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# Multiplying and Dividing Rational Expressions

Lesson 8 of 15

## Objective: Students will be to multiply and divide rational expressions.

*50 minutes*

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Multiplying and Dividing Rational Expressions which asks students to determine whether a rational expression as been properly simplified.

I also use this time to correct and record the previous day's Homework.

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This lesson begins with an area application of multiplying and dividing rational expressions (**Math Practice 4**).

*Advertisements can be purchased in the year book. You want to buy one where your image has one side that is three inches longer than the other.*

The students begin by finding the area of this advertisement. I then tell them that this advertisement turned out to be much too expensive so the image is going to be shrunk to where each side is half the original. I will give this problem to the students and then walk around and pick students to put their solutions on the board. This can be found both visually and algebraically.

Finally, I ask them if the costs of the advertisements are based on the area, what portion of the original cost will the new advertisement be? I also ask them to prove it algebraically (**Math Practice 2**). This is the key to the task as it provides them their first experience dividing rational expressions.

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The remainder of this lesson is a **Guided Practice** on multiplying and dividing Rational Expressions. Students can use their graphing calculator to graphically simplify in any way that works for them if they choose and I will ask students to share these. Please see the PowerPoint for specifics.

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to divide two rational expressions.

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This short assignment begins with several practice problems to reaffirm the students' skills. The final problem asks them to find the mistake in a simplified expression and explain how to fix it (**Math Practice 3**). This error is the most common error that I have seen when dealing with rational expressions.

This assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Quotients of Monomials
- LESSON 2: Modeling Rational Functions
- LESSON 3: Transformations of Rational Functions
- LESSON 4: Properties of Rational Functions Investigation Day 1 of 2
- LESSON 5: Properties of Rational Functions Investigation Day 2 of 2
- LESSON 6: Rational Functions Quiz
- LESSON 7: Modeling and Simplifying Rational Expressions
- LESSON 8: Multiplying and Dividing Rational Expressions
- LESSON 9: Adding and Subtraction Rational Expressions
- LESSON 10: Complex Rational Expressions
- LESSON 11: Equations with Rational Coefficients
- LESSON 12: Rational Equations
- LESSON 13: Rational Functions Review Day 1
- LESSON 14: Rational Function Review Day 2
- LESSON 15: Rational Functions Test