In several Mathematics situations we need to work with unknown numbers. In these situations, we use letters instead of numbers. We call these letters variables. Then the letters have the same operation properties as numbers. We can do this:

-To express any number: for example, even numbers have the form “2·n”, where “n” is a natural number.

-To generalize numerical properties or relationships: for example to express the commutative property of addition “a + b = b + a”

-To express and work with unknown numbers: for example to express an unknown age
John’s age → x
John’s age after 15 years → x + 15
John’s age last year : x - 1

-To express formulas: for example, the rectangle area    A = b · h

-To codify a problem mathematically and make its solution easier: After 15 years, John will be the double of age than today

x + 15 = 2·x →  x  =  15   John is 15 years old

The part of Mathematics that studies the behaviour of the expressions with letters and numbers is called ALGEBRA (from the Arabic الجبر = al-Jabr = reduction). This word was used for the first time in a book of the Persian mathematician Al-Khwarizmi, in the 9th century.

Exercise: if x is an unknown number, write an expression for each sentence:

a) Double of a number

b) Half a number

c) Double of the following number

d) Following of the double of a number

e) Half a number, plus 6 units

Solutions: a) 2x; b) x/2; c) 2(x + 1); d) 2x + 1; e) x/2 + 6