Properties of Real Numbers

1
Chapter 1

• Section 2
• Properties of Real Numbers

2
Classifications of Numbers

• Imaginary Numbers will be introduced later.

3
Real Numbers all the numbers you use in
everyday life

• The largest classification we will deal with
• Include any number that you can tell me
• Ex
• Split into Rational and Irrational Numbers

4
Real NumbersIrrational Numbers

• Numbers that cannot be written as ratios
• Decimals that never terminate and never repeat
• Square roots of positive non-perfect squares
• Ex v2, -v7, v(8/11), , 1.011011101111011111

5
Real NumbersRational Numbers

• All the numbers that can be written as a ratio
  (fraction)
• This includes terminating and repeating decimals.
• Ex 8, 10013, -54, 7/5, -3/25, 0, 0/6, -1.2,
  .09, .3333.

6
Real NumbersRational NumbersIntegers

• Complete numbers (no parts fractions or
  decimals)
• Negative, Zero, and Positive
• Each negative is the additive inverse (or
  opposite) of the positive
• Ex -543, 76, 9, 0, -34

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Real NumbersRational NumbersIntegersWhole
Numbers

• Zero and positive integers
• Ex 0, 1, 2, 3, 4,

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Real NumbersRational NumbersIntegersWhole
NumbersNatural Numbers

• Also known as Counting Numbers
• Think of young children
• Ex 1, 2, 3, 4, 5, 6,

9
Example Name the set of numbers to which each
number belongs.

• -2/3
• rational, real

10
Example Name the set of numbers to which each
number belongs.

• 9.999
• rational, real

11
Example Name the set of numbers to which each
number belongs.

• v6
• irrational, real

12
Example Name the set of numbers to which each
number belongs.

• v100
• natural, whole, integer, rational, real

13
Example Name the set of numbers to which each
number belongs.

• -23.3
• rational, real

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Properties of Real Numbers
Property Addition Multiplication
Commutative commute to move a b b a ab ba
Associative associate regroup (ab)c a(bc) (ab)c a(bc)
Identity a0a,0aa a1a, 1aa
Inverse a(-a)0 a(1/a)1,a?0
Distributive a(bc) ab ac a(bc) ab ac
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Identify the propertyExample 5

• Which Property is illustrated?
• 6 (-6) 0
• Inverse Property of Addition
• (-4 1) 2 -4 2
• Identity Property of Multiplication

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Try these Problemsp. 7 Check Understanding

• Which Property is illustrated?
• (3 0) 5 3 5
• Identity Property of Addition
• -5 2 (-3) (-5 2) (-3)
• Associative Property of Addition

17
Homework

• P.15 19-35, 49-56