Order Of Operations
Objective
Know how to use the correct order of operations to solve problems with many operations
Example
3 x 4 ÷ (3 - 1)2 =
3 x 4 ÷ (3 - 1)2 =
3 x 4 ÷ (2)2 =
3 x 4 ÷ 4 =
12 ÷ 4 =
Answer: 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Explanation
When you read a book, you read left from right, every time. Unfortunately, in math this doesn't always happen. Instead, mathematicians agreed on the following order to do their operations
Just remember GEMS
Grouping: [(2 + 32 x 4) - 2 ÷ 13]
Exponents: [(2 + 32 x 4) - 2 ÷ 13]
Multiplication and Division: [(2 + 32 x 4) - 2 ÷ 13]
Subtraction and Addition: [(2 + 32 x 4) - 2 ÷ 13]
What does this mean? Read left to right looking for things from step 1. Start again, looking for things from step 2. Then step 3. Then step 4.
I will work some examples below, but the video may be more helpful.
To watch a Khan Academy Video, click here
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Examples
Example 1
10-6x7+3
Check for grouping... no grouping
Check for exponents... no exponents
Check for multiplication and division...
10-6x7+3
10-42+3
Check for subtraction and addition...
10-42+3 (why do we do 10-42 first, instead of -42+3? Because they are both part of step 4,
-32+3 we just read left to right.)
-32+3
-29
Answer: -29
~~~~~~~~~~~~~~~~~~~
Example 2
(4x3)2
Check for grouping...
(4x3)2
122
Check for exponents...
122
144
Answer: 144
~~~~~~~~~~~~~~~~~~~
Example 3
10+42x3
Check for grouping... no grouping
Check for exponents...
10+42x3
10+16x3
Check for multiplication and division...
10+16x3
10+48
Check for subtraction and addition...
10+48
58
Answer: 58
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Practice your skills
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Ready?