Find: \(3 + 4 × 2\).
Multiplication before addition.
4 × 2 = 8 → 3 + 8 = 11.
Order of Operations (BIDMAS)
When a calculation involves multiple operations, there is a specific order that must be followed. Applying BIDMAS correctly ensures answers are accurate and avoids common exam mistakes.
Overview
BIDMAS gives the correct order to follow when a calculation involves more than one operation.
\( 3 + 4 \times 2 = 11 \quad \text{not} \quad 14 \)
If calculations are done in the wrong order, the answer will be incorrect, so BIDMAS ensures a consistent method.
What you should understand after this topic
- Understand what BIDMAS stands for
- Identify which parts of a calculation to do first
- Understand that multiplication and division are done in order from left to right
- Understand that addition and subtraction are done in order from left to right
- Solve multi-step expressions accurately
Key Definitions
BIDMAS
Brackets, Indices, Division, Multiplication, Addition, Subtraction.
Bracket
A part of the calculation grouped together, such as \( (6 - 2) \).
Index
A power, such as \( 3^2 \) or \( 5^3 \).
Expression
A mathematical calculation written using numbers and operations.
Operation
An action such as addition, subtraction, multiplication or division.
Evaluate
Work out the value of an expression.
Key Rules
Brackets first
\( 7 \times (5 - 2) = 21 \)
Indices next
\( 2 + 3^2 = 11 \)
Multiply and divide left to right
\( 20 \div 5 \times 2 = 8 \)
Add and subtract left to right
\( 10 - 4 + 1 = 7 \)
Important Reminders
D and M are the same level
Do whichever comes first from left to right.
A and S are the same level
Do whichever comes first from left to right.
Do not just read left to right
Always check whether brackets or powers appear first.
Show steps clearly
One line at a time helps prevent mistakes.
How to Solve
Step 1: Understand BIDMAS
BIDMAS tells you the correct order to carry out calculations.
B = Brackets
I = Indices
D/M = Division and Multiplication
A/S = Addition and Subtraction
Key idea: Work from highest priority to lowest.
Exam tip: Division and multiplication are equal priority.
Step 2: Work inside brackets
\( 4 + 3 \times (10 - 6) \)
First calculate inside brackets.
\(10 - 6 = 4\), so expression becomes \(4 + 3 \times 4\).
Step 3: Calculate indices
\( 2 + 5^2 \)
\(5^2 = 25\).
Then continue with the rest of the calculation.
Step 4: Multiply and divide (left to right)
\( 24 \div 6 \times 3 \)
Important: Do not always multiply first.
Division and multiplication have equal priority.
- Work from left to right.
- \(24 \div 6 = 4\).
- \(4 \times 3 = 12\).
Step 5: Add and subtract (left to right)
\( 15 - 4 + 2 \)
Important: Addition does not always come before subtraction.
- Work from left to right.
- \(15 - 4 = 11\).
- \(11 + 2 = 13\).
Step 6: Common mistakes
Wrong order
Adding before multiplying.
Ignoring brackets
Forgetting to simplify brackets first.
Not using left-to-right
Mixing up division and multiplication order.
Forgetting indices
Not calculating powers before other steps.
Step 7: Exam method summary
See directed numbers for sign rules.
- Work inside brackets.
- Calculate indices.
- Multiply and divide left to right.
- Add and subtract left to right.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics.
Edexcel
Work out \( 6 + 4 \times 3 \).
Edexcel
Work out \( (6 + 4) \times 3 \).
Edexcel
Work out \( 18 \div 3 + 5 \times 2 \).
Edexcel
Work out \( 20 - 4^2 \).
Edexcel
Work out \( 12 + 3(8 - 5)^2 \).
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on reasoning and correct application of BIDMAS.
AQA
A student evaluates 8 + 12 ÷ 3 as 20 ÷ 3. Explain the mistake and give the correct answer.
AQA
Work out \( 15 - 2 \times (3 + 4) \).
AQA
Work out \( 24 \div (6 - 2)^2 \).
AQA
Insert brackets to make the statement correct: \( 18 - 6 \div 3 \times 2 = 8 \).
AQA
Explain why \( 5 + 2^3 \times 4 \) is not equal to \( (5 + 2)^3 \times 4 \).
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising accuracy, algebraic substitution, and multi-step reasoning.
OCR
Work out \( 7 + 3^2 \times 2 \).
OCR
Work out \( (9 - 5)^3 + 6 \div 3 \).
OCR
When \( x = 4 \), work out the value of \( 3x^2 - 2x + 5 \).
