Ch 4 Sec 3: Slide #1

Columbus State Community College

Chapter 4 Section 3

Multiplying and Dividing Signed Fractions

Ch 4 Sec 3: Slide #2

Multiplying and Dividing Signed Fractions

1. Multiply signed fractions.

2. Multiply fractions that involve variables.

3. Divide signed fractions.

4. Divide fractions that involve variables.

5. Solve application problems involving multiplying and dividing fractions.

Ch 4 Sec 3: Slide #3

“ of ”

NOTE

When used with fractions, the word of indicates multiplication. For example,

13

14

of means13

14

•

Ch 4 Sec 3: Slide #4

Multiplying Fractions

Multiplying Fractions

If a, b, c, and d are numbers (but b and d are not 0), then

ab

cd

•a • cb • d

=

Ch 4 Sec 3: Slide #5

34

57

•– –

Multiplying Signed Fractions

Multiply.

(a)

EXAMPLE 1 Multiplying Signed Fractions

3 • 5 4 • 7

=1528

=

34

57

•– –

The product of two negative

numbers is positive.

The answer is in lowest terms because 15 and 28 have no common

factor other than 1.

Ch 4 Sec 3: Slide #6

Multiplying Signed Fractions

Multiply.

(b)

EXAMPLE 1 Multiplying Signed Fractions

12

35

•

12

35

•1 • 3 2 • 5

=3

10=

The answer is in lowest terms because 3 and 10 have no common

factor other than 1.

Ch 4 Sec 3: Slide #7

1

1

1

1

1

1

Using Prime Factorization to Multiply Fractions

EXAMPLE 2 Using Prime Factorization to Multiply Fractions

Multiplying a positive number times a negative

number gives a negative product.

(a) 67

1418

• –

67

1418

• – 2 • 3 • 2 • 77 • 2 • 3 • 3

= – 23

= –

Ch 4 Sec 3: Slide #8

11 1

1 11

Using Prime Factorization to Multiply Fractions

EXAMPLE 2 Using Prime Factorization to Multiply Fractions

(b) 59

2735

of

59

2735

•5 • 3 • 3 • 33 • 3 • 5 • 7

=37

=

Ch 4 Sec 3: Slide #14

1

1

Multiplying a Fraction and an Integer

EXAMPLE 3 Multiplying a Fraction and an Integer

Find23

of 45.

23

451

•2 • 3 • 3 • 5

3 • 1 =

301

= 30=

Ch 4 Sec 3: Slide #15

1

11

1

Multiplying Fractions with Variables

EXAMPLE 4 Multiplying Fractions with Variables

(a)

2 • 2 • m • m • n • n • n • 3 • 55 • 2 • 2 • 3 • m • n • n • n • n

=

mn

=

4 m2 n3

5•

1512 m n4

4 m2 n3

5•

1512 m n4

1

1

1

1

1

1

1

1

1

1

1

1

Ch 4 Sec 3: Slide #16

1

1

1

1

1

1

1

1

1

1

5 • a • 2 • 2 • 3 • b • b2 • 3 • b • 5 • 7 • a

=5 a6 b

• 12 b2

35 a

Multiplying Fractions with Variables

EXAMPLE 4 Multiplying Fractions with Variables

2 b7

=

(b) 5 a6 b

• 12 b2

35 a

Ch 4 Sec 3: Slide #17

Reciprocal of a Fraction

Two numbers are reciprocals of each other if their product is 1.

The reciprocal of the fraction is because

Reciprocal of a Fraction

ab

ba

•

ab

ba

1

1

1

1

= 1= 11

a • bb • a

=

Ch 4 Sec 3: Slide #18

Reciprocals

Find the reciprocal of each number.

1.

2.

3.

Number Reciprocal Reason

47

29

92

74

818

47

74

2828

= = 1

=29

92

1818

= 1

81

18

88

= = 1

Ch 4 Sec 3: Slide #19

Reciprocal

NOTE

Every number has a reciprocal except 0. Why not 0?

0 • (reciprocal) ≠ 1

Put any number here. When you

multiply it by 0, you get 0, never 1.

Ch 4 Sec 3: Slide #20

Dividing Fractions

Dividing Fractions

If a, b, c, and d are numbers (but b, c, and d are not 0), then we have the following.

ab

cd

÷ab

dc

•=

In other words, change division to multiplying by the reciprocal of the divisor.

Ch 4 Sec 3: Slide #21

1

4

3

1

Dividing Signed Fractions

EXAMPLE 5 Dividing Signed Fractions

(a)

34

= –

25

÷8

15–

25

÷8

15– =

25

•158

–

ReciprocalsChange division to multiplication

Ch 4 Sec 3: Slide #22

5 ÷14

Dividing Signed Fractions

EXAMPLE 5 Dividing Signed Fractions

20=

(b) 5 ÷14

=51

•41

ReciprocalsChange division to multiplication

Ch 4 Sec 3: Slide #23

Dividing Signed Fractions

EXAMPLE 5 Dividing Signed Fractions

(c) 0÷49

Division by zero is undefined.

Ch 4 Sec 3: Slide #24

1 1

1 1

1

1

a2

b3• 2 b2

a

Dividing Fractions with Variables

EXAMPLE 6 Dividing Fractions with Variables

a • a • 2 • b • bb • b • b • a

=

(a) a2

b3÷

a2 b2

=2ab

Ch 4 Sec 3: Slide #25

Dividing Fractions with Variables

EXAMPLE 6 Dividing Fractions with Variables

1 1

11

1

1

n3

6•

1

n4

n • n • n • 12 • 3 • n • n • n • n

=

(b) n3

6÷ n4

=1

6n

Ch 4 Sec 3: Slide #26

Indicator Words

Indicator Words for Multiplication

Indicator Words for Division

product

double

triple

times

twice

of (when of follows a fraction)

per

each

goes into

divided by

divided into

divided equally

Ch 4 Sec 3: Slide #27

EXAMPLE 7 Using Indicator Words – Solving Applications

(a) Alberto will spend of his paycheck on his bills. If

Alberto receives a paycheck for $480, how much will he

spend on his bills?

16

16

of 480 = 16

•4801

= 80

Alberto will spend $80 on his bills.

80

1

Using Indicator Words to Solve Application Problems

Ch 4 Sec 3: Slide #28

EXAMPLE 7 Using a Sketch – Solving Applications

(b) Bina purchased a spool containing 36 yd of ribbon. She wants

to make awards for a banquet. If each award requires yd

of ribbon, how many awards can she make?

23

23

36 ÷ = 361

•32

= 54

Bina can make 54 awards.

18

1

36 yd of ribbon

23

yd

Using a Sketch to Solve Application Problems

Ch 4 Sec 3: Slide #29

Multiplying and Dividing Signed Fractions

Chapter 4 Section 3 – Completed

Written by John T. Wallace