Beginning Algebra, 11th Edition

From the definitions of multiplication and division of real numbers,

and so

Based on this example, the quotient of a positive and a negative number can be

expressed in any of the following three forms.

- 40

8

=

40

- 8

.

40

- 8

= 40 a

1

- 8

b =-5,

- 40

8

=- 40 #

1

8

=- 5

SECTION 1.6 Multiplying and Dividing Real Numbers 53

Equivalent Forms

For any positive real numbers xand y,

x

y



x

y



x

y

.

Similarly, the quotient of two negative numbers can be expressed as a quotient of

two positive numbers.

Equivalent Forms

For any positive real numbers xand y,

x

y



x

y

.

OBJECTIVE 5 Use the rules for order of operations when multiplying and

dividing signed numbers.

Using the Rules for Order of Operations

Perform each indicated operation.

(a)

Multiply.

Definition of subtraction

Add.

(b)

Work inside the parentheses.

Multiply.

(c)

Subtract inside the parentheses.

Multiply.

=- 10 Add.

=- 6 + 1 - 42

=- 6 + 21 - 22

- 6 + 213 - 52

= 25

=- 51 - 52

- 51 - 2 - 32

=- 12

=- 18 + 6

= - 18 - 1 - 62

- 9122 - 1 - 32122

NOW TRY EXAMPLE 5

EXERCISE 5
Perform each indicated
operation.

(a)

(b)

121 - 42 - 61 - 32

- 417 - 162

- 4162 - 1 - 52152

NOW TRY ANSWERS

5. (a) 1 (b)- (^56)
   Begin inside the parentheses.
   Do notadd
   first.

(d)

Simplify the numerator and denominator separately.

or

11

5

=

- 22

- 10

,

=

- 10 - 12

21 - 52

51 - 22 - 3142

211 - 62

NOW TRY

Subtract in the numerator. Multiply in the denominator.

Write in lowest terms.