1. The Properties of Addition & Multiplication
As shown in different types of algebraic equations. Yes yes.

2. Addition Properties Closure Property Commutative Property
Identity Property
Associative Property
Inverse Property

3. What is a property? What do we mean by property?
Something that a person owns
Ex. This is Chuck’s cow. It is his property.

4. Boiling Point = 100°C Freezing Point = 0°C What is a property?
The other definition of property
A distinctive attribute or quality of something
Ex. What are the properties of water?
Boiling Point = 100°C
Freezing Point = 0°C

5. The Properties of Addition
An addition property is
“A distinctive quality unique to problems involving addition.”

6. Keyword = ORDER Commutative Property Commutative Property
The order in which two numbers are added does not change the sum
Ex = 6 + 5
Keyword = ORDER

7. Commutative Property How will I remember?
Commute = move from one place to another
(like when you commute to school every morning)
With addition, numbers can commute (move around), and we still get the same answer.

8. Keyword = GROUPED Associative Property Associative Property
The way three numbers are grouped when adding does not change the sum
Ex. (4 + 3) + 9 = 4 + (3 + 9)
Keyword = GROUPED

9. Associative Property Ex. (5+12)+13 = 5 + (12+13) How will I remember?
Associate = to hang out with someone
(like when you associate with your homies)
With addition, numbers can associate (be grouped with other numbers), and we still get the same answer.
Ex. (5+12)+13 = 5 + (12+13)

10. Identity Property Identity Property
The sum of a number and zero (0) is the number.
Ex = 14
How will I remember?
0 has no identity (poor guy). So there is no way that this nothing can change a number. He is worthless.

11. Inverse = Opposite -3.25 = 5 = 987 = -3.14… =
Inverse Property
Inverse Property
The sum of a number and its opposite is zero (0).
Ex = 0
How will I remember?
Inverse = Opposite
What’s the opposite of…
-3.25 =
5 =
987 =
-3.14… =

12. Let’s Practice

13. Which property is represented in the equation below?
8 + (-8) = 0
Inverse Property

14. Which property is represented in the equation below?
(12 + 4) +13 = 12 + (4 +13)
Associative Property

15. Which property is represented in the equation below?=
Commutative Property

16. Which property is represented in the equation below?
= 98765
Identity Property

17. This addition stuff is boring. Can’t we do multiplication now?
Yes yes young grasshopper. We can embark on the wonderful journey of multiplication properties!!!

18. Multiplication Properties
Distributive Property
Closure Property
Commutative Property
Multiplication Properties
Identity Property
Associative Property
Inverse Property

19. Keyword = ORDER Commutative Property Commutative Property
The order in which two numbers are multiplied does not change the product
Ex. 5 x 6 = 6 x 5
Keyword = ORDER

20. 5 x 6 = 6 x 5 Commutative Property How will I remember?
Commute = move from one place to another
(like when you commute to work)
With addition, numbers can commute (move around), and we still get the same answer.
5 x 6 =
6 x 5

21. Keyword = GROUPED Associative Property Associative Property
The way three numbers are grouped when multiplying does not change the product
Ex. (4 x 3) x 9 = 4 x (3 x 9)
Ex. (ab)c = a(bc)
Keyword = GROUPED

22. Associative Property Ex. (5x12)x13 = 5 x (12x13) How will I remember?
Associate = to hang out with someone
(like when you associate with your homies)
With mutliplication, numbers can associate (be grouped with other numbers), and we still get the same product.
Ex. (5x12)x13 = 5 x (12x13)

23. 1 Identity Property Identity Property I am worthless
The product of a number and 1 is the number.
Ex.
How will I remember?
Just like 0 in addition, 1 really serves no purpose in multiplication. It is worthless and has no effect on the number. It is the 0 of multiplication.
I am worthless 1

24. Inverse Property Inverse Property
The product of a number and its reciprocal is 1.
Ex.
How will I remember?
When you are inverted, you are flipped over.

25. Let’s Practice

26. Which property is represented in the equation below?
54 x 11 = 594
Closure Property

27. Which property is represented in the equation below?
31(5) = 5(31)
Commutative Property

28. Which property is represented in the equation below?
Inverse Property

29. Which property is represented in the equation below?
56342 x 1 = 56342
Identity Property

30. Which property is represented in the equation below?
(983 x 3)17 = 983(3 x 17)
Associative Property

31. LET’S RECAP

32. Associative Property
States that changing the grouping in an addition or multiplication expression does not change the sum or product.

