Session 10 (Week 5b)

Chapter 3 Rational Expressions

Section 3.2 Multiplying and Dividing Rational Expressions

1. Activities

W. Michael Kelley (2006). The Humongous Book of Calculus Problems.

Complete problems 3.9 - 3.16 [p. 30 - 33]

Wayne W. Dyer (2007). Change Your Thoughts - Change Your Life.

Read Verse 10: Living Oneness [p. 48 - 51]

Jack Weiner (2005). The Mathematics Survival Kit. Revised Edition.

Read Factoring Difference of Squares [p. 3 - 4]
Read Factoring Difference of Cubes [p. 5 - 6]

2. What's it all about?

This section involves computing the product or quotient of two or more polynomials. This is much easier than computing the sum or difference of two polynomials

3. What am I able to do, now that I am finished this section?

• multiply and/or divide two or more rational expressions

4. What will I know?

• that any expression involving multiplication and division of rational polynomials can be brought to a simpler form by carrying out the multiplication and/or division.

5. What are the key concepts?

• multiplication of polynomials

6. What are some relevant Web sites for this material?

Using your favorite search engine, and maybe one or two others, type in a few key words such as "multiplying rational expressions" or "dividing rational polynomials" .

Here are a few Web sites that I liked:

• http://www.purplemath.com/modules/rtnlmult.htm
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut9_mulrat.htm

7. What concept map can I create for this section?

The map for this section is trivial, and not worth producing.

8. What types of Mathematica activities can I create?

There is no obvious value in working through these problems with Mathematica.

9. What are some connections to other ideas?

This is basically an extension of the idea of multiplying polynomials to that of multiplying rational polynomials

10. What is my overall reaction to this section?

This section is very easy.

11. Comments on Dyer: 10. Living Oneness

This verse emphasizes that we are part of one integrated whole. Dyer comments, "Let go of your identification with your stuff and with your accomplishments. Try instead to enjoy what you do and all that flows into your life simply for the pleasure of doing and observing the flow itself."

This is definitely my approach to mathematics. It is enjoyable for its own sake. When I experience difficulties, I treat this as a signal that I do not yet understand what I am doing and go back and try again.

11. Comments on Weiner: Getting Started on Survival

This section properly belongs in Session 7 (Week 3a) on Factoring Polynomials. I will insert a copy of this activity there as well. This is a manual activity and an opportunity to use my fountain pen.