5-6 Multiplying Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

5-6 Multiplying Fractions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm Up

1. What is of 12?

2. What is of 100?

3. What is of 120?

4. What is of 100?

5. What is of 480?

6

50

60

12__

12__

12__

14 __

14 __

25

120


Problem of the Day

Your favorite uncle left one-fifth of his estate to each of his three children and the rest to his favorite charity. If his estate was worth $105,000, how much was given to charity?$42,000


MA.6.A.1.2 Multiply and divide fractions…efficiently.

Also MA.6.A.1.3

Sunshine State Standards


On average, people spend of their lives asleep. About

of the time they sleep, they dream. What fraction of

a lifetime does a person typically spend dreaming?

1

3__

1

4__

1

4__ 1

3__

• =1

12__

1

3__1

4__

1

4__ 1

3__

One way to find of is to make a model.

Find of .

Notice that there is 1 section where the shading overlaps, and the product of the numerators is 1. Notice that there are 12 sections in the model, and the product of the denominators is 12. You can use these observations to write a rule for multiplying fractions.


1

4__ 1

3__

• 1 • 1

4 • 3 _____

1

12__

=

=

Multiply the numerators.Multiply the denominators.

A person typically spends of his or her lifetime dreaming.

1

12__ The answer is in simplest

form.

Helpful Hint

Notice that when you multiply two proper fractions, the product is less than either factor.


Additional Example 1A: Multiplying Fractions

Multiply. Write each answer in simplest form.

1

4__ 2

5__• _____=

=

Multiply numerators. Multiply denominators.

2

20__

1 • 2 4 • 5

1

4__ •

2

5__

The GCF of 2 and 20 is 2.

The answer is in simplest form.=1

10__


Additional Example 1B: Multiplying Fractions


5

7__ 4

15__•

_____

=

=

Use the GCF to simplify the fractions before multiplying. The greatest common factor of 5 and 15 is 5.

4

21__

1 • 4

7 • 3

5

7__ •

4

15__


The answer is in simplest form.

1

7__ •

4

3__

1

3

=


Additional Example 1C: Multiplying Fractions


4

9__ 6

10__• ______=

=


24

90__

4 • 6

9 • 10

4

9__ •

6

10__


The answer is in simplest form.=4

15__


Check It Out: Example 1A


15

63__

____

5

21__

3 • 5

7 • 9

3

7__ 5

9__•


Check It Out: Example 1B


6

14__

____

3

7__

1 • 6

2 • 7

1

2__ 6

7__•


Check It Out: Example 1C

5

8__

_____1 • 14 • 1

1

4

__

1

1

2

5__5

8__

2

5__

•


1

4

•


Additional Example 2A: Evaluating Fraction Expressions

2

5__

1

3__ b •

2

5__

2

5__1

3__ •

_____1 • 23 • 5

2

15__

Substitute for b.1

3__

Multiply.


b =

Evaluate the expression b • for each value of b.

Write each answer in simplest form.


You can look for a common factor in a numerator and a denominator to determine whether you can simplify before multiplying.

Helpful Hint


Additional Example 2B: Evaluating Fraction Expressions

b = 3

8__

b •2

5

__

2

5

__3

8

__ •

_____3 • 14 • 5

3

20

__

Substitute for b.3

8__

Use the GCF to simplify.


1

4

2

5

__3

8

__ •

Multiply.


Additional Example 2C: Evaluating Fraction Expressions

b = 5

7__ b •

2

5__

2

5__5

7__ •

_____5 • 27 • 5

10

35__

Substitute for b.5

7__

Multiply.


The answer is in simplest form.2

7__


Check It Out: Example 2A

Evaluate the expression c • for each value of c.


c =

1

4__

1

7__

1 • 17 • 4

1

28__

_____


Check It Out: Example 2B



c =

1

4__

4

5__

4

20__

•1

4__4

5

__

1

5__


Check It Out: Example 2C



c =

1

4__

2

3__

2

12__

•1

4__2

3__

1

6__


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz


1. 2.

Evaluate the expression x • for each value of

x. Write the answer in simplest form.

3. x = 4. x =

5. At a particular college of the students take a

math class. Of these students, take basic algebra.

What fraction of all students take basic algebra?

3

5__1

4__ •

5

7__3

10__ •

1

8__

4

5__ 1

8__

2

5__

1

4__

3

20__ 3

14__

1

10__ 1

64__

1

10__


1. Multiply and identify the answer in simplest form.

A. C.

B. D.



2. Multiply and identify the answer in simplest form.

A. C.

B. D.



3. Evaluate the expression

and identify the answer in simplest form.

A. C.

B. D.



4. Evaluate the expression

and identify the answer in simplest form.

A. C. 1

B. D. 5



5. At a particular school of the students

take chemistry class. Of these students,

take organic chemistry. What fraction of all

students take organic chemistry?

A. C.

B. D. 1


5-6 Multiplying Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

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