How to Use the Order of Operations (PEMDAS Explained)

What Is the Order of Operations?

The order of operations is a set of rules that tells you which calculations to do first when an expression has more than one operation.

Without these rules, the same expression could give different answers:

Example: 2 + 3 × 4

• If you go left to right: (2 + 3) × 4 = 20 ❌
• Following order of operations: 2 + (3 × 4) = 14 ✅

The correct answer is 14 because multiplication comes before addition.

PEMDAS Explained

PEMDAS is an acronym that helps you remember the order:

| Letter | Stands for | Meaning | |---|---|---| | P | Parentheses | Do operations inside parentheses first | | E | Exponents | Calculate powers and roots next | | M | Multiplication | Then multiply... | | D | Division | ...and divide (left to right) | | A | Addition | Then add... | | S | Subtraction | ...and subtract (left to right) |

Important rules:

1. Parentheses first — always start inside the innermost parentheses
2. Exponents second — calculate all powers
3. Multiplication and Division are equal priority — do them left to right
4. Addition and Subtraction are equal priority — do them left to right

The "left to right" rule for MD and AS is crucial and often missed.

Step-by-Step Examples

Example 1: 8 + 2 × 5

1. No parentheses or exponents
2. Multiplication first: 2 × 5 = 10
3. Addition: 8 + 10 = 18

Example 2: (6 + 4) × 3²

1. Parentheses: (6 + 4) = 10
2. Exponents: 3² = 9
3. Multiplication: 10 × 9 = 90

Example 3: 24 ÷ 6 × 2

1. No parentheses, exponents, or MD vs AS confusion
2. Division and multiplication have equal priority → go left to right
3. 24 ÷ 6 = 4
4. 4 × 2 = 8

Not 24 ÷ 12 = 2 — that would be wrong!

Example 4: 5 + 3² × (8 − 2)

1. Parentheses: (8 − 2) = 6
2. Exponents: 3² = 9
3. Multiplication: 9 × 6 = 54
4. Addition: 5 + 54 = 59

Example 5: 48 ÷ (4 + 4) × 2 − 1

1. Parentheses: (4 + 4) = 8
2. Division and multiplication, left to right: 48 ÷ 8 = 6, then 6 × 2 = 12
3. Subtraction: 12 − 1 = 11

Common Traps and Mistakes

Trap 1: Multiplication doesn't always come before division

M and D have equal priority. Always go left to right.

• 12 ÷ 3 × 2 = 4 × 2 = 8 ✅
• 12 ÷ 3 × 2 = 12 ÷ 6 = 2 ❌

Trap 2: Same for addition and subtraction

• 10 − 3 + 2 = 7 + 2 = 9 ✅
• 10 − 3 + 2 = 10 − 5 = 5 ❌

Trap 3: Nested parentheses

Work from the inside out:

• 2 × ((3 + 1) × 5) = 2 × (4 × 5) = 2 × 20 = 40

Trap 4: Negative signs

Be careful with negatives and exponents:

• −3² = −(3²) = −9 (the exponent applies to 3, not −3)
• (−3)² = 9 (the exponent applies to −3)

PEMDAS vs BODMAS

Different countries use different acronyms, but they mean the same thing:

| PEMDAS (US) | BODMAS (UK) | |---|---| | Parentheses | Brackets | | Exponents | Orders | | Multiplication | Multiplication | | Division | Division | | Addition | Addition | | Subtraction | Subtraction |

Whether you learned PEMDAS, BODMAS, or BEDMAS — the rules are identical.

Practice Problems

Evaluate each expression:

1. 3 + 4 × 2
2. (5 + 3) × 2²
3. 18 ÷ 3 × 2
4. 7 + 2³ − 4
5. 100 ÷ (5 × 4) + 3²

Answers: (1) 11 (2) 32 (3) 12 (4) 11 (5) 14

Need More Help?

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