What is the Order of Operations?
The phrase “order of operations” or “PEMDAS” refers to the order in which you need to perform multiplication, division, addition, subtraction, and exponential operations in an equation.
To see the free study questions, please go to the next section.
Order of Operations – PEMDAS
The phrase PEMDAS is sometimes used to remember the correct order to perform operations in an equation.
PEMDAS means parentheses, exponents, division, multiplication, addition, and subtraction.
So, when you see an equation, you need to perform the operations from left to right in this order:
1) Parentheses – Do the operations inside parentheses or brackets first.
2) Exponents – Then perform the operations indicated by the exponents.
3) Multiplication and Division – Then do the multiplication and division from left to right.
4) Addition and Subtraction – Then do the addition and subtraction from left to right.
Some students remember the rule “PEMDAS” by using the phrase:
PEMDAS: Please Excuse My Dear Aunt Sally
Let’s look at a couple of problems on PEMDAS or order of operations.
Order of Operations PEMDAS – Basic Example
Now study this example of how to carry out the order of operations “PEMDAS” rule.
Example: 1 + 64 ÷ 4 ÷ 2 × 5 – 3 = ?
Answer: 38
In this problem, we do not have any parentheses or exponents to deal with.
So, start by doing the multiplication and division first.
Multiplication and division are performed in the same step, so you need to divide and then multiply from left to right as shown below when you have division and multiplication together like in this example.
1 + 64 ÷ 4 ÷ 2 × 5 – 3 =
1 + (64 ÷ 4) ÷ 2 × 5 – 3 =
1 + 16 ÷ 2 × 5 – 3 =
1 + (16 ÷ 2) × 5 – 3 =
1 + 8 × 5 – 3 =
1 + (8 × 5) – 3 =
1 + 40 – 3
Then do the addition and subtraction from left to right.
1 + 40 – 3 =
41 – 3 = 38
Order of Operations PEMDAS – Advanced Example
Let’s look at a more difficult example of how to carry out the order of operations “PEMDAS” rule.
Example: (4 + 5)2 + 9 ÷ 3 – 2 × 6 = ?
Answer: 72
Do the operations in the parentheses first.
(4 + 5)2 + 9 ÷ 3 – 2 × 6 =
(9)2 + 9 ÷ 3 – 2 × 6
Then do the exponential operation.
92 + 9 ÷ 3 – 2 × 6 =
(9 × 9) + 9 ÷ 3 – 2 × 6 =
81 + 9 ÷ 3 – 2 × 6
Next do the multiplication and division from left to right.
81 + 9 ÷ 3 – 2 × 6 =
81 + (9 ÷ 3) – 2 × 6 =
81 + 3 – 2 × 6 =
81 + 3 – (2 × 6) =
81 + 3 – 12
Then do the addition and subtraction from left to right.
81 + 3 – 12 =
(81 + 3) – 12 =
84 – 12 = 72
Order of Operations PEMDAS – Further Practice
If you found these exercises difficult, you should try our pre-algebra problems.
If you are testing in college math, you may also want to look at our other algebra study materials.