AlgebraStructure & Method · Book 1All Chapters

Algebraic Fractions

6-3Dividing Fractions

Overview

To divide, multiply by the reciprocal of the divisor.

Key ideas

  • (a/b) ÷ (c/d) = (a/b)·(d/c).
  • Then simplify by cancelling.
  • c, d ≠ 0.

Worked examples

Example 1

Problem. (3/4) ÷ (9/8)

Solution. (3/4)·(8/9) = 24/36 = 2/3

Example 2

Problem. (x/2) ÷ (x^2/6)

Solution. (x/2)·(6/x^2) = 3/x

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (5/6) ÷ (10/3)

  2. 2.

    ((x+1)/x) ÷ ((x+1)/x^2)

  3. 3.

    (6a/5) ÷ (3a/10)

Challenge problems

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

  1. 1.

    Divide and simplify: [(x² − 9)/(x + 2)] ÷ [(x − 3)/(x² − 4)].

  2. 2.

    Divide and simplify: (4a²/b) ÷ (8a/b²).