We can use multiplication to check a division problem. Consider Example 3(a).
12
3
= 4 , since 4 # 3 =12.
52 CHAPTER 1 The Real Number System
Division Involving 0For any real number x, with
is undefined.
Examples:
0
- 10
= 0 and
- 10
0
is undefined.
0
x
= 0 and
x
0
xZ0,
When dividing fractions, multiplying by the reciprocal works well. However,
using the definition of division directly with integers may be awkward. It is easier to
divide in the usual way and then determine the sign of the answer.
NOW TRY
EXERCISE 4
Find each quotient.
(a) (b)
(c) -
3
8
,
7
10
- 1.44
- 0.12
- 10
5
Dividing Signed NumbersThe quotient of two numbers having the samesign is positive.
The quotient of two numbers having differentsigns is negative.
Examples: and
- 15
5
=- 3
15
- 5
=-3,
- 15
- 5
= 3,
15
5
= 3,
Dividing Signed NumbersFind each quotient.
(a) (b) (c)
(d) -
1
8
, a-
3
4
b =-
1
8
#a- 4
3
b =
1
6
- 4.5
- 0.09
= 50
- 100
5
=- 20
8
- 2
=- 4
EXAMPLE 4
Remember to write in
lowest terms. NOW TRYNOW TRY ANSWERS
- (a)- 2 (b) 12 (c) - (^1528)
Multiply to check a
division problem.
This relationship between multiplication and division allows us to investigate division
by 0. Consider the quotient
Now consider
We need to find a number that when multiplied by 0 will equal 3, that is,
Noreal number satisfies this equation, since the product of any real number and 0
must be 0. Thus,
is not a number, and division by 0 is undefined. If a division problem
involves division by 0, write “undefined.”
x
0?# 0 = 3.
3
0
=?
30.
0
3
= 0 , since 0 # 3 =0.
03.
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