# 9.3 The Rational Numbers Rational numbers – A. Inverses ```9.3
The Rational Numbers
Rational numbers –
A.
Inverses (Opposites)
Recall:
Additive Inverse—is the opposite of a number.
Example 1.
3
1.
4
B.
Find the additive inverse of each of the following.
2.
− 5 .1
−9
3.
Absolute Value
Recall: Absolute Value—is the distance form 0 to a number on the number line.
Example 2.
−1
1.
8
Find the absolute value of each of the following.
1
−3
2.
3.
− 8 .2
4
C. Addition and Subtraction of Rational Numbers:
Example 3.
Find each value.
1.
1
4
− 1.4 + (−6.1)
−
2.
7 5
−
8 6
D. Multiplication of Rational Numbers
Example 4.
Find each value.
1.
− 2.2(3.2)
E.
Reciprocals of a Number
2.
3  4
⋅− 
7  5
Reciprocals:
Example 5.
4
1.
5
Find the reciprocals of the following.
2.
−
7
9
F.
Division of Rational Numbers
Find each value.
Example 6.
3  4
1.
&divide;− 
5  7
3.
− 3.6
1.2
G.
Classifying Real Numbers
1
−
6  3
&divide; − 
7  5
4.
− 3.1
− 12.4
Whole #’s
0, 1, 2, 3, 4,….
Rational #’s
3 1
, 0, 2, − 3, , , 4 , − 4 , ......
2
4 3
−
Real #’s
2.
Natural #’s
1, 2, 3, ….
Integer #’s
... − 3, − 2, − 1, 0,1, 2, 3,....
Irrational #’s
π , 2 ,− 2 , 3 ,− 3 ,....
Two types of Real Numbers
1.
Rational Numbers—any numbers that can be written as
a
, b ≠ 0 and will terminate or
b
repeat when written as a decimal.
2.
a
, b ≠ 0 and will never
b
terminate or repeat when written as a decimal.
Irrational Numbers—any numbers that cannot be written as
Example 7.
Classify each number by making a check mark in the appropriate row.
−
2
7
3.4
8
Natural number
Whole number
Integer
Rational number
Irrational number
Real number
9.3(page 525-526)
GW:
HW: