Maths
What is the order of operations (BIDMAS or PEMDAS)?
Quick answer
The order of operations is the agreed order for working out calculations: brackets, then powers, then × and ÷, then + and −. UK pupils learn it as BIDMAS; US pupils as PEMDAS.
In one sentence
The order of operations is the rule everyone follows so that a calculation like 2 + 3 × 4 has one right answer.
Explained
Try 2 + 3 × 4. If you go left to right you get 5 × 4 = 20. If you multiply first you get 2 + 12 = 14. Both can't be right, so mathematicians agreed an order. The answer is 14.
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The order is:
- Brackets first.
- Powers next (also called indices, orders or exponents).
- Multiplication and division, working left to right.
- Addition and subtraction, working left to right.
Different countries use different memory words for the same rule:
| Word | Stands for | Used in |
|---|---|---|
| BIDMAS | Brackets, Indices, Division, Multiplication, Addition, Subtraction | UK |
| BODMAS | Brackets, Orders (or "Of"), Division, Multiplication, Addition, Subtraction | UK, India, Nigeria, Australia and others |
| PEMDAS | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction | US |
| BEDMAS | Brackets, Exponents, Division, Multiplication, Addition, Subtraction | Canada |
The big trap is that the letters suggest division always comes before multiplication (BIDMAS) or the other way round (PEMDAS). It doesn't. × and ÷ are equal partners, and so are + and −. When they appear together, work from left to right. So 10 − 4 + 3 = 9, not 3.
Brackets are your tool for changing the order: 2 + 3 × 4 = 14, but (2 + 3) × 4 = 20. In algebra, this matters all the time, because 2(x + 5) is not the same as 2x + 5. And because powers come before multiplying, 2 × 3² = 2 × 9 = 18, not 6² = 36.
Examples
- 5 + 6 × 2 = 5 + 12 = 17
- (5 + 6) × 2 = 11 × 2 = 22
- 30 ÷ 5 + 1 = 6 + 1 = 7
- 30 ÷ (5 + 1) = 30 ÷ 6 = 5
- 4 + 2³ × 3 = 4 + 8 × 3 = 4 + 24 = 28
- 50 − 10 ÷ 2 + 3 = 50 − 5 + 3 = 48
Common mistakes
- Always dividing before multiplying (or always adding before subtracting) because of the letter order. Fix: same-level operations go left to right.
- Ignoring hidden brackets. In a fraction like (8 + 4) ÷ 3, the line acts like a bracket: 12 ÷ 3 = 4.
- Trusting a basic calculator. Some simple calculators work strictly left to right. Scientific calculators follow BIDMAS.
Quick quiz
Order of operations
Check what you know with 5 quick questions.
Question 1 of 5
What is 3 + 4 × 2?
Practise it
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Browse maths worksheets and look for mixed operations and algebra pages.
For grown-ups
Related topics
Powers and indices
A power (also called an index or exponent) is a small raised number showing how many times to multiply a number by itself. So 2⁴ means 2 × 2 × 2 × 2 = 16.
Algebra
Algebra is maths that uses letters, like x or n, to stand for numbers we don't know yet or numbers that can change. For example, if n + 3 = 10, then n = 7.
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Addition
Addition is putting amounts together to find a total. The sign is +, and the answer is called the sum or total, so 4 + 3 = 7.
Equations
An equation says two things are equal, using an = sign, like 2x + 1 = 9. Solving it means finding the value of the letter that makes it true, here x = 4.
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.