: >
Correct? No
Problem: Fill in the blank with <, >, or = to compare the two fractions in the following question: (2 / 4) _ (9 / 2)
CodeLlama 7B:
To compare the two fractions, we can use the following steps: 1. Multiply the two fractions together: (2/4) × (9/2) = (2 × 9) / (4 × 2) = 18 / 8 = 2 2. Compare the two fractions: 2 = 2, so the two fractions are equal. Therefore, the two fractions are equal.
Expected answer: <
Correct? No
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 7B:
The correct answer is: (6 / 3) > (10 / 2) Explanation: (6 / 3) = 2 (10 / 2) = 5 Since 2 is greater than 5, we can say that (6 / 3) is greater than (10 / 2).
Expected answer: <
Correct? No
Problem: Compare the given fractions by filling in the blank with the correct symbol (<, >, or =). (6 / 3) _ (8 / 6)
CodeLlama 7B:
The given fractions can be compared by filling in the blank with the correct symbol (<, >, or =). (6 / 3) < (8 / 6) The correct symbol is <, since (6/3) is less than (8/6).
Expected answer: >
Correct? No
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (3 / 4) _ (6 / 5)
CodeLlama 7B:
(3 / 4) < (6 / 5)
Expected answer: <
Correct? Yes
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?
CodeLlama 7B:
(3 / 4) _ (6 / 9) If we change the second fraction to (6 / 9), we get: (3 / 4) _ (6 / 9) = (3 / 4) _ (2 / 3) This changes the comparison between the two fractions because the second fraction is now smaller than the first fraction. In other words, (6 / 9) is less than (3 / 4).
Expected answer: >
Correct? No
Problem: Compare the two fractions below by filling in the blank with <, >, or =: (1 / 1) _ (3 / 1)
CodeLlama 7B:
The two fractions are (1/1) and (3/1). To compare them, we need to compare the numerators and denominators. The numerator of (1/1) is 1, and the numerator of (3/1) is 3. The denominator of (1/1) is 1, and the denominator of (3/1) is 1. Since 3 is greater than 1, we can say that (3/1) is greater than (1/1). Therefore, the correct answer is: (1/1) _ (3/1) =
Expected answer: <
Correct? Yes
Problem: Compare the following fractions by filling in the blank with <, >, or =. (7 / 6) _ (4 / 5)
CodeLlama 7B:
(7/6) < (4/5)
Expected answer: >
Correct? No
Problem: Compare the following two fractions by filling the blank with <, >, or =. (6 / 4) _ (2 / 2)
CodeLlama 7B:
(6 / 4) < (2 / 2)
Expected answer: >
Correct? No
Problem: Compare the following fractions by filling in the blank with <, >, or =. (5 / 5) _ (9 / 10)
CodeLlama 7B:
The correct comparison is: (5 / 5) < (9 / 10) Explanation: The fraction (5 / 5) is equal to 1, and the fraction (9 / 10) is greater than 1. Therefore, the correct comparison is that (5 / 5) is less than (9 / 10).
Expected answer: >
Correct? No
Problem: Fill in the blank (1 / 5) _ (1 / 1) with <, >, or = to compare the two fractions.
CodeLlama 7B:
(1 / 5) < (1 / 1) Explanation: (1 / 5) = 0.2 (1 / 1) = 1 So, (1 / 5) is less than (1 / 1).
Expected answer: <
Correct? Yes
Problem: Fill the blank with either <, >, or = to compare the two fractions in the following equation: (7 / 1) _ (4 / 2)
CodeLlama 7B:
(7 / 1) > (4 / 2) The fraction (7 / 1) is greater than the fraction (4 / 2) because the numerator of the first fraction is greater than the numerator of the second fraction.
Expected answer: >
Correct? Yes
Problem: Compare the following fractions by using <, >, or = to fill in the blank: (4 / 7) _ (9 / 4)
CodeLlama 7B:
(4/7) < (9/4)
Expected answer: <
Correct? Yes
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)?
CodeLlama 7B:
The comparison between the fractions (4/7) and (2/4) is >. The comparison between the fractions (4/7) and (9/4) is <.
Expected answer: >
Correct? Yes
Problem: Fill in the blank in the question (5 / 9) _ (4 / 7) with <, >, or = to compare the two fractions.
