PEMDAS is a widely used mnemonic designed to help students remember the standard order of operations in arithmetic and algebra.
The letters in PEMDAS stand for:
- P — Parentheses / Grouping Symbols
- E — Exponents & Roots
- M — Multiplication
- D — Division
- A — Addition
- S — Subtraction
This rule defines the precise hierarchy to evaluate expressions containing multiple operations.
How PEMDAS Works in Practice
Consider the expression: 5 + 3 × 4
It contains both addition and multiplication. According to operational precedence, multiplication takes priority over addition:
- Multiply first: 3 × 4 = 12
- Add next: 5 + 12 = 17
The correct result is 17.
Parentheses Always Come First
Grouping symbols override standard priority rules. Consider: (5 + 3) × 4
Because addition is enclosed within parentheses, it must be evaluated first:
- Parentheses first: 5 + 3 = 8
- Multiply next: 8 × 4 = 32
The final answer becomes 32.
The Left-to-Right Rule for Multiplication and Division
A common misconception with PEMDAS is assuming multiplication must always be performed before division.
Multiplication and division share equal priority. When both appear in an expression, evaluate them strictly from left to right.
Example: 24 ÷ 6 × 2
- Work from left: 24 ÷ 6 = 4
- Then multiply: 4 × 2 = 8
Addition and Subtraction Rule
Similarly, addition and subtraction hold equal rank and must also be solved from left to right.
Example: 15 − 6 + 2
- Subtract first: 15 − 6 = 9
- Add next: 9 + 2 = 11
Building Mastery Over Mnemonic Shortcuts
Memorizing the acronym is only the first step. True proficiency comes from understanding the underlying precedence levels and applying the left-to-right rule consistently.