OCR
Simplify \( 5 + 3 \times a^2 \) when \( a = 2 \).
OCR
Create an expression that equals 19 using the numbers 5, 3, and 2 with any operations and brackets.
Exam Checklist
Step 1
Look carefully for brackets.
Step 2
Check for powers or squares.
Step 3
Do division and multiplication from left to right.
Step 4
Do addition and subtraction from left to right.
Most common exam mistakes
Wrong priority
Adding or subtracting before multiplying or dividing.
Ignoring brackets
Not simplifying the bracket first.
Power mistake
Forgetting that indices come before multiplication.
Left-to-right mistake
Not working correctly when division and multiplication are mixed.
Common Mistakes
These are common mistakes students make when using the order of operations (BIDMAS) in GCSE Maths.
Adding before multiplying
Incorrect
A student adds numbers before completing multiplication.
Correct
Multiplication and division must be done before addition and subtraction. Follow BIDMAS carefully.
Ignoring brackets
Incorrect
A student works through the calculation without dealing with brackets first.
Correct
Brackets must always be evaluated first, as they override the normal order of operations.
Forgetting powers (indices)
Incorrect
A student multiplies before working out powers.
Correct
Indices (powers) come before multiplication and division. Always evaluate them early in the process.
Forcing multiplication before division
Incorrect
A student always multiplies first, even if division appears earlier.
Correct
Multiplication and division are done left to right, not in a fixed order. Follow the sequence as it appears.
Trying to do everything in one step
Incorrect
A student attempts the entire calculation mentally without showing steps.
Correct
Work step by step to avoid mistakes. Writing each stage clearly helps maintain the correct order.
Try It Yourself
Practise applying BIDMAS to evaluate numerical expressions.
Foundation
Foundation Practice
Apply BIDMAS step by step to simple expressions.
Find: \(5 + 6 × 3\).
Multiply first.
6 × 3 = 18 → 5 + 18 = 23.
Find: \((3 + 4) × 2\).
Brackets first.
3 + 4 = 7 → 7 × 2 = 14.
Find: \((5 + 2) × 3\).
Do inside brackets first.
7 × 3 = 21.
Find: \(10 - 6 ÷ 2\).
Division before subtraction.
6 ÷ 2 = 3 → 10 - 3 = 7.
Find: \(8 + 12 ÷ 4\).
Divide first.
12 ÷ 4 = 3 → 8 + 3 = 11.
Find: \(2 × 3 + 4\).
Multiply first.
2 × 3 = 6 → 6 + 4 = 10.
Find: \(9 - 3 × 2\).
Multiply first.
3 × 2 = 6 → 9 - 6 = 3.
A student says \(3 + 4 × 2 = 14\). What is wrong?
Follow BIDMAS.
Multiplication must be done first.
Find: \((6 + 2) × 5\).
Brackets first.
8 × 5 = 40.
Higher
Higher Practice
Apply BIDMAS with powers and negative numbers.
Find: \(2^3 + 4 × 2\).
Powers first.
2³ = 8, 4 × 2 = 8 → 8 + 8 = 16.
Find: \(3^2 + 5 × 2\).
Power first.
9 + 10 = 19.
Find: \(10 - 2^2 × 3\).
Power, then multiply.
2² = 4 → 4 × 3 = 12 → 10 - 12 = -2.
Find: \(12 ÷ 3 + 2^3\).
Division and power first.
12 ÷ 3 = 4, 2³ = 8 → total = 12.
Find: \(-3 + 4 × (-2)\).
Multiply first.
4 × -2 = -8 → -3 - 8 = -11.
Find: \(-6 + 2 × (-4)\).
Multiply first.
2 × -4 = -8 → -6 - 8 = -14.
Find: \((2 + 3)^2\).
Brackets then power.
5² = 25.
Find: \((4 + 1)^3\).
Add then cube.
5³ = 125.
A student says \(-3^2 = 9\). What is wrong?
Check order of operations.
-3² = -(3²) = -9.
Find: \(-2^3 + 6\).
Power first.
-8 + 6 = -2.
Games
Practise this topic with interactive games.
Games coming soon.
BIDMAS (Order of Operations) Video Tutorial
Frequently Asked Questions
What does BIDMAS stand for?
Brackets, Indices, Division, Multiplication, Addition and Subtraction.
Do I do multiplication before division?
No, you work from left to right for multiplication and division.
Why is BIDMAS important?
It ensures calculations are done in the correct order and avoids incorrect answers.