The order of operations is a foundational set of rules in mathematics that defines which operations to perform first in a multi-step expression.
Without these rules, a single mathematical expression could produce conflicting answers depending on the order in which calculations are executed.
A Clear Example
Consider the expression: 6 + 4 × 3
We do not simply calculate from left to right. Multiplication holds a higher precedence over addition.
- First step: 4 × 3 = 12
- Second step: 6 + 12 = 18
Therefore, 6 + 4 × 3 = 18.
The Standard Rules: PEMDAS
A widely used acronym to remember operational precedence is PEMDAS:
- P — Parentheses / Grouping Symbols
- E — Exponents & Radicals
- M — Multiplication
- D — Division
- A — Addition
- S — Subtraction
It is crucial to note that PEMDAS does not mean multiplication must strictly precede division, or addition before subtraction. Multiplication and division share equal priority and are evaluated from left to right. The exact same principle applies to addition and subtraction.
Step-by-Step Example
Evaluate: 20 − 8 ÷ 2
Division takes precedence over subtraction:
- 8 ÷ 2 = 4
- 20 − 4 = 16
The correct answer is 16.
Why Does Operational Precedence Matter?
The order of operations establishes a unified standard in mathematics. Whether solving basic algebra or writing computer code, following these rules ensures accurate and repeatable results worldwide.
Practice & Master PEMDAS
Building operational speed requires systematic practice. Start with basic two-step operations before advancing to multi-bracket complex expressions.
For structured study, you can download our complete 1,000-problem Order of Operations practice workbook with answer keys.