What Is a Variable in Math?
A variable is a letter (or symbol) that represents a number you do not know yet.
In x + 5 = 12, the variable is x. It represents the unknown number that makes the equation true. (x = 7, because 7 + 5 = 12.)
Variables are not new
Your child has been using variables since early elementary, they just looked different:
- __ + 5 = 12 (the blank is a variable)
- ? × 4 = 20 (the question mark is a variable)
- □ + 3 = 10 (the box is a variable)
Algebra simply uses letters (x, y, n, a) instead of blanks, question marks, or boxes. The concept is identical.
Variables can represent different things
An unknown to solve for: x + 3 = 10 → x = 7
A quantity that changes: In y = 2x + 1, both x and y are variables. As x changes, y changes too. This is how variables work in functions and graphing.
A general rule: The area formula A = l × w uses variables to express a rule that works for any rectangle, not just one specific rectangle.
Common confusion
"x is always the same number." In x + 5 = 12, x is 7. In x + 3 = 10, x is also 7. But in x + 1 = 5, x is 4. The value of a variable depends on the equation it is in.
"3x means thirty-something." In algebra, 3x means 3 × x (three times x), not a two-digit number starting with 3.
Related concepts
- How to Teach Variables and Equations: full teaching guide
- Expressions vs. equations: variables appear in both
- Functions: variables as inputs and outputs