6-4 Percent of a Number

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpMultiply.

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

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

Learn to find the percent of a number.

Course 2

6-4 Percent of a Number

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 = n Part100 90Whole Whole

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 5030

100= n

5030 · 50 = 100 · n

1,500 = 100n

1,500 100 100

= 100n

15 = n

30% of 50 is 15.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 100 to isolatethe variable.

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

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 24200100

= n24

200 · 24 = 100 · n

4,800 = 100n

4,800 100 100

= 100n

48 = n

200% of 24 is 48.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 100 to isolatethe variable.

Find the percent of each number.

Check It Out: Example 1A

Course 2

6-4 Percent of a Number

40% of 4040

100= n

4040 · 40 = 100 · n

1,600 = 100n

1,600 100 100

= 100n

16 = n

40% of 40 is 16.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 100 to isolatethe variable.

Check It Out: Example 1B

Course 2

6-4 Percent of a Number

Find the percent of each number.

150% of 64150100

= n64

150 · 64 = 100 · n

9,600 = 100n

9,600 100 100

= 100n

96 = n

150% of 64 is 96.

Write a proportion.

Set the cross products equal.

Multiply.

Divide each side by 100 to isolatethe variable.

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.

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

= 7.2Model

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 8020 40

9%

7.2

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. Estimateto 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.

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

= 8.4Model

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 4010 20

21%

8.4

Check It Out: Example 2B

Course 2

6-4 Percent of a Number

Find the percent of the number. Estimateto 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.

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.

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.

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