4-9 Multiplying Fractions by Whole Numbers

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpMultiply.

30

96

144

Course 1

4-9 Multiplying Fractions by Whole Numbers

66

120

1. 15 2

2. 12 8

3. 9 16

4. 6 11

5. 8 15

Problem of the Day

The length of three dowels are 13 inches, 27 inches, and 19 inches. How can you use the three dowels to mark off a length of 5 inches?

13 + 19 – 27

Course 1

4-9 Multiplying Fractions by Whole Numbers

Learn to multiply fractions by whole numbers.

Course 1

4-9 Multiplying Fractions by Whole Numbers

Course 1

4-9 Multiplying Fractions by Whole Numbers

Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method.

++ =

3 • = 34__1

4__

Course 1

4-9 Multiplying Fractions by Whole Numbers

31

__ 14

__ 3 • 11 • 4

______ 34

__•

There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. So 3 = .3

1__

= =Multiply numeratorsMultiply denominators

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 1A: Multiplying Fractions and Whole Numbers

Multiply. Write the answer in simplest form.

19

__

19

__71

__ 7 • 11 • 9

______

79

__

• =

=

Write 7 as a fraction. Multiply numerators and denominators.

A. 7 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 1B: Multiplying Fractions and Whole Numbers

Multiply. Write the answer in simplest form.

18

__

18

__61

__ 6 • 11 • 8

______

68

__

• =

=

Write 6 as a fraction. Multiply numerators and denominators.

34

__= Write your answer in simplest form.

B. 6 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 1C: Multiplying Fractions and Whole Numbers

Multiply. Write the answer in simplest form.

23

__

23

__81

__ 8 • 21 • 3

______

16 3

___

• =

=

Write 8 as a fraction. Multiply numerators and denominators.

13

__or 5

C. 8 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 1A

Multiply. Write the answer in simplest form.

15

__

15

__41

__ 4 • 11 • 5

______

45

__

• =

=

Write 4 as a fraction. Multiply numerators and denominators.

A. 4 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 1B

Multiply. Write the answer in simplest form.

16

__

16

__31

__ 3 • 11 • 6

______

36

__

• =

=

Write 3 as a fraction. Multiply numerators and denominators.

12

__= Write your answer in simplest form.

B. 3 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 1C

Multiply. Write the answer in simplest form.

34

__

34

__91

__ 9 • 31 • 4

______

27 4

___

• =

=

Write 9 as a fraction. Multiply numerators and denominators.

34

__or 6

C. 9 •

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 2A: Evaluating Fraction Expression

Evaluate 4x for the value of x. Write the answer in simplest form.

110

___

41

__

110

___

410

___

•

=

Write the expression.4x

4

• 110

___

=25

__

Multiply.

Substitute for x. 110

___

Write your answer in simplest form.

A. x =

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 2B: Evaluating Fraction Expression

Evaluate 4x for the value of x. Write the answer in simplest form.

38

__

41

__

38

__

12 8

___

•

=

Write the expression.4x

4

• 38

__

=32

__

Multiply.

Substitute for x.38

__

Write your answer in simplest form.12

__,or 1

B. x =

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 2A

Evaluate 3x for the value of x. Write the answer in simplest form.

19

__

31

__

19

__

39

__

•

=

Write the expression.3x

3

• 19

__

=13

__

Multiply.

Substitute for x.19

__

Write your answer in simplest form.

A. x =

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 2B

Evaluate 3x for the value of x. Write the answer in simplest form.

47

__

31

__

47

__

12 7

___

•

=

Write the expression.3x

3

• 47

__

=

Multiply.

Substitute for x.47

__

Write your answer in simplest form.57

__ 1

B. x =

Course 1

4-9 Multiplying Fractions by Whole Numbers

Sometimes the denominator of an improper fraction will divide evenly into the numerator. When this happens, the improper fraction is equivalent to a whole number, not a mixed number.

This makes sense if you remember that the fraction bar means “divided by”.

12 3

___ = 4

Course 1

4-9 Multiplying Fractions by Whole Numbers

Additional Example 3: Application

There are 25 students in the music club. Of those

students, are also in the band. How many music

club students are in the band?

3 5

__

53__To find of 25, multiply.

25 1

___35

__• 25 = •

35

__

75 5

___=

= 15

There are 15 music club students in the band.

Course 1

4-9 Multiplying Fractions by Whole Numbers

Try This: Example 3

There are 18 saltwater fish in the aquarium. Of those

fish, are blue. How many fish in the aquarium

are blue?

23

__

23

__

To find of 18, multiply.

18 1

___23

__• 18 = •

23

__

36 3

___=

= 12

There are 12 blue fish in the aquarium.

Course 1

4-9 Multiplying Fractions by Whole Numbers

Lesson Quiz

Multiply. Write each answer in simplest form.

1. 10 • 2. 6 •

Evaluate 6x for each value of x. Write your answer

in simplest form.

3. x = 4. x =

5. Alicia spent 15 minutes making a pizza. Of those

minutes were spent rolling out the crust. How many

minutes did Alicia spend rolling out the crust?

25

__ 110

__

14

__ 56

__

13

__

5 minutes

5

4 35

__

, or 112

__32

__