Order of Operations
5 minQuiz at the end
Why Order of Operations Matters
Without rules, the same expression could give different answers. BODMAS (or PEMDAS) tells us the correct order to evaluate any expression.
BODMAS
| Letter | Operation |
|---|---|
| B | Brackets |
| O | Orders (powers/roots) |
| D | Division |
| M | Multiplication |
| A | Addition |
| S | Subtraction |
Note: D and M have equal priority β work left to right. A and S have equal priority β work left to right.
Examples
3 + 4 Γ 2 β Multiplication first: 3 + 8 = 11 β (not 14)
(3 + 4) Γ 2 β Brackets first: 7 Γ 2 = 14 β
20 - 4Β² + 3 β Orders first: 20 - 16 + 3 = 4 + 3 = 7 β
18 Γ· (2 + 1) Γ 3 β Brackets: 18 Γ· 3 Γ 3 β Left to right: 6 Γ 3 = 18 β
Common Mistakes
β Doing addition before multiplication: 3 + 4 Γ 2 β 14 β Doing division before brackets: 18 Γ· (2+1) β 18 Γ· 2 + 1
When in doubt, add brackets to make the intended order explicit.