Preview Warm Up California Standards Lesson Presentation

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 24 50 48% 1 4 3 8 0.375 4 25

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

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

Additional Example 1 Continued 92 Divide both sides by 92. Simplify. n ≈ 72 66 is approximately 72% of 92.

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

Additional Example 1 Continued Check 72%  92 = 66 Substitute 72% for p. ? 0.72  92 = 66 Write as a decimal and multiply. ? 66.24  66 72% of 92 is approximately 66.

n 100 Check It Out! Example 1 What percent of 140 is 21? Method 1: Set up a proportion. Think: What number is to 100 as 21 is to 140? = number 100 part whole Set up a proportion. n 100 21 140 = Let n represent the percent. n  140 = 100  21 Find the cross products. 140n = 2100 Simplify.

Check It Out! Example 1 Continued 140 Divide both sides by 140. n = 15 Simplify. 21 is 15% of 140.

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

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

Additional Example 2A: Recreation Application 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? 1 5 First, find what percent of the grass Aimee and Ken cut. = 20% and 0.31 = 31%. 1 5 Next, subtract the percents you know from 100% to find the remaining percent. 100% – 23% – 20% – 31% = 26%. Bryn cut 26% of the grass.

Additional Example 2B: Recreation Application 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? 2 5 First, find what percent of his films are dramas and action. = 40% and 0.325 = 32.5% 2 5 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.

Check It Out! Example 2A 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? 3 5 First, find what percent of the shelves Lauren and Ling stocked. = 60% and 0.19 = 19%. 3 5 Next, subtract the percents you know from 100% to find the remaining percent. 100% – 14% – 60% – 19% = 7%. Mark stocked 7% of the shelves.

Check It Out! Example 2B 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? 1 2 First, find what percent of his CDs are rock and pop. = 50% and 0.125 = 12.5% 1 2 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.

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. Think: 55 is to 100 as what population is to 1,189,000? = 55 100 p 1,189,000 Set up a proportion. 55  1,189,000 = 100  p Find the cross products.

Additional Example 3A Continued Simplify. = 65,395,000 100 100p 100 Divide both sides by 100. 653,950 = p Simplify. 654,000 ≈ p Round to the nearest whole number. Austin has a population of approximately 654,000 people.

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

Additional Example 3B: Finding the Percent of a Number 2 3 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? 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

Additional Example 3B Continued 114,000,000 3 w = = 38,000,000 Simplify. The reservoir contained 38,000,000 gallons of water after the drought.

Choose a method: Set up an equation. Check It Out! Example 3A 2 3 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? 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.

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. Think: 35 is to 100 as what amount is to $214,000. = 35 100 s 214,000 Set up a proportion. 35  214,000 = 100  s Find the cross products.

Check It Out! Example 3B Continued 7,490,000 = 100s Simplify. = 7,490,000 100 100s 100 Divide both sides by 100. 74,900 = s Simplify. 75,000 ≈ s Round to the nearest thousand. Mr. Parson has approximately $75,000 in his savings account.

Lesson Quiz: Part I Find each percent. 20% 1. What percent of 33 is 22? 2. Of Earth’s 197 million mi2 of surface area, about 139 million mi2 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? 66 % 2 3 70.6% 25 20%

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 mi3 and the volume of Lake Erie is 116 mi3. What percent of the volume of Lake Superior is the volume of Lake Erie? 1.4 m 4%