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

Course Ratios and Proportions Warm Up Write each fraction in lowest terms

Course 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

Course Ratios and Proportions Learn to find equivalent ratios to create proportions.

Course Ratios and Proportions Vocabulary ratio equivalent ratio proportion

Course 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. 7:5 28:20

Course Ratios and Proportions Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. Reading Math 7575

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

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

Course 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.

Course Ratios and Proportions Additional Example 2: Determining Whether Two Ratios are in Proportion Simplify to tell whether the ratios form a proportion B. and A. and 2 18 Since, the ratios are in proportion = = 3 ÷ 3 27 ÷ = 1919 = 2 ÷ 2 18 ÷ = 4545 = 12 ÷ 3 15 ÷ = 3434 = 27 ÷ 9 36 ÷ = Since, the ratios are not in proportion  3434

Course Ratios and Proportions Check It Out: Example 2 Simplify to tell whether the ratios form a proportion B. and Since, the ratios are in proportion = = 3 ÷ 3 15 ÷ = 1515 = 9 ÷ 9 45 ÷ = 2727 = 14 ÷ 7 49 ÷ = 4949 = 16 ÷ 4 36 ÷ = Since, the ratios are not in proportion  A. and 9 45

Course 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 ÷ 2 42 ÷ 2 ? = 20 ÷ ÷ = ? = Since, 210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver = 2 21 Divide.

Course Ratios and Proportions Check It Out: 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? ? = 10 ÷ ÷ = ? = Since, 105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver = 2 21 Divide.

Course Ratios and Proportions Lesson Quiz: Part =; yes Find two ratios that are equivalent to each given ratio Simplify to tell whether the ratios form a proportion Possible answer:, Possible answer:, and and  ; no

Course 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? and ; yes, both equal 1818