Addition Input/Output Tables | Input Output Tables | isgb.edu.ar - Free Printable

Problem Overview:

The task involves determining the rule used by each function machine based on the input and output values provided in the tables. Each table shows a set of inputs and corresponding outputs, and the goal is to identify the mathematical operation or transformation applied to the input to produce the output.

Solution Approach:

1. Analyze Each Table Individually: For each table, observe the relationship between the input and output values.
2. Identify Patterns: Look for consistent operations such as addition, subtraction, multiplication, division, or combinations thereof.
3. Test the Rule: Ensure the identified rule works for all given input-output pairs in the table.
4. Record the Rule: Write down the rule in a clear and concise manner.

Detailed Analysis of Each Table:

#### Table 1
| Input | Output |
|-------|--------|
| 31 | 35 |
| 34 | 38 |
| 44 | 48 |
| 46 | 50 |
| 47 | 51 |

- Pattern: The output is consistently 4 more than the input.
- Rule: \( \text{Output} = \text{Input} + 4 \)

#### Table 2
| Input | Output |
|-------|--------|
| 21 | 15 |
| 24 | 18 |
| 35 | 29 |
| 40 | 34 |
| 54 | 48 |

- Pattern: The output is consistently 6 less than the input.
- Rule: \( \text{Output} = \text{Input} - 6 \)

#### Table 3
| Input | Output |
|-------|--------|
| 17 | 13 |
| 27 | 23 |
| 29 | 25 |
| 34 | 30 |
| 40 | 36 |

- Pattern: The output is consistently 4 less than the input.
- Rule: \( \text{Output} = \text{Input} - 4 \)

#### Table 4
| Input | Output |
|-------|--------|
| 20 | 10 |
| 26 | 16 |
| 38 | 28 |
| 52 | 42 |
| 59 | 49 |

- Pattern: The output is consistently half of the input minus 1.
- Rule: \( \text{Output} = \frac{\text{Input}}{2} - 1 \)

#### Table 5
| Input | Output |
|-------|--------|
| 39 | 24 |
| 45 | 30 |
| 46 | 31 |
| 53 | 38 |
| 64 | 49 |

- Pattern: The output is consistently the input minus 15.
- Rule: \( \text{Output} = \text{Input} - 15 \)

#### Table 6
| Input | Output |
|-------|--------|
| 17 | 30 |
| 19 | 32 |
| 30 | 43 |
| 41 | 54 |
| 47 | 60 |

- Pattern: The output is consistently the input plus 13.
- Rule: \( \text{Output} = \text{Input} + 13 \)

#### Table 7
| Input | Output |
|-------|--------|
| 12 | 17 |
| 35 | 40 |
| 37 | 42 |
| 42 | 47 |
| 45 | 50 |

- Pattern: The output is consistently 5 more than the input.
- Rule: \( \text{Output} = \text{Input} + 5 \)

#### Table 8
| Input | Output |
|-------|--------|
| 17 | 30 |
| 24 | 37 |
| 35 | 48 |
| 38 | 51 |
| 42 | 55 |

- Pattern: The output is consistently the input plus 13.
- Rule: \( \text{Output} = \text{Input} + 13 \)

#### Table 9
| Input | Output |
|-------|--------|
| 34 | 24 |
| 44 | 34 |
| 46 | 36 |
| 51 | 41 |
| 57 | 47 |

- Pattern: The output is consistently the input minus 10.
- Rule: \( \text{Output} = \text{Input} - 10 \)

#### Table 10
| Input | Output |
|-------|--------|
| 29 | 14 |
| 33 | 18 |
| 34 | 19 |
| 36 | 21 |
| 37 | 22 |

- Pattern: The output is consistently half of the input.
- Rule: \( \text{Output} = \frac{\text{Input}}{2} \)

#### Table 11
| Input | Output |
|-------|--------|
| 28 | 43 |
| 31 | 46 |
| 33 | 48 |
| 35 | 50 |
| 42 | 57 |

- Pattern: The output is consistently the input plus 15.
- Rule: \( \text{Output} = \text{Input} + 15 \)

#### Table 12
| Input | Output |
|-------|--------|
| 15 | 23 |
| 21 | 29 |
| 26 | 34 |
| 28 | 36 |
| 34 | 42 |

- Pattern: The output is consistently the input plus 8.
- Rule: \( \text{Output} = \text{Input} + 8 \)

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{Output} = \text{Input} + 4 \\
2. & \text{Output} = \text{Input} - 6 \\
3. & \text{Output} = \text{Input} - 4 \\
4. & \text{Output} = \frac{\text{Input}}{2} - 1 \\
5. & \text{Output} = \text{Input} - 15 \\
6. & \text{Output} = \text{Input} + 13 \\
7. & \text{Output} = \text{Input} + 5 \\
8. & \text{Output} = \text{Input} + 13 \\
9. & \text{Output} = \text{Input} - 10 \\
10. & \text{Output} = \frac{\text{Input}}{2} \\
11. & \text{Output} = \text{Input} + 15 \\
12. & \text{Output} = \text{Input} + 8 \\
\end{array}
}
\]