1. 6.2 Students will use proportions to solve percentage problems. Warm Up Rewrite each value as indicated. 1. as a percent 2. 58% as a fraction 3. as a decimal and a percent 4. What percent is 4 out of 5? 5. What percent is 10 out of 25? 24% 0.8 and 80% 80% 40% 12 50 4 5 29 50

2. 6.2 Students will use proportions to solve percentage problems. Students will use proportions to solve percentage problems when the part is missing. Why? -Sales -Tax

3. 6.2 Students will use proportions to solve percentage problems. Where do you like to shop?

4. 6.2 Students will use proportions to solve percentage problems. The Percent Proportion = number 100 part whole

5. 6.2 Students will use proportions to solve percentage problems. What is 5 percent of 200? 85% of 80 is what number? 10 68

6. 6.2 Students will use proportions to solve percentage problems. What is 37% of 828?

7. 6.2 Students will use proportions to solve percentage problems. Finding the Percent of a Number The city of Dallas, Texas has a population of approximately 1,189,000 people. The population of the city of Austin, Texas is 55% of the population of Dallas. To the nearest thousand, what is the population of Austin? Set up a proportion. = 55 100 p 1,189,000 Set up a proportion. 55  1,189,000 = 100  p Find the cross products.

8. 6.2 Students will use proportions to solve percentage problems. Additional Example 3A Continued Austin has a population of approximately 654,000 people. 65,395,000 = 100p Simplify. = 65,395,000 100 100p 100 Divide both sides by 100. 653,950 = pSimplify. 654,000 ≈ pRound to the nearest whole number. 55  1,189,000 = 100  p Find the cross products.

9. 6.2 Students will use proportions to solve percentage problems. When solving a problem when the percent is greater than 100, the number you are looking for will be greater than the number given. Helpful Hint

10. 6.2 Students will use proportions to solve percentage problems. Finding the Percent of a Number After a drought, a reservoir had only 66 % of the average amount of water. If the average amount of water is 57,000,000 gallons, how much water was in the reservoir after the drought? 2 3 Choose a method: Set up an equation. Think: What number is 66 % of 57,000,000? 2 3 w = 66 %  57,000,000 Set up an equation. 2 3 w =  57,000,000 66 % is equivalent to. 2 3 2 3 2 3

11. 6.2 Students will use proportions to solve percentage problems. Additional Example 3B Continued The reservoir contained 38,000,000 gallons of water after the drought. w = = 38,000,000 114,000,000 3 Simplify.

12. 6.2 Students will use proportions to solve percentage problems. Check It Out! Example 3A After a drought, a river had only 50 % of the average amount of water flow. If the average amount of water flow is 60,000,000 gallons per day, how much water was flowing in the river after the drought? 2 3 Choose a method: Set up an equation. Think: What number is 50 % of 60,000,000? 2 3 w = 50 %  60,000,000 Set up an equation. 2 3 w = 0.506  60,000,000 50 % is equivalent to 0.506. 2 3 w  30,400,000 Simplify. The water flow in the river was about 30,400,000 gallons per day after the drought.

13. 6.2 Students will use proportions to solve percentage problems. Check It Out! Example 3B Ms. Marvin has a savings account with approximately $214,000 in it. Mr. Parson has 35% of the amount of Ms. Marvin’s savings account. To the nearest thousand, what is the amount of Mr. Parson’s savings account? Choose a method: Set up a proportion. = 35 100 s 214,000 Set up a proportion. 35  214,000 = 100  s Find the cross products. Think: 35 is to 100 as what amount is to $214,000.

14. 6.2 Students will use proportions to solve percentage problems. Check It Out! Example 3B Continued Mr. Parson has approximately $75,000 in his savings account. 7,490,000 = 100s Simplify. = 7,490,000 100 100s 100 Divide both sides by 100. 74,900 = sSimplify. 75,000 ≈ sRound to the nearest thousand.

15. 6.2 Students will use proportions to solve percentage problems. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

16. 6.2 Students will use proportions to solve percentage problems. Lesson Quiz: Part I Find each percent. 1. What percent of 33 is 22? 2. Of Earth’s 197 million mi 2 of surface area, about 139 million mi 2 is water. Find the percent of Earth’s surface that is covered by water. 3. The Ramirez family bought a large bag of oranges during their trip to Florida. Jorge ate of the oranges, Ann ate 0.18 of the oranges, Mrs. Ramirez ate 22% of the oranges, and Mr. Ramirez ate the rest. What percent of the oranges did Mr. Ramirez eat? 70.6% 20% 66 % 2323 2525

17. 6.2 Students will use proportions to solve percentage problems. Lesson Quiz: Part II 4. Rada is 170% as tall as her brother Raj. Raj is 0.82 m tall. To the nearest tenth of a meter, how tall is Rada? 5. The volume of Lake Superior is 2900 mi 3 and the volume of Lake Erie is 116 mi 3. What percent of the volume of Lake Superior is the volume of Lake Erie? 1.4 m 4%

18. 6.2 Students will use proportions to solve percentage problems. 1. What percent of 75 is 15? A. 5 B. 10 C. 20 D. 50 Lesson Quiz for Student Response Systems

19. 6.2 Students will use proportions to solve percentage problems. 2. Denise rides her bike 4 miles. If Lindsey’s ride is 85% the length of Denise’s ride, find the length of Lindsey’s ride. A. 0.85 B. 2 C. 3.4 D. 4.85 Lesson Quiz for Student Response Systems

20. 6.2 Students will use proportions to solve percentage problems. 3. 120 is what percent of 50? A. 12 B. 50 C. 240 D. 600 Lesson Quiz for Student Response Systems