1. 2-3 Relating Addition
and Subtraction
Math Notes
Algebra and Functions 1.2

2. Inverse Operations

3. Inverse Operations
Addition and subtraction are called inverse
operations.

4. Inverse Operations
Addition and subtraction are called inverse
operations.
3 + 9 means 9 is added to 3
Subtraction can UNDO addition.

5. Inverse Operations
Addition and subtraction are called inverse
operations.
3 + 9 means 9 is added to 3
Subtraction can UNDO addition.
3

6. Inverse Operations
Addition and subtraction are called inverse
operations.
3 + 9 means 9 is added to 3
Subtraction can UNDO addition.
3 +9

7. Inverse Operations
Addition and subtraction are called inverse
operations.
3 + 9 means 9 is added to 3
Subtraction can UNDO addition.
3 +9-9

8. Inverse Operations
Addition and subtraction are called inverse
operations.
3 + 9 means 9 is added to 3
Subtraction can UNDO addition.
3 +9-9 =3

9. Inverse Operations

10. Inverse Operations
10 - 2 means 2 is subtracted from 10
Addition can UNDO subtraction.

11. Inverse Operations
10 - 2 means 2 is subtracted from 10
Addition can UNDO subtraction.
10

12. Inverse Operations
10 - 2 means 2 is subtracted from 10
Addition can UNDO subtraction.
10 - 2

13. Inverse Operations
10 - 2 means 2 is subtracted from 10
Addition can UNDO subtraction.
10 - 2 + 2

14. Inverse Operations
10 - 2 means 2 is subtracted from 10
Addition can UNDO subtraction.
10 - 2 + 2 = 10

15. Inverse Operations

16. Inverse Operations
This can also be applied to ALGEBRA

17. Inverse Operations
This can also be applied to ALGEBRA
n - 7 means 7 is subtracted from n
Addition can UNDO subtraction.

18. Inverse Operations
This can also be applied to ALGEBRA
n - 7 means 7 is subtracted from n
Addition can UNDO subtraction.
n

19. Inverse Operations
This can also be applied to ALGEBRA
n - 7 means 7 is subtracted from n
Addition can UNDO subtraction.
n-7

20. Inverse Operations
This can also be applied to ALGEBRA
n - 7 means 7 is subtracted from n
Addition can UNDO subtraction.
n - 7 +7

21. Inverse Operations
This can also be applied to ALGEBRA
n - 7 means 7 is subtracted from n
Addition can UNDO subtraction.
n - 7 +7 = n

22. Tell what you would do
to get the variable alone?
x - 20

23. Tell what you would do
to get the variable alone?
Use the
inverse
x - 20
operation
of subtraction.

24. Tell what you would do
to get the variable alone?
Use the
x - 20
inverse
operation +
of subtraction.

25. Tell what you would do
to get the variable alone?
Use the
x - 20 If you’re
inverse
operation + subtracting 20,
adding 20 will
of subtraction. undo “-”

26. Tell what you would do
to get the variable alone?
Use the
x - 20 If you’re
inverse
operation + 20 subtracting 20,
adding 20 will
of subtraction. undo “-”

27. Tell what you would do
to get the variable alone?
Use the
x - 20 If you’re
inverse
operation + 20 subtracting 20,
adding 20 will
of subtraction. undo “-”
Minus 20 and adding 20
cancels each other out.

28. Tell what you would do
to get the variable alone?
Use the
x - 20 If you’re
inverse
operation + 20 subtracting 20,
adding 20 will
of subtraction. undo “-”
Minus 20 and adding 20
cancels each other out.

29. Tell what you would do
to get the variable alone?
Use the
inverse
x If you’re
subtracting 20,
operation adding 20 will
of subtraction. undo “-”
Minus 20 and adding 20
cancels each other out.

30. Tell what you would do
to get the variable alone?
z + 100

31. Tell what you would do
to get the variable alone?
Use the
inverse
z + 100
operation
of addition.

32. Tell what you would do
to get the variable alone?
Use the
z + 100
inverse
operation -
of addition.

33. Tell what you would do
to get the variable alone?
Use the
z + 100 If you’re
inverse
operation - adding 100,
subtracting 100
of addition. will undo “+”

34. Tell what you would do
to get the variable alone?
Use the
z + 100 If you’re
inverse
operation - 100 adding 100,
subtracting 100
of addition. will undo “+”

35. Tell what you would do
to get the variable alone?
Use the
z + 100 If you’re
inverse
operation - 100 adding 100,
subtracting 100
of addition. will undo “+”
Adding 100 and subtracting 100
cancels each other out.

36. Tell what you would do
to get the variable alone?
Use the
z + 100 If you’re
inverse
operation - 100 adding 100,
subtracting 100
of addition. will undo “+”
Adding 100 and subtracting 100
cancels each other out.

37. Tell what you would do
to get the variable alone?
Use the
inverse
z If you’re
adding 100,
operation subtracting 100
of addition. will undo “+”
Adding 100 and subtracting 100
cancels each other out.

