Skip to main content
Academy11+

11+ Maths · Topic explained

Order of operations (BODMAS)

What is 2 + 3 × 4? Is it 20 or 14?

The big idea

Brackets, then Orders (powers), then × and ÷, then + and −, so everyone gets the same answer.

Picture it

Like baking a cake: you must bake it before you ice it. Some jobs always come first.

Key words

BODMAS
Brackets, Orders, Division and Multiplication, Addition and Subtraction.
brackets
( ) around a part that must be worked out first.
orders
Powers, like squared and cubed.
left to right
× and ÷ are equal partners, and so are + and −: work them from left to right.

Worked examples

  1. 1Warm-up

    Work out 2 + 3 × 4

    • × comes before +: 3 × 4 = 12
    • 2 + 12 = 14
  2. 211+ standard

    Work out (8 − 3) × 2 + 6

    • Brackets first: 8 − 3 = 5
    • Then ×: 5 × 2 = 10
    • Then +: 10 + 6 = 16
  3. 311+ standard

    Work out 20 − 8 ÷ 2 + 3²

    • Orders: 3² = 9
    • Divide: 8 ÷ 2 = 4
    • Left to right: 20 − 4 + 9 = 25
  4. 411+ standard

    Put in brackets to make it true: 4 + 6 × 3 − 1 = 29

    • Without brackets: 4 + 18 − 1 = 21
    • Try (4 + 6) × 3 − 1 = 30 − 1 = 29 ✓
    • (4 + 6) × 3 − 1 = 29

The common mistake

The mistake

12 − 4 + 2 = 6, because A comes before S in BODMAS.

Instead

Add and subtract go left to right: 12 − 4 = 8, then 8 + 2 = 10.

Why: Addition and subtraction are equal partners (so are × and ÷); BODMAS doesn't put one first.

Where it comes up in the 11+

Calculations with several operations, and 'put in brackets to make this true' puzzles.

The video

Video coming soon

We're making a short video that explains order of operations (bodmas) step by step. Until then, everything it covers is on this page.

Free printable

Order of operations (BODMAS) worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

Free account needed: it takes a minute.

Quick quiz

Have a go first, then tap to see the answer.

  1. 1. Work out 5 + 4 × 2.

    • 18
    • 13
    • 11
    • 22
    Show the answer

    13

    4 × 2 = 8 first, then 5 + 8 = 13.

  2. 2. Work out (6 + 4) ÷ 2 − 1.

    • 4
    • 7
    • 9
    • 5
    Show the answer

    4

    Brackets: 10. Then 10 ÷ 2 = 5. Then 5 − 1 = 4.

  3. 3. Work out 18 ÷ 3 × 2.

    • 3
    • 12
    • 6
    • 36
    Show the answer

    12

    Left to right: 18 ÷ 3 = 6, then 6 × 2 = 12.