What Is PEMDAS? Order of Operations Explained with Examples

PEMDAS is an acronym that helps you remember the correct order of mathematical operations. Without a standardized order, the same expression could produce different answers — which would make math impossible to use consistently.

What Does PEMDAS Stand For?

• Parentheses (also called Brackets)
• Exponents (Powers, Roots)
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

Some people remember it as "Please Excuse My Dear Aunt Sally."

Alternative Acronyms:

• BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) — used in UK and Commonwealth countries
• BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction)
• BEDMAS (Brackets, Exponents, Division/Multiplication, Addition/Subtraction)

Why Order of Operations Matters

Consider the expression: 2 + 3 × 4

If you add first: (2 + 3) × 4 = 5 × 4 = 20 (WRONG by PEMDAS)

If you multiply first: 2 + (3 × 4) = 2 + 12 = 14 (CORRECT)

The correct answer is 14. Multiplication comes before addition in the order of operations.

Step-by-Step Examples

Example 1: Basic

8 ÷ 2 × (2 + 2)

Step 1: Parentheses first → 2 + 2 = 4

Step 2: Division and Multiplication (left to right) → 8 ÷ 2 = 4, then 4 × 4 = 16

Answer: 16

Example 2: With Exponents

3 + 6 × (5 + 4) ÷ 3 − 7

Step 1: Parentheses → 5 + 4 = 9

Step 2: Multiplication → 6 × 9 = 54

Step 3: Division → 54 ÷ 3 = 18

Step 4: Addition → 3 + 18 = 21

Step 5: Subtraction → 21 − 7 = 14

Answer: 14

Example 3: Complex Expression

4 × (3² − 8) + 6 ÷ 2

Step 1: Parentheses first. Inside: Exponents first → 3² = 9

Step 2: Inside parentheses: 9 − 8 = 1

Step 3: Multiplication: 4 × 1 = 4

Step 4: Division: 6 ÷ 2 = 3

Step 5: Addition: 4 + 3 = 7

Answer: 7

Common Mistakes to Avoid

Mistake 1: Ignoring Left-to-Right Rule for Equal Precedence

Multiplication and division have equal priority and are evaluated left to right.

Incorrect: 8 ÷ 4 × 2 = 8 ÷ 8 = 1 (treating multiplication first)

Correct: 8 ÷ 4 × 2 = 2 × 2 = 4 (left to right)

Mistake 2: Adding Before Subtracting

Addition and subtraction have equal priority and are also left to right.

Incorrect: 10 − 3 + 2 = 10 − 5 = 5

Correct: 10 − 3 + 2 = 7 + 2 = 9

Mistake 3: Forgetting Implicit Multiplication

2(3) means 2 × 3 (multiplication). Some calculators treat it differently, but in standard math, it is the same.

Tips for Using PEMDAS Correctly

1. Write fractions with parentheses when needed: (a + b)/(c + d)

2. Use parentheses to clarify ambiguous expressions

3. Remember that exponents are right-associative: 2³² = 2^(3²) = 2⁹ = 512

4. When in doubt, add extra parentheses for clarity

FAQ: PEMDAS

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Yes. BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) is the same concept used in different countries.

Yes. Multiplication and division have equal priority. Evaluate them left to right.

Work from the innermost parentheses outward. For example: 2 × [(3 + 4) × 2] = 2 × [7 × 2] = 2 × 14 = 28.

Yes. The order of operations applies to all mathematical expressions, including algebra, calculus, and advanced math.

Some calculators (especially older ones) may use different conventions for implicit multiplication (e.g., 2(3) vs 2 × 3). Use parentheses to ensure correct evaluation.

The concept of order of operations developed over centuries. The PEMDAS convention became standardized in the late 19th and early 20th centuries with the rise of modern algebraic notation.