This document provides examples and explanations for calculating percentages. It begins with examples converting fractions and decimals to percentages. It then provides multiple examples of finding percentages of numbers by setting up proportions or equations. Additional examples apply these concepts to word problems involving populations, savings accounts, oranges eaten by a family, and water levels in reservoirs. A quiz at the end tests calculating percentages and applying them to heights and lake volumes.
2. 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. NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications . California Standards
4. 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? Set up a proportion. Substitute. n ๏ฝ 92 = 100 ๏ฝ 66 92 n = 6600 Find the cross products. Method 1: Set up a proportion to find the percent. Simplify. = number 100 part whole n 100 66 92 =
5. Additional Example 1 Continued n โ 72 Divide both sides by 92. 66 is approximately 72% of 92. Simplify. 92 n = 6600 92 92
6. What percent of 92 is 66? Method 2: Set up an equation. p ๏ฝ 92 = 66 Let p represent the percent. Divide both sides by 92. p ๏ป 0.72 Simplify. 66 is about 72% of 92. Additional Example 1 Continued percent ๏ฝ whole = part Set up an equation. 92 p 92 = 66 92
7. Additional Example 1 Continued Check 66.24 ๏ป 66 72% of 92 is approximately 66. 72% ๏ฝ 92 = 66 Substitute 72% for p. ? 0.72 ๏ฝ 92 = 66 Write as a decimal and multiply. ?
8. What percent of 140 is 21? Think: What number is to 100 as 21 is to 140? Set up a proportion. Let n represent the percent. n ๏ฝ 140 = 100 ๏ฝ 21 140 n = 2100 Find the cross products. Check It Out! Example 1 Method 1: Set up a proportion. Simplify. = number 100 part whole n 100 21 140 =
9. n = 15 Divide both sides by 140. 21 is 15% of 140. Check It Out! Example 1 Continued Simplify. 140 n = 2100 140 140
10. Check It Out! Example 1 Continued What percent of 140 is 21? Method 2: Set up an equation. p ๏ฝ 140 = 21 Let p represent the percent. Divide both sides by 140. p = 0.15 Simplify. 21 is 15% of 140. percent ๏ฝ whole = part Set up an equation. 140 p 140 = 21 140
11. Check It Out! Example 1 Continued 21 = 21 15% of 140 is approximately 21. Check 15% ๏ฝ 140 = 21 Substitute 15% for p. ? 0.15 ๏ฝ 140 = 21 Write as a decimal and multiply. ?
12. Additional Example 2A: Recreation Application First, find what percent of the grass Aimee and Ken cut. Four friends volunteered to cut the grass around their neighborโs 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 Next, subtract the percents you know from 100% to find the remaining percent. 100% โ 23% โ 20% โ 31% = 26%. Bryn cut 26% of the grass. = 20% and 0.31 = 31%. 1 5
13. Additional Example 2B: Recreation Application First, find what percent of his films are dramas and action. 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 Next, subtract the percents you know from 100% to find the remaining percent. 100% โ 40% โ 32.5% โ 3% โ 19.5% = 5%. 5% of Jeremyโs movie collection are independent films. = 40% and 0.325 = 32.5% 2 5
14. Check It Out! Example 2A First, find what percent of the shelves Lauren and Ling stocked. 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 Next, subtract the percents you know from 100% to find the remaining percent. 100% โ 14% โ 60% โ 19% = 7%. Mark stocked 7% of the shelves. = 60% and 0.19 = 19%. 3 5
15. Check It Out! Example 2B First, find what percent of his CDs are rock and pop. 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 Next, subtract the percents you know from 100% to find the remaining percent. 100% โ 50% โ 12.5% โ 6% โ 9.5% = 22%. 22% of Joeโs CD collection is jazz. = 50% and 0.125 = 12.5% 1 2
16. 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. Set up a proportion. 55 ๏ฝ 1,189,000 = 100 ๏ฝ p Find the cross products. Think: 55 is to 100 as what population is to 1,189,000? = 55 100 p 1,189,000
17. Additional Example 3A Continued Austin has a population of approximately 654,000 people. 65,395,000 = 100 p Simplify. Divide both sides by 100. 653,950 = p Simplify. 654,000 โ p Round to the nearest whole number. = 65,395,000 100 100 p 100
18. 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
19. 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? Choose a method: Set up an equation. 2 3 Think: What number is 66 % of 57,000,000? 2 3 w = 66 % ๏ฝ 57,000,000 Set up an equation. 2 3 w = ๏ฝ 57,000,000 66 % is equivalent to . 2 3 2 3 2 3
20. Additional Example 3B Continued The reservoir contained 38,000,000 gallons of water after the drought. w = = 38,000,000 Simplify. 114,000,000 3
21. 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? Choose a method: Set up an equation. w ๏ป 30,400,000 Simplify. The water flow in the river was about 30,400,000 gallons per day after the drought. 2 3 Think: What number is 50 % of 60,000,000? 2 3 w = 50 % ๏ฝ 60,000,000 Set up an equation. 2 3 w = 0.506 ๏ฝ 60,000,000 50 % is equivalent to 0.506. 2 3
22. 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. Marvinโs savings account. To the nearest thousand, what is the amount of Mr. Parsonโs savings account? Choose a method: Set up a proportion. Set up a proportion. 35 ๏ฝ 214,000 = 100 ๏ฝ s Find the cross products. Think: 35 is to 100 as what amount is to $214,000. = 35 100 s 214,000
23. Check It Out! Example 3B Continued Mr. Parson has approximately $75,000 in his savings account. 7,490,000 = 100 s Simplify. Divide both sides by 100. 74,900 = s Simplify. 75,000 โ s Round to the nearest thousand. = 7,490,000 100 100 s 100
24. Lesson Quiz: Part I Find each percent. 1. What percent of 33 is 22? 2. Of Earthโs 197 million mi 2 of surface area, about 139 million mi 2 is water. Find the percent of Earthโs 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% 2 5 66 % 2 3
25. 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%
