1 / 17

7-1

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

sal
Download Presentation

7-1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7-1 Ratios and Proportions Course 3 Warm Up Problem of the Day Lesson Presentation

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

  3. 7-1 Ratios and Proportions Course 3 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

  4. 7-1 Ratios and Proportions Course 3 Learn to find equivalent ratios to create proportions.

  5. 7-1 Ratios and Proportions Course 3 Insert Lesson Title Here Vocabulary ratio equivalent ratio proportion

  6. 7-1 Ratios and Proportions 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 Course 3 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.

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

  8. 7-1 Ratios and Proportions Course 3 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.

  9. 7-1 Ratios and Proportions 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 8 3 1 3 = = 64 24 64 • 2 24 • 2 = = 64 ÷ 8 24 ÷ 8 64 24 = = Course 3 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. 18 54 A. 1 3 128 48 B. 8 3

  10. 7-1 Ratios and Proportions 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 64 32 16 32 4 2 2 4 = = 32 16 32 • 2 16 • 2 = = 32 ÷ 8 16 ÷ 8 32 16 = = Course 3 Try This: Example 1 Find two ratios that are equivalent to each given ratio. Multiply or divide the numerator and denominator by the same nonzero number. 16 32 A. 2 4 64 32 B. 4 2

  11. 7-1 Ratios and Proportions Course 3 Ratios that are equivalent are said to be proportional, or in proportion. Equivalent ratios are identical when they are written in simplest form.

  12. 7-1 Ratios and Proportions 1 9 1 9 12 15 3 27 27 36 2 18 Since , the ratios are in proportion. A. B. = and and 2 18 3 27 3 ÷ 3 27 ÷ 3 2 ÷ 2 18 ÷ 2 = = = = 4 5 3 4 Since , the ratios are not in proportion.  27 36 12 15 12 ÷ 3 15 ÷ 3 27 ÷ 9 36 ÷ 9 = = = = Course 3 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

  13. 7-1 Ratios and Proportions 1 5 1 5 3 15 14 49 9 45 16 36 Since , the ratios are in proportion. B. A. = and and 9 45 3 15 9 ÷ 9 45 ÷ 9 3 ÷ 3 15 ÷ 3 = = = = 2 7 4 9 Since , the ratios are not in proportion.  14 49 16 36 16 ÷ 4 36 ÷ 4 14 ÷ 7 49 ÷ 7 = = = = Course 3 Try This: Example 2 Simplify to tell whether the ratios form a proportion. 1 5 1 5 2 7 4 9

  14. 7-1 Ratios and Proportions 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 = = Course 3 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?

  15. 7-1 Ratios and Proportions 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 = = Course 3 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?

  16. 7-1 Ratios and Proportions 8 30 12 45 Possible answer: , Possible answer: , 36 24 8 21 16 10 4 15 1. 2. 3. 4. 16 42 24 63 32 20 28 18 8 5 3 2 14 9 8 5 =  ; yes ; no Course 3 Insert Lesson Title Here 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

  17. 7-1 Ratios and Proportions 8 64 16 128 and ; yes, both equal 1 8 Course 3 Insert Lesson Title Here 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?

More Related