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# 5-11 Relating Multiplication and Division

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• ### 5-11 Relating Multiplication and Division

1. 1. 5-11 Relating Multiplication and Division Math Notes Algebra and Functions 1.2
2. 2. Inverse Operations
3. 3. Inverse Operations Multiplication and division are called inverse operations.
4. 4. Inverse Operations Multiplication and division are called inverse operations. 13 + 7 means 7 is multiplied to 13 Division can UNDO multiplication.
5. 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. 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. 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. 8. Inverse Operations
9. 9. Inverse Operations 15 ÷ 3 means 15 is divided by 3 Multiplication can UNDO division.
10. 10. Inverse Operations 15 ÷ 3 means 15 is divided by 3 Multiplication can UNDO division. (15 ÷ 3)
11. 11. Inverse Operations 15 ÷ 3 means 15 is divided by 3 Multiplication can UNDO division. (15 ÷ 3) x 3
12. 12. Inverse Operations 15 ÷ 3 means 15 is divided by 3 Multiplication can UNDO division. (15 ÷ 3) x 3 = 15
13. 13. Inverse Operations
14. 14. Inverse Operations This can also be applied to ALGEBRA
15. 15. Inverse Operations This can also be applied to ALGEBRA n ÷ 7 means n is divided by 7 Multiplication can UNDO division.
16. 16. Inverse Operations This can also be applied to ALGEBRA n ÷ 7 means n is divided by 7 Multiplication can UNDO division. n
17. 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. 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. 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. 20. Tell what you would do to get the variable alone? x ÷ 10
21. 21. Tell what you would do to get the variable alone? Use the inverse x ÷ 10 operation of division.
22. 22. Tell what you would do to get the variable alone? Use the x ÷ 10 inverse operation x of division.
23. 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. 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. 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. 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. 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. 28. Tell what you would do to get the variable alone? z x 100
29. 29. Tell what you would do to get the variable alone? Use the inverse operation z x 100 of multiplication.
30. 30. Tell what you would do to get the variable alone? Use the z x 100 inverse operation of multiplication. ÷
31. 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. 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. 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. 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. 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. 36. Tell what you would do to get the variable alone? 47 x n
37. 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. 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. 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. 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. 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. 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. 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. 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. 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. 46. Table = Math Machine Rule:
47. 47. Table = Math Machine Think of this table as a machine. Rule:
48. 48. Table = Math Machine Think of this Something goes in, table as something different a machine. comes out. Rule:
49. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 71. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Multiply by 6 156 ÷ 16 n = 26
72. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 85. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25
86. 86. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50
87. 87. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50
88. 88. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50 2
89. 89. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50 2 n
90. 90. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50 2 n
91. 91. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Divide by 25 50 2 n 4
92. 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. 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. 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. 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. 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. 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. 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. 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. 100. For each table, tell what you would do to ﬁnd n. Then ﬁnd n. Rule: Multiply by 12 48 ÷ 12 n=4
101. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.