1. Properties of Operations
Mrs. Rauch

2. Four Properties of Operations
Commutative Property
Associative Property
Identity Property
Distributive Property

3. The Commutative Property
Background
The word commutative comes from the verb “to commute.”
Definition on dictionary.com
Commuting means changing, replacing, or exchanging
People who travel back and forth to work are called commuters.
Traffic Reports given during rush hours are also called commuter reports.

4. Here are two families of commuters.
Commuter B
Commuter A
Commuter A & Commuter B changed lanes.
Remember… commute means to change.
Commuter A
Commuter B

5. Here is another example…

6. Think of this situation:
Every day you ride your bike to school.
The distance from home to school is 2 miles.
The distance from school to home is also 2 miles.

7. Home + School = School + Home
The distance from Home to School is the same as the distance from school to home.
Home + School = School + Home
H + S = S + H
A + B = B + A

8. The Commutative Property
A + B = B + A

9. The Commutative Property
The order of the numbers being added can be changed and the outcome will be the same

10. Four Properties of Operations
Commutative
Associative
Identity
Distributive

11. The Associative Property
Background
The word associative comes from the verb “to associate.”
Definition on dictionary.com
Associate means connected, joined, or related
People who work together are called associates.
They are joined together by business, and they do talk to one another.

12. Let’s look at another hypothetical situation
Three people work together.
Associate B needs to call Associates A and C to share some news.
Does it matter who he calls first?

13. Here are three associates.B
B calls A first
He calls C last A C
If he called C first, then called A, would it have made a difference?
NO!

14. (The Role of Parentheses)
In math, we use parentheses to show groups.
In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS)
So….

15. The Associative Property
The parentheses identify which two associates talked first.
(A + B) + C = A + (B + C) B B A C
THEN A
THEN C

16. The Associative Property
When three or more numbers are being added, you can regroup and have the same outcome
Ex: (2 + 8) + 4 = 2 + (8 + 4)

17. 4 Properties of Operations
Commutative
Associative
Identity
Distributive

18. The Identity Property of Addition
I am me!
You cannot change
My identity!

19. Zero is the only number you can add to something and see no change.

20. Identity Property of Addition
+ 0 =
A + 0 = A

21. Identity Property of Multiplication
One is the only number that you can multiply by something and see no change

22. Identity Property of Multiplication
• 1 =
A • 1 = A

23. Let’s practice ! Look at the problem.
Identify which property it represents.

24. The Associative Property of Addition
(9 + 8) + 7 = 9 + (8 + 7)
The Associative Property of Addition
It is the only addition property that has parentheses.

25. The Identity Property of Addition
= 12
The Identity Property of Addition
It is the only addition property that has two addends and one of them is a zero.

26. The Commutative Property of Addition
9 + 7 = 7 + 9
The Commutative Property of Addition
It is the only addition property that has numbers that change places.

27. The Commutative Property of Addition
4 + 6 = 6 + 4
The Commutative Property of Addition
Numbers change places.

28. The Identity Property of Addition
3 + 0 = 3
The Identity Property of Addition
See the zero?

29. The Associative Property of Addition
(4 + 3) + 2 = 4 + (3 + 2)
The Associative Property of Addition
It has parentheses!

30. The Identity Property of Addition
a + 0 = a
The Identity Property of Addition
Zero!

31. The Commutative Property of Addition
a + b = b + a
The Commutative Property of Addition
Moving numbers!

32. The Associative Property of Addition
(a + b) + c = a + (b + c)
The Associative Property of Addition
Parentheses! B A C