Developing math vocabulary
Order of Operations
Pronunciation: OR-der of op-uh-RAY-shunz
The order of operations is the agreed sequence used to evaluate an expression unambiguously.
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Plain language
What it means
The order of operations is the agreed sequence used to evaluate an expression unambiguously.
Formal meaning
Mathematical definition
Grouping symbols are handled first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Where it fits
Its place in mathematics
This convention keeps arithmetic and algebraic expressions consistent across classrooms, software, science, and engineering.
Why it matters
The practical reason to learn it
Without an agreed order, one expression could produce several conflicting answers.
Worked example
Evaluate carefully
Evaluate 18 ÷ 3 × 2 + 4.
- Perform division and multiplication from left to right: 18 ÷ 3 = 6, then 6 × 2 = 12.
- Add the remaining 4 to the intermediate value.
The value is 16.
Real-life example
Where this appears
A programmer follows operator precedence when writing or reviewing calculations in code.
Common mistake
What to watch for
Doing multiplication before division no matter where each appears. They have equal priority and are evaluated left to right.
Memory tip
Keep this in mind
Use parentheses when clarity matters more than relying on memory.
Little-known fact
Keep curiosity alive
Different programming languages publish precedence tables, and parentheses remain the safest way to make intent explicit.
A profession that uses this idea
Code must evaluate predictably
Programmers use precedence and grouping so formulas calculate in the intended sequence.
Explore Programmers & Data AnalystsFollow the learning trail
Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Al-Khwarizmi
A scholar whose systematic writing on calculation and equation solving helped shape algebra and whose name became the root of the word algorithm.
George Boole
George Boole was mathematician and logician. He expressed logical reasoning through algebraic operations now called Boolean algebra.
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