1. Section 2 Properties of Real Numbers
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 Numbers Irrational Numbers
Numbers that cannot be written as ratios
Decimals that never terminate and never repeat
Square roots of positive non-perfect squares
Ex: √2, -√7, √(8/11), , …

5. Real Numbers Rational 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 Numbers Rational Numbers Integers
“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

7. Real Numbers Rational Numbers Integers Whole Numbers
Zero and positive integers
Ex: 0, 1, 2, 3, 4, …

8. Real Numbers Rational Numbers Integers Whole Numbers Natural 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.√6
irrational, real

12. Example: Name the set of numbers to which each number belongs.
√100
natural, whole, integer, rational, real

13. Example: Name the set of numbers to which each number belongs.
-23.3
rational, real

14. Properties of Real Numbers
Property
Addition
Multiplication
Commutative
commute = to move
a + b = b + a
ab = ba
Associative
associate = regroup
(a+b)+c = a+(b+c)
(ab)c = a(bc)
Identity
a+0=a,0+a=a
a*1=a, 1*a=a
Inverse
a+(-a)=0
a*(1/a)=1,a≠0
Distributive
a(b+c) = ab + ac

15. Identify the property Example 5
Which Property is illustrated?
6 + (-6) = 0
Inverse Property of Addition
(-4 ∙ 1) – 2 = -4 – 2
Identity Property of Multiplication

16. Try these Problems p. 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