The problem describes a square that is cut into two equal pieces. Then one of these pieces is further cut into two equal pieces. The goal is to determine what fraction of the original square is represented by the smaller piece.

1. Problem Description

The problem describes a square that is cut into two equal pieces. Then one of these pieces is further cut into two equal pieces. The goal is to determine what fraction of the original square is represented by the smaller piece.

2. Solution Steps

Step 1: The square is initially cut into two equal pieces. Each piece represents $\frac{1}{2}$ of the original square.

Step 2: One of these halves is cut into two equal pieces. Each of these smaller pieces represents half of $\frac{1}{2}$ of the original square.

Step 3: To find the fraction of the original square represented by the smaller piece, we calculate $\frac{1}{2} \times \frac{1}{2}$.

$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Therefore, the smaller piece represents $\frac{1}{4}$ of the original square.

3. Final Answer

The shaded part is one-fourth of the original square.