1.1 Basic Concepts
Sets of Numbers
Natural Numbers
Whole Numbers
Integers
Rational Numbers
andqare integers,(all terminating or repeating decimals)
Irrational Numbers
is a real number that is not rational(all nonterminating, nonrepeating decimals)
Real Numbers
is a rational or an irrational numberAbsolute Value ae
a
aifa is positive or 0
ifa is negative5 x|x 6
5 x|x 6
E q^0 Fp
q|p5 Á,2,1, 0, 1, 2,Á 6
5 0, 1, 2, 3, 4,Á 6
5 1, 2, 3, 4,Á 6 10, 25, 143 Natural Numbers
0, 8, 47 Whole Numbers
, , 0, 4, 9 Integers, Rational NumbersIrrational NumbersReal Numbers|- 12 |= 12
| 12 |= 12
- 3,-
2
7
, 0.7, p, 11- 22 , 3 ,p
- 4
2
3
,-0.14, 0,
15
8
, 6, 0.33333Á
- 22 - 7
QUICK REVIEW
CONCEPTS EXAMPLES
1.2 Operations on Real Numbers
Addition
Same Sign:Add the absolute values. The sum has the
same sign as the given numbers.
Different Signs:Find the absolute values of the numbers,
and subtract the lesser absolute value from the greater.
The sum has the same sign as the number with the greater
absolute value.
Subtraction
For all real numbers aandb,
Multiplication and Division
Same Sign:The answer is positive when multiplying or
dividing two numbers with the same sign.
Different Signs:The answer is negative when multiplying
or dividing two numbers with different signs.
Division
For all real numbers aandb(where
aba
ba#
1
b.
bZ0),aba 1 b 2.Multiply by the reciprocal
of the divisor.
Note2
3
,
5
6
=
2
3
#^6
5=
4
5
- 24
12
- 7152 =- 35 =- 2
- 15
- 5
- 31 - 82 = 24 = 3
- 5 - 1 - 32 =- 5 + 3 =- 2
- 12 + 4 =- 112 - 42 =- 8
- 5 + 8 = 8 - 5 = 3
- 2 + 1 - 72 =- 12 + 72 =- 9
(continued)40 CHAPTER 1 Review of the Real Number System
ANSWERS(to Test Your Word Power)
1.C;Example:The set of whole numbers less than 0 is the empty set, written 2.A;Examples: a,b,c 3.D;Examples: and
4.B;Examples:3 is the reciprocal of is the reciprocal of 5.D;Example:2 and 5 are factors of 10, since both divide evenly (without
remainder) into 10. 6.B;Examples: and 7.B;Examples:6, 8.A;Examples:The term has numerical coefficient 8, and
- 10 x^3 yhas numerical coefficient -10.
34 x^102 x,- 4 ab^28 z(^13) ;- (^52) - (^25).
0. | 2 |= 2 |- 2 |= 2