Since division is defined as multiplication by the reciprocal, the rules for signs of
quotients are the same as those for signs of products.
SECTION 1.2 Operations on Real Numbers 19
Dividing Real NumbersSame sign The quotient of two nonzero real numbers with the samesign is
positive.
Different signs The quotient of two nonzero real numbers with differentsigns
is negative.
CAUTION Division by 0 is undefined. However, dividing 0 by a nonzero num-
ber gives the quotient 0. For example,
is undefined, but (since
Be careful when 0 is involved in a division problem.
0 # 6 =0).
0
6
= 0
6
0
DivisionFor all real numbers aand b(where
That is, multiply the first number (the dividend) by the reciprocal of the second
number (the divisor).
ab
a
b
a#
1
b
.
bZ0),
This suggests the following definition of division of real numbers.
There is no reciprocal for the number 0, so division by 0 is undefined.For example,
(^150) is undefined and - (^10) is undefined.
Dividing Real Numbers
Find each quotient.
(a)
(b) The reciprocal of is
(c) The reciprocal of is
This is a complex fraction(Section 7.3)—a quotient that has a fraction in the
numerator, the denominator, or both.
=- -^59 -^95.
2
3
#a-^9
5
b =
6
5
-
2
3
-
5
9
- 3 -^13.
6
- 3
= 6 a-
1
3
b =- 2
a
b=a#1
b- 12
4
=- 12 #