### Unit 5: Rational Expressions

In this unit, you will learn how to evaluate rational expressions and perform operations such as addition, multiplication, and division involving rational expressions. You will apply the concept of multiplying rational expressions to dimensional analysis, where you will convert units from single/dual unit of measurement to another.

**Completing this unit should take you approximately 17 hours.**

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

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

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.

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

### 5.1.2: Reduce Fractions

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.

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

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.

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

### 5.1.4: Reduce Polynomials

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.

Watch these videos, which discuss how to reduce polynomials.

### 5.1.5: Homework Assessment

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

### 5.2: Multiply & Divide Rational Expressions

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

### 5.2.1: Multiply & Divide Fractions

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.

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

### 5.2.2: Multiply & Divide Monomials

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.

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

### 5.2.3: Multiply & Divide Polynomials

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.

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.

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.

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

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

### 5.3: Least Common Denominator (LCD)

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

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.

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

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.

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

### 5.3.3: Polynomials

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.

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

### 5.3.4: Homework Assessment

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

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

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.

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

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

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.

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

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.

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

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

### 5.5: Dimensional Analysis

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

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.

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

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.

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

### 5.5.3: Homework Assessment

Answer all of the problems.

### Unit 5 Practice Test

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

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.

- This assessment