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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

     ·John’s age last year : x-1
-To express formulas. For example, the rectangle area    A = b · h

-To generalize the evolution of numerical series (general term)
· 1, 4, 9, 16, …, n2, …
· 2, 6, 12, 20, …, n · (n + 1), …

- 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.