for parts (a) through (d), write a fraction to approximate the shaded portion as part of the whole. \n\na…

Explanation:

Step1: Analyze the whole

The rectangle is divided into 2 equal vertical parts. One of these vertical parts is further divided into 4 equal horizontal parts. So total number of equal parts (if we consider the smallest unit) or the way to find the fraction: First, the whole can be thought of as having 2 * 4 = 8 equal small rectangles? Wait, no. Wait, the left vertical part is 1/2 of the whole, and the right vertical part is divided into 4 equal parts. Wait, actually, let's see: the whole rectangle is split into two vertical sections. The left section is a single rectangle, and the right section is split into 4 equal small rectangles. Wait, maybe another way: Let's consider the whole as being composed of 8 equal small rectangles? Wait, no, the left part is a rectangle that is equal in height to the right part which has 4 rectangles. So the left part is equivalent to 4 small rectangles (since the right has 4, same height). So total number of small rectangles (the whole) is 4 (left) + 4 (right) = 8? Wait, no, the left is a single rectangle, but its area is equal to 4 of the small right rectangles. So the whole is 4 + 4 = 8 small rectangles? Wait, the shaded part is 1 small rectangle. Wait, no, looking at the diagram: the left vertical strip is a large rectangle, and the right vertical strip is divided into 4 equal small rectangles, one of which is shaded. Wait, maybe the whole is considered as 8 parts? Wait, no, let's think again. The left strip is 1/2 of the whole, and the right strip is 1/2 of the whole, divided into 4 parts. So the right strip's 4 parts are each 1/4 of the right strip, so each is (1/2)*(1/4) = 1/8 of the whole. Wait, the shaded part is 1 of those, so 1/8? Wait, no, maybe the whole is divided into 8 equal parts? Wait, the left strip is 4 parts (since the right has 4, same height), so total 8 parts. The shaded part is 1 part. Wait, but let's check: if the right strip is 4 parts, left strip is 4 parts (same height), so total 8 parts. Shaded is 1 part. So fraction is 1/8? Wait, no, maybe I'm overcomplicating. Wait, another approach: the whole rectangle can be seen as having 2 equal vertical sections. The right section is divided into 4 equal horizontal sections. So the entire rectangle has 2 * 4 = 8 equal small rectangles (since each vertical section has 4, 2 sections). The shaded part is 1 small rectangle. So the fraction is 1/8? Wait, no, wait the left section is a single rectangle, but its area is equal to 4 small rectangles (since the right has 4, same height). So total parts: 4 (left) + 4 (right) = 8. Shaded is 1 (the small right rectangle). So fraction is 1/8? Wait, but maybe the whole is considered as 8 parts, shaded is 1. Wait, but let's check again. Alternatively, the right strip is 1/2 of the whole, and within that 1/2, it's divided into 4 parts, so each part is (1/2)/4 = 1/8 of the whole. The shaded part is 1 of those, so 1/8.

Step2: Determine the fraction

So total number of equal parts (the whole) is 8, shaded parts is 1. So the fraction is 1/8.

Answer:

$\frac{1}{8}$