MA001: College Algebra

Unit 5: Rational Expressions

• Upon successful completion of this unit, you will be able to:

  • evaluate rational expressions;
  • reduce rational expressions;
  • multiply rational expressions (with and without factoring);
  • divide rational expressions (with and without factoring);
  • find least common denominators;
  • add and subtract rational expressions (with and without common denominators); and
  • convert units using dimensional analysis (with one and two units).

• 5.1: Reduce Rational Expressions

  • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.1 Rational Expressions - Reduce Rational Expressions" URL

    Read this section. Rational expressions are just fractions and fractions of polynomials. Focus on the use of the rules of exponentiation and when we can cancel in fractions.
    

  • 5.1.1: Evaluate

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Evaluate" URL

      Complete page 94 of Wallace's workbook for practice with reducing rational expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Reduce - Evaluate" Page

      Watch this four-minute video. Pay attention to the examples being used to explain evaluate rational expressions.

  • 5.1.2: Reduce Fractions

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Reduce Fractions" URL

      Complete page 95 of Wallace's workbook for practice with reducing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Reduce - Reduce Fractions" Page

      Watch this two-minute video. Pay attention to the examples being used to explain the concept of reducing fractions in rational expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

  • 5.1.3: Reduce Monomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Monomials" URL

      Complete page 96 of Wallace's workbook for practice with reducing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Reduce - Monomials" Page

      Watch these videos. Pay attention to the examples used to explain the concepts in this unit.
      

  • 5.1.4: Reduce Polynomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Polynomials" URL

      Complete page 97 of Wallace's workbook for practice with reducing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Reduce - Polynomials" and MathIsPower4U's "Simplify Rational Expressions" Page

      Watch these videos, which discuss how to reduce polynomials.

  • 5.1.5: Homework Assessment

    • Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Reduce Rational Expressions" URL

      Answer all of the odd-numbered problems for questions 1 through 49.
      

• 5.2: Multiply & Divide Rational Expressions

  • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.2: Rational Expression - Multiply & Divide" URL

    Read this section. Again, rules for exponents are paramount, but now focus on dividing as "inverting and multiplying."
    

  • 5.2.1: Multiply & Divide Fractions

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Fractions" URL

      Complete page 98 of Wallace's workbook for practice with multiplying and dividing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Multiply and Divide - Fractions" and MathIsPower4U's "Multiplication Involving Fractions" Page

      Watch these videos, which show how to multiply and divide fractions.

  • 5.2.2: Multiply & Divide Monomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Monomials" URL

      Complete page 99 of Wallace's workbook for practice with multiplying and dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

    • Tyler Wallace's "Multiply and Divide - Monomials" and MathIsPower4U's "Multiply Rational Expressions - Monomials" and "Dividing Rational Expressions - Monomials" Page

      Watch these videos, which discuss the multiplication and division of monomials.
      

  • 5.2.3: Multiply & Divide Polynomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Polynomials" URL

      Complete page 100 of Wallace's workbook for practice with multiplying and dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Both at Once" URL

      Complete page 101 of Wallace's workbook for practice with multiplying and dividing polynomials both at once. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "Multiplying and Dividing Polynomials" Page

      Watch these videos, which discuss the multiplication and division of polynomials. Remember that you may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

    • MathIsPower4U's "Multiplying and Dividing Rational Expressions" Page

      Watch these videos if you feel like you need additional help with this topic. These videos demonstrate how to solve variations on this kind of problem. 
      

  • 5.2.4: Homework Assessment

    • Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Multiply and Divide" URL

      Answer all of the odd-numbered problems for questions 1 through 43.
      

• 5.3: Least Common Denominator (LCD)

  • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.3: Rational Expressions - Least Common Denominators" URL

    Read this section. One of the skills students have most difficulty with is adding fractions. You can make this much easier by understanding least common denominators.
    

  • 5.3.1: Numbers

    • Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Numbers" URL

      Complete page 102 of Wallace's workbook for practice with the Lowest Common Denominator (LCD). Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "LCD - Numbers" and MathIsPower4U's "Determining the Least Common Multiple Using a List of Multiples" and "Determining the Least Common Multiple Using Prime Factorization" Page

      Watch these videos, which discuss the Least Common Denominator (LCD). You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.
      

