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Order of Operations

BODMAS tells you which part of a calculation to do first, so everyone gets the same answer.

Why the Order Matters

Work out 2 + 3 \times 4 . If you go left to right you get 5 \times 4 = 20 . If you do the multiplication first you get 2 + 12 = 14 . Only one of these can be the agreed answer. Mathematics fixes this with one rule everyone follows: BODMAS .

Division and multiplication are equal priority — do whichever comes first, reading left to right. The same is true for addition and subtraction.

Example 1 — easy numbers

Work out 2 + 3 \times 4 . 1 Multiplication before addition: 3 \times 4 = 12 2 2 + 12 = 14 Answer: 14

Example 2 — with brackets

Work out (2 + 3) \times 4 . 1 Brackets first: 2 + 3 = 5 2 5 \times 4 = 20 Answer: 20

Example 3 — with a power

Work out 5 + 2^{2} . 1 Powers before addition: 2^{2} = 4 2 5 + 4 = 9 Answer: 9

Example 4 — mixing everything

Work out 3 \times (4 + 1)² - 10 \div 2 . 1 Brackets first: 4 + 1 = 5 2 Powers next: 5^{2} = 25 3 Multiplication and division, left to right: 3 \times 25 = 75, and 10 \div 2 = 5 4 Addition and subtraction last: 75 - 5 = 70 Answer: 70

Practice

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What is 10 - 2 \times 3 ?

Work out (6 + 2) \times 3 - 4 .

Your answer