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2.6 – Division of Rational Numbers
Definition
For all rational numbers a and b, the quotient
a
(or a  b ), where b  0 , is
b
the number c such that cb  a .
Dividing Positive and Negative Numbers
To divide positive and negative numbers, divide their absolute values.
Use the following rules to determine the sign of the quotient.
 When we divide a positive number by a negative number or a negative



number by a positive number, the quotient is negative.    or   



 When we divide two positive numbers or two negative numbers, the



quotient is positive.    or   



Example 1 – Divide.
a.
21
3
b.
 12
4
c.
8
2
Definition
Two rational numbers whose product is 1 are called multiplicative inverses
or reciprocals of each other.
Property of Multiplicative Inverses
For each nonzero rational number a, there is one and only one rational
number
1
1
such that a   1 .
a
a
Example 2 – Find the reciprocal.
a.
3
7
b.  8
Dividing Numbers
For all rational numbers a and b b  0 ,
a
1
a
b
b
Example 3 – Divide.
a.
9 5

8 3
b.
1 5

2 7
L16 – pg 84 (1, 3, 19, 21, 41-51 odd)
c. 
2
7

5
3