6-3 Finding Percents NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. California Standards

6-3 Finding Percents What percent of 92 is 66? Additional Example 1: 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. Simplify.

6-3 Finding Percents Additional Example 1 Continued n ≈ 72 Divide both sides by is approximately 72% of 92. Simplify. 92n =

6-3 Finding Percents What percent of 92 is 66? Method 2: Set up an equation. p  92 = 66 Let p represent the percent. Divide both sides by 92. p  0.72 Simplify. 66 is about 72% of p 92 = Additional Example 1 Continued percent  whole = part Set up an equation.

6-3 Finding Percents Additional Example 1 Continued Check  66 72% of 92 is approximately %  92 = 66 Substitute 72% for p. ? 0.72  92 = 66 Write as a decimal and multiply. ?

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. Let n represent the percent. n = n  140 = 100  n = 2100 Find the cross products. Check It Out! Example 1 Method 1: Set up a proportion. Simplify.

6-3 Finding Percents n = 15 Divide both sides by is 15% of 140. Check It Out! Example 1 Continued Simplify. 140n =

6-3 Finding Percents Check It Out! Example 1 Continued What percent of 140 is 21? Method 2: Set up an equation. p  140 = 21 Let p represent the percent. Divide both sides by 140. p = 0.15 Simplify. 21 is 15% of p 140 = percent  whole = part Set up an equation.

6-3 Finding Percents Check It Out! Example 1 Continued 21 = 21 15% of 140 is approximately %  140 = 21 Substitute 15% for p. ? 0.15  140 = 21 Write as a decimal and multiply. ? Check

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% 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.

6-3 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.

6-3 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.

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. = 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?

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

6-3 Finding Percents 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

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, % is equivalent to

6-3 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.

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 =  60,000, % is equivalent to w  30,400,000 Simplify. The water flow in the river was about 30,400,000 gallons per day after the drought.

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. = 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.

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, s 100 Divide both sides by ,900 = sSimplify. 75,000 ≈ sRound to the nearest thousand.