When a calculation contains more than one operation, the order matters. BIDMAS gives the order: Brackets, then Indices (powers and roots), then Division and Multiplication working from left to right, then Addition and Subtraction working from left to right. So 20 − 3 × 4 = 20 − 12 = 8, not 68.
BIDMAS
- Brackets
- Indices (powers and roots)
- Division and Multiplication, from left to right
- Addition and Subtraction, from left to right
Division and multiplication have equal priority, as do addition and subtraction; work through each pair from left to right.
What is BIDMAS?
BIDMAS is an agreed order for carrying out calculations, so that everyone gets the same answer. Some schools say BODMAS, where O stands for Orders, meaning powers; it is the same rule.
The common misunderstanding is that division always comes before multiplication, or addition before subtraction. They do not: within each pair, simply work from left to right.
Brackets and indices first
Anything in brackets is worked out first. Then powers and roots. An index applies only to the number it is attached to, so in 3 + 2 × 5² the square applies to the 5 alone: 5² = 25, then 2 × 25 = 50, then 3 + 50 = 53.
Multiplication and division before addition and subtraction
Once brackets and indices are done, sweep through the calculation doing every multiplication and division from left to right. Only then do the additions and subtractions. In 12 ÷ 2 + 5 × 2, the division and multiplication give 6 and 10, and the sum is 16.
Negative numbers and powers
Brackets change the meaning of a power with a negative number. (−3)² means −3 × −3 = 9, but −3² means −(3²) = −9. Calculators follow this rule too, so type the brackets when you mean the whole negative number to be squared.
Inserting brackets
Some questions ask you to add brackets to make a calculation correct. Try brackets around different pairs of numbers and work out each version. For example, 6 + 4 × 2 equals 14 without brackets, but (6 + 4) × 2 equals 20.
Worked examples
Example 1. Work out 20 − 3 × 4.
- Multiplication first: 3 × 4 = 12.
- Then subtract: 20 − 12.
Answer: 8.
Example 2. Work out (9 + 6) ÷ 3.
- Brackets first: 9 + 6 = 15.
- Then divide: 15 ÷ 3.
Answer: 5.
Example 3. Work out 3 + 2 × 5².
- Index first: 5² = 25.
- Then multiply: 2 × 25 = 50.
- Then add: 3 + 50.
Answer: 53.
Example 4. Work out 40 ÷ (3 + 5) × 3.
- Brackets: 3 + 5 = 8.
- Division and multiplication from left to right: 40 ÷ 8 = 5, then 5 × 3.
Answer: 15.
Example 5. Work out (−3)² + 4, and explain why it differs from −3² + 4.
- (−3)² = −3 × −3 = 9, so (−3)² + 4 = 13.
- −3² means −(3²) = −9, so −3² + 4 = −5.
Answer: 13. The brackets make the whole of −3 squared.
Example 6. Insert one pair of brackets to make 6 + 4 × 2 = 20 true.
- Without brackets, 6 + 8 = 14, which is too small.
- Bracketing 6 + 4 gives 10 × 2.
Answer: (6 + 4) × 2 = 20.
Common mistakes
- Working strictly from left to right. 20 − 3 × 4 is 8, not 68; multiply before subtracting.
- Always dividing before multiplying. Division and multiplication are equal; work left to right.
- Applying a power to too much. In 2 × 5², only the 5 is squared.
- Squaring a negative without brackets. (−3)² = 9 but −3² = −9.
- Ignoring brackets on a calculator. Type brackets exactly as written in the question.
How BIDMAS is examined
Order of operations is tested at Foundation tier in Edexcel GCSE (1MA1) and in Edexcel International GCSE (4MA1), usually on non-calculator papers. Typical questions:
- work out a calculation with mixed operations
- work out a calculation with brackets and powers
- insert brackets to make a statement correct
- spot and explain an error in someone else's working
For unlimited practice, use the GCSE number revision engine. The order of operations worksheet has questions with answers.
BIDMAS is needed throughout substitution into formulae and written calculation methods.
Frequently asked questions
What does BIDMAS stand for?
Brackets, Indices, Division, Multiplication, Addition, Subtraction.
Do you divide before you multiply?
Not necessarily. Division and multiplication have equal priority, so work from left to right.
What is the difference between BIDMAS and BODMAS?
Nothing important. The O in BODMAS stands for Orders, which means powers, the same as Indices.