Home > Pre-Algebra > Integers > Order of Operations

## Order of Operations

#### Introduction

When you are given a math problem to work out that contains different functions, order of operations tells you which order to complete the sums in.

You can remember order of operations using the acronym PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction).

## Lesson

The key rule with order of operations is to follow PEMDAS. That means that you solve the sums in the following order:

First: Parenthesis - symbols like this ( ) that go around parts of an equation. Second: Exponents - symbols like this $^{2}$ that tell you how many times to multiply a number together. Third: Multiplication - represented by a symbol like this x Fourth: Division - represented by a symbol like this ÷ or / Fifth: Addition - represented by a symbol like this + Sixth: Subtraction - represented by a symbol like this -

So, if we take the following sum:

$2^{3} + 5 - (3 * 4) = ?$

We would use PEMDAS to work out that the first thing to solve is the sum in the parenthesis:

$2^{3} + 5 - (3 * 4) = ?$

$2^{3} + 5 - 12 = ?$

We then solve the exponent:

$2^{3} + 5 - 12 = ?$

($2^{3} = 8$)

$8 + 5 - 12 = ?$

$8 + 5 - 12 = ?$

$13 - 12 = ?$

And finally the subtraction:

$13-12 = ?$

$13-12 = 1$

If you have a sum that contains only addition and subtraction, you can solve this left to right.

If you have a sum that contains only multiplication and division, you can solve this left to right.

## Examples

$10 + 2 * 8 - 3$
$10 + 2 * 8 - 3$
$10 + 16 - 3$
$26 - 3$
$23$
$([1 + 2] * 3 + 6) / (2 + 3)$
$([1 + 2] * 3 + 6) / (2 + 3)$
$(3 * 3 + 6) / (2 + 3)$
$(9 + 6) / (2 + 3)$
$15 / (2 + 3)$
$15 / 5$
$3$
$4 + 2 * (3 + 5 - 1)$
$4 + 2 * (3 + 5 - 1)$
$4 + 2 * (3 + 4)$
$4 + 2 * 7$
$4 + 14$
$18$