# How do you simplify 3(7 + 4 - 2) ÷ 9 - 7 using order of operations?

Feb 19, 2016

$3 \left(7 + 4 - 2\right) \div 9 - 7 = - 4$

#### Explanation:

The order of operations is parentheses, exponents, multiplication and division, and then addition and subtraction.

Parentheses:
First, we evaluate any parts of the expression within parentheses. In this case, the only operations within parentheses are addition and subtraction, so we can just go from left to right.

$3 \textcolor{red}{\left(7 + 4 - 2\right)} \div 9 - 7 = 3 \textcolor{red}{\left(11 - 2\right)} \div 9 - 7$

$= 3 \textcolor{red}{\left(9\right)} \div 9 - 7$

There are no more expressions within parentheses which we need to evaluate, meaning we can move on to the next step.

Exponents:
This expression contains no exponents, and so we move on.

Multiplication and Division:
Now we evaluate any multiplication or division operations, going from left to right.

$\textcolor{red}{3 \left(9\right)} \div 9 - 7 = \textcolor{red}{27} \div 9 - 7$

$\textcolor{red}{27 \div 9} - 7 = \textcolor{red}{3} - 7$

There are no more multiplication or division operations, and so we move to the final step.

$\textcolor{red}{3 - 7} = \textcolor{red}{- 4}$
$3 \left(7 + 4 - 2\right) \div 9 - 7 = - 4$