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

2. 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

3. 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

4. Learn to find equivalent ratios to create proportions.

5. Vocabulary
ratio
equivalent ratio
proportion

6. 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: :20

7. 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

8. 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

9. 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

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