What is a letter for?

In algebra, a letter stands for a number that we do not yet know, or a number that may vary.

This is not an unnecessary complication: it is what allows us to write a rule just once instead of rewriting it for each case.

An example

‘The perimeter of a square is four times its side.’

P = 4 x c

This single line replaces an infinite number of sentences: if the side is 3, the perimeter is 12; if it is 7.5, the perimeter is 30. The formula says it all in one go.

Notation conventions

Three shortcuts to be aware of, as they are used everywhere:

Written as	This means
3a	3 x a — the ‘x’ is implied
a^2	a x a
ab	a x b

However, a3 is not written: the number always comes before the letter.

Replacing a letter with its value

This is known as evaluating an expression. We substitute, then calculate following the order of operations:

Pour x = 5 :   3x + 2  =  3 x 5 + 2  =  15 + 2  =  17

Note: 3x + 2 is not equal to 5x. You cannot add a number of x’s to a number on its own — this is the subject of the next lesson.