7-7 Percent of a Number Learn to find the percent of a number.

7-7 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. Part 67 = nPart Whole

7-7 Percent of a Number Find the percent of each number. Additional Example 1A: Using Proportions to Find Percents of Numbers 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.

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

7-7 Percent of a Number Additional Example 1B: Using Proportions to Find Percents of Numbers 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.

7-7 Percent of a Number Find the percent of each number. Check It Out: Example 1A 40% of = n · 40 = 100 · n 1,600 = 100n 1, = 100n 16 = n 40% of 40 is 16. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

7-7 Percent of a Number Check It Out: Example 1B Find the percent of each number. 150% of = n · 64 = 100 · n 9,600 = 100n 9, = 100n 96 = n 150% of 64 is 96. Write a proportion. Set the cross products equal. Multiply. Divide each side by 100 to isolate the variable.

7-7 Percent of a Number In addition to using proportions, you can find the percent of a number by using decimal equivalents.

7-7 Percent of a Number Find the percent of the number. Check whether your answer is reasonable. Additional Example 2A: Using Decimal Equivalents to Find Percents of Numbers 9% of 80 9% of 80 = 0.09 · 80 = 7.2 Model Since 10% of 80 = 8, a reasonable answer for 9% of 80 is 7.2. Write the percent as a decimal and multiply. 0 20% 40% 60% 80% 100% % 7.2

7-7 Percent of a Number Additional Example 2B: Using Decimal Equivalents to Find Percents of Numbers 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% of 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.

7-7 Percent of a Number Find the percent of the number. Check whether your answer is reasonable. Check It Out: Example 2A 21% of 40 21% of 40 = 0.21 · 40 = 8.4 Model Since 20% of 40 = 8, a reasonable answer for 21% of 40 is 8.4. Write the percent as a decimal and multiply. 0 20% 40% 60% 80% 100% % 8.4

7-7 Percent of a Number Check It Out: Example 2B Find the percent of the number. Estimate to check whether your answer is reasonable. 6% of 18 6% of 18 = 0.06 · 18 = 1.08 Estimate 5% of 20 = 1, so 6% of 18 is close to 1. Thus 1.08 is a reasonable answer. Write the percent as a decimal and multiply.

7-7 Percent of a Number 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 · 6,157 2,462.8 The number of people 19 or younger was about 2,463 million. Write the percent as a decimal. Multiply.

7-7 Percent of a Number 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 · 6,157 3,694.2 The number of people 19 or older was about 3,694 million. Write the percent as a decimal. Multiply.