A graphical representation of all the properties of multiplication. This is the foundation for algebra. Unfortunately most students have poor conceptual understanding and therefore turn to rote learning math. And that's where the disaster begins.

1. Properties of Multiplication

2. Properties of Multiplication
Commutativ
e Property

3. Properties of Multiplication
Commutativ
e Property
Associative
Property

4. Properties of Multiplication
Commutativ
e Property
Associative
Property
Distributive
Property

5. Properties of Multiplication
Commutativ
e Property
Associative
Property
Distributive
Property
multiplicative inverse

6. Commutative PropertyCommutative Property
of Multiplication

7. 36 x 4

8. 36 x 4
1
4

9. 36 x 4
1
2
4

10. 36 x 4
1
2
3
4

11. 36 x 4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4

12. 36 x 4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4

13. 36 x 4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4

14. 36 x 4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
36 times 4

15. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
36 times 4

16. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
36 times 4

17. How?How?

18. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
1

19. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
21

20. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
3
1 2

21. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
4
3
1 2

22. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4

23. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4

24. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4

25. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4

26. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
1 time 36

27. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
2 times 36

28. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
3 times 36

29. 36 x 4 is the same as
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4
4 times 36

30. 36 x 4 is the same as 4 x 36
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1
2
3
4
5
6
4 (4 times 36)

31. 36 x 4 is the same as 4 x 36
A x B = B x A
Commutative PropertyCommutative Property
of
MultiplicationMultiplication

32. Associative PropertyAssociative Property
of Multiplication

33. 4 x (3 x 5) = (4 x 3) x 5

34. 4 x (3 x 5) = (4 x 3) x 5
brackets first

35. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first

36. 4 x (3 x 5) = (4 x 3) x 5
brackets first
(3 times 5)

37. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)

38. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
( )

39. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
( )

40. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
( )

41. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
( )

42. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times ( )

43. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times ( )

44. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times ( )

45. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times ( )

46. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times ( )

47. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x (3 times 5)
4 times (
60
)

48. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times (
60
)

49. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times (
60
(4 times 3)
)

50. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times (
60
(4 times 3) x 5
)

51. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
()

52. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
()

53. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
()

54. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
()

55. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
()

56. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)

57. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

58. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

59. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

60. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

61. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

62. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

63. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

64. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5

65. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x (3 times 5)
4 times ( )
60
(4 times 3) x 5
( times 5)
12 times 5
60

66. 4 x (3 x 5) = (4 x 3) x 5

67. 4 x (3 x 5) = (4 x 3) x 5
brackets first

68. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first

69. 4 x (3 x 5) = (4 x 3) x 5
brackets first
15

70. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x 15

71. 4 x (3 x 5) = (4 x 3) x 5
brackets first
4 x 15
60

72. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x 15
60

73. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x 15 12
60

74. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x 15 12 x 5
60

75. 4 x (3 x 5) = (4 x 3) x 5
brackets first brackets first
4 x 15 12 x 5
60 60

76. A x (B x C) = (A x B) x C
Associative PropertyAssociative Property
of
MultiplicationMultiplication
4 x (3 x 5) = (4 x 3) x 5

77. Distributive PropertyDistributive Property
of Multiplication

78. 4 x (30 + 6) =

79. 4 x (30 + 6) = 4 x 30

80. 4 x (30 + 6) = 4 x 30 +

81. 4 x (30 + 6) = 4 x 30 + 4 x 6

82. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6)

83. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6)

84. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6)

85. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6)

86. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6)

87. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

88. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

89. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

90. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

91. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

92. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

93. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

94. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

95. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 times (30+6) 4 times 30 + 4 times 6

96. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x (30 + 6)

97. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 36
4 x (30 + 6)

98. 4 x (30 + 6) = 4 x 30 + 4 x 6
3 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

99. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 30 + 4 x 6
3 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

100. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 30 + 4 x 6
120
3 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

101. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 30 + 4 x 6
120 +
3 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

102. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 30 + 4 x 6
120 + 24
3 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

103. 4 x (30 + 6) = 4 x 30 + 4 x 6
4 x 30 + 4 x 6
120 + 24
1443 6
x 4
1 4 4
2
4 x 36
4 x (30 + 6)

104. 4 x (30 + 6) = 4 x 30 + 4 x 6
A x (B + C) = A x B + A x C

105. 4 x (30 + 6) = 4 x 30 + 4 x 6
A x (B + C) = A x B + A x C
A x (B – C) = A x B – A x C
and also

106. Distributive PropertyDistributive Property
of
MultiplicationMultiplication over Addition
A x (B + C) = A x B + A x C
A x (B – C) = A x B – A x C

107. Distributive PropertyDistributive Property
of
MultiplicationMultiplication
A x (B + C) = A x B + A x C
A x (B – C) = A x B – A x C

108. Multiplicative Inverse

109. 4 x = 1?
Multiplicative Inverse

110. 4 x = 1?
Multiplicative Inverse
4 times = 1?

111. Multiplicative Inverse
4 x = 1? 4 times = 1?

112. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
4

113. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
4
1
4

114. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
4
1
4
1
4

115. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
4
1
4
1
4
1
4

116. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
4
1
4
1
4
1
4
1

117. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
So, the Multiplicative Inverse of 4 is
1
4

118. Multiplicative Inverse
4 x = 1? 4 times = 1?
1
So, the Multiplicative Inverse of 4 is
1
4
And, the Multiplicative Inverse of is 41
4

119. Multiplicative Inverse
Multiplicative Inverse is also called Reciprocal

120. Multiplicative Inverse
Multiplicative Inverse is also called Reciprocal
Multiplicative Inverse
or
Reciprocal
1
4
of 4 is

121. Multiplicative Inverse
Multiplicative Inverse is also called Reciprocal
Multiplicative Inverse
or
Reciprocal
1
4
of 4is