Order of operations (PEMDAS / BODMAS), explained

When an expression has more than one operation, everyone needs to reach the same answer. The order of operations is the shared rule for that. In English it is remembered as PEMDAS; elsewhere as BODMAS. Both describe the same order.

The rule, in order

• Parentheses (brackets) first.
• Exponents (powers and roots) next.
• Multiplication and Division, left to right.
• Addition and Subtraction, left to right.

A first example

Multiplication comes before addition, so it is not simply left to right. Take $3 + 4 \times 2$.

With brackets and powers

Clear the brackets first, then powers, then the rest. Take $(6 + 2) \times 3^2$.

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The mistakes that change the answer

• Multiplication and division share a rank; work left to right. $12 \div 2 \times 3 = 18$, not $2$.
• Addition and subtraction also share a rank; left to right again. $8 - 3 + 2 = 7$, not $3$.
• A minus sign in front of a power applies after the power: $-3^2 = -9$, while $(-3)^2 = 9$.

Work down the list: brackets, powers, then multiply and divide, then add and subtract, always left to right within a rank.