Definition
Variable
A variable is a symbol that represents a value that may vary, be unknown, or stand for any number.
What it means
A variable is a name tag for a value, not the value itself. Its role comes from the problem. The same letter can hold one unknown value in an equation, change through a table, or represent every allowed number in a rule.
Remember it
The symbol is the name tag; the value is what it stands for.
Example
In p = 3n + 1, n and p are variables. If n = 4, then p = 13. When n changes, p changes according to the same rule.
Watch for
The multiplication sign × is an operation symbol, not a variable, even though it can look like the letter x.
Common mix-up
A variable does not always change during one problem; it may represent one fixed but unknown value that must be found.
Exact meaning
A variable is a symbol representing a value. Depending on context, it may be an unknown to determine, a quantity that changes, an input or output, or a general number in a statement.