Course 1

5-7 Multiplying Fractions5-7 Multiplying Fractions

Course 1

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 1

5-7 Multiplying Fractions

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

Course 1

5-7 Multiplying Fractions

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

Course 1

5-7 Multiplying Fractions

Learn to multiply fractions.

Course 1

5-7 Multiplying Fractions

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

3__

1

4__

1

4__

1

4__ 1

3__

1

4__ 1

3__

• =1

12__

One way to find of is to make a model.

Find of .

Course 1

5-7 Multiplying Fractions

You can also multiply fractions without making a model.

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.

Course 1

5-7 Multiplying Fractions

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__

Course 1

5-7 Multiplying Fractions

Additional Example 1B: Multiplying Fractions

Multiply. Write each answer in simplest form.

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__

Multiply numerators. Multiply denominators.

The answer is in simplest form.

1

7__ •

4

3__

1

3

=

Course 1

5-7 Multiplying Fractions

Additional Example 1C: Multiplying Fractions

Multiply. Write each answer in simplest form.

4

9__ 6

10__• ______=

=

Multiply numerators. Multiply denominators.

24

90__

4 • 6

9 • 10

4

9__ •

6

10__

The GCF of 24 and 90 is 6.

The answer is in simplest form.=4

15__

Course 1

5-7 Multiplying Fractions

Check It Out: Example 1A

Multiply. Write each answer in simplest form.

1

2__ 3

6__• _____=

=

Multiply numerators. Multiply denominators.

3

12__

1 • 3 2 • 6

1

2__ •

3

6__

The GCF of 3 and 12 is 3.

The answer is in simplest form.=1

4__

Course 1

5-7 Multiplying Fractions

Check It Out: Example 1B

Multiply. Write each answer in simplest form.

3

7__ 5

9__•

_____

=

=

Use the GCF to simplify the fractions before multiplying. The greatest common factor of 3 and 9 is 3.

5

21__

1 • 5

7 • 3

3

7__ •

5

9__

Multiply numerators. Multiply denominators.

The answer is in simplest form.

1

7__ •

5

3__

1

3

=

Course 1

5-7 Multiplying Fractions

Check It Out: Example 1C

Multiply. Write each answer in simplest form.

3

7__ 5

15__• ______=

=

Multiply numerators. Multiply denominators.

15105____

3 • 5 7 • 15

3

7__ •

5

15__

The GCF of 15 and 105 is 15.

The answer is in simplest form.=1

7__

Course 1

5-7 Multiplying Fractions

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.

The answer is in simplest form.

b =

Evaluate the expression b • for each value of b.

Write each answer in simplest form.

Course 1

5-7 Multiplying Fractions

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

Helpful Hint

Course 1

5-7 Multiplying Fractions

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.

The answer is in simplest form.

1

4

2

5

__3

8

__ •

Multiply.

Course 1

5-7 Multiplying Fractions

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 GCF of 10 and 35 is 5.

The answer is in simplest form.2

7__

Course 1

5-7 Multiplying Fractions

Check It Out: Example 2A

Evaluate the expression c • for each value of c.

Write each answer in simplest form.

c =

1

4__

1

7__ c •

1

4__

1

4__1

7__ •

_____1 • 17 • 4

1

28__

Substitute for c.1

7__

Multiply.

The answer is in simplest form.

Course 1

5-7 Multiplying Fractions

Check It Out: Example 2B

c = 2

7__ c •

1

4

__

1

4

__2

7

__ •

_____1 • 17 • 2

1

14

__

Substitute for c.2

7__

Use the GCF to simplify.

The answer is in simplest form.

1

2

1

4

__2

7

__ •

Multiply.

Course 1

5-7 Multiplying Fractions

Check It Out: Example 2C

c = 4

7__ c •

1

4__

1

4__4

7__ •

_____4 • 17 • 4

4

28__

Substitute for c.4

7__

Multiply.

The GCF of 4 and 28 is 4.

The answer is in simplest form.1

7__

Course 1

5-7 Multiplying Fractions

Lesson Quiz

Multiply. Write each answer in simplest form.

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__