Chapter 1.7, Problem 16P

Use the Distributive Property to simplify each expression.

$\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$

To determine

To find: The simplified form of the expression $\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$ .

Answer to Problem 16P

The simplified form of the expression $\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$ is $\frac{4}{9}m-\frac{4}{9}$ .

Explanation of Solution

Given:

The expression is $\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$ .

Calculation:

Solve the expression $\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$ using distributive property as follows:

  $\begin{array}{c}\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)=\frac{2}{3}\left(\frac{2}{3}m\right)+\frac{2}{3}\left(-\frac{2}{3}\right)\\ =\frac{4}{9}m-\frac{4}{9}\end{array}$

Thus, the simplified form of the expression $\frac{2}{3}\left(\frac{2}{3}m-\frac{2}{3}\right)$ is $\frac{4}{9}m-\frac{4}{9}$ .