# How do you simplify 6/2-1*6² using order of operations?

Dec 22, 2015

$\frac{6}{2} - 1 \cdot {6}^{2} = - 33$

#### Explanation:

The order of operations is:

Parentheses
Exponents
Multiplication
Division
Subtraction

Now, multiplication and division actually have the same priority, as do addition and subtraction, but it wont hurt to follow the given order, either.

Let's see how it applies to the expression $\frac{6}{2} - 1 \cdot {6}^{2}$

Parentheses:
There are no parentheses in the given expression, so we can skip this.

Exponents:
We have one exponent to evaluate: $\frac{6}{2} - 1 \cdot {6}^{\textcolor{red}{2}}$

As ${6}^{2} = 6 \cdot 6 = 36$ we have

$\frac{6}{2} - 1 \cdot {6}^{2} = \frac{6}{2} - 1 \cdot 36$

Multiplication:
We have one instance of multiplication to evaluate: $\frac{6}{2} - 1 \textcolor{red}{\cdot} 36$

As $1 \cdot 36 = 36$ we have

$\frac{6}{2} - 1 \cdot 36 = \frac{6}{2} - 36$

Division:
We have one instance of division to evaluate: $6 \textcolor{red}{\div} 2 - 1$

As $\frac{6}{2} = 3$ we have

$\frac{6}{2} - 36 = 3 - 36$

We have one instance of subtraction to evaluate: $3 \textcolor{red}{-} 36$
As $3 - 36 = - 33$ we have our final result.
$\frac{6}{2} - 1 \cdot {6}^{2} = - 33$