1. Pre-Algebra 7-1 Ratios and Proportions Warm Up Write each fraction in lowest terms. Pre-Algebra 7-1 Ratios and Proportions 14 16 1. 9 72 3. 24 64 2. 45 120 4. 7878 3838 1818 3838

2. Pre-Algebra 7-1 Ratios and Proportions Learn to find equivalent ratios to create proportions.

3. Pre-Algebra 7-1 Ratios and Proportions Vocabulary ratio equivalent ratio proportion

4. Pre-Algebra 7-1 Ratios and Proportions Ratios can be written in several ways. A colon is often used. 90:3 and name the same ratio. Reading Math 90 3

5. Pre-Algebra 7-1 Ratios and Proportions 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.

6. Pre-Algebra 7-1 Ratios and Proportions Example 1: Finding Equivalent Ratios Find two ratios that are equivalent to each given ratio. B. 18 54 1313 128 48 8383 A. = 9 27 = 9 2 27 2 = 9 ÷ 9 27 ÷ 9 9 27 = Two ratios equivalent to are and. 9 27 18 54 1313 Two ratios equivalent to are and. 64 24 128 48 8383 = 64 2 24 2 = 64 ÷ 8 24 ÷ 8 64 24 = 64 24 = Multiply or divide the numerator and denominator by the same nonzero number.

7. Pre-Algebra 7-1 Ratios and Proportions Example 2 Find two ratios that are equivalent to each given ratio. B. 16 32 1212 64 32 2121 A. = 8 16 = 8 2 16 2 = 8 ÷ 8 16 ÷ 8 8 16 = Two ratios equivalent to are and. 8 16 32 1212 Two ratios equivalent to are and. 32 16 64 32 2121 = 32 2 16 2 = 32 ÷ 16 16 ÷ 16 32 16 = 32 16 = Multiply or divide the numerator and denominator by the same nonzero number.

8. Pre-Algebra 7-1 Ratios and Proportions Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

9. Pre-Algebra 7-1 Ratios and Proportions Example 3: Determining Whether Two Ratios are in Proportion Simplify to tell whether the ratios form a proportion. 12 15 B. and 27 36 3 27 A. and 2 18

10. Pre-Algebra 7-1 Ratios and Proportions Example 4 Simplify to tell whether the ratios form a proportion. 14 49 B. and 16 36 3 15 A. and 9 45

11. Pre-Algebra 7-1 Ratios and Proportions Lesson Review Find two ratios that are equivalent to each given ratio. 8 30 1. 16 42 2. 16 10 3. 36 24 4. Simplify to tell whether the ratios form a proportion. 16 60 4 15 Possible answer:, 8 21 32 84 Possible answer:, and 32 20 and 28 18