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6-3. Percent of a Number. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 6-3. Percent of a Number. Course 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. 13.5. 25.84. 6-3. Percent of a Number.

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6 3

6-3

Percent of a Number

Course 2

Warm Up

Problem of the Day

Lesson Presentation


6 3

6-3

Percent of a Number

Course 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

13.5

25.84


6 3

6-3

Percent of a Number

Course 2

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


6 3

6-3

Percent of a Number

Course 2

Learn to find the percent of a number.


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6-3

Percent of a Number

Part

n

Part

67

=

Whole

Whole

90

100

Course 2

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.


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6-3

Percent of a Number

Course 2

Additional Example 1A: 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 to isolate

the variable.

=

100

100

15 = n

30% of 50 is 15.


6 3

6-3

Percent of a Number

Helpful Hint

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

Course 2


6 3

6-3

Percent of a Number

Course 2

Additional Example 1B: 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

Divide each side by 100 to isolate

the variable.

100n

=

100

100

48 = n

200% of 24 is 48.


6 3

6-3

Percent of a Number

Course 2

Try This: Example 1A

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 to isolate

the variable.

=

100

100

16 = n

40% of 40 is 16.


6 3

6-3

Percent of a Number

Course 2

Try This: Example 1B

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

Divide each side by 100 to isolate

the variable.

100n

=

100

100

96 = n

150% of 64 is 96.


6 3

6-3

Percent of a Number

Helpful Hint

When you are solving problems with percents, of usually means “times.”

Course 2

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


6 3

6-3

Percent of a Number

Course 2

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

Find the percent of the number. Estimate to check whether your answer is reasonable.

A. 9% of 80

Write the percent as a decimal and multiply.

9% of 80 = 0.09 · 80

= 7.2

Estimate

10% · 80 = 8, so 9% of 80 is less than 8. Thus 7.2 is a reasonable answer.


6 3

6-3

Percent of a Number

Course 2

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.

B. 3% of 12

3% of 12 = 0.03 · 12

Write the percent as a decimal and multiply.

= 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.


6 3

6-3

Percent of a Number

Course 2

Insert Lesson Title Here

Try This: Example 2A

Find the percent of the number. Estimate to check whether your answer is reasonable.

A. 21% of 50

21% of 50 = 0.21 · 50

Write the percent as a decimal and multiply.

= 10.5

Estimate

20% · 50 = 10, so 21% of 50 is a little more than 10. Thus 10.5 is a reasonable answer.


6 3

6-3

Percent of a Number

Course 2

Try This: Example 2B

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

Estimate

5% · 20 = 1, so 6% of 18 is close to 1. Thus 1.08 is a reasonable answer.


6 3

6-3

Percent of a Number

Course 2

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.

Multiply.

2,462.8

The number of people 19 or younger was about 2,463 million.


6 3

6-3

Percent of a Number

Course 2

Try This: 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.

The number of people 19 or older was about 3,694 million.


6 3

6-3

Percent of a Number

Course 2

Insert Lesson Title Here

Lesson Quiz

Find the percent of each number.

1. 25% of 8

2. 40% of 110

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


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