# Letters instead of numbers

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

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

- To generalize numerical properties or relationships. For example to express the addition commutative property “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

- To codify a problem mathematically and make its resolution easier. For example: "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 by the Persian mathematician Al-Khwarizmi, in the 9th century.

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