Question

divide the square into eighths.

Explanation:

Step1: Recall fraction division concept

To divide a square into eighths, we can first divide it into halves, then quarters, then eighths. Or use equal divisions (e.g., 8 equal parts). A common way is to divide the square into 8 equal - sized smaller squares or rectangles. For example, we can divide the square horizontally into 4 equal strips (by making 3 horizontal lines) and vertically into 2 equal strips (by making 1 vertical line), or vice - versa. The total number of parts will be \(4\times2 = 8\). Another way is to divide it into 8 equal triangles, but the rectangle/square division is simpler.

Step2: Visualize the division

If we consider the square, we can draw 3 horizontal lines that are equally spaced and 1 vertical line that is equally spaced (or 1 horizontal and 3 vertical) such that the area of each sub - region is equal. For example, if the side length of the square is \(s\), and we divide the height into 4 equal parts (each of height \(\frac{s}{4}\)) and the width into 2 equal parts (each of width \(\frac{s}{2}\)), then each small rectangle will have an area of \(\frac{s}{4}\times\frac{s}{2}=\frac{s^{2}}{8}\), which is one - eighth of the area of the original square (\(s\times s = s^{2}\)).

Answer:

To divide the square into eighths, we can divide it into 8 equal - area regions. One way is to draw 3 equally - spaced horizontal lines and 1 equally - spaced vertical line (or 1 horizontal and 3 vertical lines) such that the square is partitioned into 8 smaller rectangles (or other shapes like triangles) of equal area. (The actual drawing would involve creating 8 congruent parts within the square. For example, if we consider the square, we can split it into 2 columns and 4 rows of equal - sized rectangles. Each rectangle will have an area that is \(\frac{1}{8}\) of the square's area.)