Mathematics

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MAT 221 Introduction to Algebra

Mathematics

Running Head: SIMPLIFYING EXPRESSIONS
Running head should use a shortened version of the title if the title is long! All capital
letters for the title and the words Running and Head should be capitalized as well.
Simplifying Expressions (full title; centered horizontally & vertically)
First Name Last Name
MAT 221
Dr. XXXXXXX XXXXXXXX
Date
1
SIMPLIFYING ALGEBRAIC EXPRESSIONS
2
Simplifying Expressions
Be sure to have a centered title on page 1 of your papers.
[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.
YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD
APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! 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 movement of terms to different locations within
expressions and the operation symbol in front of the term will move as well. The associative
property is used to group like terms together so they can all be combined. Like terms must have
the same variable raised to the same power, or with the same exponent.
While simplifying the following expressions, the properties of real numbers will be used
and identified. 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 demonstrate everything needed in the actual assignment.]
A) 3a(a – 7) + 6(a –7)
The given expression
3a2 – 21a + 6a – 42
The distributive property removes the parentheses.
3a2 – 15a – 42
Like terms are combined by adding coefficients.
SIMPLIFYING ALGEBRAIC EXPRESSIONS
3
This expression is now fully simplified because nothing else can be computed. In this
example it was not necessary to change the order of any of the terms because 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
Distributive property removes the parentheses.
5w + 7w – 4w – 7 – 21 + 36
Like terms are arranged together using the
commutative property to switch places. 5w, 7w, and
-4w are like variable terms while
-7, -21, and 36
are like constant terms. These can all be added or
subtracted.
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 because 8w
and 8 cannot be added.
C) 0.03(0.7m + 24n) – 0.9(-0.06n – 18m)
0.021m + 0.72n + 0.054n + 16.2m
The given expression
The distributive property removes the
parentheses.
0.021m + 16.2m + 0.72n + 0.054n
Like terms are arranged together using the
commutative property. All terms are
variable terms but only those with the same
variable may be combined.
SIMPLIFYING ALGEBRAIC EXPRESSIONS
16.221m + 0.774n
4
Like terms are combined by adding
coefficients.
This one only looked more complicated because of the decimal numbers, which require the
decimals lined up to add or subtract. 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. DO NOT INCLUDE
PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO
SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE
CONNECTED TO OTHER CONCEPTS.]
SIMPLIFYING ALGEBRAIC EXPRESSIONS
Reference
Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY:
McGraw-Hill Publishing.
Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR
UNDERLINE.
Textbook should ALWAYS be included in every assignment! Be sure to use appropriate
indentation (hanging), font (Arial or Times New Roman), and size (12).
5
Tips for Writing in Math Classes
In addition to the weekly homework, lab, and discussion posts, the Math courses at Ashford also include
written assignments. Do not let this intimidate you. While this may be unlike other math classes in the
past, the purpose of this is let you examine a math concept that has a direct correlation to the use of
mathematics in the “real world,” and to have you explain how and why you solved a problem in a
particular way, allowing you to further develop your critical thinking skills with regard to mathematics.
The purpose of this short “guide” is to prepare you for completing these writing assignments, since the
format will be slightly different than the other writing assignments you have here at Ashford. However,
the basic 5 paragraph essay should still be the basis for your written assignments in Math.
Introduction:
Your introduction needs to do three main things:
Introduce the specific concept examined in the assignment (i.e. inequalities, Pythagorean
quadratics, etc).
Introduce or reference the specific question or real world application being asked (i.e. BMI,
navigation)
Have a clear statement that describes how the concept examined in the assignment is important to
a “real world” setting.
As with all introductions, this should be about 5-6 sentences in length.
Body Paragraphs:
This is where your assignment diverges from a more traditional essay. Here is where you will solve the
specific problem being asked, and explain how and why this is important.
In order to do this, you will need to:
Restate the problem in your own words. Solve the problem demonstrating your understanding of
the concepts examined in the essay, making sure to include each mathematical step (in other
words, show your work). This will count as a “paragraph.”
If there is a visual that you used that would like to include, you may attach a scanned
copy of it separately, and reference it here (i.e. see attached visual). Please note that this
visual must be created by you and cannot be a scanned copy of the text or other class
wide visual.
Include a discussion that incorporates the answers of each additional question asked in the
prompt. Depending on the questions asked, this will usually be 2 paragraphs in length.
In your discussion, make sure to incorporate the weekly vocabulary terms listed in the
assignment, and place these in bold type. These should be fully integrated into your discussion,
and should not just be definitions.
Conclusion
Your conclusion should be a paragraph (at least 5 sentences) that includes the following:
An application of the concept examined to the particular problem solved
A summary of the problem and your method of solving it
A statement of what you learned
A statement of how this concept can be used in the real world.
APA format:
All assignments submitted at Ashford must be in APA format. Therefore, please make sure to include a
properly formatted reference and title page, and make sure your paper is in an APA font, such as 12 pt.
Courier New or Times New Roman. With regard to internal citations, you don’t need to cite the textbook
if the problem you are solving is from the textbook, but you will need to cite any outside sources. Please
make sure that the text is listed in your reference section however, along with any other sources you used
in working on the assignment.
Plagiarism:
Plagiarism, or the use of another person’s words are thoughts, is academically and intellectually dishonest
and not permitted at Ashford. Please make sure everything you turn in is new and original work, and is
written in your own words. Copy and pasting portions of your discussion off the internet will result in
automatically failing the assignment.
Assignment:
Simplifying Expressions
•
•
•
•
Use the properties of real numbers to simplify the following expressions:
o 2 a ( a- 5) + 4 ( a- 5)
o 2 w – 3 + 3 (w- 4) – 5 (w- 6)
o 0.05 (0.3 m + 35 n) – 0. 8 (- 0. 09n – 22 m)
Write a two- three page paper that is formatted in APA style. Format your math work as
shown in the Instructor Guidance and be concise in your reasoning. In the body of your
essay, do the following;
Demonstrate your solution to the above problems, making sure to include all mathematical
work. 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 and the
properties used on the right.
Explain why the properties of real numbers are important to know when working with algebra.
In what ways are they useful for simplifying algebraic expressions?
Incorporate 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
approprilately in sentences describing your math work)
o Simplify
o Like terms
o Coefficient
o Distributive
o Removing parentheses
No plagiarism please or copy and pasted work. Pay close attention to details.
...

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