How The Properties of Real Numbers are Used, and Why They are Important, in the Simplification of Algebraic Expressions
For this weeks lesson we are going to show how the properties of Real numbers are used, and why they are important, in the simplification of expressions. In order to do this we must first identify the properties of real numbers. Then we will use the properties to simplify some example expressions to show them in action. Finally we will discuss the importance of the use of the properties in order to help simplify the expressions we worked.
Real numbers have three basic properties that are fundamental to working, simplifying, and solving all algebraic expressions. The Commutative, Associative, and Distributive properties. The Commutative Property, A+B = B+A or AB = BA, states that changing the order of two numbers either being added or multiplied, does not change the value of it. The two sides are called equivalent expressions because they look different but have the same value. The Associative Property, A + (B + C) = (A + B) + C or A(BC) = (AB)C, states that changing the grouping of numbers that are either being added or multiplied does not change the value of it. The two sides are equivalent to each other (Seward, 2012). It is important to know that neither the Commutative or Associative properties work with subtraction or division. A simple trick to learn to combat any subtraction obstacles is to change the subtraction of a positive integer into the addition of a negative one. (x - 2) = (x + (-2) (Stapel, 2012). The Distributive property, a(b + c) = ab + ac, or (a +b)c = ac + bc is used when you have a term being multiplied times two or more terms that are being added or subtracted in a parentheses. You distribute the terms by multiplying every term inside the parenthesis by the outside term (Seward, 2011).
Now with the Properties of Real numbers defined we will put them to work using them to simplify three examples....