4-7 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

4-7 Multiplying Fractions and Mixed Numbers

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm Up

1. What is

2. What is

3. What is

12

815

12 of 24?12 of 16?12 of 30?

4. What is 14 of 28? 7

Course 2


Problem of the Day

Caitlin was watching television. In a weather forecast at midnight the forecaster indicated that it would be cloudy for exactly 72 hours and then would be sunny. Caitlin called the station to tell the forecaster he was wrong. How did she know?

There are 24 hours in a day, so 72 hours equals 3 days. In 3 days it would be midnight again, not sunny.

Course 2


Learn to multiply fractions and mixed numbers.

Course 2


The San Francisco-Oakland Bay Bridge, which opened in 1936,is a toll bridge used by drivers traveling between the two cities. In 1977 , the toll for a car crossing the

bridge was of the toll in 2001.38

To find the toll in 1977, you will need to multiply the toll in 2001 by a fraction.

Course 2


In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was

Additional Example 1: Transportation Application

23

of the toll in 2001. What was the toll in 1995?

23

6 · = 23

+ 23

23

23

23

23

+ + + + +

= 123

=41

Simplify.

= $4.00 Write the fraction as a decimal.

The George Washington Bridge toll for a car was $4.00 in 1995.

+ + + +13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

1 1 1 1

Course 2


In 2002, the fee to park in a parking garage was

$4. In 2000 the fee was of the fee in 2002.

What was the fee in 2000?

Try This: Example 1

34

4 · = 34

+ 34

34

34

+ +

= 124

=31

Simplify.

= $3.00 Write the fraction as a decimal.

The fee to park in the parking garage was $3.00 in 2000.

34

+14

14

14

14

14

14 + +1

414

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

1 1 1

Course 2


To multiply fractions, multiply the numerators to find the product’snumerator. Then multiply the denominators to find the product’sdenominator.

Course 2


Multiply. Write the answer in simplest form.

Additional Example 2A: Multiplying Fractions

A. –12 · 34

–12 · 34

= – 121

· 34

Write –12 as a fraction.

= – 12 · 31 · 4

3

1Simplify.

91

= – = –9 Multiply numerators.Multiply denominators.

You can write any integer as a fraction with a denominator of 1.

Remember!

Course 2



Additional Example 2B: Multiplying Fractions

B. · 8

= Simplify.

Multiply numerators.Multiply denominators.

313

1

1

= 18

38

·13

13

· 3 8·

Course 2



Additional Example 2C: Multiplying Fractions

C. · 5

The signs are different, so the answer will be negative.


423

–

45

·23

– =23

· 4 5·

–

= 8 15

–

Course 2



Try This: Example 2A

A. –16 · 14

–16 · 14

= – 161

· 14

Write –16 as a fraction.

= – 16 · 11 · 4

4

1Simplify.

41

= – = –4 Multiply numerators.Multiply denominators.

Course 2



Try This: Example 2B

B. · 9

= Simplify.


616

1

1

= 19

69

·16

16

· 6 9·

Course 2



Try This: Example 2C

C. · 8

The signs are different, so the answer will be negative.


137

–

18

·37

– =37

· 1 8·

–

= 3 56

–

Course 2



Additional Example 3A: Multiplying Mixed Numbers

Write the mixed number as an improper fraction.

Simplify.


A. 2

25

· 1 23 = 2

5· 53

= 25

· 53

1

1

5· 1 2

3

= 23

Course 2



Additional Example 3B: Multiplying Mixed Numbers

Write the mixed numbers as improper fractions.

Simplify.

B. 4 15

· 2 17

415

· 17

= 215

·157

= 5·

71521

1

3

1

3

= 91

or 9 Multiply numerators.Multiply denominators.

2

Course 2



Additional Example 3C: Multiplying Mixed Numbers


C. 23 · 4 2

56

23 · 4 2

56 = 20

3· 22

5

203

· 225

=4

1


Simplify.

3= 88 or 291

3

Course 2



Try This: Example 3A

Write the mixed number as an improper fraction.

Simplify.


A. 3

35

· 2 13 = 3

5· 73

= 35

· 73 1

1

5· 2 1

3

= or 175

Course 2


25


Try This: Example 3B


Simplify.

B. 3 36

· 1 13

336

· 13

= 216

· 43

= 6·

3421

1

7

3

2


1

= 143

or 423

Course 2



Try This: Example 3C


C. 16 · 1 1

33

16 · 1 1

33 = 19

6· 4

3

196

· 43

=3

2


Simplify.

9= 38 or 4 2

9

Course 2


Lesson Quiz: Part 1

Multiply. Write each answer in simplest terms.

1. 18

· 56

2. 5 56 · 1

2

3. 5 110

·123

4. 316

· 4 23

78

3512

or 1112

2

17 2

12

or 8

548

Course 2


Lesson Quiz: Part 2

Multiply. Write the answer in simplest terms.

5. A recipe for clam chowder calls for 2 14 pounds of

butter. If you prepare one-half of the recipe, how

much butter do you need?

1 18

pounds

Course 2


Documents

4-7 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation