Warm-Up
 To which set(s) of numbers does each number belong?
1. 2
2. -2
3. π
4. √3
5. 0
6. 0.5
1.1 Properties of Real Numbers
Objectives: Students will be able to graph and order
real numbers and to identify and use properties of real
numbers.
Subsets of Numbers
 Natural, Whole, Integers, Rational, Irrational, Real
Numbers
Classifying Numbers
 To which set does each number belong:
1.
7
2.
0.8
3.
29
4.
144
Opposites and Reciprocals
 The ___________________ or additive inverse if any
number a is –a.
 Example: ____ and ____ are additive inverses.
_____ and _____ are opposites.
 The reciprocal or _________________ ___________ of
any non-zero number a is 1
a
 The product of reciprocals is ____.
Examples: Find the additive inverse and
multiplicative inverse of each number.
400
2. 4.2
3. -0.25
1.
4.
4

9
Name the property illustrated
3( x  9)  3 x  27
3(9 x)  (3  9) x
Absolute Value
 The absolute value of a number is it’s _______________
from zero on a number line.
 Example:  15  15
 Simplify each of the following:
1
1
23
 15
 23
 15
 10  6
 16
Properties of Real Numbers
 Commutative
a b  ba
ab  ba
 Associative
( a  b)  c  a  (b  c )
( ab)c  a (bc )
 Identity
a0  a
 Inverse
a  (a)  0
 Distributive
a (b  c)  ab  ac
a 1  a
1
a 1
a