Input Output Boxes - Free Printable

Problem Overview:

The task involves filling in the missing values in "In and Out Boxes" based on given rules. Each box has an "In" column and an "Out" column, and a rule that describes how to transform the "In" value into the "Out" value. The goal is to apply the rule to fill in the missing values and determine the rule when it is not provided.

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Solution:

#### Part a:
- Rule: Subtract 1
- Given:
- In: 0, 3, 7
- Out: 1, _, _
- Solution:
- For In = 0: \( 0 - 1 = -1 \)
- For In = 3: \( 3 - 1 = 2 \)
- For In = 7: \( 7 - 1 = 6 \)
- Filled Box:
- In: 0, 3, 7
- Out: -1, 2, 6

#### Part b:
- Rule: Add 5
- Given:
- In: 0, 3, 7
- Out: 5, _, 15
- Solution:
- For In = 0: \( 0 + 5 = 5 \) (already given)
- For In = 3: \( 3 + 5 = 8 \)
- For In = 7: \( 7 + 5 = 12 \) (but the given Out is 15, so there might be a typo. Assuming the rule is correct, we use 12.)
- Filled Box:
- In: 0, 3, 7
- Out: 5, 8, 12

#### Part c:
- Rule: Add 2
- Given:
- In: 3, 7, 11
- Out: 5, _, 10
- Solution:
- For In = 3: \( 3 + 2 = 5 \) (already given)
- For In = 7: \( 7 + 2 = 9 \)
- For In = 11: \( 11 + 2 = 13 \) (but the given Out is 10, so there might be a typo. Assuming the rule is correct, we use 13.)
- Filled Box:
- In: 3, 7, 11
- Out: 5, 9, 13

#### Part d:
- Rule: Subtract 5
- Given:
- In: 5, 8, 9
- Out: 0, _, 10
- Solution:
- For In = 5: \( 5 - 5 = 0 \) (already given)
- For In = 8: \( 8 - 5 = 3 \)
- For In = 9: \( 9 - 5 = 4 \) (but the given Out is 10, so there might be a typo. Assuming the rule is correct, we use 4.)
- Filled Box:
- In: 5, 8, 9
- Out: 0, 3, 4

#### Part e:
- Rule: Subtract 10
- Given:
- In: 20, 30, 80
- Out: _, 40, _
- Solution:
- For In = 20: \( 20 - 10 = 10 \)
- For In = 30: \( 30 - 10 = 20 \) (but the given Out is 40, so there might be a typo. Assuming the rule is correct, we use 20.)
- For In = 80: \( 80 - 10 = 70 \)
- Filled Box:
- In: 20, 30, 80
- Out: 10, 20, 70

#### Part f:
- Rule: Add 4
- Given:
- In: 5, 8, 9
- Out: 9, _, 11
- Solution:
- For In = 5: \( 5 + 4 = 9 \) (already given)
- For In = 8: \( 8 + 4 = 12 \)
- For In = 9: \( 9 + 4 = 13 \) (but the given Out is 11, so there might be a typo. Assuming the rule is correct, we use 13.)
- Filled Box:
- In: 5, 8, 9
- Out: 9, 12, 13

#### Part g:
- Rule: Not given
- Given:
- In: 3, 8, 13
- Out: 6, 10, 11, 16
- Solution:
- Observing the pattern:
- For In = 3: \( 3 \times 2 = 6 \)
- For In = 8: \( 8 \times 1.25 = 10 \)
- For In = 13: \( 13 \times 0.846 \approx 11 \)
- For In = 16: \( 16 \times 1 = 16 \)
- The rule appears to be multiplying by a decreasing factor.
- Rule: Multiply by a decreasing factor (e.g., \( \times 2, \times 1.25, \times 0.846, \times 1 \))

#### Part h:
- Rule: Not given
- Given:
- In: 3, 4, 7
- Out: 1, 4, 8
- Solution:
- Observing the pattern:
- For In = 3: \( 3 - 2 = 1 \)
- For In = 4: \( 4 \times 1 = 4 \)
- For In = 7: \( 7 \times 1.143 \approx 8 \)
- The rule appears to involve subtraction and multiplication.
- Rule: Subtract 2, then multiply by a factor (e.g., \( -2, \times 1, \times 1.143 \))

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{a. In: } 0, 3, 7 \quad \text{Out: } -1, 2, 6 \\
\text{b. In: } 0, 3, 7 \quad \text{Out: } 5, 8, 12 \\
\text{c. In: } 3, 7, 11 \quad \text{Out: } 5, 9, 13 \\
\text{d. In: } 5, 8, 9 \quad \text{Out: } 0, 3, 4 \\
\text{e. In: } 20, 30, 80 \quad \text{Out: } 10, 20, 70 \\
\text{f. In: } 5, 8, 9 \quad \text{Out: } 9, 12, 13 \\
\text{g. Rule: Multiply by a decreasing factor} \\
\text{h. Rule: Subtract 2, then multiply by a factor}
\end{array}
}
\]