38. Tell what you would do
to get the variable alone?
47 + n

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

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

41. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)

42. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)
-

43. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)
- If you’re adding 47,
subtracting 47 will
undo “+”

44. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)
- 47 If you’re adding 47,
subtracting 47 will
undo “+”

45. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)
- 47 If you’re adding 47,
subtracting 47 will
undo “+”
Adding 47 and subtracting 47
cancels each other out.

46. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n + 47
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE
PROPERTY)
- 47 If you’re adding 47,
subtracting 47 will
undo “+”
Adding 47 and subtracting 47
cancels each other out.

47. Tell what you would do
to get the variable alone?
WATCH OUT! Use the
Before using the inverse operation
n
inverse operation, of addition.
switch the order
of the addends.
(COMMUTATIVE If you’re adding 47,
PROPERTY) subtracting 47 will
undo “+”
Adding 47 and subtracting 47
cancels each other out.

48. Table = Math Machine
Rule:

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

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

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.
Rule:

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.
Rule: Add 5

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: Add 5
8

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.
Let place the
number 8
into the machine. Rule: Add 5
8

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.
Let place the
number 8
into the machine. Rule: Add 5
8 13

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: Add 5
8 13

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: Add 5
8 13
10

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: Add 5
8 13
10

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: Add 5
8 13
10 15

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: Add 5
8 13
10 15
17

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: Add 5
8 13
10 15
17

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: Add 5
8 13
10 15
17 22

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: Subtract 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: Subtract 8
8

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: Subtract 8
8

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: Subtract 8
8 0

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: Subtract 8
8 0
10

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: Subtract 8
8 0
10

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: Subtract 8
8 0
10 2

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: Subtract 8
8 0
10 2
17

71. 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: Subtract 8
8 0
10 2
17

72. 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: Subtract 8
8 0
10 2
17 9

73. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16

74. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48

75. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48

76. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32

77. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103

78. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103

79. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103 87

80. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103 87
n

81. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103 87
n

82. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103 87
n 150

83. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 16
48 32
103 87
n 150
We know a number was entered.

84. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER 16 was Rule: Subtract 16
subtracted, the
answer was 150.
48 32
103 87
n 150
We know a number was entered.

85. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 16 was with 150 and
Rule: Subtract 16
subtracted, the inverse operations
answer was 150. to find n?
48 32
103 87
n 150
We know a number was entered.

86. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 16 was with 150 and
Rule: Subtract 16
subtracted, the inverse operations
answer was 150. to find n?
48 32
Apply the inverse
103 87 operation of the
rule to 150.
n 150
We know a number was entered.

87. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 16 was with 150 and
Rule: Subtract 16
subtracted, the inverse operations
answer was 150. to find n?
48 32
Apply the inverse
103 87 operation of the
rule to 150.
n 150 150
+16
We know a number was entered. n = 166

88. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25

89. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20

90. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20

91. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45

92. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n

93. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n

94. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n 80

95. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n 80
75

96. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n 80
75

97. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n 80
75 100

98. For each table, tell what you would
do to find n. Then find n.
Rule: Add 25
20 45
n 80
75 100
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 25 was Rule: Add 25
added, the
answer was 80.
20 45
n 80
75 100
We know a number was entered.

100. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 25 was with 80 and
Rule: Add 25
added, the inverse operations
answer was 80. to find n?
20 45
n 80
75 100
We know a number was entered.

101. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 25 was with 80 and
Rule: Add 25
added, the inverse operations
answer was 80. to find n?
20 45
Apply the inverse
n 80 operation of the
rule to 80.
75 100
We know a number was entered.

102. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 25 was with 80 and
Rule: Add 25
added, the inverse operations
answer was 80. to find n?
20 45
Apply the inverse
n 80 operation of the
rule to 80.
75 100 80
-25
We know a number was entered. n = 55

103. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50

104. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n

105. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n

106. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100

107. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200

108. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200

109. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200 150

110. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200 150
500

111. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200 150
500

112. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200 150
500 250

113. For each table, tell what you would
do to find n. Then find n.
Rule: Subtract 50
n 100
200 150
500 250
We know a number was entered.

114. For each table, tell what you would
do to find n. Then find n.
We know that
AFTER 50 was Rule: Subtract 50
subtracted, the
answer was 100.
n 100
200 150
500 250
We know a number was entered.

115. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 50 was with 100 and
Rule: Subtract 50
subtracted, the inverse operations
answer was 100. to find n?
n 100
200 150
500 250
We know a number was entered.

116. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 50 was with 100 and
Rule: Subtract 50
subtracted, the inverse operations
answer was 100. to find n?
n 100
Apply the inverse
200 150 operation of the
rule to 100.
500 250
We know a number was entered.

117. For each table, tell what you would
do to find n. Then find n.
We know that What can we do
AFTER 50 was with 100 and
Rule: Subtract 50
subtracted, the inverse operations
answer was 100. to find n?
n 100
Apply the inverse
200 150 operation of the
rule to 100.
500 250 100
+50
We know a number was entered. n = 150