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.
Solve x/8 = 3/4.
- 2.
Solve 5/x = 10/14.
- 3.
Solve 2/3 = (x − 1)/9.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: (x + 2)/5 = (x − 1)/3.
- 2.
If 3/a = 5/b and a + b = 24, find a and b.