1. Properties of Numbers

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

3. Commutative
Property

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

5. Algebra terms commute
when they trade places

6. This is a statement of the
commutative property
for addition:

7. It also works for
multiplication:

8. Associative
Property

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

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

11. In algebra:

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

13. In algebra:

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

15. The Associative Property also works for multiplication:

16. Distributive
Property

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

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

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

21. 4(2x+3) =8x +12 This is an example of the distributive property. 2x +3

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

23. Identity
Property

24. The
identity
property
makes me
think
about my
identity.

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

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

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

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

29. 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

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

31. The distributive property contains both addition and multiplication:

32. The
End