Ratio and Proportion

7-2Proportions

Overview

A proportion sets two ratios equal: a/b = c/d. Cross-multiply: ad = bc.

Key ideas

  • Cross-multiply only when one ratio equals another.
  • Solve the resulting equation.
  • Check whether your answer keeps the proportion true.

Worked examples

Example 1

Problem. Solve 3/x = 9/15.

Solution. 9x = 45 → x = 5.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solve x/8 = 3/4.

  2. 2.

    Solve 5/x = 10/14.

  3. 3.

    Solve 2/3 = (x − 1)/9.

Challenge problems

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

  1. 1.

    Solve: (x + 2)/5 = (x − 1)/3.

  2. 2.

    If 3/a = 5/b and a + b = 24, find a and b.