relationships that are always true for real numbers are called _____________, which are rules used...

Relationships that are always true

for real numbers are called

_____________, which are rules

used to rewrite and compare

expressions.

properties

PROPERTY DEFINITION EXAMPLE

CommutativeProperty

Addition

Multiplication

AssociativeProperty

Addition

Multiplication

Distributive Property

Changing Orderdoes not change the outcome

1 + 2 = 2 + 1a + b = b + a1 ● 2 = 2 ● 1a b = b a

(8 + 6) + 7 = 8 + (6 + 7)(a + b) + c = a + (b + c)4● (5 ●9) = (4 ●5) ● 9(ab) ● c = a ● (bc )

10 (1 + 7) = 10 ● 1 + 10 ●715(x - 4) = 15 ● x – 15 ●4

RegroupingOrder stays the same only ( ) move(Change who you associate

[hang out] with)

a(b + c) = ab + aca(b - c) = ab - ac

Property Definition Example

Identity Properties

Addition Addition

Multiplication Multiplication

Inverse Properties

Addition Addition

Multiplication Multiplication

Adding “0” = no change

Multiply by 1= no change

a + (-a) = 0

-17 + 0 = -17

1● 99y = 99y

14 + (-14) = 0

Property Definition Example

Zero Property of Multiplication

Multiplication Property of –1

Multiply by 0, you get 0

Multiply by -1, you change the sign

(7003)(0) = 0

-1(a) = -a-1(2) = -2-1(-5) = 5

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.

F. A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. 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.

$7.75 + $2.40 + $1.25 = (7.75 +1.25 + 2.40) = 9.00 + 2.40 = 11.40

3●4 ●6 ●10 = 720

Using Properties for Mental Calculations

Writing Equivalent Expressions

(5 ● 3)n 15n

(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