Order of Operations (BODMAS)

In short: The order of operations tells you which part of a calculation to do first: Brackets, Orders (powers and roots), Division and Multiplication, then Addition and Subtraction (BODMAS). Multiplying and dividing go left to right, and so do adding and subtracting.

Before you start

• Your times tables up to $12\times 12$, and division facts.
• A square is a number times itself: $3^2=9$. A square root goes backwards: $\sqrt{64}=8$ because $8\times 8=64$.

BODMAS

Brackets inside brackets

Square brackets $[]$ work just like round ones. When brackets are inside other brackets, start with the innermost pair.

Turning words into a calculation

Selective test questions often hide the operations in words.

• "the sum of" means add
• "the difference between" means subtract (bigger minus smaller)
• "the product of" means multiply
• "the quotient of" means divide
• "increase by" means add, "decrease by" means subtract
• "a dozen" is 12

Quick summary

• BODMAS: Brackets, Orders (powers and roots), Division and Multiplication, Addition and Subtraction.
• $\times$ and $÷$ are equal partners: go left to right. So are $+$ and $-$.
• Work from the innermost brackets outwards.
• Learn the words: sum, difference, product, quotient, increase, decrease.
• Look for friendly pairs like $8\times 125=1000$ to make sums easier.

Quiz