1. 5-11 Relating
Multiplication and
Division
Math Notes
Algebra and Functions 1.2

2. Inverse Operations

3. Inverse Operations
Multiplication and division are called inverse
operations.

4. Inverse Operations
Multiplication and division are called inverse
operations.
13 + 7 means 7 is multiplied to 13
Division can UNDO multiplication.

5. Inverse Operations
Multiplication and division are called inverse
operations.
13 + 7 means 7 is multiplied to 13
Division can UNDO multiplication.
(13 x 7)

6. Inverse Operations
Multiplication and division are called inverse
operations.
13 + 7 means 7 is multiplied to 13
Division can UNDO multiplication.
(13 x 7) ÷ 13

7. Inverse Operations
Multiplication and division are called inverse
operations.
13 + 7 means 7 is multiplied to 13
Division can UNDO multiplication.
(13 x 7) ÷ 13 = 7

8. Inverse Operations

9. Inverse Operations
15 ÷ 3 means 15 is divided by 3
Multiplication can UNDO division.

10. Inverse Operations
15 ÷ 3 means 15 is divided by 3
Multiplication can UNDO division.
(15 ÷ 3)

11. Inverse Operations
15 ÷ 3 means 15 is divided by 3
Multiplication can UNDO division.
(15 ÷ 3) x 3

12. Inverse Operations
15 ÷ 3 means 15 is divided by 3
Multiplication can UNDO division.
(15 ÷ 3) x 3 = 15

13. Inverse Operations

14. Inverse Operations
This can also be applied to ALGEBRA

15. Inverse Operations
This can also be applied to ALGEBRA
n ÷ 7 means n is divided by 7
Multiplication can UNDO division.

16. Inverse Operations
This can also be applied to ALGEBRA
n ÷ 7 means n is divided by 7
Multiplication can UNDO division.
n

17. Inverse Operations
This can also be applied to ALGEBRA
n ÷ 7 means n is divided by 7
Multiplication can UNDO division.
n ÷7

18. Inverse Operations
This can also be applied to ALGEBRA
n ÷ 7 means n is divided by 7
Multiplication can UNDO division.
n ÷7 x7

19. Inverse Operations
This can also be applied to ALGEBRA
n ÷ 7 means n is divided by 7
Multiplication can UNDO division.
n ÷7 x7 =n

20. Tell what you would do
to get the variable alone?
x ÷ 10

21. Tell what you would do
to get the variable alone?
Use the
inverse
x ÷ 10
operation
of division.

22. Tell what you would do
to get the variable alone?
Use the
x ÷ 10
inverse
operation x
of division.

23. Tell what you would do
to get the variable alone?
Use the
x ÷ 10 If you’re
inverse
operation x dividing 10,
multiplying 20
of division. will undo “÷”

24. Tell what you would do
to get the variable alone?
Use the
x ÷ 10 If you’re
inverse
operation x 10 dividing 10,
multiplying 20
of division. will undo “÷”

25. Tell what you would do
to get the variable alone?
Use the
x ÷ 10 If you’re
inverse
operation x 10 dividing 10,
multiplying 20
of division. will undo “÷”
Dividing by 20 and multiplying 20
cancels each other out.

26. Tell what you would do
to get the variable alone?
Use the
x ÷ 10 If you’re
inverse
operation x 10 dividing 10,
multiplying 20
of division. will undo “÷”
Dividing by 20 and multiplying 20
cancels each other out.

27. Tell what you would do
to get the variable alone?
Use the
inverse
x If you’re
dividing 10,
operation multiplying 20
of division. will undo “÷”
Dividing by 20 and multiplying 20
cancels each other out.

28. Tell what you would do
to get the variable alone?
z x 100

29. Tell what you would do
to get the variable alone?
Use the
inverse operation
z x 100
of multiplication.

30. Tell what you would do
to get the variable alone?
Use the z x 100
inverse operation
of multiplication. ÷

31. Tell what you would do
to get the variable alone?
Use the z x 100 If you’re
multiplying by
inverse operation
of multiplication. ÷ 100,
dividing by 100
will undo “x”

32. Tell what you would do
to get the variable alone?
Use the z x 100 If you’re
multiplying by
inverse operation
of multiplication. ÷ 100 100,
dividing by 100
will undo “x”

33. Tell what you would do
to get the variable alone?
Use the z x 100 If you’re
multiplying by
inverse operation
of multiplication. ÷ 100 100,
dividing by 100
will undo “x”
Multiplying by 100 and dividing by 100
cancels each other out.

34. Tell what you would do
to get the variable alone?
Use the z x 100 If you’re
multiplying by
inverse operation
of multiplication. ÷ 100 100,
dividing by 100
will undo “x”
Multiplying by 100 and dividing by 100
cancels each other out.

35. Tell what you would do
to get the variable alone?
Use the
inverse operation
z If you’re
multiplying by
100,
of multiplication. dividing by 100
will undo “x”
Multiplying by 100 and dividing by 100
cancels each other out.

36. Tell what you would do
to get the variable alone?
47 x n

37. Tell what you would do
to get the variable alone?
WATCH OUT!
Before using the
47 x n
inverse operation,
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)

38. Tell what you would do
to get the variable alone?
WATCH OUT!
Before using the
inverse operation,
switch the order
of the factors.
n x 47
(COMMUTATIVE
PROPERTY)

39. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)

40. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)
÷

41. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)
÷ If you’re multiplying
by 47,
dividing by 47 will
undo “x”

42. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)
÷ 47 If you’re multiplying
by 47,
dividing by 47 will
undo “x”

43. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)
÷ 47 If you’re multiplying
by 47,
dividing by 47 will
undo “x”
Multiplying by 47 and dividing by 47
cancels each other out.

44. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n x 47
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE
PROPERTY)
÷ 47 If you’re multiplying
by 47,
dividing by 47 will
undo “x”
Multiplying by 47 and dividing by 47
cancels each other out.

45. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n
inverse operation, of multiplication.
switch the order
of the factors.
(COMMUTATIVE If you’re multiplying
PROPERTY) by 47,
dividing by 47 will
undo “x”
Multiplying by 47 and dividing by 47
cancels each other out.

46. Table = Math Machine
Rule:

47. Table = Math Machine
Think of this
table as
a machine.
Rule:

48. Table = Math Machine
Think of this Something goes in,
table as something different
a machine. comes out.
Rule:

49. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule:

50. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5

51. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Let place the
number 8
into the machine. Rule: Multiply by 5
8

52. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Let place the
number 8
into the machine. Rule: Multiply by 5
8

53. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Let place the
number 8
into the machine. Rule: Multiply by 5
8 40

54. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40

55. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10

56. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10

57. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10 50

58. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10 50
17

59. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10 50
17

60. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Multiply by 5
8 40
10 50
17 170

61. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2

62. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8

63. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8

64. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4

65. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10

66. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10

67. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10 5

68. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10 5
24

69. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10 5
24

70. Table = Math Machine
Think of this Something goes in, You can program
table as something different each machine to do
a machine. comes out. whatever you want.
Rule: Divide by 2
8 4
10 5
24 12

71. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
156 ÷ 16
n = 26

72. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13
156 ÷ 16
n = 26

73. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13
156 ÷ 16
n = 26

74. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
156 ÷ 16
n = 26

75. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16
156 ÷ 16
n = 26

76. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16
156 ÷ 16
n = 26

77. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16 96
156 ÷ 16
n = 26

78. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16 96
n
156 ÷ 16
n = 26

79. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16 96
n
156 ÷ 16
n = 26

80. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16 96
n 156
156 ÷ 16
n = 26

81. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 6
13 78
16 96
n 156
156 ÷ 16
We know a number was entered. n = 26

82. For each table, tell what you would
We know that
do to find n. Then find n.
AFTER n was
multiplied by 6,
the answer was Rule: Multiply by 6
156.
13 78
16 96
n 156
156 ÷ 16
We know a number was entered. n = 26

83. For each table, tell what you would
We know that
do to find n. Then find n.
AFTER n was
What can we do
multiplied by 6,
with 156 and
the answer was Rule: Multiply by 6 inverse operations
156.
to find n?
13 78
16 96
n 156
156 ÷ 16
We know a number was entered. n = 26

84. For each table, tell what you would
We know that
do to find n. Then find n.
AFTER n was
What can we do
multiplied by 6,
with 156 and
the answer was Rule: Multiply by 6 inverse operations
156.
to find n?
13 78
Apply the inverse
16 96 operation of the
rule to 156.
n 156
156 ÷ 16
We know a number was entered. n = 26

85. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25

86. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50

87. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50

88. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2

89. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n

90. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n

91. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n 4

92. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n 4
150

93. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n 4
150

94. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n 4
150 6

95. For each table, tell what you would
do to find n. Then find n.
Rule: Divide by 25
50 2
n 4
150 6
We know a number was entered.

96. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was
divided by 25, the Rule: Divide by 25
answer was 4.
50 2
n 4
150 6
We know a number was entered.

97. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was What can we do
divided by 25, the with 4 and
Rule: Divide by 25
answer was 4. inverse operations
to find n?
50 2
n 4
150 6
We know a number was entered.

98. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was What can we do
divided by 25, the with 4 and
Rule: Divide by 25
answer was 4. inverse operations
to find n?
50 2
Apply the inverse
n 4 operation of the
rule to 4.
150 6
We know a number was entered.

99. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was What can we do
divided by 25, the with 4 and
Rule: Divide by 25
answer was 4. inverse operations
to find n?
50 2
Apply the inverse
n 4 operation of the
rule to 4.
150 6 4
x25
We know a number was entered. n = 100

100. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
48 ÷ 12
n=4

101. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n
48 ÷ 12
n=4

102. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n
48 ÷ 12
n=4

103. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
48 ÷ 12
n=4

104. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10
48 ÷ 12
n=4

105. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10
48 ÷ 12
n=4

106. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10 120
48 ÷ 12
n=4

107. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10 120
15
48 ÷ 12
n=4

108. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10 120
15
48 ÷ 12
n=4

109. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10 120
15 180
48 ÷ 12
n=4

110. For each table, tell what you would
do to find n. Then find n.
Rule: Multiply by 12
n 48
10 120
15 180
48 ÷ 12
n=4
We know a number was entered.

111. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was
multiplied by 12,
the answer was Rule: Multiply by 12
100.
n 48
10 120
15 180
48 ÷ 12
n=4
We know a number was entered.

112. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was
What can we do
multiplied by 12,
with 48 and
the answer was Rule: Multiply by 12 inverse operations
100.
to find n?
n 48
10 120
15 180
48 ÷ 12
n=4
We know a number was entered.

113. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER n was
What can we do
multiplied by 12,
with 48 and
the answer was Rule: Multiply by 12 inverse operations
100.
to find n?
n 48
Apply the inverse
10 120 operation of the
rule to 48.
15 180
48 ÷ 12
n=4
We know a number was entered.