Properties of Numbers

InAlgebra County

We’ll learn 5 properties:•Commutative Property•Associative Property•Distributive Property•Identity•Inverse

CommutativeProperty

We commutewhen we go back and forth

from work to home.

Algebra terms commute when they trade places

x y

y x

This is a statement of thecommutative property

for addition:

x y y x

It also works for multiplication:

xy yx

AssociativeProperty

To associate with someone means that we like to

be with them.

The tiger and the pantherare associating with eachother.

They are leaving thelion out.

( )

In algebra:

( )x y z

The panther has decided tobefriend the lion.

The tiger is left out.

( )

In algebra:

( )x y z

This is a statement of theAssociative Property:

( ) ( )x y z x y zThe variables do not change

their order.

The Associative Propertyalso works for multiplication:

( ) ( )xy z x yz

DistributiveProperty

We have already used thedistributive property.

Sometimes executives askfor help in distributing

papers.

The distributive property onlyhas one form.

Not one foraddition . . .and one for

multiplication

. . .because both operations areused in one property.

4(2x+3)

We multiply here:

We add here:

4(2x+3)=8x+12

This is an exampleof the distributive

property.

Here is the distributiveproperty using variables:

( )x y z xy xz

IdentityProperty

The identity

property makes

me thinkaboutmy

identity.

The identity property for addition asks,

“What can I add to myselfto get myself back again?

_x x0

The above is the identity propertyfor addition.

_x x0

is the identity elementfor addition.0

The identity property for multiplication

asks, “What can I multiply to myself

to get myself back again?

(_ )x x1

The above is the identity propertyfor multiplication.

1

is the identity elementfor multiplication.1

(_ )x x

InverseProperty

We learned about the inverseproperty when we did zero pairs.

2 ( 2) 0

The inverse property is related

to the identity property.

This is the identity element

for addition.

2 ( 2) 0

This is the inverse element

for addition.

2 ( 2) 0

The whole thing is the inverse property.

A statement of the inverseproperty for addition is:

( ) 0x x

What is the identityelement formultiplication?

2 ( 2) 01

To keep the same pattern,

it wouldgo here.

Therefore. . .

1

To keep the same pattern,

it wouldgo here.

2(_ )12

A statement of the inverseproperty for multiplication is:

1 1xx

Some examples of the inverseproperty for multiplication are:

15 15

2 3 13 2

Here are the 4 propertiesthat have to do with

addition:x + y = y + x

x + (y + z)= (x + y) + z

x + 0 = x

x + (-x) = 0

Commutative

Associative

Identity

Inverse

Here are the 4 propertiesfor multiplication:

xy = yxx(yz)= (xy)z

Commutative

Associative

Identity

Inverse

1x x 1 1xx

The distributive propertycontains both addition

and multiplication:

Distributive

( )x y z xy xz

TheEnd