Chapter 1.5, Problem 73STP

To determine

Rewrite the expression $6\frac{1}{9}\left(9\right)$ using distributive property and then evaluate it.

Answer to Problem 73STP

The value of the expression $6\frac{1}{9}\left(9\right)$ is $55$ .

Explanation of Solution

Given:

The expression is $6\frac{1}{9}\left(9\right)$ .

Calculation:

The distributive law of multiplication over addition or subtraction states that $a\left(b\pm c\right)=ab\pm ac$ , where $a$ , $b$ and $c$ are real numbers.

The expression $6\frac{1}{9}\left(9\right)$ is simplified using distributive property as follows:

  $\begin{array}{c}6\frac{1}{9}\left(9\right)=\left(6+\frac{1}{9}\right)\left(9\right)\\ =\left(6\times 9\right)+\left(\frac{1}{9}\times 9\right)\\ =54+1\\ =55\end{array}$

Thus, the value of the expression $6\frac{1}{9}\left(9\right)$ is $55$ .