100% original work please

Read the following instructions in order to complete this assignment, and review the example of how to complete the math required for this assignment:

• Use the properties of real numbers to simplify the following expressions:
  
  
  • 2a(a – 5) + 4(a – 5)
  • 2w – 3 + 3(w – 4) – 5(w – 6)
  • 0.05(0.3m + 35n) – 0.8(-0.09n – 22m)
     
• Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, please make sure to include:
  
  
  • Your solution to the above problem, making sure to include all mathematical work.
    
    
    • Plan the logic necessary to complete the problem before you begin writing. For examples of the math required for this assignment, please review Elementary and Intermediate Algebra and the example of how to complete the math required for this assignment.
    • Show every step of the process of simplifying and identify which property of real numbers was used in each step of your work.  Please include your math work on the left; the properties used on the right.
  • A discussion of why the properties of real numbers are important to know when working with algebra. In what ways are they useful for simplifying algebraic expressions?
  • The incorporation of the following five math vocabulary words into the text of your paper. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):
    
    
    • Simplify
    • Like terms
    • Coefficient
    • Distribution
    • Removing parentheses

For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.

 

INSTRUCTOR GUIDANCE EXAMPLE: Week One Assignment

[The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. The following paragraph is not an introduction to the paper but rather the discussion called for in part 2 of the instructions.]

The properties of algebra are important to know and understand how they work because in simplifying and solving methods one must be able to properly move terms around and put expressions and equations into the simplest form possible. The distributive property, sometimes called distribution is used to apply multiplication across two or more terms inside of parentheses and results in the removal of the parentheses.

The commutative property allows us to move terms to different locations 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.

[Notice that these expressions are not the same as in the assignment, although they are similar enough to demonstrated everything which is needed in the actual assignment.]

A) 3a(a – 7) + 6(a –7) 3a2 – 21a + 6a – 42 3a2 – 15a – 42

The given expression
The distributive property removes the parentheses. Like terms are combined by adding coefficients. This expression is now fully simplified.

In this example it was not necessary to change the order of any of the terms as the like terms were already together in the middle of the expression in step 2.

B) 5w – 7 + 7(w – 3) – 4(w – 9) 5w – 7 + 7w – 21 – 4w + 36 5w + 7w – 4w – 7 – 21 + 36

12w – 4w – 28 + 36 8w + 8

The given expression
The distributive property removes the parentheses. Like terms are arranged together using the commutative property to switch places.
Two of the variable terms are added and two
of the constant terms are also added.
The remaining pairs of like terms are added.
This expression is now fully simplified.

C) 0.03(0.7m + 24n) – 0.9(-0.06n – 18m) 0.021m + 0.72n + 0.054n + 16.2m

0.021m + 16.2m + 0.72n + 0.054n

The given expression
The distributive property removes the parentheses.
Like terms are arranged together using the commutative property.

16.221m + 0.774n Like terms are combined by adding coefficients.

This one only looked more complicated because of the decimal numbers. The basic steps are not any different from the other examples.