Question
Hadley has 3/6 of a box of white envelopes and 1/3 of a box of gray envelope when full each box of envelopes has the same number of envelopes Hadley said she was for over nine of a box when she puts the white envelopes in gray envelopes together which statement describes this situation select the two statement that apply A How do we answer is incorrect because 3/6 is equal to 1/2 and 4/9 is less than 1/2 B Hadley answer isn't correct because 3/6 + 1/3 equals 5/6 C How do we answer is incorrect because 3/6 + 1/3 equals 2/6 D Hadley answer is correct because 3 and 1 is 4 and 6 and 3 is 9
Answers
GPT-4o mini
To analyze the situation, let's first convert the quantities of envelopes into a common fraction:
1. Hadley has \( \frac{3}{6} \) of a box of white envelopes, which simplifies to \( \frac{1}{2} \).
2. Hadley has \( \frac{1}{3} \) of a box of gray envelopes.
Now let's find a common denominator to add these two fractions. The least common denominator for \(2\) and \(3\) is \(6\):
- Convert \( \frac{1}{3} \) into sixths: \( \frac{1}{3} = \frac{2}{6} \).
Now we can add the two fractions:
\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]
Now we'll evaluate the statements provided:
A. **Hadley's answer is incorrect because \( \frac{3}{6} \) is equal to \( \frac{1}{2} \) and \( \frac{4}{9} \) is less than \( \frac{1}{2} \)**
- This statement is misleading. While \( \frac{3}{6} \) is indeed \( \frac{1}{2} \), the comparison with \( \frac{4}{9} \) is irrelevant to the total Hadley found. This statement does not correctly analyze the situation.
B. **Hadley's answer isn't correct because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \)**
- This statement is correct. Hadley's total is \( \frac{5}{6} \) which is indeed less than a full box (1), so she is not over a box.
C. **Hadley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{2}{6} \)**
- This statement is incorrect. As shown, \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \), not \( \frac{2}{6} \).
D. **Hadley's answer is correct because \( 3 + 1 = 4 \) and \( 6 + 3 = 9 \)**
- This statement is not a valid justification for Hadley’s answer. It does not accurately analyze the fractions in the context of the problem.
Given this evaluation, the correct statements that apply are:
- **B**: Hadley's answer isn't correct because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \).
- **You could argue that A is misleading; hence it may not count as correct. The clear answer is just B**.
So **the best choice is only** **B**.
1. Hadley has \( \frac{3}{6} \) of a box of white envelopes, which simplifies to \( \frac{1}{2} \).
2. Hadley has \( \frac{1}{3} \) of a box of gray envelopes.
Now let's find a common denominator to add these two fractions. The least common denominator for \(2\) and \(3\) is \(6\):
- Convert \( \frac{1}{3} \) into sixths: \( \frac{1}{3} = \frac{2}{6} \).
Now we can add the two fractions:
\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]
Now we'll evaluate the statements provided:
A. **Hadley's answer is incorrect because \( \frac{3}{6} \) is equal to \( \frac{1}{2} \) and \( \frac{4}{9} \) is less than \( \frac{1}{2} \)**
- This statement is misleading. While \( \frac{3}{6} \) is indeed \( \frac{1}{2} \), the comparison with \( \frac{4}{9} \) is irrelevant to the total Hadley found. This statement does not correctly analyze the situation.
B. **Hadley's answer isn't correct because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \)**
- This statement is correct. Hadley's total is \( \frac{5}{6} \) which is indeed less than a full box (1), so she is not over a box.
C. **Hadley's answer is incorrect because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{2}{6} \)**
- This statement is incorrect. As shown, \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \), not \( \frac{2}{6} \).
D. **Hadley's answer is correct because \( 3 + 1 = 4 \) and \( 6 + 3 = 9 \)**
- This statement is not a valid justification for Hadley’s answer. It does not accurately analyze the fractions in the context of the problem.
Given this evaluation, the correct statements that apply are:
- **B**: Hadley's answer isn't correct because \( \frac{3}{6} + \frac{1}{3} \) equals \( \frac{5}{6} \).
- **You could argue that A is misleading; hence it may not count as correct. The clear answer is just B**.
So **the best choice is only** **B**.