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Pre-Algebra Homework

Pre-Algebra Homework. Page 344 #9-25. 7-1. Ratios and Proportions. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 7-1. Ratios and Proportions. 45 120. 14 16. 9 72. 24 64. 1. 3. 2. 4. Pre-Algebra. Warm Up Write each fraction in lowest terms. 7 8. 3 8. 1

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Pre-Algebra Homework

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  1. Pre-Algebra Homework Page 344 #9-25

  2. 7-1 Ratios and Proportions Warm Up Problem of the Day Lesson Presentation Pre-Algebra

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

  4. 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

  5. Today’s Learning Goal Assignment Learn to find equivalent ratios to create proportions.

  6. BrainPOP Videos http://www.brainpop.com/math/ratioproportionandpercent/proportions/ http://www.brainpop.com/math/ratioproportionandpercent/ratios/

  7. Vocabulary ratio equivalent ratio proportion

  8. 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 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.

  9. Reading Math Ratios can be written in several ways. A colon is often used. 90:3 and name the same ratio. 90 3

  10. 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.

  11. 9 27 9 • 2 27 • 2 = = Two ratios equivalent to are and . Two ratios equivalent to are and . 9 27 9 ÷ 9 27 ÷ 9 64 24 9 27 128 48 18 54 1 3 8 3 = = 64 24 64 • 2 24 • 2 = = 64 ÷ 8 24 ÷ 8 64 24 = = Additional Example 1: Finding Equivalent Ratios Find two ratios that are equivalent to each given ratio. Multiply or divide the numerator by the same nonzero number. 18 54 A. 1 3 128 48 B. 8 3

  12. 8 16 8 • 2 16 • 2 = = Two ratios equivalent to are and . Two ratios equivalent to are and . 8 16 8 ÷ 4 16 ÷ 4 32 16 8 16 16 32 64 32 2 4 4 2 = = 32 16 32 • 2 16 • 2 = = 32 ÷ 8 16 ÷ 8 32 16 = = Try This: Example 1 Find two ratios that are equivalent to each given ratio. Multiply or divide the numerator by the same nonzero number. 16 32 A. 2 4 64 32 B. 4 2

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

  14. 1 9 1 9 12 15 3 27 27 36 2 18 Since , the ratios are in proportion. B. A. = and and 2 18 3 27 2 ÷ 2 18 ÷ 2 3 ÷ 3 27 ÷ 3 = = = = 4 5 3 4 Since , the ratios are not in proportion.  12 15 27 36 12 ÷ 3 15 ÷ 3 27 ÷ 9 36 ÷ 9 = = = = Additional Example 2: Determining Whether Two Ratios are in Proportion Simplify to tell whether the ratios form a proportion. 1 9 1 9 4 5 3 4

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

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

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

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

  19. 8 64 16 128 and ; yes, both equal 1 8 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?

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