Course 2 3-10 Multiplying Fractions and Mixed Numbers 3-10 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem

Course 2

3-10Multiplying Fractions and Mixed Numbers3-10 Multiplying Fractions and Mixed

Numbers

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

3-10Multiplying Fractions and Mixed Numbers

Warm Up

What is of each of the following?

1. 24 2. 16

3. 30 4. 28

12 8

15

12

14

Course 2


Problem of the Day

At midnight Caitlin heard a forecaster say that it would be cloudy for exactly 72 hours and then would be sunny. Caitlin knew the forecaster was wrong. Explain.

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 1939 , the toll for a car crossing the

bridge was of the toll in 2005. 215

To find the toll in 1939, you would need to multiply the toll in 2005 by a fraction. See Example 1 in your textbook.

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 that toll. What was the toll in 1995?

23

6 · = 23

+ 23

23

23

23

23

+ + + + +

= 123

=41

Simplify.

= $4.00 Divide 4 by 1 to 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?

Check It Out: Example 1

34

4 · = 34

+ 34

34

34

+ +

= 124

=31

Simplify.

= $3.00 Divide 3 by 1 to 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

–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

· 8

= Simplify.

Multiply numerators.Multiply denominators.

313

1

1

= 18

38

·13

13

· 3 8·

Course 2



Additional Example 2C: Multiplying Fractions

· 4

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


135

–

·35

14

– =35

· 1 4·

–

= 3 20

–

Course 2



Check It Out: Example 2A

–16 · 14

–16 · 14

= – 161

· 14

Write –16 as a fraction.

= – 16 · 11 · 4

4

1Simplify.

41

= – = –4 Multiply numerators.Multiply denominators.

Course 2



Check It Out: Example 2B

· 9

= Simplify.


616

1

1

= 19

69

·16

16

· 6 9·

Course 2



Check It Out: Example 2C

· 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.


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.

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


23 · 4 2

56

23 · 4 2

56 = 20

3· 22

5

203

· 225

=4

1


Simplify.

3= 88 or 291

3

Course 2



Check It Out: Example 3A

Write the mixed number as an improper fraction.

Simplify.


3

35

· 2 13 = 3

5· 73

= 35

· 73 1

1

5· 2 1

3

= or 175

25

Course 2



Check It Out: Example 3B


Simplify.

3 36

· 1 13

336

· 13

= 216

· 43

= 6·

3421

1

7

3

2


1

= 143

or 423

Course 2




16 · 1 1

33

16 · 1 1

33 = 19

6· 4

3

196

· 43

=3

2


Simplify.

9= 38 or 4 2

9

Check It Out: Example 3C

Course 2


Lesson Quiz: Part I

Multiply. Write each answer in simplest terms.

1. 18

· 56

2. 5 56

· 12

3. 5 110

·123

4. 316

· 4 23

78

3512

or 1112

2

17 2

12

or 8

548

Course 2


Lesson Quiz: Part II

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?

118

pounds

Documents

Course 2 3-10 Multiplying Fractions and Mixed Numbers 3-10 Multiplying Fractions and Mixed Numbers Course 2 Warm Up Warm Up Problem of the Day Problem