The document discusses five properties of multiplication: the commutative property, associative property, identity property, zero property, and distributive property. It provides examples to illustrate each property, such as how the order of factors does not change the product under the commutative property or how grouping factors differently does not change the result under the associative property. Examples are also given for how the product is the other factor under the identity property and is zero when zero is a factor under the zero property.

1. 4-1 Multiplication
Properties
Math Notes
Algebra and Functions 1.3

2. Five Properties

3. Five Properties
Commutative Property

4. Five Properties
Commutative Property
Associate Property

5. Five Properties
Commutative Property
Associate Property
Identity Property

6. Five Properties
Commutative Property
Associate Property
Identity Property
Zero Property

7. Five Properties
Commutative Property
Associate Property
Identity Property
Zero Property
Distributive

8. Commutative Property

9. Commutative Property
The order in which numbers are multiplied
does not change the product.

10. Commutative Property
The order in which numbers are multiplied
does not change the product.
3 x 5=

11. Commutative Property
The order in which numbers are multiplied
does not change the product.
3 x 5 = 15

12. Commutative Property
The order in which numbers are multiplied
does not change the product.
5 x 3 = 15

13. Commutative Property
The order in which numbers are multiplied
does not change the product.
5 x 3 = 15
5 x 3=

14. Commutative Property
The order in which numbers are multiplied
does not change the product.
5 x 3 = 15
5 x 3 = 15

15. Commutative Property
The order in which numbers are multiplied
does not change the product.
5 x 3 = 15
3 x 5 = 15

16. Associative Property

17. Associative Property
The way in which factors are grouped does
not change the product.

18. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.

19. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 =

20. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 = 12 x 2 =

21. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 = 12 x 2 = 24

22. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 = 12 x 2 = 24
3 x (4 x 2) =

23. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 = 12 x 2 = 24
3 x (4 x 2) = 3x8=

24. Associative Property
The way in which factors are grouped does
not change the product.
When you see ( ) parentheses, do the work
with the ( ) first.
(3 x 4) x 2 = 12 x 2 =24
3 x (4 x 2) = 3 x 8 = 24

25. Identity Property

26. Identity Property
When 1 is one of the two factors, the
product is the other factor.

27. Identity Property
When 1 is one of the two factors, the
product is the other factor.
16 x 1 = 16

28. Identity Property
When 1 is one of the two factors, the
product is the other factor.
16 x 1 = 16
nx1=n

29. Zero Property

30. Zero Property
When 0 is a factor, the product is 0

31. Zero Property
When 0 is a factor, the product is 0
16 x 0 = 0

32. Zero Property
When 0 is a factor, the product is 0
16 x 0 = 0
0x7=0

33. Name the property used.

34. Name the property used.
23 x 0

35. Name the property used.
23 x 0
76 x 1 = 76

36. Name the property used.
23 x 0
76 x 1 = 76
10 x 12 = 12 x 10

37. Name the property used.
23 x 0
76 x 1 = 76
10 x 12 = 12 x 10
(6 x 4) x 8 = 6 x (4 x 8)

38. Name the property used.
Zero Property
23 x 0 See the 0 (zero)?
76 x 1 = 76
10 x 12 = 12 x 10
(6 x 4) x 8 = 6 x (4 x 8)

39. Name the property used.
Zero Property
23 x 0 See the 0 (zero)?
Identity Property
Multiplied by 1
76 x 1 = 76
10 x 12 = 12 x 10
(6 x 4) x 8 = 6 x (4 x 8)

40. Name the property used.
Zero Property
23 x 0 See the 0 (zero)?
Identity Property
Multiplied by 1
76 x 1 = 76 Commutative
See the numbers
10 x 12 = 12 x 10 switched?
(6 x 4) x 8 = 6 x (4 x 8)

41. Name the property used.
Zero Property
23 x 0 See the 0 (zero)?
Identity Property
Multiplied by 1
76 x 1 = 76 Commutative
See the numbers
10 x 12 = 12 x 10 switched?
(6 x 4) x 8 = 6 x (4 x 8)
Associative Property
6 x 4 is multiplied first and 4 x 8 was multiplied first
Product did not change.

42. Distributive Property

43. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.

44. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3

45. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x

46. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x 14

47. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x 14

48. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x

49. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)

50. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10)

51. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) (3 x 4)

52. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) + (3 x 4)

53. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) + (3 x 4)
30

54. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) + (3 x 4)
30 12

55. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) + (3 x 4)
30 + 12

56. Distributive Property
Think of one factor as the sum of two
addends. Then multiply each addend by
the other factor and add the products.
3 x (10 + 4)
(3 x 10) + (3 x 4)
30 + 12 = 42