Order of Operations

Consider the expression 3 + 4 × 2. If you add first, you get 14. If you multiply first, you get 11. Which is correct? Without a standard set of rules, the same expression could produce different answers. The order of operations eliminates this ambiguity and ensures everyone arrives at the same result.

PEMDAS

The standard order of operations is remembered by the acronym PEMDAS:

Letter	Step	Details
P	Parentheses	Evaluate expressions inside parentheses (or brackets) first
E	Exponents	Evaluate powers and roots
M / D	Multiplication / Division	Work left to right (equal priority)
A / S	Addition / Subtraction	Work left to right (equal priority)

Important: Multiplication and Division are at the same level -- perform them left to right in the order they appear. The same applies to Addition and Subtraction.

Example 1 -- Basic PEMDAS

Evaluate: 3 + 4 × 2

No parentheses or exponents.
Multiply first: 4 × 2 = 8.
Then add: 3 + 8 = 11.

The correct answer is 11.

Example 2 -- With Parentheses and Exponents

Evaluate: 2 × (3 + 5)² - 10

Parentheses: (3 + 5) = 8.
Exponents: 8² = 64.
Multiply: 2 × 64 = 128.
Subtract: 128 - 10 = 118.

Example 3 -- Left-to-Right Rule

Evaluate: 24 ÷ 4 × 3

Division and multiplication are equal priority, so work left to right.
24 ÷ 4 = 6.
6 × 3 = 18.

The answer is 18, not 2 (which you would get if you multiplied first).

Common Mistake

Many students think multiplication always comes before division, or that addition always comes before subtraction. This is incorrect. M and D share the same priority and are done left to right. The same is true for A and S. Think of PEMDAS as P-E-MD-AS, with MD and AS each being a single tied step.

Practice Problems

1. Evaluate: 8 + 12 ÷ 4

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Divide first: 12 ÷ 4 = 3. Then add: 8 + 3 = 11.

2. Evaluate: (6 + 2) × 3 - 4

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Parentheses: 8. Multiply: 8 × 3 = 24. Subtract: 24 - 4 = 20.

3. Evaluate: 5 + 3² × 2

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Exponents: 3² = 9. Multiply: 9 × 2 = 18. Add: 5 + 18 = 23.

4. Evaluate: 18 - 6 ÷ 3 + 2 × 4

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Division: 6 ÷ 3 = 2. Multiplication: 2 × 4 = 8. Then left to right: 18 - 2 + 8 = 24.

5. Evaluate: 4 × (10 - 3)² ÷ 7

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Parentheses: 10 - 3 = 7. Exponents: 7² = 49. Left to right: 4 × 49 = 196, then 196 ÷ 7 = 28.

Lesson Summary

The order of operations (PEMDAS) ensures a single, consistent interpretation of every mathematical expression. Work in this order: Parentheses, Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right). Remember that M/D and A/S each share equal priority and are resolved left to right.