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Constants

(KS3, Year 7)

A constant is a number with a fixed value - its value does not change.

Dictionary Definition

The Merriam-Webster dictionary defines a constant as "a number that is assumed not to change value in a given mathematical discussion."

Real Examples of Constants

In algebra, some values always stay the same. They are constants. Numbers are examples of constants - a number can only have one value. 2 can only have a value of 2.

Sometimes we use letters to stand in for constants. These letters will still stand in for a number which will always be the same. For example, π (pi) always has a value of 3.14.

In algebra, numbers that are not constants are called variables - they can change in value.

Understanding Constants

It is easier to understand constants with an example. Let's look at an algebraic equation. Consider a linear equation:

a linear equation with constants

The 2 and the 1 are both constants. They both have a fixed value. The x and the y are variables. We can change their value. The values of x and y must keep both sides of the equation the same. The left hand side (y) must be the same as the right hand side (2x + 1).

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

The constants are the same in each case and show which pairs of x and y are allowed by the equation. Different constants would mean different pairs of x and y would be allowed by the equation.

a linear equation with different constants