33. Associative Property ONLY works with addition and multiplication!
a + (b + c) is the same as (a + b) + c
a x (b x c) is the same as (a x b) x c

34. Associative Property – Example 1
a = 4, b = 8 , c = 3
4 + (8 + 3) = ???

35. Show each side is equal by simplifying and solving
Associative Example 2
Show each side is equal by simplifying and solving
4 x (8 x 3) = (4 x 8) x 3
Simplify:
Solve:

36. Apply the Associative Property
3 + (4 + 5) =
(3 + 4) + 5

37. Apply the Associative Property
(12 + 9) +15 =
12 + (9 + 15)

38. Apply the Associative Property
(48 + 7) + 32 =
48 + (7 + 32)

39. Prove the Associative Property
Simplify each side to show equivalency
(12 + 4) + 2 = 12 + (4 + 2)
Simplify:
Solve: =
18 = 18

40. Prove the Associative Property
Simplify each side to show equivalency
30 + (5 + 15) = (30 + 5) + 15
Simplify:
Solve: =
50 = 50

41. Check Yo’ Self 1. 2. 3. b. (8 + 1) + 2 c. k + (g + m)
Simplify: =
Solve: 18 = 18 3.
a. 3
b. 4

42. Commutative Property
States that two or more terms can be added in any order without changing the sum, and two more terms can be multiplied in any order without changing the product.

43. Commutative Property ONLY works with addition and multiplication!
a + b = b + a
a x b = b x a

44. Commutative Property – Example 3
5 + 9 = ???

45. Commutative Property- Example 4
Use the commutative property to rewrite each number sentence in two different ways.
= __________________
_________________

46. Apply the Commutative Property=

47. Apply the Commutative Property=

48. Apply the Commutative Property=

49. Commutative Challenge: Associative or Commutative Property?
(3 + 5) + 7 = 7 + (3 + 5)
Commutative

50. Check Yo’ Self 1. b
c. d + m 4. B

51. Distributive Property
A number outside parenthesis must be multiplied by everything inside
Ex.
3(5 + 2) = 3x5 + 3x2
Keyword = SHARED

52. Distributive Property
A number outside parenthesis must be multiplied by everything inside
Ex.
How will I remember?
Distribute means “to share.”
The outside number must be distributed (shared) with every other number.
3(5 + 2) = 3x5 + 3x2

53. Distributive Property
Think of it like this…
Ex. 3(5 + 2) = ???
** 3 is the candy.
We must share the candy with everyone.
That is, we must share 3 with 5 & 2. 3
(5 + 2)
3x5 + 3x2

54. Distributive Property
Think of it like this…
Ex. 6(2 + 7) = ??? 6
(2 + 7)
There is too much of a spotlight on 6. The spotlight must be shared with 2 and 7
6(2) + 6(7) 54

55. Distributive Property
Think of it like this…
Ex. -10(3 + 9) = ???
(3 + 9)
Uh oh! Don’t lose the negative sign as you distribute the spotlighted number!!
-10
-10(3) + -10(9)
-120

56. Distributive Property
Think of it like this…
Ex. -5(4 – 7) = ??? -5
(4 – 7)
Make sure you know where your negative signs are in this problem!!!!!
-5(4) - -5(7)
-20 – (-35) 15

57. And now it’s time for … No!! It can’t be!! Say it ain’t so!!
Yes class. It’s time for variables!!! Mwahahaha!!!

58. Distributive Property
Think of it like this…
Ex. 3(x + 4) = ??? 3
(x + 4)
There is too much of a spotlight on 3. The spotlight must be shared with x and 4
3(x) + 3(4)
3x + 12

59. Distributive Property
Think of it like this…
Ex. -11(x + 5) = ???
(x + 5)
Uh oh! Don’t lose the negative sign as you distribute the spotlighted number!!
-11
-11(x) + -11(5)
-11x + -55

60. Distributive Property
Think of it like this…
Ex. -5(2x – y) = ??? -5
(2x – y)
Make sure you know where your negative signs are in this problem!!!!!
-5(2x) - -5(y)
-10x – (-5y)

61. Let’s Practice

62. Distributive Property
Share,
share,
share!
1. 4(6 + 5) 2. 6(3 + 8) 3. 15(12 + t) 4. -6(x + 12) (3 + r) (4 + t) 7. -9(6 + p) 8. -5(7 + t)