Developing math vocabulary
Variable
Pronunciation: VAIR-ee-uh-bul
A variable is a symbol that represents a number or another mathematical object.
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Plain language
What it means
A variable is a symbol that represents a number or another mathematical object.
Formal meaning
Mathematical definition
A variable is a placeholder whose value may be unknown, allowed to change, or selected from a stated domain.
Where it fits
Its place in mathematics
Variables let mathematics describe patterns, general rules, equations, functions, formulas, and data relationships.
Why it matters
The practical reason to learn it
One expression can represent many cases instead of requiring a separate calculation for each value.
Worked example
Evaluate with a variable
Evaluate 3x + 2 when x = 5.
- Substitute 5 for x.
- Compute 3 × 5 + 2.
The value is 17.
Real-life example
Where this appears
A programmer uses variables to store values that a program reads, changes, and calculates.
Common mistake
What to watch for
Assuming a variable must be x or must always represent one unknown number.
Memory tip
Keep this in mind
State what the variable represents and include units when the situation has them.
Little-known fact
Keep curiosity alive
The word variable is used in both mathematics and programming, but the exact behavior depends on context.
A profession that uses this idea
Variables make rules reusable
Programmers and analysts name changing values so one procedure can handle many inputs.
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Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
François Viète
François Viète was lawyer, cryptanalyst, and algebraist. He introduced systematic letter notation for known and unknown quantities and advanced symbolic algebra.
René Descartes
A French thinker who helped unite algebra and geometry by representing curves and shapes with coordinates and equations.
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