Area Diagrams - Algebra 1

7.8.1 Area Diagrams

7.8.1 • Area Diagrams

Warm Up

A rectangle of width 6 units is divided horizontally into sections that are 3 units long and 4 units long. The labels 3 and 4 are along the left side of the rectangle and 6 is across the top.

Explain why the diagram shows that $6 (3 + 4) = 6 \cdot 3 + 6 \cdot 4$ .

Compare your answer:

The entire diagram represents the product $6 (3 + 4)$ . The upper half represents $6 \cdot 3$ while the lower half represents $6 \cdot 4$ .

Draw a diagram to show that $5 (x + 2) = 5 x + 10$ .

Compare your answer:

Diagrams will vary, but should show a large rectangle with two sub-rectangles, with one sub-rectangle representing $5 \cdot x$ , and the other representing $5 \cdot 2$ . For example:

A rectangle of width 5 units is divided horizontally into sections that are x units long and 2 units long. The labels x and 2 are along the left side of the rectangle and 5 is across the top.