Read the following instructions in order to complete this assignment and review the [example](http://managedcourse.next.ecollege.com/pub/content/1c4a7cbc-859b-4f4d-8798-0e285261a492/MAT221.W1.AssignmentExample.pdf) of how to complete the math required for

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) The given expression

3a 2 – 21a + 6a – 42 The distributive property removes the parentheses.

3a 2 – 15a – 42 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) The given expression

5w – 7 + 7w – 21 – 4w + 36 The distributive property removes the parentheses.

5w + 7w – 4w – 7 – 21 + 36 Like terms are arranged together using the

commutative property to switch places.

12w – 4w – 28 + 36 Two of the variable terms are added and two

of the constant terms are also added.

8w + 8 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) The given expression

0.021m + 0.72n + 0.054n + 16.2m The distributive property removes the

parentheses.

0.021m + 16.2m + 0.72n + 0.054n 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.

[The conclusion paragraph must be written by each individual student and the content will vary

depending on what the student decides to include in their summary. NOTE: this example does

not demonstrate APA format for a paper. The student is responsible for the proper formatting of

his or her own work.]