Order of Operations Cheat Sheet

Parentheses/Brackets

Perform operations inside parentheses or brackets first. Work from the innermost set outwards.

Example: (2 + 3) * 4 = 5 * 4 = 20

Exponents/Orders

Evaluate exponents (powers and roots).

Example: 3^2 = 3 * 3 = 9

Multiplication and Division

Perform multiplication and division from left to right.

Example: 12 / 3 * 2 = 4 * 2 = 8

Addition and Subtraction

Perform addition and subtraction from left to right.

Example: 5 + 3 - 2 = 8 - 2 = 6

Parentheses

Parentheses ( ) are used to group parts of an expression.

Example: 2 * (3 + 4)

Brackets

Brackets [ ] are used to group parts of an expression, often nested inside parentheses.

Example: [2 * (3 + 4)] + 1

Braces

Braces { } are used to group parts of an expression, often nested inside brackets.

Example: {[2 * (3 + 4)] + 1} / 3

Fraction Bars

Fraction bars act as grouping symbols, the numerator and denominator are evaluated separately.

Example: (2 + 4) / (5 - 2) = 6 / 3 = 2

Left to Right

When you have multiple operations of the same precedence (e.g., multiplication and division), work from left to right.

Example: 10 / 2 * 5 = 5 * 5 = 25

Implied Multiplication

Multiplication can be implied by placing a number next to a parenthesis. Perform this multiplication after evaluating the parenthesis.

Example: 2(3 + 4) = 2 * 7 = 14

Careful with Negatives

Pay close attention to negative signs. A negative sign directly in front of a parenthesis applies to the entire expression inside.

Example: -(2 + 3) = -5