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1 Basic Math Review
Numbers
NATURAL NUMBERS
{1, 2, 3, 4, 5, …}
WHOLE NUMBERS
{0, 1, 2, 3, 4, …}
INTEGERS
{…, 3, 2, 1, 0, 1, 2, …}
RATIONAL NUMBERS
All numbers that can be written in the form , where a
and b are integers and .
IRRATIONAL NUMBERS
Real numbers that cannot be written as the quotient of two
integers but can be represented on the number line.
REAL NUMBERS
Include all numbers that can be represented on the number
line, that is, all rational and irrational numbers.
PRIME NUMBERS
A prime number is a number greater than 1 that has only
itself and 1 as factors.
Some examples:
2, 3, and 7 are prime numbers.
COMPOSITE NUMBERS
A composite number is a number that is not prime. For
example, 8 is a composite number since
8 = 2 . # 2 # 2 = 23
Rational Numbers
Real Numbers
23, 22.4, 21 , 0, 0.6, 1, etc. 4_ 2 5
25VN
Irrational
Numbers
Integers p 23, 22, 21, 0, 1, 2, 3, p
Whole Numbers 0, 1, 2, 3, p
Natural Numbers 1, 2, 3, p
3,
VN2, p, etc.
b Z 0
a>b
–5 –4 –3
Negative integers Positive integers
The Number Line
Zero
–2 –1 0 1 2 3 4 5
ISBN-13:
ISBN-10:
978-0-321-39476-7
0-321-39476-3
9 780321 394767
90000
Int Properties
Identity Property of Zero:
Inverse Property:
Commutative Property:
Associative Property:
PROPERTIES OF MULTIPLICATION
Property of Zero:
Identity Property of One: , when .
Inverse Property: , when .
Commutative Property:
Associative Property:
PROPERTIES OF DIVISION
Property of Zero: , when .
Property of One: , when .
Identity Property of One:
Absolute Value
The absolute value of a number is always ≥ 0.
If , .
If , .
For example, and . In each case, the
ƒ -5 ƒ = 5 ƒ 5 ƒ = 5
a 6 0 ƒ a ƒ = a
a 7 0 ƒ a ƒ = a
a
1 = a # 1
a Z 0 a
a = 1
a Z 0
0
a = 0
a # 1b # c2 = 1a # b2 # c
a # b = b # a
a # a Z 0
1
a = 1
a # 1 = a a Z 0
a # 0 = 0
a + 1b + c2 = 1a + b2 + c
a + b = b + a
a + 1-a2 = 0
a + 0 = a
Key Words
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