In short: BIDMAS tells you the order to do operations in: Brackets, Indices, Division and Multiplication, then Addition and Subtraction. Work through it in that order, and treat division and multiplication as equal rank (left to right), just like addition and subtraction. This gives one correct answer every time.
Knowing how to use BIDMAS is a foundation skill for GCSE Foundation maths, because it decides the correct order of operations in any calculation with more than one step. Get the order wrong and a perfectly good calculation gives the wrong answer. This guide explains what BIDMAS stands for and shows you how to apply it step by step, with a worked example.
The reliable method
BIDMAS is the order you must follow when a calculation mixes different operations.
- Brackets first. Work out anything inside brackets before anything else.
- Indices next. Deal with powers and square roots, such as 5² or √9.
- Division and Multiplication next. These share equal rank, so work through them from left to right as they appear.
- Addition and Subtraction last. These also share equal rank, so again work left to right.
- Write each step out so you can see the calculation shrinking towards a single answer.
The key idea is that the D and M go together, and the A and S go together. Within each of those pairs, you simply work left to right rather than always doing one before the other.
A worked example
Work out 6 + 2 × (4 + 1)² − 8 ÷ 4 using BIDMAS.
Apply BIDMAS one stage at a time.
Brackets:
- (4 + 1) = 5, so the calculation becomes 6 + 2 × 5² − 8 ÷ 4
Indices:
- 5² = 25, so it becomes 6 + 2 × 25 − 8 ÷ 4
Division and Multiplication (left to right):
- 2 × 25 = 50
- 8 ÷ 4 = 2
- Now the calculation is 6 + 50 − 2
Addition and Subtraction (left to right):
- 6 + 50 = 56
- 56 − 2 = 54
So the answer is 54. Each stage replaces part of the calculation with a single number, so the line gets shorter until only the answer is left.
This works because BIDMAS gives everyone the same rules, so a calculation has exactly one correct answer rather than depending on the order you happen to read it in.
Common mistakes to avoid
- Trap: always doing multiplication before division. Treating the M as higher than the D. Fix: division and multiplication share equal rank, so go left to right.
- Trap: always doing addition before subtraction. Treating the A as higher than the S. Fix: addition and subtraction also share equal rank, so go left to right.
- Trap: ignoring the brackets. Working from the left and skipping the brackets. Fix: brackets are always first, no matter where they sit in the calculation.
- Trap: forgetting that a power applies only to what it sits on. Squaring more than intended. Fix: in 2 × 5², only the 5 is squared, giving 2 × 25, not (2 × 5)².
Frequently asked questions
What does BIDMAS stand for and what order do you use it? BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. You work in that order, but division and multiplication share equal rank (left to right), and so do addition and subtraction.
Do you always do multiplication before division in BIDMAS? No. Multiplication and division are equal in rank, so you work through them from left to right in the order they appear. The same is true for addition and subtraction.
What is the difference between BIDMAS and BODMAS? They are the same rule with different names. The I in BIDMAS stands for Indices, and the O in BODMAS stands for Order, but both mean powers and roots. The order of operations is identical.
Why does the order of operations matter? Without an agreed order, the same calculation could give different answers. BIDMAS sets one fixed order so that everyone reaches the same correct result every time.
How do brackets change a calculation? Anything inside brackets is worked out first, which can completely change the answer. For example, 2 × (3 + 4) = 14, but 2 × 3 + 4 = 10, because the brackets force the addition to happen before the multiplication.
Practise this
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