Dictionary Definition
The Merriam-Webster dictionary defines a variable as "a quantity that may assume any one of a set of values; a symbol representing a variable."Real Examples of Variables
In algebra, some values are fixed, while others are allowed to vary. The values that are allowed to vary are variables. They are represented by letters and symbols:
Understanding Variables
It is easier to understand variables with an example. Let's look at an algebraic equation. Consider a linear equation:
x = 1 ∴ y = 2x + 1 = 2 × 1 + 1 = 3
x = 2 ∴ y = 2x + 1 = 2 × 2 + 1 = 5
x = 3 ∴ y = 2x + 1 = 2 × 3 + 1 = 7
Why Are Variables Useful?
There are two uses for variables:- A variable can stand in for a number that we don't know yet. This 'unknown' can then be found, like solving a puzzle.
For example, x stands for a number we don't know yet in the equation shown below.
Using algebra, x = 1.
- A variable can stand in for many different numbers. The value the variable takes varies.
For example, in a function, a variable is used as an input. By putting different numbers in, the function gives different numbers out.
The variable x can take a value of 1, 2, 3 etc.
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