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# Algebra

Algebra is a part of mathematics (math) where letters (a,b,c,...) or other symbols are used to represent unknown numbers.

In algebra, addition, subtraction, multiplication, and division are used to find numbers (values) in a math problem (equation) when they are not known.

An example would be to find x (the variable) in the math problem (equation): x âˆ’ 5 = 2
Using algebra, one can add five to both sides of the equal sign (=). (x âˆ’ 5 + 5 = 2 + 5), so the answer is: x = 7

In other words,

On the left:
x âˆ’ 5 + 5 = a negative 5 and a positive 5 equal 0 leaving just the "x"
On the right:
= 2 + 5 a positive 2 plus a positive 5 equal 7
Rewriting the equation:
x âˆ’ 0 = 7
so
x = 7
7 âˆ’ 5 = 2

This is called "elementary algebra", or basic algebra. There's also abstract algebra, linear algebra, and universal algebra.

Algebra can be used to solve real problems because the rules of algebra work in real life and numbers can be used to represent the values of real things.

For example, if I give 5 coins to a friend and have 10 left over, how many did I have before? We are trying to find out how many I had before, so we will call that x. How many coins I had before minus how many I gave to my friend equals how many coins I have now, so x âˆ’ 5 = 10. We can add five to each side to find that x âˆ’ 5 + 5 = 10 + 5; so x = 15. X, the number I had before, equals 15. I had 15 coins before.

## Writing algebra

In algebra, adding z to y (or y plus z) is written as y + z. In algebra, subtracting z from y (or y minus z) is written as y - z.

In algebra, multiplying y by z (or y times z) can be written in 4 ways: y Ã— z, y*z, y(z), or yz. yz is the most usual form of writing the product of y and z in algebra.

When we multiply a number and a letter in algebra, we write the number in front of the letter. When the number is one, then one is not written because one times anything is that thing and so is not necessary.

In algebra, dividing y by z is written as y */* z or y/z. y/z is more commonly used.

## Graphing algebra

Algebra also introduces graphing and the basic formula y=mx+b where b is the y-intercept of the graph and m is the slope. This formula applies to the coordinates of the graph or (x,y).

## History

The word "algebra" is a Latin form of the Arabic word Al-Jabr ("casting") and comes from a mathematics book Al-Maqala fi Hisab-al Jabr wa-al-Muqabilah, ("Essay on the Computation of Casting and Equation") written in the 9th century by a famous Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, who was a Zoroastrian born in Kharazm in Iran. He flourished under Al-Ma'moun in Baghdad, Iraq through 813-833 AD, and died around 840 AD. The book was brought into Europe and translated into Latin in the 12th century. The book was then given the name 'Algebra'.