Beside

BODMAS: The Order of Operations Made Simple

In one line: BODMAS is a rule that tells you which part of a calculation to do first: Brackets, then Orders (powers and roots), then Division and Multiplication from left to right, then Addition and Subtraction from left to right.

Why it works

A calculation like 5 + 3 × 2 could give 16 or 11 depending on what you do first, and maths only works if everyone gets the same answer. BODMAS is the agreed order that makes every calculation have one correct answer. Calculators, spreadsheets and computer programs all follow this same order, so learning it now helps with algebra, science formulas and coding later.

Think of it like: Think of getting dressed in the morning. You put on socks before shoes, and underwear before trousers, because the order matters. If you put your shoes on first, you end up with a very different (and wrong) result. BODMAS is the getting-dressed order for maths: brackets go on first, then orders, and so on. (Where this breaks: Getting dressed has one strict step after another, but BODMAS has two pairs of equal partners. Division and multiplication are equal, so you do whichever comes first reading left to right. Addition and subtraction work the same way. The letters' order in the word does not mean D always beats M, or A always beats S.)

Worked example

Work out 8 + (6 − 2)² ÷ 2 × 3

  1. Brackets first: 6 − 2 = 4, so the calculation becomes 8 + 4² ÷ 2 × 3.
  2. Orders next (an order is a power, like 'squared'): 4² = 4 × 4 = 16, so it becomes 8 + 16 ÷ 2 × 3.
  3. Division and multiplication, working left to right: 16 ÷ 2 = 8, then 8 × 3 = 24, so it becomes 8 + 24.
  4. Addition and subtraction, working left to right: 8 + 24 = 32.

Answer: 32

Common mistakes

  • Doing the whole calculation strictly from left to right, so 5 + 3 × 2 becomes 16 — fix it by finding and doing the multiplication or division before any adding or subtracting.
  • Always doing division before multiplication because D comes before M in the word — fix it by treating them as equal partners and working left to right, so 24 ÷ 4 × 2 is 6 × 2 = 12.
  • Always doing addition before subtraction, so 20 − 18 + 2 becomes 0 — fix it by working left to right, giving 2 + 2 = 4.
  • Reading a power such as 3² as 3 × 2 = 6 — fix it by remembering that 3² means 3 × 3 = 9.

Try it · 1 of 3

Free · no sign-up
What is 5 + 3 × 2?

Questions parents ask

What year do kids learn BODMAS?

In Australia and the UK, children usually meet the order of operations in Year 6 and build on it through Years 7 and 8, adding powers and more complex brackets. In the US, students start with parentheses in Grade 5 and add exponents in Grade 6.

What is the difference between BODMAS, BIDMAS and PEMDAS?

They are the same rule with different names. BODMAS uses 'Orders' and BIDMAS uses 'Indices' (both mean powers like squared), while PEMDAS, used in the US, says Parentheses and Exponents instead of Brackets and Orders.

Why does my child get different answers on different calculators?

Most scientific calculators follow BODMAS, but some basic calculators work strictly left to right as you press each key. Encourage your child to use brackets on the calculator, or to check with a scientific calculator, so the order is clear.

How can I help my child with BODMAS at home?

Ask them to talk through each step aloud and underline the part they will do next before calculating. Short daily puzzles, such as making the number 10 from four given numbers using brackets, build confidence and make the rule feel like a game.