What a Variable Is

Notebooks cost 3 dollars each, and you have not decided how many to buy. The cost is 3 times the number of notebooks, whatever that number turns out to be. Mathematics gives the unknown number a letter, say n, and writes the cost as 3n. A letter that stands for a number is called a variable, because the number it stands for can vary.

A number written right next to a letter is multiplied by it: 3n means 3 × n. The dot is left out because nothing else could be meant, and dropping it keeps longer lines easy to read. So when n is 4, 3n is 12, never 34: the digits are not glued together, they are multiplied.

A calculation with a letter in it, like n + 4 or 3n, is an expression. The value of n + 4 depends on the number chosen for n. It is a recipe: give it a number for n and it gives you a number back. When n is 1, n + 4 is 5; when n is 20, it is 24.