# Multiplying and Dividing Rational Expressions

### Multiplying and Dividing Rational Expressions

Student Outcomes

• Students multiply and divide rational expressions and simplify using equivalent expressions.

### New York State Common Core Math Algebra II, Module 1, Lesson 24

Worksheets for Algebra II, Module 1, Lesson 24

Classwork

If 𝑎, 𝑏, 𝑐, and 𝑑 are rational expressions with 𝑏 ≠ 0, 𝑑 ≠ 0, then

a/b ∙ c/d = ac/bd

Exercises

Example 1

Make a conjecture about the product 𝑥3/4𝑦 ∙ 𝑦2/𝑥. What will it be? Explain your conjecture, and give evidence that it is correct.

Example 2

Find the following product:

Exercises 1–3

1. Summarize what you have learned so far with your neighbor.
2. Find the following product and reduce to lowest terms
3. Find the following product and reduce to lowest terms

Example 3

Find the quotient and reduce to lowest terms:

Exercises 4–5

1. Find the quotient and reduce to lowest terms:
2. Simplify the rational expression.

Lesson Summary

In this lesson, we extended multiplication and division of rational numbers to multiplication and division of rational expressions.

• To multiply two rational expressions, multiply the numerators together and multiply the denominators together, and then reduce to lowest terms.
• To divide one rational expression by another, multiply the first by the multiplicative inverse of the second, and reduce to lowest terms.
• To simplify a complex fraction, apply the process for dividing one rational expression by another.

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