  • 5.3.2: Monomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Monomials" URL

      Complete page 103 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "LCD - Monomials" and Bigbend Emporium's "Least Common Multiple (LCM) with Variables" Page

      Watch these videos, which discuss the Least Common Denominator with monomials.

  • 5.3.3: Polynomials

    • Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Polynomials" URL

      Complete page 104 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "LCD - Polynomials" Page

      Watch this five-minute video, which discusses the Least Common Denominator with polynomials.
      

  • 5.3.4: Homework Assessment

    • Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Least Common Denominator" URL

      Answer questions 11-20. If necessary, use the videos and information in this subunit to help you solve these problems.
      

• 5.4: Add & Subtract Rational Expressions

  • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.4: Rational Expressions - Add & Subtract" URL

    Read this section and complete the corresponding workbook assignment for this subunit. Notice that most of the work involves finding a common denominator; once that is done, we simply need to be careful with multiplication.
    

  • 5.4.1: Add & Subtract Fractions

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Fractions" URL

      Complete page 105 of Wallace's workbook for practice with adding and subtracting fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "Add and Subtract - Common Denominator" Page

      Watch this five-minute video. Pay attention to the examples being used to explain how to add and subtract fractions.
      

  • 5.4.2: Add & Subtract Rational Expressions with Different Denominators

    • 5.4.2.1: Different Denominator - Part 1

      • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.5: Add and Subtract Rational Expressions: Different Denominator (Part 1)" URL

        Read this section and complete the corresponding workbook assignment for the subunit.
        

      • Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Common Denominator" URL

        Complete page 106 of Wallace's workbook for practice with adding and subtracting common denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
        

      • Tyler Wallace's "Add and Subtract - Different Denominators Part 1" Page

        Watch this five-minute video. Pay attention to the examples used to explain adding and subtracting when there are different denominators. Here, one would first obtain a common denominator for the expressions involved and then proceed as in subunit 5.4.2.1 above.
        

    • 5.4.2.2: Different Denominator - Part 2

      • Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Different Denominators" URL

        Complete page 107 of Wallace's workbook for practice with adding and subtracting different denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
        

      • Tyler Wallace's "Add and Subtract - Different Denominators Part 2" Page

        Watch this five-minute video which discusses adding and subtracting when there are different denominators. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
        

  • 5.4.3: Homework Assessment

    • Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Add and Subtract" URL

      Answer the odd-numbered problems for questions 1 through 43.
      

• 5.5: Dimensional Analysis

  • Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.8: Rational Expressions - Dimensional Analysis" URL

    Read this section and complete the corresponding workbook assignment for this subunit. Notice how converting from minutes to hours or feet to miles or cups to gallons all have the same foolproof method: canceling units of measurement.
    

  • 5.5.1: Convert Single Unit

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Dimensional Analysis - Convert Single Unit" URL

      Complete page 108 of Wallace's workbook for practice with dimensional analysis in which you convert single units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "Dimensional Analysis - Convert Single Unit" Page

      Watch this five-minute video which discusses converting single units. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.
      

  • 5.5.2: Convert Dual Unit

    • Tyler Wallace's "Beginning Algebra Lab Notebook: Dimensional Analysis - Convert Two Units" URL

      Complete page 109 of Wallace's workbook for practice with dimensional analysis with converting dual units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.
      

    • Tyler Wallace's "Dimensional Analysis - Convert Two Units" Page

      Watch this five-minute video, which discusses converting dual units.
      

  • 5.5.3: Homework Assessment

    • Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Dimensional Analysis" URL

      Answer all of the problems.
      

• Unit 5 Practice Test

  • Tyler Wallace's "Beginning and Intermediate Algebra: Unit 5 Practice Test" URL

    Review Unit 5 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 5 Practice Test - Answer Key".
    

• Unit 5 Assessment

  • Unit 5 Assessment Quiz

    Take this assessment to see how well you understood this unit.

    • This assessment does not count towards your grade. It is just for practice!
    • You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
    • You can take this assessment as many times as you want, whenever you want.