# Mathematics Principles V11

Clive W. Humphris

ALGEBRA 0: Simplest of Algebra.

Algebra is a mathematical sentence that expresses numerical quantities and their relationships as a string of letters and numbers.

Algebraic formulae is a method of defining a problem in writing as a statement that can sometimes be reorganised or simplified. In this example solving the problem of finding the perimeter and area of a rectangle or square will demonstrate the most basic of algebra and how it might be simplified. Once we have the formula in its simplest terms we can then apply it to any similar problem, knowing it will always produce the correct result.

Note there are just two variables [a] and [b]. The perimeter being a total of all four sides, two of which are the same length [a] and the other two also of same length [b] their sum given the variable [c]. The area is the product of the width [a] multiplied by the height [b] and assigned to the variable [d]. During the simplification process the actual values of the variables are not required and should only be applied at the final level.

The perimeter [c] expression can be simplified into a more familiar algebraic form, whereas the expression for finding the area [d] does not require further simplification. By convention multiplication signs are not normally included in algebraic expressions.