The order of operations is the agreed sequence for evaluating a math expression so everyone gets the same answer. The common mnemonic is PEMDAS (BODMAS in some countries).
| Step | Operation |
|---|---|
| P | Parentheses (grouping) |
| E | Exponents (powers, roots) |
| MD | Multiplication & Division — left to right |
| AS | Addition & Subtraction — left to right |
The key subtlety
Multiplication and division share a tier and are done left to right, not multiplication first — same for addition and subtraction. So 8 ÷ 2 × 4 = (8 ÷ 2) × 4 = 16, not 8 ÷ (2×4).
Worked example
3 + 4 × 2² − (5 − 1): parentheses first (5−1=4), then the exponent (2²=4), then multiply (4×4=16), then add/subtract left to right → 3 + 16 − 4 = 15.
Frequently asked questions
What does PEMDAS stand for? Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Is multiplication always before division? No — they’re equal; work left to right.
Why do we need an order? So every expression has one unambiguous answer.
When an expression gets long, add your own parentheses to make the intended order explicit — it costs nothing and prevents the ambiguity that trips up people and spreadsheets alike. Clarity beats cleverness in any formula someone else will read.