Order of Operations (BIDMAS): GCSE & IGCSE Maths Explained
The BIDMAS order of operations gives a consistent method for evaluating expressions in GCSE and IGCSE Maths: Brackets first, then Indices, then Division and Multiplication (equal priority, worked left to right), and finally Addition and Subtraction. This page explains each stage with step-by-step worked examples, highlights the common errors that cost marks, and shows how to apply BIDMAS correctly in exam-style questions.
Are there any brackets?
Simplify everything inside them first. Work outwards from the innermost bracket.
Any indices (powers or roots)?
Evaluate them next. For example 2 cubed is 8, or the square root of 25 is 5.
Any division or multiplication?
Equal priority. Work left to right when both appear. Do not always multiply first.
Any addition or subtraction?
Equal priority. Work left to right. The minus sign belongs to the number after it.
Why Do We Need BIDMAS?
Why can't we all just solve a sum however we want? Click the operations below in any order you like. The correct BIDMAS answer is 4. See what happens if you do them in a different order.
How to Solve a Calculation Using BIDMAS: Step by Step
When a calculation mixes several operations, the order you carry them out changes the answer. BIDMAS tells you what to do first:
- Brackets: simplify anything grouped in brackets first.
- Indices: evaluate powers and roots next.
- Division and Multiplication: equal priority. When both appear, work from left to right.
- Addition and Subtraction: equal priority. When both appear, work from left to right.
Work through one operation at a time, rewriting the whole expression on each new line. This keeps your working clear and makes mistakes easy to spot.
Quick example calculation using BIDMAS: to evaluate \( 3 + 4 \times 2^2 \), apply indices first to get \( 3 + 4 \times 4 \), then multiply to get \( 3 + 16 \), then add to get \( 19 \).
Worked Examples
💡 Example 1
Evaluate \( 12 - 9 \div (8 - 5) \times 2^3 + 7 \)
\( 12 - 9 \div \textcolor{#b91c1c}{(8-5)} \times 2^3 + 7 \)
\( = 12 - 9 \div \textcolor{#b91c1c}{3} \times 2^3 + 7 \)
What's happening?
Brackets first. \( 8 - 5 = 3 \).
\( 12 - 9 \div 3 \times \textcolor{#b91c1c}{2^3} + 7 \)
\( = 12 - 9 \div 3 \times \textcolor{#b91c1c}{8} + 7 \)
What's happening?
Indices next. \( 2^3 = 8 \).
\( 12 - \textcolor{#b91c1c}{9 \div 3} \times 8 + 7 \)
\( = 12 - \textcolor{#b91c1c}{3} \times 8 + 7 \)
\( = 12 - \textcolor{#b91c1c}{3 \times 8} + 7 \)
\( = 12 - \textcolor{#b91c1c}{24} + 7 \)
What's happening?
Division and multiplication share priority, so go left to right: divide first, then multiply.
\( \textcolor{#b91c1c}{12 - 24} + 7 \)
\( = \textcolor{#b91c1c}{-12} + 7 \)
\( = \textcolor{#b91c1c}{-5} \)
What's happening?
Addition and subtraction share priority, so go left to right. \( 12 - 24 = -12 \), then add 7.
💡 Example 2
Evaluate \( 30 \div 5 + (3 + 2)^2 - 9 \)
\( 30 \div 5 + \textcolor{#b91c1c}{(3+2)}^2 - 9 \)
\( = 30 \div 5 + \textcolor{#b91c1c}{5}^2 - 9 \)
What's happening?
Brackets first. \( 3 + 2 = 5 \). The square still applies to the result.
\( 30 \div 5 + \textcolor{#b91c1c}{5^2} - 9 \)
\( = 30 \div 5 + \textcolor{#b91c1c}{25} - 9 \)
What's happening?
Indices next. \( 5^2 = 25 \).
\( \textcolor{#b91c1c}{30 \div 5} + 25 - 9 \)
\( = \textcolor{#b91c1c}{6} + 25 - 9 \)
What's happening?
Division before any addition or subtraction. \( 30 \div 5 = 6 \).
\( \textcolor{#b91c1c}{6 + 25} - 9 \)
\( = \textcolor{#b91c1c}{31} - 9 \)
\( = \textcolor{#b91c1c}{22} \)
What's happening?
Left to right through addition and subtraction.
💡 Example 3
Evaluate \( 4 + 3 \times (10 - 2 \times 3) \)
\( 4 + 3 \times \textcolor{#b91c1c}{(10 - 2 \times 3)} \)
\( = 4 + 3 \times (10 - \textcolor{#b91c1c}{6}) \)
\( = 4 + 3 \times \textcolor{#b91c1c}{4} \)
What's happening?
Brackets first, but BIDMAS applies inside the bracket too. Multiply before subtracting: \( 2 \times 3 = 6 \), then \( 10 - 6 = 4 \).
\( 4 + \textcolor{#b91c1c}{3 \times 4} \)
\( = 4 + \textcolor{#b91c1c}{12} \)
\( = \textcolor{#b91c1c}{16} \)
What's happening?
Bracket is gone, so multiply before adding. \( 3 \times 4 = 12 \), then add 4.
💡 Example 4
Evaluate \( \dfrac{20 - 4^2}{2} + \sqrt{9} \)
\( \dfrac{20 - \textcolor{#b91c1c}{4^2}}{2} + \sqrt{9} \)
\( = \dfrac{20 - \textcolor{#b91c1c}{16}}{2} + \sqrt{9} \)
\( = \dfrac{20 - 16}{2} + \textcolor{#b91c1c}{\sqrt{9}} \)
\( = \dfrac{20 - 16}{2} + \textcolor{#b91c1c}{3} \)
What's happening?
A fraction bar acts like a bracket. Indices include roots, so \( 4^2 = 16 \) and \( \sqrt{9} = 3 \).
\( \dfrac{\textcolor{#b91c1c}{20 - 16}}{2} + 3 \)
\( = \dfrac{\textcolor{#b91c1c}{4}}{2} + 3 \)
What's happening?
Simplify the top of the fraction first. \( 20 - 16 = 4 \).
\( \textcolor{#b91c1c}{\dfrac{4}{2}} + 3 \)
\( = \textcolor{#b91c1c}{2} + 3 \)
\( = \textcolor{#b91c1c}{5} \)
What's happening?
Divide before adding. \( 4 \div 2 = 2 \), then add 3.
🔑 Key Points
- BIDMAS order: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
- Division and multiplication have the same priority. So do addition and subtraction. When operations share priority, work left to right.
- Rewrite the full expression on each new line. One operation per step.
- A bracket only affects what sits inside it. A power outside a bracket, like \( (3+2)^2 \), applies once the bracket is simplified.
- A fraction bar acts like a bracket. Simplify the top and bottom separately before dividing.
- Estimate your answer first. If the working gives something very different, check your order.
⚠️ Common Pitfalls
- Doing multiplication before division, or addition before subtraction. They are equal priority, so go left to right.
- Squaring before simplifying the bracket, for example writing \( (3+2)^2 \) as \( 3 + 4 \). Simplify the bracket first, then square.
- Treating a minus sign like a separator. In \( 12 - 24 + 7 \), the minus belongs to the 24: subtract first, then add.
- Skipping lines. Doing two operations at once is where errors creep in.
- Missing an invisible multiplication. \( 3(4+1) \) means \( 3 \times (4+1) \).