AlgebraStructure & Method · Book 1All Chapters

Ratio and Proportion

7-1Ratios

Overview

A ratio compares two quantities by division. Written a:b, a/b, or ‘a to b.’

Key ideas

  • Simplify like any fraction.
  • Units must match before comparing.
  • A rate is a ratio of two different units (mph).

Worked examples

Example 1

Problem. Express 12:18 in simplest form.

Solution. 2:3

Example 2

Problem. 240 mi in 4 h. Rate?

Solution. 60 mph

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Simplify 15:25.

  2. 2.

    $48 for 6 books → unit rate.

  3. 3.

    Simplify 14 to 49.

Challenge problems

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

  1. 1.

    The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?

  2. 2.

    A map scale is 1:25000. If two towns are 8 cm apart on the map, what is the actual distance?