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Origins:

The word algebra originated from the title of the book ilm al-jabr w'almuqabala, a book written during the ninth century the an Arabian mathematician named al-Khworizimi. The original title was translated as the science of restoration and reduction, basically meaning transposing and combining similar terms of equations. Translated in Latin to al-jabr (the union of broken parts) led to the term we now refer to as Algebra. Algebra was brought from ancient Babylon, Egypt and India to Europe via Italy by the Arabs.

Fundamentals:

Essentially, Algebra evolved from the rules and operations of arithmetic which begins with the four operations: addition, subtraction, multiplication and division of numbers. Operations in algebra follow the same rules as those in arithmetic. Algebra uses variables which is a symbol that represents a number and expressions which are mathematical statements that use numbers and or variables. The second example below is an example of an expression. Algebra involves equations which are statements that two numbers or expressions are equal.

5 + 5 = 2 x 5
5 + 5 = 10

n + n = 2 x n
5 + 5 = 2n (When 2n is written, it is understood that 2 is multiplied by n)

In Algebra, symbols or letters are introduced as a sort of shorthand which is used to abbreviate and simplify long and often complicated statements.

Algebra is illustrated by many formulas used in science, computer programs and the workplace industry.

Properties of Addition and Multiplication:

A Basic property of equality:

If a = b and c = d, then a + c = b + d and ac = bd.

The above property states that the same number can be added to both sides of the equality and that both sides of the equality can be multiplied by the same number.

Properties of Negatives:

111-(-a) = 0
11 (-a)b = - (ab) = a(-b)
(-a)(-b) = ab
11(-1)a = -a

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