1. Properties of Real Numbers

2. Relationships that are always true for real numbers are called _____________, which are rules used to rewrite and compare expressions.
properties

3. Order stays the same only ( ) move
PROPERTY
DEFINITION
EXAMPLE
Commutative
Property
Addition
Multiplication
Associative
Distributive Property
1 + 2 = 2 + 1
a + b = b + a
Changing Order
does not change
the outcome
1 ● 2 = 2 ● 1
a b = b a
(8 + 6) + 7 = 8 + (6 + 7)
(a + b) + c = a + (b + c)
Regrouping
Order stays the same only ( ) move
4● (5 ●9) = (4 ●5) ● 9
(ab) ● c = a ● (bc )
(Change who you associate [hang out] with)
a(b + c) = ab + ac
a(b - c) = ab - ac
10 (1 + 7) = 10 ● ●7
15(x - 4) = 15 ● x – 15 ●4

4. -17 + 0 = -17 1● 99y = 99y a + (-a) = 0 14 + (-14) = 0 Property
Definition
Example
Identity Properties
Addition
Multiplication
Inverse Properties
Adding “0” = no change
= -17
Multiply by 1= no change
1● 99y = 99y
a + (-a) = 0
14 + (-14) = 0

5. Multiply by 0, you get 0 (7003)(0) = 0 -1(a) = -a -1(2) = -2
Property
Definition
Example
Zero Property of Multiplication
Multiplication Property of –1
Multiply by 0,
you get 0
(7003)(0) = 0
-1(a) = -a
-1(2) = -2
-1(-5) = 5
Multiply by -1,
you change the sign

6. Identifying Properties (What property is shown in each example?)
Zero Property of Multiplication
Associative Prop. of Addition
Identity of Addition (Additive Identity)
Identity of Multiplication (Multiplicative Identity)
Commutative Prop. (Addition)
The “z” and the √ y have been switched.

7. Using Properties for Mental Calculations
F. A movie ticket costs $ A drink costs $ Popcorn costs $ What is the total cost for a ticket, a drink, and popcorn? Use mental math.
G. A can hold 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math.
$ $ $1.25 = ( ) =
= 11.40
3●4 ●6 ●10 = 720

8. Writing Equivalent Expressions
(7b + 4) + 8
7b + ( 4 + 8)
7b + 12 1 6x
(2.1 ● 4.5)x
9.45x
6 + (3 + 4h)
(6 + 3) + 4h
9+ 4h