1. Course 3 6-3 Finding Percents 6-3 Finding Percents Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Course 3 6-3 Finding Percents Warm Up Rewrite each value as indicated. 1. as a percent 2. 25% as a fraction 3. as a decimal 4. 0.16 as a fraction 48% 0.375 4 25 24 50 3 8 1 4

3. Course 3 6-3 Finding Percents Problem of the Day A number between 1 and 10 is halved, and the result is squared. This gives an answer that is double the original number. What is the starting number? 8

4. Course 3 6-3 Finding Percents Learn to find percents.

5. Course 3 6-3 Finding Percents What percent of 92 is 66? Additional Example 1A: Finding the Percent One Number Is of Another Think: What number is to 100 as 66 is to 92? = number 100 part whole Set up a proportion. Substitute. n 100 66 92 = n  92 = 100  66 92n = 6600 Find the cross products. Method 1: Set up a proportion to find the percent.

6. Course 3 6-3 Finding Percents Additional Example 1A Continued n ≈ 72 = 72 100 66 92 The proportion is reasonable. Solve for n. 92 6600 n = 66 is approximately 72% of 92.

7. Course 3 6-3 Finding Percents Additional Example 1B: Finding the Percent One Number Is of Another What percent of 220 is 88? Method 2: Set up an equation to find the percent. p  220 = 88 Set up an equation. Divide both sides by 220. p = 0.4 0.4 is 40%. So 88 is 40% of 220. 220p 220 = 88 220

8. Course 3 6-3 Finding Percents Additional Example 1B Continued Check 88 = 88 40% of 220 is 88. 40%  220 = 88 Substitute 40% for p. ? 0.40  220 = 88 Write a decimal and multiply. ?

9. Course 3 6-3 Finding Percents What percent of 140 is 21? Think: What number is to 100 as 21 is to 140? = number 100 part whole Set up a proportion. Substitute. n 100 21 140 = n  140 = 100  21 140n = 2100 Find the cross products. Check It Out: Example 1A Method 1: Set up a proportion to find the percent.

10. Course 3 6-3 Finding Percents n = 15 The proportion is reasonable. Solve for n. 140 2100 n = 21 is 15% of 140. = 15 100 21 140 Check It Out: Example 1A Continued

11. Course 3 6-3 Finding Percents Check It Out: Example 1B What percent of 110 is 11? Method 2: Set up an equation to find the percent. p  110 = 11 Set up an equation. 11 110 p =Solve for p. p = 0.1 0.1 is 10%. So 11 is 10% of 110.

12. Course 3 6-3 Finding Percents Additional Example 1B Continued Check 11 = 11 10% of 110 is 11. 10%  110 = 11 Substitute 10% for p. ?.10  110 = 11 Write a decimal and multiply ?

13. Course 3 6-3 Finding Percents Additional Example 2A: Recreation Application First, find what percent of the grass Aimee and Ken cut. = 20% and 0.31 = 31%. 1515 Four friends volunteered to cut the grass around their neighbor’s house. Jay cut 23% of the grass, Aimee cut of the grass, Ken cut 0.31 of the grass, and Bryn cut the rest. What percent of the grass did Bryn cut? 1515 Next, subtract the percents you know from 100% to find the remaining percent. 100% - 23% - 20% - 31% = 26%. Bryn cut 26% of the grass.

14. Course 3 6-3 Finding Percents Additional Example 2B: Recreation Application First, find what percent of his films are dramas and action. = 40% and 0.325 = 32.5% 2525 Jeremy organizes his movie collection by genre. of his collection are dramas, 0.325 are action films, 3% are documentaries, 19.5% are comedies, and the rest of his movies are independent films. What percent of his movie collection are independent films? 2525 Next, subtract the percents you know from 100% to find the remaining percent. 100%  40%  32.5%  3%  19.5% = 5%. 5% of Jeremy’s movie collection are independent films.

15. Course 3 6-3 Finding Percents Check It Out: Example 2A First, find what percent of the shelves Lauren and Ling stocked. = 60% and 0.19 = 19%. 3535 Four store employees stock the shelves at the Electronics Store. Francisco stocked 14% of the shelves, Lauren stocked of the shelves, Ling stocked 0.19 of the shelves, and Mark stocked the rest. What percent of the shelves did Mark stock? 3535 Next, subtract the percents you know from 100% to find the remaining percent. 100% - 14% - 60% - 19% = 7%. Mark stocked 7% of the shelves.

16. Course 3 6-3 Finding Percents Check It Out: Example 2B First, find what percent of his CDs are rock and pop. = 50% and 0.125 = 12.5% 1212 Joe organizes his CD collection by genre. of his collection is rock, 0.125 is pop, 6% is classical, 9.5% is country, and the rest of his CDs are jazz. What percent of his CD collection is jazz? 1212 Next, subtract the percents you know from 100% to find the remaining percent. 100%  50%  12.5%  6%  9.5% = 22%. 22% of Joe’s CD collection is jazz.

17. Course 3 6-3 Finding Percents Additional Example 3A: 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? Choose a method: Set up a proportion. = 55 100 p 1,189,000 Set up a proportion. 55  1,189,000 = 100  p Find the cross products. Think: 55 is to 100 as what population is to 1,189,000.

18. Course 3 6-3 Finding Percents Additional Example 3A Continued Austin has a population of approximately 654,000. 65,395,000 = 100p Simplify. = 65,395,000 100100 Divide both sides by 100. 653,950 = pSimplify. 654,000 ≈ pRound to the nearest whole number.

19. Course 3 6-3 Finding Percents When solving a problem with a percent greater than 100, look for the number that will be greater than the number given. Helpful Hint

20. Course 3 6-3 Finding Percents Additional Example 3B: 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

21. Course 3 6-3 Finding Percents 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.

22. Course 3 6-3 Finding Percents 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 = 30,400,000Simplify.

23. Course 3 6-3 Finding Percents Check It Out: Example 3A Continued The water flow in the river was 30,400,000 gallons per day after the drought.

24. Course 3 6-3 Finding Percents 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.

25. Course 3 6-3 Finding Percents Check It Out: Example 3B Continued Mr. Parson has approximately $75,000 in his savings account. 7,490,000 = 100s Simplify. = 7,490,000 100100 Divide both sides by 100. 74,900 = sSimplify. 75,000 ≈ sRound to the nearest whole number.

26. Course 3 6-3 Finding Percents 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

27. Course 3 6-3 Finding Percents 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%