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. Problem of the Day In a group of 60 triangular and square tiles, 25% are red, and 75% are blue. The ratio of triangles to squares is 1:2. Seventy percent of the squares are blue. Find the number of each kind of tile (red or blue squares or triangles). 3 red triangles, 17 blue triangles, 12 red squares, 28 blue squares Course 2 6-4 Percent of a Number

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

5. 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. Part 67 = nPart 100 90 Whole

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. Find the percent of each number. Check It Out: Example 1A Course 2 6-4 Percent of a Number 40% of 40 40 100 = n 40 40 · 40 = 100 · n 1,600 = 100n 1,600 100 = 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.

10. Check It Out: Example 1B Course 2 6-4 Percent of a Number Find the percent of each number. 150% of 64 150 100 = n 64 150 · 64 = 100 · n 9,600 = 100n 9,600 100 = 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.

11. Course 2 6-4 Percent of a Number In addition to using proportions, you can find the percent of a number by using decimal equivalents.

12. Find the percent of the number. Check whether your answer is reasonable. Additional Example 2A: Using Decimal Equivalents to Find Percents of Numbers Course 2 6-4 Percent of a Number 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% 0 60 80 20 40 9% 7.2

13. 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.

14. Find the percent of the number. Check whether your answer is reasonable. Check It Out: Example 2A Course 2 6-4 Percent of a Number 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% 0 30 40 10 20 21% 8.4

15. Check It Out: Example 2B Course 2 6-4 Percent of a Number 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% · 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.

16. 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.

17. Check It Out: Example 3 Course 2 6-4 Percent of a Number 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 3,694.2 The number of people 19 or older was about 3,694 million. Write the percent as a decimal. Multiply.

18. 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