1. Properties of Real Numbers
Section 1.2
Properties of Real Numbers

2. Real Numbers Living Things R = Rat Rational Irrational IRR Animals
Plants I
Integers
Mammals W
Whole
Dogs N
Natural
Border Collies

3. Real Numbers Ex: ½ , 0.3, 1, 2, 2, , , -1.07 Irrational Numbers
Integers
Ex: …, -2, -1, 0, 1, 2, …
Whole Numbers
Ex: 0, 1, 2, 3 …
Natural Numbers
Ex: 1, 2, 3 …

4. Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, …
Textbook: Page 5
Natural Numbers: 1, 2, 3, …
Numbers used for counting
Whole Numbers: 0, 1, 2, 3, …
Natural Numbers and 0
Integers: …, -2, -1, 0, 1, 2, …
Natural Numbers, 0, and their opposites
Rational Numbers:
Repeating or terminating decimal
Irrational Numbers: cannot be written as a ratio of integers; non-repeating or non-terminating decimals

5. Graphing on a Number Line:2 4 -2 -4
Rational, Real 1. 2. 3. 4. 5.
Irrational, Real
Natural, Whole, Integer, Rational, Real
White Boards
Integer, Rational, Real
Irrational, Real

6. The opposite (additive inverse) of any number a is –a
When you add together, = 0
The Identity Element!
The reciprocal (multiplicative inverse) of any nonzero number a is
When you multiply together, = 1

7. White Boards Opp. Rec. Opp. Rec. Opp. Rec. Mixed Number:
Improper Fraction:
White Boards
Opp.
Rec.
Opp.
Rec.
Opp.
Rec.

8. Properties of Real Numbers
Property
Addition
Multiplication
Closure
Commutative
Associative
Identity
Inverse
Distributive
Words
a + b is a real number.
ab is a real number.
Order
a + b = b + a
ab = ba
Group
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Mirror
a + 0 = a, 0 + a = a
a  1 = a, 1  a = a
Undo
a + (-a) = 0
a  = 1, a ≠ 0
1st x 1st + 1st x 2nd
a(b + c) = ab + ac
Identifying Properties of Real Numbers:
1. (-7)(2  5) = (-7)(5  2)
 ( 8 + 0) = 3  8
[2 + (-3)] = (-5 + 2) + (-3)
White Boards
Commutative Property of Multiplication
Identity Property of Addition
Associative Property of Addition

9. Absolute Value
Absolute value of a real number is the distance from zero on the number line.
= 4
= – 18
= 1.5

10. page 9
White Boards
79.
81.