1. 4-3 Identifying and Writing Proportions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 4-3 Identifying and Writing Proportions Warm Up Find the unit rate. 1. 18 miles in 3 hours 2. 6 apples for $3.30 3. 3 cans for $0.87 4. 5 CD’s for $43 6 mi/h $0.55 per apple $0.29 per can $8.60 per CD

3. 4-3 Identifying and Writing Proportions Problem of the Day Bob made a square table top with 100 white square tiles. He painted the tiles along the edge of the table red. How many tiles are red? 36

4. 4-3 Identifying and Writing Proportions Learn to find equivalent ratios and to identify proportions.

5. 4-3 Identifying and Writing Proportions Vocabulary equivalent ratios proportion

6. 4-3 Identifying and Writing Proportions Students in Mr. Howell’s math class are measuring the width w and the length l of their faces. The ratio of l to w is 6 inches to 4 inches for Jean and 21 centimeters to 14 centimeters for Pat.

7. 4-3 Identifying and Writing Proportions 6464 21 14 These ratios can be written as the fractions and. Since both simplify to, they are equivalent. Equivalent ratios are ratios that name the same comparison. 3232

8. 4-3 Identifying and Writing Proportions An equation stating that two ratios are equivalent is called a proportion. The equation, or proportion, below states that the ratios and are equivalent. 6464 21 14 6464 = 21 14 Read the proportion by saying “six is to four as twenty-one is to fourteen.” Reading Math 6464 = 21 14

9. 4-3 Identifying and Writing Proportions If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

10. 4-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Additional Example 1A: Comparing Ratios in Simplest Forms, 24 51 72 128 72 ÷ 8 128 ÷ 8 = 9 16 24 ÷ 3 51 ÷ 3 = 8 17 Simplify. 24 51 Simplify. 72 128 8 17 Since =, the ratios are not proportional. 9 16

11. 4-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Additional Example 1B: Comparing Ratios in Simplest Forms, 150 105 90 63 90 ÷ 9 63 ÷ 9 = 10 7 150 ÷ 15 105 ÷ 15 = 10 7 Simplify. 150 105 Simplify. 90 63 10 7 Since =, the ratios are proportional. 10 7

12. 4-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Check It Out: Example 1A, 54 63 72 144 72 ÷ 72 144 ÷ 72 = 1 2 54 ÷ 9 63 ÷ 9 = 6767 Simplify. 54 63 Simplify. 72 144 6767 Since =, the ratios are not proportional. 1212

13. 4-3 Identifying and Writing Proportions Determine whether the ratios are proportional. Check It Out: Example 1B, 135 75 9494 9 4 135 ÷ 15 75 ÷ 15 = 9 5 Simplify. 135 75 is already in simplest form. 9 4 9595 Since =, the ratios are not proportional. 9494

14. 4-3 Identifying and Writing Proportions Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice. Additional Example 2: Comparing Ratios Using a Common Denominator Write the ratios of rice to water for 12 servings and for 40 servings. Ratio of rice to water, 12 servings: 3636 Ratio of rice to water, 40 servings: 10 19 3636 = 3 · 19 6 · 19 = 57 114 10 19 = 10 · 6 19 · 6 = 60 114 57 114 60 114 Write the ratio as a fraction. Write the ratio as a fraction Write the ratios with a common denominator, such as 114. Since =, the two ratios are not proportional. 191040 6312 Cups of Water Cups of Rice Servings of Rice

15. 4-3 Identifying and Writing Proportions Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans. Check It Out: Example 2 Write the ratios of beans to water for 8 servings and for 35 servings. Ratio of beans to water, 8 servings: 4343 Ratio of beans to water, 35 servings: 13 9 4343 = 4 · 9 3 · 9 = 36 27 13 9 = 13 · 3 9 · 3 = 39 27 36 27 39 27 Write the ratio as a fraction. Write the ratio as a fraction Write the ratios with a common denominator, such as 27. 91335 348 Cups of WaterCups of BeansServings of Beans Since =, the two ratios are not proportional.

16. 4-3 Identifying and Writing Proportions You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number.

17. 4-3 Identifying and Writing Proportions Additional Example 3: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: A. 3535 3535 = 3 · 2 5 · 2 6 10 = Multiply both the numerator and denominator by any number such as 2. 3535 = 6 10 Write a proportion. B. 28 16 28 16 = 28 ÷ 4 16 ÷ 4 28 16 = 7474 = 7474 Divide both the numerator and denominator by any number such as 4. Write a proportion.

18. 4-3 Identifying and Writing Proportions Check It Out: Example 3 Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. Possible Answers: A. 2323 2323 = 2 · 3 3 · 3 6969 = Multiply both the numerator and denominator by any number such as 3. 2323 = 6969 Write a proportion. B. 16 12 16 12 = 16 ÷ 4 12 ÷ 4 16 12 = 4343 = 4343 Divide both the numerator and denominator by any number such as 4. Write a proportion.

19. 4-3 Identifying and Writing Proportions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 4-3 Identifying and Writing Proportions Lesson Quiz: Part I Determine whether the ratios are proportional. 1. 9 30, 12 40 2. 12 21, 10 15 Find a ratio equivalent to each ratio. Then use the ratios to write a proportion. 3. 3838 4. 3737, ; not proportional 4747 2323 15 40 ; = 3 8 15 40, ; proportional 3 10 3 10 9 21 ; = 3737 9 21

21. 4-3 Identifying and Writing Proportions Lesson Quiz: Part II 5. In preschool, there are 5 children for every one teacher. In another preschool there are 20 children for every 4 teachers. Determine whether the ratios of children to teachers are proportional in both preschools. 5151 = 20 4

22. 4-3 Identifying and Writing Proportions 1. Determine whether the ratios are proportional., A.proportional B. not proportional Lesson Quiz for Student Response Systems 12 20 18 30

23. 4-3 Identifying and Writing Proportions 2. Determine whether the ratios are proportional., A.proportional B. not proportional Lesson Quiz for Student Response Systems 21 56 14 49

24. 4-3 Identifying and Writing Proportions 3. Identify a ratio equivalent to. Then use the ratios to write a proportion. A.; =C. ; = B.; =D. ; = Lesson Quiz for Student Response Systems 10 35 10 45 5 35 5 45 2929 2929 2929 10 35 10 45 2929 2929 5 35 5 45

25. 4-3 Identifying and Writing Proportions 4. Identify a ratio equivalent to. Then use the ratios to write a proportion. A.; =C. ; = B.; =D. ; = Lesson Quiz for Student Response Systems 12 15 12 18 12 20 15 20 4545 4545 4545 12 15 12 18 4545 4545 12 20 15 20

26. 4-3 Identifying and Writing Proportions 5. In one school, there are 12 students for every classroom. In another school, there are 36 students for every 4 classrooms. Determine whether the ratios of students to classrooms are proportional in both schools. A. = ; C. ≠ ; proportional not proportional B. = ; D. ≠ ; proportional not proportional Lesson Quiz for Student Response Systems 12 36 12 1 1313 36 3 12 1 12 4 36 4 36 1