The Distributive Property, Part 3


For this exercise, you’ll need a sheet of paper, pencil/pen. Attempt the solution to a problem before you click to see the answer. Click “New” when you are ready to do more.

Activity #1

Practice the Distributive Property with Models.

The model below is the distributive property for 2 x (3 + 4). The entire rectangle in the applet below represents 2 x (3 x 4). The shaded region represents 2 x 3, and the unshaded region represents 2 x 4. Always note that the shaded portion will represent the first multiplication of the numbers that you choose, while the unshaded portion will represent the second multiplication.

  • Enter values for a, b, and c in the boxes below to obtain different instances of the distributive property.
  • To ensure a nice picture, choose the value of a to be at most 5, b to be at most 4, and c to be at most 5.

Activity #2

Match Equivalent Expressions.

Draw lines to match each expression in column 1 to an equivalent expression in column 2. If you get stuck, consider drawing a diagram in the second applet below.

Activity #3

Apply the Distributive Property to write Equivalent Expressions.

In the following activity, you are going to use the distributive property to write equivalent expressions. The instructions on how to interact with the applet are given below.

  • In each row, use the distributive property to write an equivalent expression.
  • If you get stuck, consider drawing a diagram in the applet below the table.

  • Write an equivalent expression for the given expression. Try to do as many problems as you can in this activity.

Challenge #1

A rectangle with dimensions 6 cm and W cm is partitioned into two smaller rectangles.

Explain why each of these expressions represents the area, in cm2, of the shaded region.

(1.) 6W – 24

(2.) 6(W – 4)

Challenge #2

Challenge #3

Quiz Time