Algebra Demystified 2nd Ed

Chapter 1 FraCtions 3

PRACTICE

Perform the multiplication with the rule ab⋅cd = bdac.

1.

7

6

1

4

⋅=

2.

8

15

6

5

⋅=

3.

5

3

9

10

⋅=

4.

40

9

2

3

⋅=

5.^3
7

30

4

⋅=

SOLUTIONS

1.^7
6

1

4

71

64

7

24

⋅=⋅

⋅

=

2.^8
15

6

5

86

15 5

48

75

⋅=⋅

⋅

=

3.^5
3

9

10

59

310

45

30

⋅=⋅

⋅

=

4.^40
9

2

3

40 2

93

80

27

⋅=⋅

⋅

=

5.^3
7

30

4

330

74

90

28

⋅=⋅

⋅

=

Multiplying Fractions and Whole Numbers

We now develop a rule for multiplying a whole number and a fraction. To see

how we can multiply a fraction by a whole number, we use a pie chart to find

the product 4 2

9

⋅.

The shaded region in Figure 1-5 represents^29.

We want a total of four of these shaded regions. See Figure 1-6.

As we can see, four of the^29 regions give us a total of eight^19 ’s. This is

why 4 2

9

⋅ is 4 2

9

42

9

8

⋅= 9

⋅ =.

In general, when multiplying W⋅ab (where W is a whole number), we have

Wa⋅ of the^1 b fractions. This fact gives us the multiplication rule W a

b

Wa

b

⋅=.

✔SOLUTIONS

PRACTICE

Perform the multiplication with the rule