Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Write each fraction in simplest form. Warm Up Write each fraction in simplest form. 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

A proportion is an equation that states that two ratios are equivalent A proportion is an equation that states that two ratios are equivalent. Ratios that are equivalent are said to be proportional. Equivalent ratios are identical when they are written in simplest form.

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

Simplify to tell whether the ratios form a proportion. Check It Out: Example 2 Simplify to tell whether the ratios form a proportion. Since , the ratios are in proportion. 1 5 = 3 15 A. and 9 45 3 15 = = 3 ÷ 3 15 ÷ 3 1 5 9 45 = = 9 ÷ 9 45 ÷ 9 1 5 14 49 = = 14 ÷ 7 49 ÷ 7 2 7 Since , the ratios are not in proportion. 2 7  4 9 14 49 B. and 16 36 16 36 = = 16 ÷ 4 36 ÷ 4 4 9

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? Since , 210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver. 2 21 = 4 42 ? = 20 210 4 ÷ 2 42 ÷ 2 ? = 20 ÷ 10 210 ÷ 10 Divide. 2 21 =

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? Since , 105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver. 2 21 = 2 21 ? = 10 105 ? = 10 ÷ 5 105 ÷ 5 2 21 Divide. 2 21 =

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 15 15

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

Lesson Quiz: Part II 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 64 16 128 and ; yes, both equal 1 8

Lesson Quiz for Student Response Systems 1. Identify the two ratios that are equivalent to the given ratio. A. B. C. D. 18 18

Lesson Quiz for Student Response Systems 2. Simplify to tell whether the ratios form a proportion. A. B. C. D. 19 19

Lesson Quiz for Student Response Systems 3. A bakery has 20 carrot muffins and 60 blueberry muffins. At the end of the day, 15 carrot muffins and 45 blueberry muffins were sold. What ratio of each type of muffin was sold? Are the ratios proportional? A. B. C. D. 20 20