Order of Operations: Getting BODMAS Right

Do calculations in the wrong order and you get the wrong answer, even with perfect arithmetic. BODMAS is the rule that fixes that.

When a calculation has several operations, the order you do them in changes the answer. To make sure everyone gets the same result, maths follows a fixed order, remembered as BODMAS.

1What BODMAS stands for

The BODMAS ladder. Work down it in order; division/multiplication and addition/subtraction each rank equally.

B — Brackets first
O — Orders (powers and roots)
DM — Division and Multiplication, left to right
AS — Addition and Subtraction, left to right

The key subtlety: division and multiplication rank equally (do them left to right), and so do addition and subtraction. BODMAS is not strictly top-to-bottom for those pairs.

Worked ExampleWorked example: 3 + 4 × 2² − (5 − 1)

1
Brackets: (5 − 1) = 4, giving 3 + 4 × 2² − 4.
Always clear brackets first.
2
Orders: 2² = 4, giving 3 + 4 × 4 − 4.
Powers come before ×, ÷, + and −.
3
Multiply: 4 × 4 = 16, giving 3 + 16 − 4.
× before + and −.
4
Add and subtract left to right: 3 + 16 = 19, then 19 − 4 = 15.
The final answer is 15.

⚠️

The classic error: doing 3 + 4 first in '3 + 4 × 2'. Multiplication comes before addition, so it is 3 + 8 = 11, not 7 × 2 = 14.

💡

When in doubt, add your own brackets to show the order you intend — it keeps long calculations organised and easy to check.

BODMAS underpins every calculation you'll ever do, from Grade 8 arithmetic to Grade 12 calculus. Getting it automatic now prevents a whole category of avoidable mistakes.