Question

How to decompose a rectangle into two or three smaller rectangles to demonstrate the distributive property?

Answer 1

Answer:

See explanation

Step-by-step explanation:

The distibutive property states that for all real numbers a, b and c

$(a+b)c=ac+bc$

Draw a rectangle with length of (a+b) units and width of c units. The area of this rectangle is

$(a+b)c\ un^2.$

Divide this rectangle into two rectangles: first rectangle with the length of a units and the width of c units and the second rectangle with the length of b units and the width of c units. The area of these rectangles are

$a\cdot c\ \text{and}\ b\cdot c$

These two rectangles together form initial rectangle, so the sum of the area of two smaller rectangles is the area of the bigger rectangle.