For Parents/Math/What Is the Order of Operations (PEMDAS)?

What Is the Order of Operations (PEMDAS)?

2 min read4th–6th
Algebra

The order of operations is the set of rules that determines which calculations to perform first in a math expression.

Without these rules, 3 + 4 × 2 could be 14 (add first) or 11 (multiply first). The order of operations says: multiply first. The answer is 11.

The rules (PEMDAS)

  1. Parentheses — do what is inside parentheses first
  2. Exponents — calculate powers and roots
  3. Multiplication and Division — left to right (equal priority)
  4. Addition and Subtraction — left to right (equal priority)

Important: Multiplication and division have the same priority — work left to right. Same for addition and subtraction.

Example

Solve: 2 + 3 × (4 + 1)² ÷ 5

  1. Parentheses: (4 + 1) = 5 → 2 + 3 × 5² ÷ 5
  2. Exponents: 5² = 25 → 2 + 3 × 25 ÷ 5
  3. Multiplication/Division (left to right): 3 × 25 = 75, then 75 ÷ 5 = 15 → 2 + 15
  4. Addition: 2 + 15 = 17

Common mistakes

Doing addition before multiplication: 3 + 4 × 2 = 14 is wrong. Multiply first: 3 + 8 = 11.

Always doing multiplication before division: They are equal priority. 12 ÷ 3 × 2 = 8 (left to right), not 12 ÷ 6 = 2.

Thinking PEMDAS means M always comes before D: The M and D are worked left to right, as are A and S.

Related concepts

Related reading

Learning path

After this

How to Teach Order of Operations (Beyond PEMDAS)

4th–5th

Related articles

Math Expectations: 6th Through 8th Grade

A clear guide to the math skills your child should master in grades 6 through 8 — from ratios and proportions to algebra, integers, geometry transformations, and functions. The bridge to high school math.

6 min read6th–8th

What Is the Distributive Property?

The distributive property is one of the most useful rules in math — and most kids use it without knowing its name. Here is what it means and why it matters.

2 min read4th–6th

What Is an Inequality in Math?

A clear explanation of inequalities — greater than, less than, and the symbols that express them. Written for parents helping with math.

2 min read6th–7th

What Is the Difference Between an Equation and an Expression?

Equations and expressions are two of the most confused terms in math. Here is the simple difference — and why it matters for your child's understanding.

2 min read5th–7th

Adaptive math that teaches itself

Lumastery handles the daily math lessons, adapts to each child’s level, and gives you weekly reports on their progress.

Join the Waitlist