5-5 Multiplying Fractions by Whole Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation...

5-5 Multiplying Fractions by Whole Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpMultiply.

30

96

144

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


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 • =14__ 1

4__ 1

4__ 1

4__ 3

4__++ =


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

Notice that when you multiply a proper fraction and a number greater than 1, the product is between the factors.


Additional Example 1A: Multiplying Fractions and Whole Numbers

Multiply. Write each answer in simplest form.

Method 1: Use repeated addition.

19

__

19

__

79

__

• =

=

7 •

Write 7 • as addition. Add the numerators.

19__1

9__ + + + + + +

19

__ 19

__ 19

__ 19

__ 19

__19

__7


Additional Example 1B: Multiplying Fractions and Whole Numbers


Method 1: Use repeated addition.

18

__

18

__

68

__

• =

=

34

__= Write your answer in simplest form.

6 •

18

__ + + + + + 18

__ 18

__ 18

__ 18

__ 18

__ Write 6 • as addition.

Add the numerators.

18__

6


Additional Example 1C: Multiplying Fractions and Whole Numbers


Method 2: Multiply.

23

__

23

__81

__ 16 3

___• =

13

__= 5

8 •

Multiply.

Write your answer in simplest form.


Check It Out: Example 1A


3

4__

274__ or

9 •

34

__6


Check It Out: Additional Example 1B


2

5__

85__

or

4 •

35

__1


Check It Out: Additional Example 1C


5

6__

256__ or

5 •

16

__4


Additional Example 2A: Evaluating Fraction Expressions

Evaluate 4x for each value of x. Write each 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.

x =


Additional Example 2B: Evaluating Fraction Expressions


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

x =




19

__

19__

•3 = 13

__

x =


Check It Out: Example 2B


25

__

25

__•3

x =

= 15

__65

__ or 1


Check It Out: Example 2C


56__

56

__•3

x =

=12

__156__ or 2


Sometimes the denominator of an improper fraction will divide into the numerator without a remainder. When this happens, the improper fraction is equivalent to a whole number, not a mixed number.

12 3

___ = 4

means 12 ÷ 3.12 3

Remember!


Additional Example 3: Music 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.

Divide 75 by 5 and write your answer in simplest form.



There are 50 people on the football team. Of those people, are also on the basketball team. How many people on the football team are also on the basketball team?

15__ =

15__

50 • 10


Check It Out: Example 3B

There are 16 players on the baseball team. Of these players, are girls. How many girls play on the baseball team?

14__ =

14_

16 • 4


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz


1. 2.

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

simplest form.

3. 4.

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?

5 minutes

5

4 35

__

, or 112

__32

__


1. Multiply and identify the answer in simplest form.

A. 10 C. 6

B. 8 D. 4



2. Multiply and identify the answer in simplest form.

A. C.

B. 1 D.



3. Evaluate and identify the

answer in the simplest form.

A. C.

B. D.



4. Evaluate and identify the

answer in the simplest form.

A. 5 C. 3

B. 4 D. 1



5. Peter spent 40 minutes doing his math

homework. Of those minutes, were spent

referring to additional materials. How many

minutes did he spend referring to additional

materials?

A. 10 min C. 20 min

B. 15 min D. 25 min


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