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

Course Finding Percents Warm Up Rewrite each value as indicated. 1. as a percent 2. 25% as a fraction 3. as a decimal as a fraction 48%

Course 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

Course Finding Percents Learn to find percents.

Course 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 = n  92 = 100  66 92n = 6600 Find the cross products. Method 1: Set up a proportion to find the percent.

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

Course 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 = is 40%. So 88 is 40% of p 220 =

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

Course 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 = n  140 = 100  n = 2100 Find the cross products. Check It Out: Example 1A Method 1: Set up a proportion to find the percent.

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

Course 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 p =Solve for p. p = is 10%. So 11 is 10% of 110.

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

Course Finding Percents Additional Example 2A: Recreation Application First, find what percent of the grass Aimee and Ken cut. = 20% and 0.31 = 31% 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.

Course Finding Percents Additional Example 2B: Recreation Application First, find what percent of his films are dramas and action. = 40% and = 32.5% 2525 Jeremy organizes his movie collection by genre. of his collection are dramas, 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.

Course Finding Percents Check It Out: Example 2A First, find what percent of the shelves Lauren and Ling stocked. = 60% and 0.19 = 19% 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.

Course Finding Percents Check It Out: Example 2B First, find what percent of his CDs are rock and pop. = 50% and = 12.5% 1212 Joe organizes his CD collection by genre. of his collection is rock, 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.

Course 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. = 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.

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

Course 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

Course 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, % is equivalent to

Course Finding Percents Additional Example 3B Continued The reservoir contained 38,000,000 gallons of water after the drought. w = = 38,000, ,000,000 3 Simplify.

Course 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 =  60,000, % is equivalent to w = 30,400,000Simplify.

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

Course 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. = 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.

Course 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, Divide both sides by ,900 = sSimplify. 75,000 ≈ sRound to the nearest whole number.

Course 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 %

Course 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%