Learn BODMAS — step by step

Understanding BODMAS: Why order matters

BODMAS (or BIDMAS/PEMDAS) is a compact memory aid to decide which parts of an expression you solve first. Below we break it down with step-by-step worked problems, pitfalls and practice.

What BODMAS means

• Brackets — parentheses & grouping
• Orders — exponents, squares, roots
• Division and Multiplication — same level, left to right
• Addition and Subtraction — same level, left to right

Worked examples

Example: Evaluate 4 + 3 × (2 + 6) ÷ 4

1. Brackets → (2 + 6) = 8
2. Multiplication/Division left-to-right → 3 × 8 ÷ 4 = 24 ÷ 4 = 6
3. Addition → 4 + 6 = 10

Practice

1. 7 + (3 × 2)²
2. 18 ÷ 3 × 2 + 5
3. 5 + 12 ÷ (2 × 3)
4. (8 - 3) × 4 + 6 ÷ 3

Answers

1. 43
2. 17
3. 7
4. 22

When you feel confident, try these problems on the interactive puzzles at Mathsteaser.com.

5 Quick Tips to Avoid BODMAS Mistakes

Scan for brackets, rewrite powers early, underline left-to-right sequences, check units, and always re-evaluate ambiguous expressions step by step.

Practice Set — Mixed Operations (Beginner)

1. 9 - 3 × 2 + 8
2. (5 + 5) ÷ 2 + 7
3. 2³ + 4 × (6 - 2)
4. 36 ÷ (3 × 2) + 1
5. 7 + 4 × 3 - 6 ÷ 2

Teacher Resource: 10 Minute BODMAS Warm-up

A quick set of rapid-fire problems you can use at the start of class to warm students up for mental math.