CodeLlama 7B:
(5 / 9) < (4 / 7) Explanation: (5 / 9) = 0.555555... (4 / 7) = 0.571428... Since (5 / 9) is less than (4 / 7), we can conclude that 5/9 is smaller than 4/7.
Expected answer: <
Correct? Yes
Problem: Compare the following fractions and fill in the blank with <, >, or =: (8 / 3) _ (7 / 3)
CodeLlama 7B:
(8/3) < (7/3) Explanation: (8/3) = 8/3 = 2 (7/3) = 7/3 = 2 So, (8/3) is less than (7/3).
Expected answer: >
Correct? No
Problem: In the equation: (5 / 1) _ (2 / 2), replace the underscore with one of the following signs: <, >, or = to compare the two fractions.
CodeLlama 7B:
The correct answer is: (5 / 1) > (2 / 2) Explanation: The first fraction is greater than the second fraction because the numerator of the first fraction (5) is greater than the numerator of the second fraction (2).
Expected answer: >
Correct? Yes
Problem: Compare the following fractions and fill in the blank with either <, >, or =: (5 / 8) _ (3 / 3)
CodeLlama 7B:
(5/8) < (3/3) The correct answer is <.
Expected answer: <
Correct? Yes
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)
CodeLlama 7B:
(5/4) > (3/3) The correct answer is >.
Expected answer: >
Correct? Yes
Problem: Determine which symbol : <, >, or =, is appropriate to fill the blank in the following comparison: (5 / 8) _ (6 / 10)
CodeLlama 7B:
The appropriate symbol to fill the blank in the comparison is "=". The comparison is between two fractions, and the symbol "=" is used to indicate that the two fractions are equal. Therefore, the correct answer is: (5 / 8) = (6 / 10)
Expected answer: >
Correct? No
Problem: Compare the two fractions by filling in the blank with <, >, or =: (5 / 10) _ (6 / 6)
CodeLlama 7B:
(5 / 10) < (6 / 6) Explanation: (5 / 10) = 0.5 (6 / 6) = 1 Since 0.5 is less than 1, we say that (5 / 10) is less than (6 / 6). Therefore, we write: (5 / 10) < (6 / 6)
Expected answer: <
Correct? Yes
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?
CodeLlama 7B:
(5 / 10) _ (6 / 1) = (5 / 10) > (6 / 1) Explanation: (5 / 10) = 0.5 (6 / 1) = 6 Since 0.5 is less than 6, we say that (5 / 10) is less than (6 / 1). Therefore, we write: (5 / 10) < (6 / 1)
Expected answer: <
Correct? Yes
Problem: Compare these two fractions by filling in the blank with <, >, or =. (5 / 4) _ (2 / 4)
CodeLlama 7B:
(5 / 4) < (2 / 4) Explanation: (5 / 4) = 1.25 (2 / 4) = 0.5 So, (5 / 4) is greater than (2 / 4).
Expected answer: >
Correct? No
Problem: Compare the values of the following fractions by using <, >, or = to fill in the blank: (6 / 10) _ (6 / 10)
CodeLlama 7B:
The fractions are equal, so we can fill in the blank with "=". (6 / 10) = (6 / 10) Therefore, the comparison is: (6 / 10) = (6 / 10) So, the fractions are equal.
Expected answer: =
Correct? Yes
Problem: Please compare these two fractions and fill the blank with <, >, or =. (6 / 8) _ (2 / 9)
CodeLlama 7B:
(6/8) < (2/9) Explanation: (6/8) = 3/4 (2/9) = 1/4 So, (6/8) is less than (2/9).
Expected answer: >
Correct? No
Problem: Fill in the blank with <, =, or > after comparing the fractions below: (2 / 10) _ (6 / 2)
CodeLlama 7B:
(2 / 10) < (6 / 2) The correct answer is <.
Expected answer: <
Correct? Yes
Problem: Let's modify the previous problem slightly. Fill in the blank with <, =, or > after comparing the fractions: (2 / 10) _ (6 / 9)
CodeLlama 7B:
(2 / 10) > (6 / 9) The correct answer is >.
