OBJECTIVE 4 Use the reciprocal of a number to apply the definition of
division. Recall that the result of division is called the quotient.The quotient of
two numbers is found by multiplying by the reciprocal,or multiplicative inverse,
of the second number.
SECTION 1.6 Multiplying and Dividing Real Numbers 51
Integer 18 20 15 7 1
1, 18 1, 20 1, 15 1, 7 1, 1
2, 9 2, 10 3, 5
Pairs of 3, 6 4, 5
factors- 3, - 6 - 4, - 5
- 2, - 9 - 2, - 10
- 1, - 18 - 1, - 20 - 3, - 5
- 1, - 15
- 1, - 7 - 1, - 1
- 1, - 15
Multiplicative Inverse
Number (Reciprocal)
45
58 - (^85)
1
5 , or -^
1
5
10
0.3, or 3
3
101
4A number and its multiplicative
inverse have a product of 1.For
example,
4 #^14 =^44 =1.
Reciprocal or Multiplicative InversePairs of numbers whose product is 1 are called reciprocals,or multiplicative
inverses,of each other.
The table in the margin shows several numbers and their multiplicative inverses.
Definition of DivisionFor any real numbers xand y, with
That is, to divide two numbers, multiply the first by the reciprocal, or multi-
plicative inverse, of the second.
Example:
- 8
4
=- 8 #
1
4
= 2
x
y
x#
1
y
yZ0,.
NOTE Recall that an equivalent form of is where xis called the dividend
and yis called the divisor.For example, - 48 =- 8 ,4.
xy x, y,
Since division is defined in terms of multiplication, all the rules for multiplying
signed numbers also apply to dividing them.
Using the Definition of DivisionFind each quotient, using the definition of division.
(a) (b)
- 10
2
=- 10 #
1
2
xy=x# (^1) y =- 5
12
3
= 12 #
1
3
= 4
EXAMPLE 3
NOW TRY
EXERCISE 3
Find each quotient, using the
definition of division.
(a) (b)
(c) -
5
6
,
17
9
9.81
- 0.9
15
- 3
NOW TRY ANSWERS
- (a)- 5 (b)-10.9 (c)- 3415
(c) (d)
NOW TRY-
2
3
, a-
4
5
b =-
2
3
#a- 5
4
b =
5
6
- 1.47
- 7
=-1.47a-
1
7
b =0.21
Remember to
write in lowest
terms.