Lesson 2: Order of Operations

Property

When simplifying mathematical expressions perform the operations in the following order:

1. Parentheses and other Grouping Symbols: Simplify all expressions inside parentheses or other grouping symbols, working on the innermost parentheses first.
2. Exponents: Simplify all expressions with exponents.
3. Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
4. Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.

A common way to remember this is the phrase 'Please Excuse My Dear Aunt Sally'.

Examples

• To simplify $10 - 2 \cdot 3$, you perform multiplication before subtraction: $10 - 6 = 4$.
• To simplify $(10 - 2) \cdot 3$, you perform the operation in parentheses first: $8 \cdot 3 = 24$.
• To simplify $5 + (4-1)^2 \div 3$, you start with parentheses ($5+3^2 \div 3$), then exponents ($5+9 \div 3$), then division ($5+3$), and finally addition, which gives $8$.

Explanation

This is the official rulebook for solving math problems. Following this order (PEMDAS) ensures everyone gets the same correct answer. Always handle groups first, then powers, then multiplication/division, and finally addition/subtraction from left to right.

Property

Common misconceptions include: working strictly left to right without considering operation hierarchy, treating multiplication and division as having different precedence levels, and incorrectly handling negative signs and parentheses.

Examples