Preview Warm Up California Standards Lesson Presentation

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 13.5 25.84

6-4 Percent of a Number Standards California NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Also covered: NS2.4

The human body is made up mostly of water 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. Part 67 = n 100 90 Whole

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

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

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

Check It Out! Example 1 Find the percent of each number. A. 40% of 40 40 100 n 40 = Write a proportion. 40 · 40 = 100 · n Set the cross products equal. 1,600 = 100n Multiply. 1,600 100n = Divide each side by 100. 100 100 16 = n 40% of 40 is 16.

Check It Out! Example 1 Find the percent of each number. B. 150% of 64 150 100 n 64 = Write a proportion. 150 · 64 = 100 · n Set the cross products equal. 9,600 = 100n Multiply. 9,600 100n = Divide each side by 100. 100 100 96 = n 150% of 64 is 96.

In addition to using proportions, you can find a percent of a number by using decimal equivalents.

Write the percent as a decimal and multiply. Additional Example 2: Using Decimal Equivalents to Find Percents of Numbers Find the percent of the number. Check whether your answer is reasonable. A. 9% of 80 9% of 80 = 0.09 · 80 Write the percent as a decimal and multiply. = 7.2 Check Since 10% of 80 = 8, a reasonable answer for 9% of 80 is 7.2. 20% 40% 60% 80% 100% 60 80 20 40 9% 7.2

Additional Example 2: Using Decimal Equivalents to Find Percents of Numbers Find the percent of the number. Estimate to check whether your answer is reasonable. B. 3% of 12 3% of 12 = 0.03 · 12 Write the percent as a decimal and multiply. = 0.36 Check 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. Check It Out! Example 2 Find the percent of the number. Check whether your answer is reasonable. A. 21% of 40 21% of 40 = 0.21 · 40 Write the percent as a decimal and multiply. = 8.4 Check Since 20% of 40 = 8, a reasonable answer for 21% of 40 is 8.4. 20% 40% 60% 80% 100% 30 40 10 20 21% 8.4

Check It Out! Example 2 Find the percent of the number. Estimate to check whether your answer is reasonable. B. 6% of 18 6% of 18 = 0.06 · 18 Write the percent as a decimal and multiply. = 1.08 Check 5% · 20 = 1, so 6% of 18 is close to 1. Thus 1.08 is a reasonable answer.

Additional Example 3: Geography Application 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 Write the percent as a decimal. = 2,462.8 Multiply. ≈ 2,463 Round to the nearest whole number. The number of people 19 or younger was about 2,463 million.

Write the percent as a decimal. Check It Out! Example 3 The estimated world population in 2001 was 6,157 million. About 60% of the people were above 19 years of age. What was the approximate number of people 19 or older, to the nearest million? Find 60% of 6,157 million. 0.60 · 6,157 Write the percent as a decimal. = 3,694.2 Multiply. ≈ 3,694 Round to the nearest whole number. The number of people 19 or older was about 3,694 million.

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? 2 44 144 0.36 357