# 12.5: Multiplication and Division of Rational Expressions

Difficulty Level:

**At Grade**Created by: CK-12## Learning Objectives

At the end of this lesson, students will be able to:

- Multiply rational expressions involving monomials.
- Multiply rational expressions involving polynomials.
- Multiply a rational expression by a polynomial.
- Divide rational expressions involving polynomials.
- Divide a rational expression by a polynomial.
- Solve real-world problems involving multiplication and division of rational expressions.

## Vocabulary

NONE

## Teaching Strategies and Tips

Use the ordinary fractions in Example 1 to motivate multiplying and dividing variable rational expressions.

Use Example 2 to point out that an answer can be more readily obtained by reducing common factors *before* multiplying.

- Suggest students to factor all polynomial expressions as much as possible first.

## Error Troubleshooting

In *Review Questions* 9, 12, and 16, remind students to write the expression on the right as a fraction with denominator equal to , and then proceed to multiply or divide.

General Tip: Remind students to rewrite division problems as multiplication problems.

General Tip: In a division problem, some students will invert the first fraction. Remind students to invert the second.

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asymptotes
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CK.MAT.ENG.TE.1.Algebra-I.12
Common Misconceptions
Concept Check and Troubleshooting
constant of proportionality
cross products
denominator
Differentiated Instruction
direct variation
division of polynomials
Enrichment
Inquiry Process
inverse variation
joint variation
least common denominator
least common multiple
monomial
numerator
Pacing
polynomial
polynomials
prime factorization
Problem Sets
Problem Solving
Quizzes
random sampling
rational expressions
rational functions
Science Inquiry
Solution Key
Solutions
stratified sampling
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
Worksheets

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Solutions
Solution Key
Answers
(41 more)
Problem Sets
Tests
Teacher Edition
Quizzes
Assessment
Inquiry Process
Testing
Problem Solving
Concept Check and Troubleshooting
Enrichment
Teaching Strategies
Differentiated Instruction
cross products
direct variation
polynomials
rational expressions
rational functions
denominator
numerator
constant of proportionality
asymptotes
binomial
monomial
biased samples
stratified sampling
random sampling
prime factorization
least common multiple
least common denominator
polynomial
joint variation
division of polynomials
inverse variation
Pacing
Common Misconceptions
Science Inquiry
Teaching Strategies and Tips
Activities
Worksheets
CK.MAT.ENG.TE.1.Algebra-I.12

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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