Order of Operations (BIDMAS)
Applying brackets, indices, division, multiplication, addition and subtraction in the correct order.
What is Order of Operations (BIDMAS)?
When a calculation has more than one operation, you must follow a specific order to get the right answer. This order is remembered using the acronym BIDMAS: Brackets, Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right).
BIDMAS questions appear frequently in the 11+ exam, either as standalone calculations or as part of larger problems. Getting the order wrong can lead to a completely different answer.
Step-by-Step Method
Do Brackets first
Work out anything inside brackets before doing anything else.
Then Indices (powers)
Calculate squares, cubes and other powers.
Then Division and Multiplication from left to right
These have equal priority – work from left to right, doing whichever comes first.
Then Addition and Subtraction from left to right
Again, equal priority – work from left to right.
Show each step clearly
Write out each step of the calculation on a new line so you do not lose track.
Worked Examples
3 + 4 x 2 = ?
Working
- Multiplication before addition: 4 x 2 = 8.
- Then add: 3 + 8 = 11.
- (Not 3 + 4 = 7, then 7 x 2 = 14 – that is wrong!)
(8 + 2) x 3 – 1 = ?
Working
- Brackets first: 8 + 2 = 10.
- Then multiply: 10 x 3 = 30.
- Then subtract: 30 – 1 = 29.
24 / (3 + 5) + 2 squared = ?
Working
- Brackets first: 3 + 5 = 8.
- Division: 24 / 8 = 3.
- Indices: 2 squared = 4.
- Addition: 3 + 4 = 7.
Common Mistakes
Working from left to right and ignoring BIDMAS (e.g. getting 3 + 4 x 2 = 14).
Always do multiplication and division before addition and subtraction.
Thinking division always comes before multiplication.
Division and multiplication have EQUAL priority. Work from left to right.
Forgetting to complete everything inside brackets before moving on.
Brackets are always first. Solve the entire bracket expression before using the result.
Top Tips
- Remember BIDMAS: Brackets, Indices, Division, Multiplication, Addition, Subtraction.
- Division and Multiplication are on the same level – do them left to right.
- Addition and Subtraction are on the same level – do them left to right.
- When in doubt, add brackets to make the order clear to yourself.
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Put these techniques into action with our free practice papers.
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