7 1 Ratios and Proportions PreAlgebra Homework Page

7 -1 Ratios and Proportions Pre-Algebra Homework Page 344 #9 -25 Pre-Algebra

7 -1 Ratiosand and. Proportions Warm Up Problem of the Day Lesson Presentation Pre-Algebra

7 -1 Ratios and Proportions Warm Up Write each fraction in lowest terms. 1. 14 16 7 8 2. 24 64 3 8 3. 9 72 1 8 4. 45 120 3 8 Pre-Algebra

7 -1 Ratios and Proportions 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 Pre-Algebra

7 -1 Ratios and Proportions Today’s Learning Goal Assignment Learn to find equivalent ratios to create proportions. Pre-Algebra

7 -1 Ratios and Proportions Brain. POP Videos http: //www. brainpop. com/math/ratioproportionandperce nt/proportions/ http: //www. brainpop. com/math/ratioproportionandperce nt/ratios/ Pre-Algebra

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

7 -1 Ratios and Proportions Relative density is the ratio of the density of a substance to the density of water at 4°C. The relative density of silver is 10. 5. This means that silver is 10. 5 times as heavy as an equal volume of water. The comparisons of water to silver in the table are ratios that are all equivalent. Comparisons of Mass of Equal Volumes of Water and Silver Water 1 g 2 g 3 g 4 g Silver 10. 5 g 21 g 31. 5 g 42 g Pre-Algebra

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

7 -1 Ratios and Proportions Additional Example 1: Finding Equivalent Ratios Find two ratios that are equivalent to each given ratio. Multiply or divide the 9 9 • 2 18 numerator by the same = A. = 27 27 • 2 54 nonzero number. 9 9÷ 9 1 Two ratios equivalent = = 27 27 ÷ 9 3 to 9 are 18 and 1. 27 54 3 64 • 2 64 128 = = B. 24 24 • 2 48 8 64 = 64 ÷ 8 = 24 ÷ 8 3 24 Pre-Algebra Two ratios equivalent to 64 are 128 and 8. 24 48 3

7 -1 Ratios and Proportions Try This: Example 1 Find two ratios that are equivalent to each given ratio. Multiply or divide the 8 8 • 2 16 numerator by the same = A. = 16 16 • 2 32 nonzero number. 8 8÷ 4 2 Two ratios equivalent = = 16 16 ÷ 4 4 to 8 are 16 and 2. 16 32 4 32 B. 16 = 32 = 16 Pre-Algebra 32 • 2 = 64 16 • 2 32 32 ÷ 8 4 = 16 ÷ 8 2 Two ratios equivalent to 32 are 64 and 4. 16 32 2

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. Pre-Algebra

7 -1 Ratios and Proportions Additional Example 2: Determining Whether Two Ratios are in Proportion Simplify to tell whether the ratios form a proportion. A. 3 and 2 27 18 3 3÷ 3 1 = = 27 27 ÷ 3 9 2 2÷ 2 1 = = 18 18 ÷ 2 9 B. 12 and 27 12 = 12 ÷ 3 = 4 15 36 15 15 ÷ 3 5 27 27 ÷ 9 3 = 36 36 ÷ 9 = 4 Pre-Algebra 1 1 Since = , 9 9 the ratios are in proportion. Since 4 3 , 5 4 the ratios are not in proportion.

7 -1 Ratios and Proportions Try This: Example 2 Simplify to tell whether the ratios form a proportion. A. 3 and 9 15 45 3 3÷ 3 = = 15 15 ÷ 3 9 9÷ 9 = = 45 45 ÷ 9 B. 14 and 16 49 36 14 14 ÷ 7 2 = 49 49 ÷ 7 = 7 1 5 16 16 ÷ 4 4 = 36 36 ÷ 4 = 9 Pre-Algebra 1 1 Since = , 5 5 the ratios are in proportion. Since 2 4 , 7 9 the ratios are not in proportion.

7 -1 Ratios and Proportions Additional Example 3: Earth Science Application At 4°C, four cubic feet of silver has the same mass as 42 cubic feet of water. At 4°C, would 210 cubic feet of water have the same mass as 20 cubic feet of silver? 4 ? 20 = 42 210 4 ÷ 2 ? 20 ÷ 10 = 42 ÷ 2 210 ÷ 10 2 2 = 21 21 Pre-Algebra Since 2 = 2 , 21 21 210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver.

7 -1 Ratios and Proportions Try This: Example 3 At 4°C, two cubic feet of silver has the same mass as 21 cubic feet of water. At 4°C, would 105 cubic feet of water have the same mass as 10 cubic feet of silver? 2 ? 10 = 21 105 ? 10 ÷ 5 2 = 105 ÷ 5 21 2 2 = 21 21 Pre-Algebra Since 2 = 2 , 21 21 105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver.

7 -1 Ratios and Proportions Lesson Quiz: Part 1 Find two ratios that are equivalent to each given ratio. 1. 4 15 Possible answer: 8 , 12 30 45 2. 8 Possible answer: 16 , 24 42 63 21 Simplify to tell whether the ratios form a proportion. 3. 16 and 32 8 = 8; yes 20 5 5 10 4. 36 and 28 18 24 Pre-Algebra 3 14 ; no 2 9

7 -1 Ratios and Proportions Lesson Quiz: Part 2 5. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. What ratio of juice is missing from each bottle? Are the ratios proportional? 8 and 16 ; yes, both equal 1 8 64 128 Pre-Algebra