Expected answer: <
Correct? No
Problem: Determine which of the following fractions is greater by filling in the blank with <, >, or =. (2 / 7) _ (9 / 4)
CodeLlama 7B:
To determine which fraction is greater, we need to compare the numerators and denominators. (2/7) = 2/7 (9/4) = 9/4 Since 9/4 is greater than 2/7, we can say that (9/4) is greater than (2/7). Therefore, the correct answer is: (9/4) > (2/7)
Expected answer: <
Correct? No
Problem: Compare the following fractions by filling in the blank with <, >, or =. (1 / 1) _ (2 / 10)
CodeLlama 7B:
The correct comparison is: (1 / 1) < (2 / 10) Explanation: The fraction (1 / 1) is equal to 1, and the fraction (2 / 10) is equal to 2/10 = 1/5. Since 1 is less than 1/5, the correct comparison is that (1 / 1) is less than (2 / 10).
Expected answer: >
Correct? No
Problem: Compare the results of the following fractions by filling the blank with <, >, or =. (8 / 2) _ (10 / 9)
CodeLlama 7B:
(8/2) < (10/9)
Expected answer: >
Correct? No
Problem: Determine the relationship between the fractions by filling in the blank in the following equation with either <, >, or =: (3 / 2) _ (9 / 8)
CodeLlama 7B:
The relationship between the fractions can be determined by comparing the numerators and denominators. (3 / 2) = (9 / 8) Comparing the numerators, we see that 3 = 9, so the fractions are equal. Therefore, the relationship between the fractions is: (3 / 2) = (9 / 8) This is an equality, denoted by the symbol "=".
Expected answer: >
Correct? No
Problem: Compare the following quantities by filling in the blank with <, >, or =: (4 / 6) _ (6 / 10)
CodeLlama 7B:
(4 / 6) < (6 / 10)
Expected answer: >
Correct? No
Problem: Fill in the blank with the correct symbol to compare the following fractions: (8 / 10) _ (1 / 1)
CodeLlama 7B:
To compare the following fractions, we need to find their common denominator. In this case, the common denominator is 10. So, we can write the first fraction as: (8/10) = 8/10 And the second fraction as: (1/1) = 1/1 Now we can compare the two fractions by converting them to the same denominator: (8/10) = 8/10 = 8/10 (1/1) = 1/1 = 1/1 Both fractions are equal, so we can say that: (8/10) = (1/1) Therefore, the correct symbol to compare the two fractions is the equal sign (=).
Expected answer: <
Correct? No
Problem: Using either <, >, or =, compare the following fractions by filling in the blank: (5 / 1) _ (5 / 8)
CodeLlama 7B:
The correct comparison is: (5 / 1) > (5 / 8) This is because 5/1 is greater than 5/8.
Expected answer: >
Correct? Yes
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 7B:
The correct symbol to use in the statement is "<". (6 / 5) < (9 / 6) This is because the first fraction (6/5) is less than the second fraction (9/6).
Expected answer: <
Correct? Yes
Problem: Compare the following fractions by filling in the blank: (7 / 5) _ (1 / 10) You can use <, > or =.
CodeLlama 7B:
(7/5) > (1/10)
Expected answer: >
Correct? Yes
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.
CodeLlama 7B:
(1/5) < (1/10)
Expected answer: >
Correct? No
Problem: Compare the two fractions and fill in the blank with <, >, or =. (10 / 8) _ (10 / 1)
CodeLlama 7B:
(10 / 8) _ (10 / 1) = (10 / 8) _ (10) = (10 / 8) _ 10 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10 / 8) _ 2 = (10
Expected answer: <
Correct? No
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =: (3 / 2) _ (4 / 6)
CodeLlama 7B:
(3/2) < (4/6)
Expected answer: >
Correct? No
Problem: Compare the following two fractions by filling in the blank with <, >, or =. (9 / 7) _ (4 / 6)
CodeLlama 7B:
The correct comparison is: (9 / 7) < (4 / 6) Explanation: (9 / 7) = 1 1/2 (4 / 6) = 1/2 Since 1 1/2 is less than 1/2, the first fraction is less than the second fraction. Therefore, the correct answer is "<".
Expected answer: >
Correct? No
Problem: Fill in the blank in the following comparison with a <, >, or = sign. (8 / 7) _ (8 / 8)
CodeLlama 7B:
The correct comparison is: (8 / 7) < (8 / 8) Explanation: (8 / 7) = 1.14 (8 / 8) = 1 So, (8 / 7) is less than (8 / 8).
