1. Section Concepts 1.5 Homework questions? Slide 1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. Section Concepts 1.5 Applications of Rational Equations and Proportions Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Solving Proportions 2.Applications of Proportions

3. DEFINITIONProportion Slide 3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

4. Section Concepts 1.5 Solving Proportions Slide 4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 – Cross multiply Step 2 – Set the cross products equal to each other Step 3 – Solve the equation Step 4 – Check your solution

5. Example 1Solving a Proportion Slide 5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

6. Example 2Solving a Proportion Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the proportion.

7. Example 3Solving a Proportion Slide 7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the proportion.

8. Example 4Solving a Proportion Slide 8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the proportion.

9. Example 5Solving a Proportion Slide 9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the proportion.

10. Example 6Solving a Proportion Slide 10 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solve the proportion for V f.

11. Section Concepts 1.5 Solving Proportion Applications Slide 11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Step 1 – Read the problem Step 2 – Set up a proportion Step 3 – Make sure the units of measure are in the same order on each side Step 4 – Solve the proportion Step 5 – Check your solution

12. Example 7Using a Proportion in an Application Slide 12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For a recent year, the population of Alabama was approximately 4.2 million. At that time, Alabama had seven representatives in the U.S. House of Representatives. In the same year, North Carolina had a population of approximately 7.2 million. If representation in the House is based on population in equal proportions for each state, how many representatives did North Carolina have?

13. Example Solution: 7Using a Proportion in an Application (continued) Slide 13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14. Example 8Using a Proportion in an Application Slide 14 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A university has a ratio of students to faculty of 105 to 2. If the student population at the university is 15,750, how many faculty members are needed?

15. Example 9Using a Proportion in an Application Slide 15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Cooking oatmeal requires 1 cup of water for every ½ cup of oats. How many cups of water will be required for ¾ cup of oats?

16. Example 10You Try Slide 16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. b.A certain fertilizer is applied at a rate of 6 pounds per 150 square feet. How many square feet can be fertilized with 20 pounds of fertilizer? c.In Minneapolis, there were 30 homeless persons visible for every 1050 homeless in shelters. If the number of homeless visible on the street grew to 75, how many would you expect to find in shelters?

17. Example 10You Try Slide 17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a.

18. Example 10You Try Slide 18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. b.A certain fertilizer is applied at a rate of 6 pounds per 150 square feet. How many square feet can be fertilized with 20 pounds of fertilizer?

19. Example 10You Try Slide 19 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. c. In Minneapolis, there were 30 homeless persons visible for every 1050 homeless in shelters. If the number of homeless visible on the street grew to 75, how many would you expect to find in shelters?

20. Example 11You Try Two More! – Set these up. Slide 20 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a.Biologists catch, tag, and release 125 trout in a pond. Later, 200 trout are caught and checked for tags. Forty of these trout are found to have tags. Write a proportion to estimate the total trout population in the pond. b.A health department estimates that 8 vials of a malaria serum will treat 100 people. At this rate, how many vials are needed to treat 175 people? Write a proportion.

21. Section Concepts 1.5 Applications of Rational Equations and Proportions Slide 21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Solving Proportions 2.Applications of Proportions