Let’s solve each table one by one. We’ll use the rule given in the middle column to find missing inputs or outputs.
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Top Left Table: Rule = +6
We add 6 to input to get output, OR subtract 6 from output to get input.
- Output = 12 → Input = 12 - 6 =
6
- Input = 7 → Output = 7 + 6 =
13
- Output = 15 → Input = 15 - 6 =
9
- Output = 8 → Input = 8 - 6 =
2
- Output = 18 → Input = 18 - 6 =
12
Filled table:
Input | Rule | Output
6 | +6 | 12
7 | +6 | 13
9 | +6 | 15
2 | +6 | 8
12 | +6 | 18
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Top Right Table: Rule = -8
Subtract 8 from input to get output, OR add 8 to output to get input.
- Output = 1 → Input = 1 + 8 =
9
- Output = 2 → Input = 2 + 8 =
10
- Output = 9 → Input = 9 + 8 =
17
- Input = 11 → Output = 11 - 8 =
3
- Input = 18 → Output = 18 - 8 =
10
Filled table:
Input | Rule | Output
9 | -8 | 1
10 | -8 | 2
17 | -8 | 9
11 | -8 | 3
18 | -8 | 10
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Middle Left Table: Rule = ×6
Multiply input by 6 to get output, OR divide output by 6 to get input.
- Input = 2 → Output = 2 × 6 =
12
- Output = 48 → Input = 48 ÷ 6 =
8
- Output = 36 → Input = 36 ÷ 6 =
6
- Input = 9 → Output = 9 × 6 =
54
- Input = 12 → Output = 12 × 6 =
72
Filled table:
Input | Rule | Output
2 | ×6 | 12
8 | ×6 | 48
6 | ×6 | 36
9 | ×6 | 54
12 | ×6 | 72
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Middle Right Table: Rule = ÷12
Divide input by 12 to get output, OR multiply output by 12 to get input.
- Output = 10 → Input = 10 × 12 =
120
- Input = 132 → Output = 132 12 =
11
- Input = 12 → Output = 12 ÷ 12 =
1
- Output = 3 → Input = 3 × 12 =
36
- Input = 72 → Output = 72 ÷ 12 =
6
Filled table:
Input | Rule | Output
120 | 12 | 10
132 | ÷12 | 11
12 | ÷12 | 1
36 | 12 | 3
72 | ÷12 | 6
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Bottom Left Table: Rule = +7
Add 7 to input to get output.
- Input = 7 → Output = 7 + 7 =
14
- Input = 11 → Output = 11 + 7 =
18
- Input = 5 → Output = 5 + 7 =
12
- Input = 1 → Output = 1 + 7 =
8
- Input = 2 → Output = 2 + 7 =
9
Filled table:
Input | Rule | Output
7 | +7 | 14
11 | +7 | 18
5 | +7 | 12
1 | +7 | 8
2 | +7 | 9
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Bottom Right Table: Rule = ÷7
Divide input by 7 to get output, OR multiply output by 7 to get input.
- Input = 21 → Output = 21 ÷ 7 =
3
- Output = 10 → Input = 10 × 7 =
70
- Input = 63 → Output = 63 ÷ 7 =
9
- Output = 6 → Input = 6 × 7 =
42
- Input = 28 → Output = 28 ÷ 7 =
4
Filled table:
Input | Rule | Output
21 | ÷7 | 3
70 | ÷7 | 10
63 | ÷7 | 9
42 | ÷7 | 6
28 | ÷7 | 4
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Final Answer:
Top Left (+6):
Inputs: 6, 7→13, 9, 2, 12
Outputs: 12, 13, 15, 8, 18
Top Right (-8):
Inputs: 9, 10, 17, 11→3, 18→10
Outputs: 1, 2, 9, 3, 10
Middle Left (×6):
Inputs: 2→12, 8, 6, 9→54, 12→72
Outputs: 12, 48, 36, 54, 72
Middle Right (÷12):
Inputs: 120, 132→11, 12→1, 36, 72→6
Outputs: 10, 11, 1, 3, 6
Bottom Left (+7):
Outputs: 14, 18, 12, 8, 9
Bottom Right (÷7):
Outputs: 3, 10←70, 9, 6←42, 4
(Or full pairs: 21→3, 70→10, 63→9, 42→6, 28→4)
All blanks filled correctly using the rules.
Parent Tip: Review the logic above to help your child master the concept of input output machine worksheet.
