1. Properties of Numbers
10/20/2016

2. Do you remember these Properties of Addition?
Commutative Property of Addition
The numbers move around
a + b = b + a
Associative Property of Addition
Grouping with parentheses
(a + b) + c = a + (b + c)
Identity Property of Addition
The identity of the problem does not change
a + 0 = a

3. In multiplication, you will see these same properties, plus 2 more…

4. Five Properties of Multiplication
These are the basically the same as addition
Commutative
Associative
Identity
These belong to multiplication only
Zero
Distributive

5. Multiplicative (Do you see most of the word “multiply” in this word?
Let’s review the addition properties— from the multiplicative perspective…
Multiplicative (Do you see most of the word “multiply” in this word?

6. The Commutative Property of Multiplication

7. The Commutative Property
Background
The word commutative comes from the verb “to commute.”
Definition on dictionary.com
Commuting means changing, replacing, exchanging, switching places, trading places
People who travel back and forth to work are called commuters.

8. Here are two families of commuters.
Hi!
Remember us?
Commuter B
Commuter A
Commuter A & Commuter B changed lanes.
Remember… commute means to switch places.
Commuter A
Commuter B

9. The Commutative Property
A • B = B • A

10. Here is another example…

11. 3 groups of 5 = 5 groups of 3
3 x 5 =
5 x 3 = =
15 kids
15 kids

12. What commutative means to multiplication…
Remember… in Lesson 1-11 we said that the word “of” means multiply
3 groups of 5 = 5 groups of 3
3 • 5 = 5 • 3
a • b = b • a

13. The Associative Property of Multiplication

14. 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 have to talk to one another.

15. 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?

16. 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!

17. (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….

18. 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

19. Also known as the zero property of the addition
Property #3a
The Identity Property
of Addition
Also known as the zero property of the addition
Make foldable

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

21. 0 is the only number you can add to something and see no change.

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

23. The Identity Property of Multiplication
Property #3b
The Identity Property
of Multiplication
Make foldable

24. The Identity Property
I am me!
You cannot change
My identity!

25. 1 is the only number you can multiply something by and see no change.

26. Identity Property of Multiplication
x 1 =
a x 1 = a

27. Identity Property of Multiplication
x 1 =
x 1 =
x 1 =
a x 1 = a

28. These are 3 of the Properties of Multiplication
Commutative Property of Multiplication
The numbers move around
a • b = b • a
Associative Property of Multiplication
Grouping with parentheses
(a • b) • c = a • (b • c)
Identity Property of Multiplication
The identity of the problem does not change
a • 1 = a

29. There are two more properties which are unique to multiplication
The Zero Property
The Distributive Property

30. The Zero Property of Multiplication
Make foldable

31. The Zero Property of Multiplication
This looks like a mixture of the identity property of addition and the identity property of multiplication…
Be careful not to mix them up!

32. If I have 2 pockets with NO money in them, then I have NO money!
The Zero Property
Any time you multiply a number by zero, your answer is zero!
If I have 2 pockets with NO money in them, then I have NO money!
2 • 0 = 0
The End

33. The Distributive Property of Multiplication

34. The Distributive Property
Background
The word distributive comes from the verb “to distribute.”
Definition on dictionary.com
Distributing refers to passing things out or delivering things to people

35. The Distributive Property
a(b + c) = (a • b) + (a • c)
A times the sum of b and c = a times b plus a times c
Let’s plug in some numbers first.
Remember that to distribute means delivering items, or handing them out.
Here is how this property works:
5(2 + 3) = (5 • 2) + (5 • 3)

36. You have sold many items for the RCMS fundraiser!
You went to two houses on one street and three houses on a different street. Every family bought 5 items!
5(2 + 3) = (5 • 2) + (5 • 3)
You went to two houses on one street and three houses on a different street. Every family bought 5 items!

37. You will be distributing 5 items to each house.2 3 5 4 1

38. 5(2 + 3) = (5 • 2) + (5 • 3)
You distributed (delivered) these all in one trip.
There are (2+3) five houses all together.
You need to deliver 5 gifts to each house.
You need to put 25 items on your wagon at one time.
5 items x 5 houses = 25 items all together

39. 5(2 + 3) = (5 • 2) + (5 • 3)
and 10
You distributed your items in two trips (+).
On the first trip you distributed 5 items to each of 2 houses (5 x 2 = 10).
On the second trip you distributed 5 items to each of 3 houses (5 x 3 = 15).
That means you distributed (delivered) 10 items plus 15 items. That makes 25 items altogether. + 15 25

40. The Distributive Property
Make 1 trip. You have 5 houses. You need to bring 5 items to each house. You need 25 items on your wagon.
DISTRIBUTION CENTER
5(2 + 3)

41. The Distributive Property
Make 2 trips. You have 2 houses for your first trip and you need to bring 5 items to each house. You have 3 houses on your second trip and need to bring 5 items to each house. When your second trip is over, you will have distributed 25 items.
DISTRIBUTION CENTER
(5 • 2) + (5 • 3)

42. How do I tell the properties apart?
Commutative
Numbers switch places
Associative
Parentheses on both sides
Only multiplication on each side
Identity
Multiply by 1
Zero Property
Multiply by zero
Distributive
Parentheses on each side
One side has a multiplication sign AND a plus sign

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

44. The Distributive Property
4(5 + 6) = (4 • 5) + (4 • 6)
The Distributive Property
of Multiplication
3 numbers on one side—4 on the other
Multiplication AND addition
3 sets of parentheses

45. 987 • 1 = 987
The Identity Property
of Multiplication
Times 1

46. Zero Property of Multiplication
3 • 0 = 0
Zero Property of Multiplication
Times zero

47. The Associative Property of Multiplication
(1 • 2) • 3 = 1 • (2 • 3)
The Associative Property of Multiplication
Same 3 numbers
Multiplication only
2 sets of parentheses

48. The Commutative Property
6 • 11 = 11 • 6
The Commutative Property
of Multiplication
Same 2 numbers
Numbers switched places

49. The Commutative Property
9 • 7 = 7 • 9
The Commutative Property
of Multiplication
Same 2 numbers
Numbers switched places

50. Zero Property of Multiplication
12 • 0 = 0
Zero Property of Multiplication
Times zero

51. The Associative Property of Multiplication
(9 • 8) • 7 = 9 • (8 • 7)
The Associative Property of Multiplication
Same 3 numbers
Multiplication only
2 sets of parentheses

52. The Distributive Property
9(8 + 7) = (9 • 8) + (9 • 7)
The Distributive Property
of Multiplication
3 numbers on one side—4 on the other
Multiplication AND addition
3 sets of parentheses

53. 9 • 1 = 9
The Identity Property
of Multiplication
Times 1

54. a • 1 = a
The Identity Property
of Multiplication

55. The Commutative Property
a • b = b • a
The Commutative Property
of Multiplication

56. The Associative Property
(a + b) + c = a + (b + c)
The Associative Property
of Multiplication B A C

57. a • 0 = 0
The Zero Property
of Multiplication

58. The Distributive Property
a(b • c) = (a • b) + (a • c)
The Distributive Property
of Multiplication

59. Ticket Out the Door