The order of operations
When a calculation has more than one operation, we follow a set order so everyone gets the same answer. Do the work inside brackets first, then × and ÷ from left to right, and finally + and − from left to right.
Key idea
Order: Brackets → × ÷ (left to right) → + − (left to right).
Worked example
Worked example
Work out 6 × 5 + 40 ÷ 8.
Do × and ÷ first: 6 × 5 = 30 and 40 ÷ 8 = 5.
Now add: 30 + 5 = 35.
Why brackets matter
Brackets change the answer. 100 ÷ (2 + 3) means add first: 2 + 3 = 5, then 100 ÷ 5 = 20. Without brackets the answer would be different, so always solve brackets first. When two operations are at the same level, such as × and ÷ together, or + and − together, simply work from left to right and do not jump ahead. Take one small step at a time and rewrite the shorter calculation before moving on, so you do not lose track.
Remember
- Brackets come first, every time.
- × and ÷ are done before + and −.
- Same level? Work from left to right.
- Rewrite the line after each step.