Question

hadley has \\(\frac{3}{6}\\) of a box of white envelopes and \\(\frac{1}{3}\\) of a box of gray envelopes. when full, each box of envelopes has the same number of envelopes. hadley said she has \\(\frac{4}{9}\\) of a box when she puts the white envelopes and gray envelopes together. which statements describe the situation? select the two statements that apply. (1 point) hadleys answer is incorrect because \\(\frac{3}{6}\\) is equal to \\(\frac{1}{2}\\), and \\(\frac{4}{9}\\) is less than \\(\frac{1}{2}\\) \\(square\\) hadleys answer is incorrect because \\(\frac{3}{6}\\) plus \\(\frac{1}{3}\\) equals \\(\frac{5}{6}\\) \\(square\\) hadleys answer is incorrect because \\(\frac{3}{6}\\) plus \\(\frac{1}{3}\\) equals \\(\frac{2}{6}\\) \\(square\\) hadleys answer is correct because 3 and 1 is 4, and 6 and 3 is 9. \\(square\\)

Explanation:

Step1: Simplify $\frac{3}{6}$

$\frac{3}{6} = \frac{1}{2}$

Step2: Add the two fractions

First, rewrite $\frac{1}{3}$ with denominator 6: $\frac{1}{3} = \frac{2}{6}$
Then calculate: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

Step3: Verify Hadley's error

Hadley claimed the sum is $\frac{4}{9}$. Since $\frac{5}{6} \approx 0.833$ and $\frac{4}{9} \approx 0.444$, and $\frac{1}{2}=0.5$, $\frac{4}{9}<\frac{1}{2}$ while $\frac{3}{6}=\frac{1}{2}$, so her answer is wrong.

Answer:

A. Hadley's answer is incorrect because $\frac{3}{6}$ is equal to $\frac{1}{2}$, and $\frac{4}{9}$ is less than $\frac{1}{2}$
B. Hadley's answer is incorrect because $\frac{3}{6}$ plus $\frac{1}{3}$ equals $\frac{5}{6}$