Algebraic Fractions

6-2Multiplying Fractions

Overview

(a/b)(c/d) = ac/bd. Factor first, then cancel common factors before multiplying.

Key ideas

  • Factor every numerator and denominator.
  • Cancel across the equality sign.
  • Watch domain restrictions.

Worked examples

Example 1

Problem. (2/3)(9/4)

Solution. = 18/12 = 3/2

Example 2

Problem. (x/(x+1)) · ((x+1)/x^2)

Solution. = 1/x

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (3/5)(10/9)

  2. 2.

    ((x+2)/x)·(x/(x+2))

  3. 3.

    (6a/b)(b^2/3)

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Multiply and simplify: [(x² − 4)/(x + 3)] · [(x + 3)/(x − 2)].

  2. 2.

    Multiply and simplify: (3a²b/5c) · (10c²/9ab²).