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Pre-Algebra · Quick Reference
Order of Operations Cheat Sheet
In one line: order of operations is the agreed-upon set of rules for which calculation to do first in an expression with multiple operations — without it, the same expression could give different answers to different people.
Key Ideas
1PEMDAS. Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right) — the standard order for evaluating expressions.
2Parentheses First. Always simplify everything inside parentheses (or other grouping symbols) before anything else.
3Exponents Next. After parentheses, evaluate any exponents (powers) in the expression.
4Multiplication and Division Together. These are done left to right, in the order they appear — multiplication is not automatically done before division.
5Addition and Subtraction Together. Like multiplication/division, these are also done left to right, in the order they appear.
Worked Examples
Evaluate 3 + 4 x 2.
11
Evaluate (3 + 4) x 2.
14
Evaluate 2 + 3^2 x 2.
20
Formulas
PEMDAS: Parentheses, Exponents, Multiply/Divide (left to right), Add/Subtract (left to right)
Practice Yourself
Evaluate 5 + 2 x 3.
11
Evaluate (5 + 2) x 3.
21
Evaluate 10 - 4 / 2.
8