Properties of Numbers

We’ll learn 4 properties: Commutative Property Associative Property Distributive Property Identity

Commutative Property

We commute when we go back and forth from work to home.

Algebra terms commute when they trade places

This is a statement of the commutative property for addition:

It also works for multiplication:

Associative Property

To associate with someone means that we like to be with them.

( ) The tiger and the panther are associating with each other. They are leaving the lion out. ( )

In algebra:

( ) The panther has decided to befriend the lion. The tiger is left out. ( )

In algebra:

This is a statement of the Associative Property: The variables do not change their order.

The Associative Property also works for multiplication:

Distributive Property

We have already used the distributive property. Sometimes executives ask for help in distributing papers.

The distributive property only has one form. Not one for addition . . .and one for multiplication . . .because both operations are used in one property.

We add here: 4(2x+3) We multiply here:

4(2x+3) =8x +12 This is an example of the distributive property. 2x +3

Here is the distributive property using variables: y +z x xy xz

Identity Property

The identity property makes me think about my identity.

The identity property for addition asks, “What can I add to myself to get myself back again?

The above is the identity property for addition. is the identity element for addition.

The identity property for multiplication asks, “What can I multiply to myself to get myself back again?

The above is the identity property for multiplication. is the identity element for multiplication.

Here are the 3 properties that have to do with addition: x + y = y + x Commutative Associative x + (y + z)= (x + y) + z x + 0 = x Identity

Here are the 3 properties for multiplication: Commutative xy = yx Associative x(yz)= (xy)z Identity

The distributive property contains both addition and multiplication:

The End