Ratios and Proportions 5-1 Ratios and Proportions Course 3 Warm Up Problem of the Day Lesson Presentation

Write each fraction in lowest terms. Warm Up Write each fraction in lowest terms. 14 16 1. 7 8 24 64 2. 3 8 9 72 3. 1 8 45 120 4. 3 8

Problem of the Day A magazine has page numbers from 1 to 80. What fraction of those page numbers include the digit 5? 17 80

Learn to find equivalent ratios to create proportions.

Vocabulary ratio equivalent ratio proportion

A ratio is a comparison of two quantities by division A ratio is a comparison of two quantities by division. In one rectangle, the ratio of shaded squares to unshaded squares is 7:5. In the other rectangle, the ratio is 28:20. Both rectangles have equivalent shaded areas. Ratios that make the same comparison are equivalent ratios. 7:5 28:20

Ratios can be written in several ways Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. Reading Math 7 5

Additional Example 1: Finding Equivalent Ratios Find two ratios that are equivalent to each given ratio. Multiply or divide the numerator and denominator by the same nonzero number. = 9 27 = 9 • 2 27 • 2 18 54 A. 9 27 = = 9 ÷ 9 27 ÷ 9 1 3 Two ratios equivalent to are and . 9 27 18 54 1 3 = 64 • 2 24 • 2 64 24 = 128 48 Two ratios equivalent to are and . 64 24 128 48 8 3 B. 64 24 = = 64 ÷ 8 24 ÷ 8 8 3

Check It Out: Example 1 Find two ratios that are equivalent to each given ratio. Multiply or divide the numerator and denominator by the same nonzero number. = 8 16 = 8 • 2 16 • 2 16 32 A. 8 16 = = 8 ÷ 4 16 ÷ 4 2 4 Two ratios equivalent to are and . 8 16 32 2 4 32 16 = = 32 • 2 16 • 2 64 32 Two ratios equivalent to are and . 32 16 64 4 2 B. 32 16 = = 32 ÷ 8 16 ÷ 8 4 2

Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.