Maths · Number & Negatives
Order of operations
BIDMAS/BODMAS with brackets and negatives.
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What is BIDMAS?
BIDMAS tells us the order to do operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction. Some people say BODMAS (using 'Orders' instead of 'Indices'). Always work out what is inside brackets first. Then follow the rest of the order.
Working with Negatives
Negative numbers can appear anywhere in a calculation. Remember that subtracting a negative is the same as adding. For example, 5 – (–3) becomes 5 + 3. When multiplying or dividing, two negatives make a positive.
Brackets Come First
Always simplify inside brackets before doing anything else. If there are operations inside brackets, follow BIDMAS inside them too. Work from the innermost brackets outwards if there are brackets inside brackets.
Multiplication and Division Together
When you have multiplication and division in the same problem, work from left to right. The same rule applies to addition and subtraction. They have equal priority, so just go left to right.
Common Mistakes to Avoid
Do not ignore brackets or do addition before multiplication. Watch out for negative signs, especially after brackets. Always check if a minus sign belongs to a number or is an operation between two numbers.
Worked examples
1. Calculate: 8 + 3 × (5 – 2)
- Brackets first: 5 – 2 = 3
- Now we have: 8 + 3 × 3
- Multiply before adding: 3 × 3 = 9
- Finally add: 8 + 9 = 17
2. Calculate: 20 – (–4) + 6 ÷ 2
- Work out the brackets: – (–4) = + 4, so 20 + 4
- Now we have: 20 + 4 + 6 ÷ 2
- Division before addition: 6 ÷ 2 = 3
- Add from left to right: 20 + 4 + 3 = 27
3. Calculate: (10 – 4) × 2 – 3
- Brackets first: 10 – 4 = 6
- Now we have: 6 × 2 – 3
- Multiply before subtract: 6 × 2 = 12
- Finally subtract: 12 – 3 = 9
Try it yourself
Calculate: 15 – 2 × (4 + 1)
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