1. Course 3 5-1 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

2. Course 3 5-1 Ratios and Proportions Warm Up Write each fraction in lowest terms. 14 16 1. 9 72 3. 24 64 2. 45 120 4. 7878 3838 1818 3838

3. Course 3 5-1 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

4. Course 3 5-1 Ratios and Proportions Learn to find equivalent ratios to create proportions.

5. Course 3 5-1 Ratios and Proportions Vocabulary ratio equivalent ratio proportion

6. Course 3 5-1 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. 7:5 28:20

7. Course 3 5-1 Ratios and Proportions Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio. Reading Math 7575

8. Course 3 5-1 Ratios and Proportions Additional Example 1: Finding Equivalent Ratios Find two ratios that are equivalent to each given ratio. B. 18 54 1313 128 48 8383 A. = 9 27 = 9 2 27 2 = 9 ÷ 9 27 ÷ 9 9 27 = Two ratios equivalent to are and. 9 27 18 54 1313 Two ratios equivalent to are and. 64 24 128 48 8383 = 64 2 24 2 = 64 ÷ 8 24 ÷ 8 64 24 = 64 24 = Multiply or divide the numerator and denominator by the same nonzero number.

9. Course 3 5-1 Ratios and Proportions Check It Out: Example 1 Find two ratios that are equivalent to each given ratio. B. 16 32 2424 64 32 4242 A. = 8 16 = 8 2 16 2 = 8 ÷ 4 16 ÷ 4 8 16 = Two ratios equivalent to are and. 8 16 32 2424 Two ratios equivalent to are and. 32 16 64 32 4242 = 32 2 16 2 = 32 ÷ 8 16 ÷ 8 32 16 = 32 16 = Multiply or divide the numerator and denominator by the same nonzero number.

10. Course 3 5-1 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.

11. Course 3 5-1 Ratios and Proportions Additional Example 2: Determining Whether Two Ratios are in Proportion Simplify to tell whether the ratios form a proportion. 12 15 B. and 27 36 3 27 A. and 2 18 Since, the ratios are in proportion. 1919 = 1919 1919 = 3 ÷ 3 27 ÷ 3 3 27 = 1919 = 2 ÷ 2 18 ÷ 2 2 18 = 4545 = 12 ÷ 3 15 ÷ 3 12 15 = 3434 = 27 ÷ 9 36 ÷ 9 27 36 = Since, the ratios are not in proportion. 4545  3434

12. Course 3 5-1 Ratios and Proportions Check It Out: Example 2 Simplify to tell whether the ratios form a proportion. 14 49 B. and 16 36 Since, the ratios are in proportion. 1515 = 1515 1515 = 3 ÷ 3 15 ÷ 3 3 15 = 1515 = 9 ÷ 9 45 ÷ 9 9 45 = 2727 = 14 ÷ 7 49 ÷ 7 14 49 = 4949 = 16 ÷ 4 36 ÷ 4 16 36 = Since, the ratios are not in proportion. 2727  4949 3 15 A. and 9 45

13. Course 3 5-1 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 ÷ 2 42 ÷ 2 ? = 20 ÷ 10 210 ÷ 10 2 21 = 2 21 4 42 ? = 20 210 Since, 210 cubic feet of water would have the same mass at 4°C as 20 cubic feet of silver. 2 21 = 2 21 Divide.

14. Course 3 5-1 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 ÷ 5 105 ÷ 5 2 21 2 21 = 2 21 2 21 ? = 10 105 Since, 105 cubic feet of water would have the same mass at 4°C as 10 cubic feet of silver. 2 21 = 2 21 Divide.

15. Course 3 5-1 Ratios and Proportions Lesson Quiz: Part 1 8585 8585 =; yes Find two ratios that are equivalent to each given ratio. 4 15 1. 8 21 2. 16 10 3. 36 24 4. Simplify to tell whether the ratios form a proportion. 8 30 12 45 Possible answer:, 16 42 24 63 Possible answer:, and 32 20 and 28 18 3232 14 9  ; no

16. Course 3 5-1 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 64 16 128 and ; yes, both equal 1818