Math · Algebraic Thinking

Order of Operations

Math has grammar rules too! Follow PEMDAS so everyone solves the same problem and lands on the same answer.
🪜The PEMDAS Order
1P Parentheses first — do everything inside grouping symbols ( ).Brackets [ ] and braces { } count too. ( )
2E Exponents next — the small raised power, like 5³.5³ = 5 × 5 × 5 = 125. xⁿ
3MD Multiply & Divide — a tie! Do them left to right.Whichever comes first as you read. × ÷
4AS Add & Subtract — also a tie! Do them left to right.Last of all, reading left to right. + −
🧮Solve It Step by Step
3 + (4 − 1)² × 2
P 3 + (4 − 1) ² × 2 4 − 1 = 3 E 3 + × 2 3² = 3 × 3 = 9 M 3 + 9 × 2 9 × 2 = 18 A 3 + 18 3 + 18 = 21 = 21 🎉
Work top to bottom: P → E → M → A. One operation at a time!
⚖️Ties & a Calculator Check
↔️It's a tie? Go left → right
20 ÷ 4 × 5 20 ÷ 4 = 5 5 × 5 = 25 = 25 ✅
× and ÷ don't fight — do whichever comes first reading left to right.
🧮Why 14, not 20?
2 + 3 × 4 multiply first 3 × 4 = 12 → 2 + 12 = 14 ✅ (not 20)
A good calculator multiplies before it adds — that's the order of operations at work.
🔑Key Terms
🛣️PEMDAS Parentheses, Exponents, Multiply/Divide, Add/Subtract — the order to follow.
🔵Parentheses The symbols ( ) that group parts of a problem so they're done first.
⬆️Exponent A small raised number telling how many times to multiply the base by itself.
🔍Evaluate To find the value of an expression by doing all its operations.
Operation A math action: adding, subtracting, multiplying, or dividing.
📦Grouping Symbol Any ( ), [ ], or { } used to keep math parts together.
Remember: do P → E → MD → AS, and break every tie by reading left to right — then everyone gets the same answer!
✏️ Math Anchor Chart · Order of Operations
From ClickClass — hundreds of free printables at clickclassedu.com/printables