2.4

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

2.4

Multiplying Fractions and Mixed Numbers

Martin-Gay, Basic Mathematics, 4e 22


Multiplying Fractions

Multiplying FractionsTo multiply two fractions, multiply the numerators and multiply the denominators.If a, b, c, and d represent positive whole numbers we have

a c a c

b d b d

P 141-142



Examples

Multiply.

a.

b.

c.

1 1

11 3

1 1

11 3

2 3

7 5

2 3

7 5

6

35

2 4

3 7

1

33

8

21

P 141-142



Examples

Multiply and simplify.

a.

b. 2 3 14

7 8 15

2 3 2 7

7 2 2 2 3 5

3 2 2 2

2 2 11

3 8

4 11

6

11

1

10

P 141-142



Practice Problems


1.

2.

3.

4.

P 141-142

78

53

56

15

7

5

8

3

6

1

3

1

63

11

18

1

8

5

55

6

855

56

440

30

8

3

15

4

120

12

1012

112

10

1

No common factors

No common Factors


4410

310

44

3



Practice Problems


5.

6.

7.

P 142

75

202

75

452

7

20

5

2

16

33

11

4

42211

31122

4

3

16

25

10

3

6

1

165232

5531

1622

5


64

5

7

42

7

8



Multiplying Fractions and Mixed Numbers or Whole Numbers

Multiplying Fractions and Mixed Numbers of Whole NumbersTo multiply with mixed numbers or whole numbers, first write any mixed or whole numbers as fractions and then multiply as usual.

P 143



Examples

Multiply.

a.

b. 2 3

59 8

2 43

9 8

8 7

3 8

2 72

3 8

7

3

2 2 2 7

3 2 2 2

1

or 23

2 43

3 3 2 2 2

43 7

136 36

P 143



Example

Multiply.

7

108

5 2 7

1 2 2 2

35

4

3or 8

4

P 143



Practice Problems


8.

9.

10.

11.

P 143-144

152

85

3

11or

3

4

15

8

2

12

183

2

13

182

1262

4

32

5

13

45

1116

45

1144

15

1135

15

56

1

5

351

565

3

218or

3

56

5

48or

5

44

Multiplying Fractions and Mixed Numbers or Whole Numbers

532

425

13

632



Example

Multiply. Check by estimating.

2 12 1

9 4

20 5

9 4 25 7

or 29 9

5 2 2 5

3 3 2 2

Let’s check by estimating.

22

9rounds to 2, rounds to 1, and 2 · 1 = 2.

The estimate is close to the exact value, so our answer is reasonable.

11

4

P 144



Example

An estimate for the measure of an adult’s wrist is of the waist size. If Jorge has a 34-inch waist, estimate the size of his wrist.

1

4

17 2 1

1 2 2

17

2

1or 8

234 1

1 4

Jorge’s wrist is about inches.1

82

P 145



Practice Problem 14 similar

SOLUTION

About 1/3 of all plant and animal species in the United States are at risk of becoming extinct. There are 20,439 known species of plants and animals in the United States. How many species are at risk of extinction?

204393

1

13

204391

13

681331

6813

P 145

Solving Problems by Multiplying Fractions



DONE

2.4

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