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

Warm Up Multiply      Course Percent of a Number

Learn to find the percent of a number. Course Percent of a Number

Course 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 Whole

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

Find the percent of each number. Additional Example 1A: Using Proportions to Find Percents of Numbers Course Percent of a Number 30% of = n · 50 = 100 · n 1,500 = 100n 1, = 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.

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

Additional Example 1B: Using Proportions to Find Percents of Numbers Course Percent of a Number Find the percent of each number. 200% of = n · 24 = 100 · n 4,800 = 100n 4, = 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.

Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers Course 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

Additional Example 3: Geography Application Course 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 · 6,157 2,462.8 The number of people 19 or younger was about 2,463 million. Write the percent as a decimal. Multiply.

Lesson Quiz Find the percent of each number % of % of 110 Find the percent of each number. Check whether your answer is reasonable % of % of 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 Course Percent of a Number 357

Warm Up Solve. 1. 4x = x = x = x = Course Solving Percents Problems 7

Learn to solve problems involving percents. Course Solving Percents Problems

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 Solving Percents Problems

Proportion Method n 100 = Part Whole Part Whole n · 24 = 100 · n = 1,650 n = Sloths spend about 69% of the day sleeping! Course Solving Percents Problems

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

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

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

Solve. Check It Out: Example 1B 8 is 40% of what number? = 8n8n n · 40 = 100 · 8 40n = n 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 Solving Percents Problems

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 = 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 Solving Percents Problems 225n 225 = Divide each side by 225. n = 8

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 = 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 Solving Percents Problems 800n 800 = Divide each side by 800. n = 7

Lesson Quiz Solve is 42% of what number? 2. What percent of 292 is 73? % 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 Solving Percents Problems