Expected answer: >
Correct? No
Problem: Fill in the blank with the correct symbol (<, >, =) to compare these two fractions: (5 / 5) _ (4 / 6)
CodeLlama 7B:
To compare these two fractions, we need to compare their values. (5 / 5) = (4 / 6) This is equivalent to: 5 = 4 This is true, so the two fractions are equal. Therefore, the correct symbol to use is "=".
Expected answer: >
Correct? No
Problem: Compare the following fractions and use <, >, or = to fill the blank: (10 / 10) _ (4 / 10)
CodeLlama 7B:
(10 / 10) = (4 / 10) Therefore, the answer is =.
Expected answer: >
Correct? No
Problem: Compare the following fractions and fill in the blank with <, >, or =. (8 / 1) _ (4 / 9)
CodeLlama 7B:
The correct comparison is: (8 / 1) > (4 / 9) Explanation: 8 is greater than 4, and 1 is greater than 9, so the fraction (8 / 1) is greater than the fraction (4 / 9).
Expected answer: >
Correct? Yes
Problem: Compare the values of the two fractions below by choosing either <, >, or = to fill in the blank: (9 / 3) _ (4 / 8)
CodeLlama 7B:
The correct comparison is: (9 / 3) > (4 / 8) Explanation: (9 / 3) = 3 (4 / 8) = 0.5 So, (9 / 3) is greater than (4 / 8).
Expected answer: >
Correct? Yes
Problem: Compare the fractions in the expression (10 / 7) _ (9 / 6). Fill in the blank with <, >, or =.
CodeLlama 7B:
The expression (10 / 7) _ (9 / 6) can be simplified as follows: (10 / 7) = 1 4/7 (9 / 6) = 1 5/6 Now, we can compare the fractions: 1 4/7 = 1 5/6 (greater than) Therefore, the expression (10 / 7) _ (9 / 6) is greater than 1.
Expected answer: <
Correct? No
Problem: Compare the following fractions, and complete the statement: (10 / 8) _ (3 / 1) Fill the blank space with <, >, or =.
CodeLlama 7B:
(10/8) _ (3/1) = < Explanation: (10/8) = 1 1/2 (3/1) = 3 Therefore, (10/8) _ (3/1) = 1 1/2 < 3, so the correct answer is <.
Expected answer: <
Correct? Yes
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 7B:
The relationship between the two fractions is: (3 / 2) = (3 / 5) This is because the numerator of the first fraction is 3, and the numerator of the second fraction is 3. The denominator of the first fraction is 2, and the denominator of the second fraction is 5. So, we can simplify the fractions by dividing the numerators by the denominators: (3 / 2) = (3 ÷ 2) = (1.5) (3 / 5) = (3 ÷ 5) = (0.6) Now we can compare the two fractions: (1.5) = (0.6) This means that the two fractions are equal.
Expected answer: >
Correct? No
Problem: Compare the following two fractions by filling in the blank with <, >, or =. (4 / 10) _ (2 / 2)
CodeLlama 7B:
The correct answer is <. (4/10) = (2/2) The fraction (4/10) is less than the fraction (2/2).
Expected answer: <
Correct? Yes
Problem: Compare the two fractions and fill in the blank with <, >, or =: (6 / 7) _ (2 / 10)
CodeLlama 7B:
(6 / 7) < (2 / 10) Explanation: (6 / 7) = 0.85 (2 / 10) = 0.2 Since 0.85 is less than 0.2, we say that (6 / 7) is less than (2 / 10). Therefore, we fill in the blank with <.
Expected answer: >
Correct? No
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (9 / 7) _ (10 / 3)
CodeLlama 7B:
The values of the fractions can be compared by dividing the numerators by the denominators. (9 / 7) = 1.2857 _ (10 / 3) = 3.3333 Comparing the values, we see that (9 / 7) is less than (10 / 3), so we fill in the blank with <. Therefore, the correct answer is: (9 / 7) < (10 / 3)
Expected answer: <
Correct? Yes
Problem: Compare the following two fractions by filling in the blank with <, >, or =. (8 / 8) _ (2 / 8)
CodeLlama 7B:
The two fractions can be compared by dividing the numerators by the denominators. (8 / 8) = (2 / 8) 8/8 = 2/8 8 = 2 Therefore, the two fractions are equal. ### Answer: =
Expected answer: >
Correct? No
Problem: Evaluate the following expression by comparing the two fractions using <, >, or =: (4 / 3) _ (1 / 8)
CodeLlama 7B:
The expression can be simplified as follows: (4 / 3) _ (1 / 8) = (4 / 3) / (1 / 8) = 4 / 3 / 1 / 8 = 4 / 24 = 1 / 6 Therefore, the expression is equal to 1/6.
