Title: LESSON: Order of Operations
Course: Mathematics Essentials Q1 > Section: Week 2

Order of Operations

INTRODUCTION

Order of Operations

READ: Evaluating Expressions

Evaluating Numerical Expressions with the Four Operations

What is an expression? To understand what an expression is, let’s compare it with an equation. An equation is a number sentence that can be solved. It has an equal sign where one side of the equals sign is equal to the other side of the equals sign.

Example

This is an equation. It has an equals sign and can be solved.

What is an expression then? An expression is a number sentence without an equals sign. It can be simplified and/or evaluated.

Example

Now this expression can be confusing because it has both addition and multiplication in it. Do we need to add or multiply first? To figure this out, we are going to learn something called the Order of Operations. The Order of Operation is a way of evaluating expressions. It lets you know what order to complete each operation in.

Order of Operations

P - parentheses

E - exponents

MD - multiplication or division in order from left to right

AS - addition or subtraction in order from left to right

Take a few minutes to write these down in a notebook.

Example

Here we have an expression with addition and multiplication. We can look at the order of operations and see that multiplication comes before addition. We need to complete that operation first.

When we evaluate this expression using order of operations, our answer is 20.

What would have happened if we had NOT followed the order of operations?

Example

We probably would have solved the problem in order from left to right.

This would have given us an incorrect answer. It is important to always follow the order of operations.

READ: Evaluating Expressions with Grouping Symbols

Evaluating Numerical Expressions Using Powers and Grouping Symbols

We can also use the order of operations when we have exponent powers and grouping symbols like parentheses. Let’s review where exponents and parentheses fall in the order of operations.

Order of Operations

P - parentheses

E - exponents

MD - multiplication or division in order from left to right

AS - addition or subtraction in order from left to right

According to the order of operations parentheses comes first. We always do the work in parentheses first. Then we evaluate exponents.

Example

In this example, we can see that we have four things to look at. We have 1 set of parentheses, addition, subtraction in the parentheses and multiplication. We can evaluate this expression using the order of operations.

Our answer is 6.

What about when we have parentheses and exponents?

Example

We start by using the order of operations. It says we evaluate parentheses first.

$$(3)( 2) = 6$$

$$35 + 3^2 -6(7)$$

Next, we evaluate exponents.

$$3^2=9$$

$$35+9-6(7)$$

Next, we complete multiplication or division in order from left to right. We have multiplication.

Next, we complete addition and/or subtraction in order from left to right.

Our answer is 2.

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

EXAMPLE 4

Check Yourself! Order of Operations