Order of Operations Explained

The order of operations is an agreement mathematicians use so everyone gets the same value for the same expression.

Quick idea

Do parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Steps

1. Simplify anything inside parentheses or grouping symbols.
2. Evaluate exponents.
3. Move left to right through multiplication and division.
4. Move left to right through addition and subtraction.

Worked example

Evaluate 3 plus 4 times 2.

Full solution

Step-by-step walkthrough

Step 1

Multiplication happens before addition.

Step 2

Four times 2 is 8.

Step 3

Then add 3 to get 11.

Common mistake

PEMDAS does not mean all multiplication before all division no matter where they appear. Multiplication and division share a level, so work left to right.

Practice problems

1. Evaluate 6 + 2 x 5.
2. Evaluate (6 + 2) x 5.
3. Evaluate 18 / 3 x 2.

Answers

1. 16
2. 40
3. 12

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Solve One-Step Equations
• How to Solve Two-Step Equations
• How to Simplify Exponents