# Order of Operations (MDAS)

In this section, you are going to learn to use parentheses in your calculations. The reason to use parentheses is to change the order of operations. But what is the order of operations?

The order of operations decides in which order you do your calculations. At this stage, I call the order of operations MDAS (the initials of Multiplication, Division, Addition and Subtraction).

Rule

### MDAS

• First, do all Multiplication and Division.

• Then, do all Addition and Subtraction.

Let’s take a look at some examples:

Example 1

Calculate $6+3\cdot 2$.

Now, think MDAS. First you multiply and divide, then you add and subtract. Here’s how you do it: $\begin{array}{llll}\hfill 6+3\cdot 2& =6+6\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =12\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

Calculate $4-2\cdot 6+3$.

Think MDAS. First you multiply and divide, then you add and subtract. Here’s how you do it: $\begin{array}{llll}\hfill 4-2\cdot 6+3& =4-12+3\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 3

Calculate $12÷4-6+8\cdot 5$.

Think MDAS. First you multiply and divide, then you add and subtract. Here is how you do it: $\begin{array}{llll}\hfill 12÷4-6+8\cdot 5& =3-6+40\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-3+40\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =37\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 4

Calculate $72÷8-6\cdot 4+16+32÷8$.

Think MDAS. First you multiply and divide, then you add and subtract. Here’s how you do it:

$\begin{array}{llll}\hfill 72& ÷8-6\cdot 4+16+32÷8\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =9-24+16+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

$\begin{array}{llll}\hfill 72÷8-6\cdot 4+16+32÷8& =9-24+16+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$