1.3

Operations and order of operations

Cambridge IGCSE Mathematics (0580)  · Unit 1: Number  · 9 flashcards

Operations and order of operations is topic 1.3 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Types of number, Fractions, decimals and percentages and Powers and roots.  In one line: BIDMAS/BODMAS stands for Brackets, Indices (or Orders), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This is the order in which mathematical operations should be performed.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 1 definition, 2 key concepts and 1 application card — covering the precise wording mark schemes reward.  Use the definition card to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

The correct order of operations according to BIDMAS/BODMAS

BIDMAS/BODMAS stands for Brackets, Indices (or Orders), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This is the order in which mathematical operations should be performed.

Questions this Operations and order of operations deck will help you answer

Key Concept Flip

Evaluate: 12 + 6 ÷ 3 - 2 × 4

Answer Flip

Following the order of operations (BIDMAS/BODMAS), divide first: 6 ÷ 3 = 2. Then multiply: 2 × 4 = 8. Finally, add and subtract from left to right: 12 + 2 - 8 = 6.

Definition Flip

What is the correct order of operations according to BIDMAS/BODMAS?

Answer Flip

BIDMAS/BODMAS stands for Brackets, Indices (or Orders), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This is the order in which mathematical operations should be performed.

Key Concept Flip

Simplify: (5 + 3) × 2 - 4²

Answer Flip

First, solve the bracket: (5 + 3) = 8. Then, calculate the index: 4² = 16. Next, multiply: 8 × 2 = 16. Finally, subtract: 16 - 16 = 0.

Key Concept Flip

Explain the importance of following the order of operations.

Answer Flip

Following the order of operations ensures that mathematical expressions are evaluated consistently and correctly. Without a standard order, different people could arrive at different answers for the same problem.

Key Concept Flip

Calculate: (1/2 + 1/4) ÷ 3/4

Answer Flip

First add the fractions inside the bracket: 1/2 + 1/4 = 3/4. Then, divide by 3/4 which is the same as multiplying by 4/3: (3/4) × (4/3) = 1.

Key Concept Flip

Evaluate: 2.5 × 4 + 6.3 ÷ 3

Answer Flip

First, multiply: 2.5 × 4 = 10. Then, divide: 6.3 ÷ 3 = 2.1. Finally, add: 10 + 2.1 = 12.1

Key Concept Flip

What happens if you ignore the order of operations?

Answer Flip

Ignoring the order of operations leads to incorrect results.

Example: If you calculate 2 + 3 × 4 as (2 + 3) × 4 = 20 instead of 2 + (3 × 4) = 14, you get a wrong answer.
Key Concept Flip

Sarah buys 3 apples at $0.75 each and 2 oranges at $0.60 each. She pays with a $5 bill. How much change does she receive? Write the equation.

Answer Flip

The total cost is (3 × 0.75) + (2 × 0.60) = 2.25 + 1.20 = $3.45. Her change is 5 - 3.45 = $1.55. The equation reflects order of operations.

Key Concept Flip

Simplify: 5 + (2³ - 4) ÷ 2

Answer Flip

First, solve the index within the brackets: 2³ = 8. Then, continue the brackets 8-4 = 4. Divide: 4 ÷ 2 = 2. Finally, add: 5 + 2 = 7.

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1.2 Fractions, decimals and percentages 1.4 Powers and roots

Key Questions: Operations and order of operations

What is the correct order of operations according to BIDMAS/BODMAS?

BIDMAS/BODMAS stands for Brackets, Indices (or Orders), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This is the order in which mathematical operations should be performed.

More topics in Unit 1 — Number

Operations and order of operations sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

1.1 Types of number

10 flashcards
1.2 Fractions, decimals and percentages

10 flashcards
1.4 Powers and roots

9 flashcards
1.5 Ratio, proportion and rate

18 flashcards
1.6 Approximation and estimation

10 flashcards
1.7 Limits of accuracy

9 flashcards
1.8 Surds

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

add subtract multiply divide BIDMAS BODMAS order of operations brackets indices operations with fractions operations with decimals

Key terms covered in this Operations and order of operations deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

The correct order of operations according to BIDMAS/BODMAS

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How to study this Operations and order of operations deck

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