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The BODMAS rule: order of operations, explained with examples
What BODMAS means (and PEMDAS and BIDMAS), the order to do brackets, powers, division, multiplication, addition and subtraction, worked examples, common mistakes, and free practice worksheets.
When a sum has more than one operation, everyone must do them in the same order, or two people would get different answers. That agreed order is called BODMAS in India and the UK, BIDMAS in some UK schools and PEMDAS in the US. They are the same rule.
What the letters mean
| BODMAS | PEMDAS | Meaning |
|---|---|---|
| Brackets | Parentheses | Work out anything in brackets first |
| Orders | Exponents | Powers and roots, like 3² or √16 |
| Division and Multiplication | Multiplication and Division | Same level: work left to right |
| Addition and Subtraction | Addition and Subtraction | Same level: work left to right |
The most important detail: division and multiplication are equal partners, and so are addition and subtraction. Within each pair, go from left to right.
Worked examples
- 6 + 4 × 3 = 6 + 12 = 18 (multiply before adding)
- (6 + 4) × 3 = 10 × 3 = 30 (brackets first)
- 20 − 12 ÷ 4 + 2² = 20 − 3 + 4 = 21
- 8 ÷ 2 × 4 = 4 × 4 = 16 (left to right, not 8 ÷ 8)
- 3 + 6 × (5 + 4) ÷ 3 − 7 = 3 + 6 × 9 ÷ 3 − 7 = 3 + 18 − 7 = 14
Common mistakes
- Adding first because it comes first. In 5 + 2 × 3 the answer is 11, not 21.
- Doing all multiplication before any division. 12 ÷ 3 × 2 is 8 (left to right), not 2.
- Forgetting that a power belongs only to the number next to it. −3² means −(3²) = −9, but (−3)² = 9.
Practise
- Order of operations worksheets (BODMAS / PEMDAS) with answer keys.
- The 24 game: make 24 with four numbers, a fun way to use brackets.
- Maths Practice for instant feedback.
Common questions
What is the full form of BODMAS?
Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction.
Is BODMAS the same as PEMDAS?
Yes. They give the same answers; only the words differ. Both say multiplication and division are done together from left to right, and so are addition and subtraction.
What is the answer to 6 ÷ 2(1 + 2)?
Using the standard left-to-right rule, 6 ÷ 2 × 3 = 3 × 3 = 9. It goes viral because the missing × sign makes it look ambiguous; good maths writing adds brackets to avoid that.
This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.