Question
Haley has 3/6 Of a box of white envelopes and 1/3 Of a box of great envelopes one for each box of envelopes has the same number of envelopes haley says she has 4/9 of a Box when she puts the white envelopes and great envelopes together which statement describes the situation select two statements that apply
Haley's answer is incorrect becauase 3/6 Is equal to 1/2 and 1/4 is less then 1/2
Haley's answer is incorrect because 3/6 plus 1/3 equals 5/6
Haley's answer is incorrect because 3/6 plus 1/3 Equals 2/6
Haley's answer is correct because3 and 1 is 4 and 6 and 3 is 9
Haley's answer is incorrect becauase 3/6 Is equal to 1/2 and 1/4 is less then 1/2
Haley's answer is incorrect because 3/6 plus 1/3 equals 5/6
Haley's answer is incorrect because 3/6 plus 1/3 Equals 2/6
Haley's answer is correct because3 and 1 is 4 and 6 and 3 is 9
Answers
GPT-4o mini
To analyze Haley's claim and determine which statements are correct, let’s break down the fractions she provided.
1. Haley has \( \frac{3}{6} \) of a box of white envelopes:
- Simplifying \( \frac{3}{6} \) gives \( \frac{1}{2} \).
2. She has \( \frac{1}{3} \) of a box of great envelopes.
To add these two fractions, we need a common denominator. The least common multiple of the denominators (6 and 3) is 6.
- Convert \( \frac{1}{3} \) to a fraction with a denominator of 6:
\[
\frac{1}{3} = \frac{2}{6}
\]
Now we can add the two fractions:
\[
\text{White envelopes: } \frac{3}{6} + \text{Great envelopes: } \frac{2}{6} = \frac{5}{6}
\]
Now, we evaluate Haley's claim:
- She claims that when putting the two together, she has \( \frac{4}{9} \) of a box, which is incorrect based on our calculations of \( \frac{5}{6} \).
Now, let's analyze the statements provided:
1. **Haley's answer is incorrect because \( \frac{3}{6} \) is equal to \( \frac{1}{2} \) and \( \frac{1}{3} \) is less than \( \frac{1}{2} \)**: This statement is irrelevant to the correctness of her total. It's not valid to conclude her answer is incorrect based solely on comparing fractions.
2. **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{5}{6} \)**: This statement is correct. It accurately calculates the total number of envelopes she has.
3. **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{2}{6} \)**: This statement is incorrect because it miscalculates the sum of the fractions.
4. **Haley's answer is correct because \( 3 + 1 = 4 \) and \( 6 + 3 = 9 \)**: This reasoning is incorrect because \( \frac{5}{6} \) does not equal \( \frac{4}{9} \), and the arithmetic does not justify her answer.
Thus, the two statements that apply to the situation are:
- **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{5}{6} \)**.
- The other statements do not provide valid reasoning for arriving at the correct conclusion.
The only correct conclusion is the second statement listed above.
1. Haley has \( \frac{3}{6} \) of a box of white envelopes:
- Simplifying \( \frac{3}{6} \) gives \( \frac{1}{2} \).
2. She has \( \frac{1}{3} \) of a box of great envelopes.
To add these two fractions, we need a common denominator. The least common multiple of the denominators (6 and 3) is 6.
- Convert \( \frac{1}{3} \) to a fraction with a denominator of 6:
\[
\frac{1}{3} = \frac{2}{6}
\]
Now we can add the two fractions:
\[
\text{White envelopes: } \frac{3}{6} + \text{Great envelopes: } \frac{2}{6} = \frac{5}{6}
\]
Now, we evaluate Haley's claim:
- She claims that when putting the two together, she has \( \frac{4}{9} \) of a box, which is incorrect based on our calculations of \( \frac{5}{6} \).
Now, let's analyze the statements provided:
1. **Haley's answer is incorrect because \( \frac{3}{6} \) is equal to \( \frac{1}{2} \) and \( \frac{1}{3} \) is less than \( \frac{1}{2} \)**: This statement is irrelevant to the correctness of her total. It's not valid to conclude her answer is incorrect based solely on comparing fractions.
2. **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{5}{6} \)**: This statement is correct. It accurately calculates the total number of envelopes she has.
3. **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{2}{6} \)**: This statement is incorrect because it miscalculates the sum of the fractions.
4. **Haley's answer is correct because \( 3 + 1 = 4 \) and \( 6 + 3 = 9 \)**: This reasoning is incorrect because \( \frac{5}{6} \) does not equal \( \frac{4}{9} \), and the arithmetic does not justify her answer.
Thus, the two statements that apply to the situation are:
- **Haley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} = \frac{5}{6} \)**.
- The other statements do not provide valid reasoning for arriving at the correct conclusion.
The only correct conclusion is the second statement listed above.