2-3 Relating Addition and Subtraction
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The document discusses inverse operations of addition and subtraction. It provides examples of how addition and subtraction undo each other, such as 3 + 9 - 9 = 3 and 10 - 2 + 2 = 10. It explains this concept also applies to algebra, for example n - 7 + 7 = n. The document then discusses using inverse operations to isolate a variable, working through examples like x - 20 + 20 to get x and n + 47 - 47 to get n. It introduces a concept of a "math machine" table where numbers can be input with a rule (like add 5) to transform the number and output a different number.
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2-3 Relating Addition and Subtraction
- 1. 2-3 Relating Addition and Subtraction Math Notes Algebra and Functions 1.2
- 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
- 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
- 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 youre 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 鍖nd n. Then 鍖nd n. Rule: Subtract 16
- 74. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48
- 75. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48
- 76. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32
- 77. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103
- 78. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103
- 79. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103 87
- 80. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103 87 n
- 81. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103 87 n
- 82. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 16 48 32 103 87 n 150
- 83. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n? 48 32 103 87 n 150 We know a number was entered.
- 86. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd 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 鍖nd n. Then 鍖nd n. Rule: Add 25
- 89. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20
- 90. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20
- 91. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45
- 92. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n
- 93. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n
- 94. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n 80
- 95. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n 80 75
- 96. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n 80 75
- 97. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Add 25 20 45 n 80 75 100
- 98. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n? 20 45 n 80 75 100 We know a number was entered.
- 101. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd 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 鍖nd n. Then 鍖nd n. Rule: Subtract 50
- 104. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n
- 105. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n
- 106. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100
- 107. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200
- 108. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200
- 109. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200 150
- 110. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200 150 500
- 111. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200 150 500
- 112. For each table, tell what you would do to 鍖nd n. Then 鍖nd n. Rule: Subtract 50 n 100 200 150 500 250
- 113. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd n? n 100 200 150 500 250 We know a number was entered.
- 116. For each table, tell what you would do to 鍖nd n. Then 鍖nd 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 鍖nd 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 鍖nd n. Then 鍖nd 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 鍖nd 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