Question

question 8 of 10 approximately what portion of the box is shaded blue? a. $\frac{1}{2}$ b. $\frac{5}{9}$ c. $\frac{3}{4}$ (with an image of a rectangle having a white upper section and a blue lower section)

Explanation:

Step1: Analyze the visual

The box (rectangle) has a blue - shaded region and a white region. Visually, the blue - shaded part is more than half? Wait, no, let's re - examine. Wait, actually, looking at the rectangle, the blue part seems to occupy about two - thirds? Wait, no, the options are $\frac{1}{2}$, $\frac{5}{8}$, and $\frac{3}{4}$. Wait, first, let's estimate the height of the blue region relative to the total height of the rectangle.

Suppose the total height of the rectangle is divided into 8 equal parts (for easier comparison with the fractions). $\frac{1}{2}=\frac{4}{8}$, $\frac{5}{8}$ is 5 out of 8, and $\frac{3}{4}=\frac{6}{8}$. Looking at the diagram, the blue region's height is more than half (4/8) and less than 3/4 (6/8). Among the options, $\frac{5}{8}$ is between $\frac{1}{2}$ and $\frac{3}{4}$. Let's check the visual again: the white region is a smaller strip at the top, and the blue region is the larger part. If we compare the height, the blue part is about 5/8 of the total height.

Step2: Compare with options

• Option A: $\frac{1}{2} = 0.5$. If the blue part were $\frac{1}{2}$, the white and blue parts would be equal in height, but in the diagram, the blue part is taller than the white part, so A is incorrect.
• Option B: $\frac{5}{8}=0.625$. This seems to match the visual as the blue part is more than half (0.5) and less than 3/4 (0.75).
• Option C: $\frac{3}{4} = 0.75$. The blue part does not seem to be 3/4 of the height, as the white part is still a noticeable portion, so C is incorrect.

Answer:

B. $\frac{5}{8}$