This paper will provide information on how to utilize the properties of real numbers to simplify several expressions. This paper will provide the necessary steps that are needed in the process of simplifying and identify which property of real numbers was used, as well as why the prosperities of real numbers are important to know when working with algebra, and finally this paper will explain several vocabulary words that are used to explain each mathematical problem.

The properties of algebra are necessary to know and understand how they work since in simplifying and solving techniques one must be able to correctly move terms around and put expressions and equations into the simplest possible forms. The distributive property is used to apply multiplication across two or more terms inside of parentheses and results in the removal of the parentheses. The commutative property permits us to move terms to different settings within expressions, while the associative property is used to group like terms together so they can all be combined. I will now demonstrate how the properties of real numbers are used while I simplify the following expressions. The math work will be aligned on the left while the discussion of properties is on the right side of each line. 2a(a – 5) + 4(a – 5) The given expression 2a -10a +4a-20 The distributive property removes the parentheses 2a^2 -6a - 20 Like terms are combined by adding coefficient 2w-3+3(w-4)-5(w-6) The given expression...