Order of Operations

The rules that tell you which part of an expression to evaluate first.

Definition

Order of operations is the agreed-upon sequence for evaluating an expression when it contains more than one operation. The acronym BEDMAS (or PEMDAS) summarises the sequence:

Step	BEDMAS	PEMDAS
1	Brackets	Parentheses
2	Exponents	Exponents
3	Division	Multiplication
3	Multiplication	Division
4	Addition	Addition
4	Subtraction	Subtraction

Division and multiplication have equal priority — work left to right. Same for addition and subtraction.

Step-by-step evaluation

Evaluate $3 + 4 \times 2$ .

Multiplication before addition:

3 + 4 \times 2 = 3 + 8 = 11

Not $14$ . If you add first you get the wrong answer.

Brackets change everything

Evaluate $(3 + 4) \times 2$ .

Brackets first:

(3 + 4) \times 2 = 7 \times 2 = 14

Left to right for equal-priority operations

$12 \div 4 \times 3$ — division and multiplication have the same priority, so go left to right:

12 \div 4 \times 3 = 3 \times 3 = 9

Not $12 \div 12 = 1$ .

Try it

Evaluate without a calculator:

2 + 3^2 \times (8 - 5)

Solution

Brackets first: $8 - 5 = 3$

Exponent: $3^2 = 9$

Multiply: $9 \times 3 = 27$

Add: $2 + 27 = \mathbf{29}$

Related concepts

Expressions

Uses this

Combinatorics Number Theory Basics

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