Algebra/Order of Operations

Introduction

Order of Operations: A way of evaluating expressions with more than one operation. These rules govern precedence in mathematical operations.

For Example: When faced with $4+2\times 3$, how do you proceed?

There are two apparent options:

$4+2\times 3$

$=6\times 3$

$=18$

OR

$4+2\times 3$

$=4+6$

$=10$

Which is correct?

We must follow the correct order of operations so that this expression has a necessarily unique value.

For the above example, the correct answer is 10.

Now, let's find out why?

The Actual Order

Solve equations in this order.

• Parentheses (evaluate what's inside them)
• Exponents
• Multiplication and/or division from left to right
• Addition and/or subtraction from left to right

An Easy Way of Remembering

Use this memory tool to help remember the order! Please Excuse My Dear Aunt Sally

or

Please Eat My Dear Aunt Sally

NB An alternative form of this is brackets, indices, division, multiplication, addition, subtraction (BIDMAS).

Examples

Order of Operations - Examples

Expression	Evaluation	Operation
4 × 2 + 1	= 4 × 2 + 1	Multiplication
	= 8 + 1	Addition
	= 9
12 - 9 ÷ 3	= 12 - 9 ÷ 3	Division
	= 12 - 3	Subtraction
	= 9
3 + 12 ÷ (5 - 2)	= 3 + 12 ÷ (5 - 2)	Parentheses
	= 3 + 12 ÷ 3	Division
	= 3 + 4	Addition
	= 7
7 × 10 - (2 × 4)2	= 7 × 10 - (2 × 4)2	Parentheses
	= 7 × 10 - 82	Exponents
	= 7 × 10 - 64	Multiplication
	= 70 - 64	Subtraction
	= 6

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Practice Problems

Evaluate the numerical expression
Evaluate the expression for the given value of the variable
Evaluate the fraction expression for the given value of the variable
55+98 9^2-7(8+4)