Order of Operations (PEMDAS / BODMAS) Explained
When an expression has more than one operation, the order you work in changes the answer. The order of operations is the agreed rule that makes everyone get the same result.
The rule
Work through an expression in this order:
- Parentheses (brackets) first.
- Exponents (powers and roots).
- Multiplication and division, from left to right.
- Addition and subtraction, from left to right.
In the United States this is taught as PEMDAS. In the UK and many other countries it is BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). They describe the same rule. Multiplication and division share one level, and so do addition and subtraction, so you move left to right within each level.
Worked examples
| Expression | Steps | Answer |
|---|---|---|
| 2 + 3 × 4 | 3 × 4 = 12, then 2 + 12 | 14 |
| (2 + 3) × 4 | 2 + 3 = 5, then 5 × 4 | 20 |
| 18 ÷ 3 × 2 | Left to right: 18 ÷ 3 = 6, then 6 × 2 | 12 |
| 10 − 2² + 1 | 2² = 4, then 10 − 4 = 6, then 6 + 1 | 7 |
Using a basic calculator correctly
Many basic calculators, including the Standard mode on CalcWindow, work like a desk calculator: they apply each operation when you press the next one. If you type 2 + 3 × 4 = in that order, the calculator adds first and gives 20, not 14.
3 × 4 in one window, then add 2 to the result. Opening two calculator windows side by side makes this easy: use one for the inner part and one for the final step.Common mistakes
- Doing multiplication before division. They have equal priority, so go left to right.
- Forgetting that a minus sign belongs to the number after it. In 5 − 3 + 2 the answer is 4, not 0.
- Ignoring parentheses. Anything inside brackets is calculated before the rest.
For powers and roots, see the scientific calculator guide.