1. 6-4 Percent of a Number Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Multiply. 1. 0.05  20 2. 0.32  15 3. 0.06  25 4. 0.75  18 5. 0.34  76 1 4.8 1.5 Course 2 6-4 Percent of a Number 13.5 25.84

3. Learn to find the percent of a number. Course 2 6-4 Percent of a Number

4. Course 2 6-4 Percent of a Number The human body is made up mostly of water. In fact, about 67% of a person’s total (100%) body weight is water. If Cameron weighs 90 pounds, about how much of his weight is water? Recall that a percent is a part of 100. Since you want to know the part of Cameron’s body that is water, you can set up and solve a proportion to find the answer. % 67 = nPart 100 90 100 Whole

5. Using a proportion… % = “IS” 100 “OF” WHOLE PART PERCENT

6. Find the percent of each number. Additional Example 1A: Using Proportions to Find Percents of Numbers Course 2 6-4 Percent of a Number 30% of 50 30 100 = n 50 30 · 50 = 100 · n 1,500 = 100n 1,500 100 = 100n 15 = n 30% of 50 is 15. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

7. Course 2 6-4 Percent of a Number When solving a problem with a percent greater than 100%, the part will be greater than the whole. Helpful Hint

8. Additional Example 1B: Using Proportions to Find Percents of Numbers Course 2 6-4 Percent of a Number Find the percent of each number. 200% of 24 200 100 = n 24 200 · 24 = 100 · n 4,800 = 100n 4,800 100 = 100n 48 = n 200% of 24 is 48. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

9. Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers Course 2 6-4 Percent of a Number Find the percent of the number. Estimate to check whether your answer is reasonable. 3% of 12 3% of 12 = 0.03 · 12 = 0.36 Estimate 5% · 12 = 0.6, so 3% of 12 is a little less than 0.6. Thus 0.36 is a reasonable answer. Write the percent as a decimal and multiply. “OF” MEANS MULTIPLY

10. Additional Example 3: Geography Application Course 2 6-4 Percent of a Number The estimated world population in 2001 was 6,157 million. About 40% of the people were 19 or younger. What was the approximate number of people 19 or younger, to the nearest million? Find 40% of 6,157 million. 0.40 · 6,157 2,462.8 The number of people 19 or younger was about 2,463 million. Write the percent as a decimal. Multiply.

11. Lesson Quiz Find the percent of each number. 1. 25% of 8 2. 40% of 110 Find the percent of each number. Check whether your answer is reasonable. 3. 150% of 96 4. 0.3% of 120 5. Whitmer Middle School has 850 students. If 42% of the students bought lunch on Monday, how many student bought lunch on Monday? 44 2 Insert Lesson Title Here 144 0.36 Course 2 6-4 Percent of a Number 357

12. Warm Up Solve. 1. 4x = 90 2. 8x = 96 3. 12x = 180 4. 26x = 182 22.5 12 15 Course 2 6-5 Solving Percents Problems 7

13. Learn to solve problems involving percents. Course 2 6-5 Solving Percents Problems

14. Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day 16.5 hours is, you can use a proportion or an equation. Course 2 6-5 Solving Percents Problems

15. Proportion Method n 100 = 16.5 24 Part Whole Part Whole n · 24 = 100 · 16.5 24n = 1,650 n = 68.75 Sloths spend about 69% of the day sleeping! Course 2 6-5 Solving Percents Problems

16. Solve. Additional Example 1A: Using Proportions to Solve Problems with Percents What percent of 40 is 25? n 100 = 25 40 n · 40 = 100 · 25 40n = 2,500 40n 40 = 2,500 40 n = 62.5 25 is 62.5% of 40. Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to isolate the variable. Course 2 6-5 Solving Percents Problems

17. Solve. Additional Example 1B: Using Proportions to Solve Problems with Percents 15 is 25% of what number? 25 100 = 15 n n · 25 = 100 · 15 25n = 1,500 25n 25 = 1,500 25 n = 60 15 is 25% of 60. Write a proportion. Set the cross products equal. Multiply. Divide each side by 25 to isolate the variable. Course 2 6-5 Solving Percents Problems

18. Solve. Check It Out: Example 1A What percent of 50 is 10? n 100 = 10 50 n · 50 = 100 · 10 50n = 1,000 50n 50 = 1,000 50 n = 20 10 is 20% of 50. Write a proportion. Set the cross products equal. Multiply. Divide each side by 50 to isolate the variable. Course 2 6-5 Solving Percents Problems

19. Solve. Check It Out: Example 1B 8 is 40% of what number? 40 100 = 8n8n n · 40 = 100 · 8 40n = 800 40n 40 = 800 40 n = 20 8 is 40% of 20. Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to isolate the variable. Course 2 6-5 Solving Percents Problems

20. A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18? Additional Example 3: Finding Sales Tax n 100 = 18 225 n · 225 = 100 · 18 8% of $225 is $18. The sales tax is 8%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $225 is $18? 225n = 1800 Course 2 6-5 Solving Percents Problems 225n 225 = 1800 225 Divide each side by 225. n = 8

21. A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56? Check It Out: Example 3 n 100 = 56 800 n · 800 = 100 · 56 7% of $800 is $56. The sales tax is 7%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $800 is $56? 800n = 5600 Course 2 6-5 Solving Percents Problems 800n 800 = 5600 800 Divide each side by 800. n = 7

22. Lesson Quiz Solve. 1. 21 is 42% of what number? 2. What percent of 292 is 73? 3. 112% of what number is 84? 4. What percent of 1,340 is 13.4? 5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate? 25% 50 Insert Lesson Title Here 75 1% 6% Course 2 6-5 Solving Percents Problems