What you'll learn
This topic covers the order of operations — the rules that tell you which calculation to do first, summarised as BIDMAS (or BODMAS). In this guide you will learn what each letter means, how to handle brackets, indices, division and multiplication, addition and subtraction, and how to apply the order to longer calculations. Getting the order right is essential for every numerical answer.
Key terms and definitions
BIDMAS/BODMAS — Brackets, Indices/Orders, Division/Multiplication, Addition/Subtraction.
Brackets — grouping symbols showing what to calculate first.
Indices (orders) — powers and roots.
Operation — an arithmetic action (+, −, ×, ÷).
Term — a part of an expression separated by + or − signs.
Core concepts
What BIDMAS means
BIDMAS gives the order: Brackets first, then Indices (powers and roots), then Division and Multiplication, then Addition and Subtraction. BODMAS is the same with "Orders" for indices. Following this order guarantees one correct answer.
Brackets first
Always work out anything inside brackets first. If brackets are nested, work from the innermost outwards. For example, in 2 × (3 + 4), do 3 + 4 = 7 first, then 2 × 7 = 14.
Indices next
After brackets, deal with indices — powers and roots. In 5 + 2³, the power comes first: 2³ = 8, then 5 + 8 = 13.
Division and multiplication
Division and multiplication have equal priority and are done left to right as they appear. In 12 ÷ 2 × 3, work left to right: 6 × 3 = 18 (not 12 ÷ 6).
Addition and subtraction
Finally, addition and subtraction, also of equal priority, are done left to right. In 10 − 4 + 2, work left to right: 6 + 2 = 8 (not 10 − 6).
Worked examples
Example 1: Brackets and multiplication
Work out 3 + 2 × (5 − 1).
Brackets: 5 − 1 = 4. Multiply: 2 × 4 = 8. Add: 3 + 8 = 11.
Example 2: Indices
Work out 4 + 3².
Index first: 3² = 9. Add: 4 + 9 = 13.
Example 3: Left to right
Work out 20 ÷ 4 × 2.
Left to right: 20 ÷ 4 = 5, then 5 × 2 = 10.
Common mistakes and how to avoid them
Adding before multiplying. Multiplication comes before addition.
Doing × before ÷ always. They are equal — work left to right.
Ignoring indices. Powers come before multiplication and addition.
Skipping brackets. Always do inside brackets first.
Working right to left. For equal-priority operations, go left to right.
Exam technique for Order of Operations
Write out BIDMAS to remind yourself of the order.
Do brackets first, innermost outwards.
Evaluate indices before multiplying or adding.
Treat × and ÷ as equal, left to right; likewise + and −.
Show each step to avoid slips.
Quick revision summary
The order of operations is given by BIDMAS/BODMAS: Brackets, Indices (orders), Division and Multiplication, then Addition and Subtraction. Always work out brackets first (innermost outwards), then indices (powers and roots). Crucially, division and multiplication have equal priority and are done left to right as they appear — so 12 ÷ 2 × 3 = 18, not 2 — and likewise addition and subtraction are equal and done left to right. Following this order guarantees a single correct answer. The common errors are adding before multiplying, always doing × before ÷ (rather than left to right), ignoring indices, skipping brackets, and working right to left for equal operations. Write out BIDMAS, do brackets then indices, treat × and ÷ (and + and −) as equal left to right, and show each step.