1. Holt CA Course 1 5-4 Solving Proportions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 5-4 Solving Proportions Warm Up Determine whether the ratios are proportional. 1. 5858, 15 24 2. 12 15, 16 25 3. 15 10, 20 16 4. 14 18, 42 54 yes no yes no Evaluate the expression. (16 – 8)  3 + (100  10) A. 2 B. 18 C. 34 D. 104

3. Holt CA Course 1 5-4 Solving Proportions Number Sense (NS1.3) - Use proportions to solve problems (e.g., determine the value of N if = Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Number Sense (NS1.3) - Use proportions to solve problems (e.g., determine the value of N if =, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Also covered: AF2.2, AF2.3 California Standards 47474747 N 21

4. Holt CA Course 1 5-4 Solving Proportions Objective: You will learn how to solve proportions by using cross products.

5. Holt CA Course 1 5-4 Solving Proportions Vocabulary cross product

6. Holt CA Course 1 5-4 Solving Proportions For two ratios, the product of the numerator in one ratio and the denominator in the other is a cross product. If the two ratios form a proportion, then the cross products are equal. 5 · 6 = 30 2 · 15 = 30 = 2525 6 15

7. Holt CA Course 1 5-4 Solving Proportions You can use the cross product rule to solve proportions with variables.

8. Holt CA Course 1 5-4 Solving Proportions Use cross products to solve the proportion. Example 1: Solving Proportions Using Cross Products = m5m5 9 15

9. Holt CA Course 1 5-4 Solving Proportions Check It Out! Example 2 Use cross products to solve the proportion. 6767 = m 14

10. Holt CA Course 1 5-4 Solving Proportions Check It Out! Example 3 Use cross products to solve the proportion. 7 84 = 12 h

11. Holt CA Course 1 5-4 Solving Proportions Check It Out! Example 4 Use cross products to solve the proportion. 5 140 = 12 v

12. Holt CA Course 1 5-4 Solving Proportions Check It Out! Example 5 Use cross products to solve the proportion. 1.2 n = 8 12

13. Holt CA Course 1 5-4 Solving Proportions Check It Out! Example 6 Use cross products to solve the proportion. n 9.3 = 6868

14. Holt CA Course 1 5-4 Solving Proportions Objective: You will learn how to solve proportions in word problems by using cross products.

15. Holt CA Course 1 5-4 Solving Proportions Warm Up Determine whether the ratios are proportional. 1. 5858, 15 24 2. 12 15, 16 25 3. 15 10, 20 16 4. 14 18, 42 54 yes no yes no

16. Holt CA Course 1 5-4 Solving Proportions It is important It is important to set up proportions correctly when working with word problems. Each ratio must compare corresponding quantities in the same order. 16 mi 4 hr = 8 mi x hr 16 mi 8 mi = 4 hr x hr 16 mi 4 hr = 8 hr x mi

17. Holt CA Course 1 5-4 Solving Proportions A piglet can gain 3 pounds in 36 hours. If this rate continues, when will the piglet reach 18 pounds? Example 1: Problem-Solving Application

18. Holt CA Course 1 5-4 Solving Proportions S. Petey drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles? Example 2: Problem-Solving Application

19. Holt CA Course 1 5-4 Solving Proportions The ratio of dogs to cats at a kennel is exactly 4 to 5. If there are 36 dogs at the kennel, how many cats are at the kennel? Example 3: Problem-Solving Application

20. Holt CA Course 1 5-4 Solving Proportions Pho Toeh reduced a print that was 9 inches wide and 15 inches long. If the width of the reduction is 3 inches, what is the length? Example 4: Problem-Solving Application

21. Holt CA Course 1 5-4 Solving Proportions Home Learning On-Line Tutoring

22. Holt CA Course 1 5-4 Solving Proportions Lesson Quiz Use cross products to solve each proportion. 1. 25 20 = 45 t 2. x9x9 = 19 57 3. 2323 = r 36 4. n 10 = 28 8 t = 36x = 3 r = 24 n = 35 5. Carmen bought 3 pounds of bananas for $1.08. June paid $ 1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy? 5 pounds