Expected answer: >
Correct? No
Problem: Compare the following fractions by completing the sentence with the appropriate symbol (<, >, or =): (4 / 6) _ (6 / 10)
CodeLlama 7B:
(4 / 6) < (6 / 10)
Expected answer: >
Correct? No
Problem: Compare the two fractions by filling the blank using <, >, or =. Here's the question: (9 / 6) _ (6 / 8)
CodeLlama 7B:
The two fractions can be compared by filling the blank with the appropriate symbol. (9 / 6) = (6 / 8) The two fractions are equal.
Expected answer: >
Correct? No
Problem: Compare the following fractions by filling in the blank with one of the following symbols: <, >, or =. (2 / 6) _ (8 / 7)
CodeLlama 7B:
The correct comparison is: (2 / 6) < (8 / 7) Explanation: (2 / 6) = 0.33 (8 / 7) = 1.14 Since 0.33 is less than 1.14, we use the symbol < to indicate that the first fraction is less than the second fraction.
Expected answer: <
Correct? Yes
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 7B:
In this case, the comparison between the two fractions would be: (2 / 7) > (8 / 7) Explanation: (2 / 7) = 0.28 (8 / 7) = 1.14 Since 0.28 is less than 1.14, we use the symbol > to indicate that the first fraction is less than the second fraction.
Expected answer: <
Correct? No
Problem: Compare the following fractions by filling in the blank with <, >, or =. (9 / 6) _ (4 / 10)
CodeLlama 7B:
(9/6) < (4/10)
Expected answer: >
Correct? No
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 7B:
The correct answer is: (6 / 8) > (5 / 1) Explanation: (6 / 8) = 3/4 (5 / 1) = 5/1 So, (6 / 8) is greater than (5 / 1) in value.
Expected answer: <
Correct? No
Problem: Compare these two fractions by filling in the blank with <, >, or =. (8 / 4) _ (1 / 10)
CodeLlama 7B:
(8/4) < (1/10)
Expected answer: >
Correct? No
Problem: Compare the values of the following expressions by filling in the blank with <, >, or =. (6 / 3) _ (8 / 2)
CodeLlama 7B:
(6 / 3) _ (8 / 2) = (6 / 3) _ 4 = 6 _ 4 = 24 < 32. Therefore, the expression (6 / 3) _ (8 / 2) is less than 32.
Expected answer: <
Correct? Yes
Problem: Please compare the following two fractions and fill the blank with one of the symbols: <, >, or =: (4 / 6) _ (6 / 3)
CodeLlama 7B:
The two fractions can be compared as follows: (4 / 6) = (6 / 3) The comparison is: (4 / 6) = (6 / 3) The answer is: =
Expected answer: <
Correct? No
Problem: Fill in the blank with <, >, or = to compare the fractions 6 / 7 and 3 / 1 properly.
CodeLlama 7B:
To compare the fractions 6/7 and 3/1 properly, we need to use the correct comparison operator. Since 6/7 is less than 3/1, we can use the comparison operator < to say that 6/7 is less than 3/1. So, the correct statement is: 6/7 < 3/1
Expected answer: <
Correct? Yes
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.
CodeLlama 7B:
To compare the fractions 6/7 and 9/1, we need to use the correct comparison operator. Since 6/7 is less than 9/1, we can use the comparison operator < to say that 6/7 is less than 9/1. So, the correct statement is: 6/7 < 9/1
Expected answer: <
Correct? Yes
Problem: Compare the values of the following fractions by filling in the blank with <, >, or =. (6 / 10) _ (9 / 10)
CodeLlama 7B:
(6 / 10) < (9 / 10)
Expected answer: <
Correct? Yes
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)?
CodeLlama 7B:
If we compare the fractions (1 / 10) and (9 / 10), we can see that (1 / 10) is less than (9 / 10). So, the answer to the comparison would be: (1 / 10) < (9 / 10)
Expected answer: <
Correct? Yes
Problem: Compare the two fractions by filling in the blank with <, >, or =. (6 / 8) _ (4 / 9)
CodeLlama 7B:
(6 / 8) < (4 / 9)
Expected answer: >
Correct? No