2. Chapter 6 Lesson 5 Using the Percent Proportion pgs. 288-292 What you will learn: Use the percent proportion to solve problems What you will learn: Use the percent proportion to solve problems

3. Vocabulary Part (288): numerator Base (288): denominator Percent Proportion (288): comparing a percent, written as a fraction, whose base is 100 to a proportion part base Part (288): numerator Base (288): denominator Percent Proportion (288): comparing a percent, written as a fraction, whose base is 100 to a proportion part base

4. Key Concept (288) Percent Proportion Words: part = percent base 100 Symbols: a = p, where a is the part, b 100 b is the base and p is the percent. Words: part = percent base 100 Symbols: a = p, where a is the part, b 100 b is the base and p is the percent.

5. Example 1: Find the Percent Seventy-two is what percent of 160? Seventy-two is being compared to 160. So, 72 is the part and 160 is the base. Let p represent the percent. a = P ----> 72 = P b 100 160 100 Find the cross products: 72  100 = 160  P Simplify: 7200=160P Divide: 7200 = 160P 160 160 Solve: 45 = P So, 72 is 45% of 160 Seventy-two is what percent of 160? Seventy-two is being compared to 160. So, 72 is the part and 160 is the base. Let p represent the percent. a = P ----> 72 = P b 100 160 100 Find the cross products: 72  100 = 160  P Simplify: 7200=160P Divide: 7200 = 160P 160 160 Solve: 45 = P So, 72 is 45% of 160

6. Example 2: Find the Percent What percent of 5 is 8? Eight is being compared to 5. So 8 is the part and 5 is the base. Let P represent the percent. a = P ----> 8 = P b 100 5 100 Cross Products: 8  100 =5  P Simplify: 800=5P Divide: 800 = 5P 5 5 Solve: 160 = P So, 160% of 5 is 8 What percent of 5 is 8? Eight is being compared to 5. So 8 is the part and 5 is the base. Let P represent the percent. a = P ----> 8 = P b 100 5 100 Cross Products: 8  100 =5  P Simplify: 800=5P Divide: 800 = 5P 5 5 Solve: 160 = P So, 160% of 5 is 8

7. Example 3: Apply the Percent Proportion If 12 of the 75 animals in a pet store are parakeets, what percent are parakeets? a = P = 12 = P b 100 75 100 Cross Products: 12  100 = 75  P Simplify: 1200 = 75P Divide: 1200 = 75P 75 75 Solve: 16 = P So, 16% of the animals are Parakeets If 12 of the 75 animals in a pet store are parakeets, what percent are parakeets? a = P = 12 = P b 100 75 100 Cross Products: 12  100 = 75  P Simplify: 1200 = 75P Divide: 1200 = 75P 75 75 Solve: 16 = P So, 16% of the animals are Parakeets

8. Concept Summary (289) Types of Percent Problems TypeExampleProportion Find the % 3 is what percent of 4? 3 = P 4 100 Find the partWhat number is 75% of 4? a = 75 4 100 Find the base3 is 75% of what number 3 = 75 b 100

9. Example 4: Find the Part What number is 3.5% of 750? The percent is 3.5 and the base is 750. Let a represent the part. a = P ------> a = 3.5 b 100 750 100 Cross Products: a  100 = 750  3.5 Simplify: 100a = 2625 Divide: 100a = 2625 100 100 Solve: a = 26.25 So, 3.5% of 750 is 26.25 What number is 3.5% of 750? The percent is 3.5 and the base is 750. Let a represent the part. a = P ------> a = 3.5 b 100 750 100 Cross Products: a  100 = 750  3.5 Simplify: 100a = 2625 Divide: 100a = 2625 100 100 Solve: a = 26.25 So, 3.5% of 750 is 26.25

10. Example 5: Apply the Percent Proportion Of the fish in an aquarium, 26% are angelfish. If the aquarium contains 50 fish, how many are angelfish? To find 26% of 50, let b represent the base, 50, and let p represent the percent 26% in the percent proportion. Let a represent the part. a = P ---> a = 26 b 100 50 100 a  100 = 50  26 100a = 1300 a = 13 So, 13 fish are angelfish Of the fish in an aquarium, 26% are angelfish. If the aquarium contains 50 fish, how many are angelfish? To find 26% of 50, let b represent the base, 50, and let p represent the percent 26% in the percent proportion. Let a represent the part. a = P ---> a = 26 b 100 50 100 a  100 = 50  26 100a = 1300 a = 13 So, 13 fish are angelfish

11. Example 6: Find the Base 27 is 90% of what number? The percent is 90% and the part is 27. Let b represent the base. a = P ----> 27 = 90 b 100 b 100 Cross Products: 27  100 = b  90 Simplify: 2700 = 90b Divide: 2700 = 90b 90 90 Solve: 30= b So, 27 is 90% of 30 27 is 90% of what number? The percent is 90% and the part is 27. Let b represent the base. a = P ----> 27 = 90 b 100 b 100 Cross Products: 27  100 = b  90 Simplify: 2700 = 90b Divide: 2700 = 90b 90 90 Solve: 30= b So, 27 is 90% of 30

12. Your Turn! Use the percent proportion to solve each problem, round to the nearest tenth. 17 is what percent of 85? 36 is 72% of what number? What is 84% of 150? What is 0.3% of 750? 17 is what percent of 85? 36 is 72% of what number? What is 84% of 150? What is 0.3% of 750? 17 = P 85 100 P = 20 20% 36 = 72 b 100 b = 50 a = 84 150 100 a = 126 a = 0.3 750 100 a = 2.25

13. Make sure you carefully Read & understand what The question is asking! Extra Practice by the door! Quiz Tomorrow! (6-4 & 6-5)