Definition
Order of operations
The order of operations is the agreed sequence for evaluating an expression so everyone gets the same value.
What it means
An expression can contain several operations. Follow the shared order instead of simply reading every symbol from left to right. Multiplication and division share one level, so do whichever comes first. Addition and subtraction also share one level.
Remember it
Group, powers, multiply-or-divide left to right, add-or-subtract left to right.
Example
Evaluate 18 − 6 ÷ 3 + 2 × 4. Division and multiplication first: 18 − 2 + 8. Then left to right: 16 + 8 = 24.
Watch for
PEMDAS, BODMAS, and BIDMAS are reminders, not separate rules; they must not make multiplication always beat division or addition always beat subtraction.
Common mix-up
Do not calculate 18 − 6 first just because it appears first; division has higher precedence.
Exact meaning
Evaluate grouping symbols first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. Grouping symbols can change that order.