Question

Look at the diagram below. An input and an output are filled in.
Which rules would make this input-output pair true?
input
12
rule
Input Output Arrow
?
Input Output Arrow
output
7
Could be a rule for this input-output pair Could not be a rule for this input-output pair
Add 2, then divide by 2.
Subtract 5.
Divide by 2, then add 1.
Subtract 3, then divide by 5.
Divide by 6.
If odd, subtract 9. If even, write 3.

Answer 1

To determine which rules could make the input-output pair (12 -> 7) true, let's analyze each provided rule step by step.

1. **Add 2, then divide by 2.**
- Start with 12: \(12 + 2 = 14\)
- Then divide by 2: \(14 / 2 = 7\)
- This rule **could make the input-output pair true**.

2. **Subtract 5.**
- Start with 12: \(12 - 5 = 7\)
- This rule **could make the input-output pair true**.

3. **Divide by 2, then add 1.**
- Start with 12: \(12 / 2 = 6\)
- Then add 1: \(6 + 1 = 7\)
- This rule **could make the input-output pair true**.

4. **Subtract 3, then divide by 5.**
- Start with 12: \(12 - 3 = 9\)
- Then divide by 5: \(9 / 5 = 1.8\) (not equal to 7)
- This rule **could not make the input-output pair true**.

5. **Divide by 6.**
- Start with 12: \(12 / 6 = 2\)
- This rule **could not make the input-output pair true**.

6. **If odd, subtract 9. If even, write 3.**
- The input 12 is even, so according to the rule, we would write 3.
- This rule **could not make the input-output pair true**.

In summary, the rules that **could make the input-output pair true** are:
- Add 2, then divide by 2.
- Subtract 5.
- Divide by 2, then add 1.

The rules that **could not make the input-output pair true** are:
- Subtract 3, then divide by 5.
- Divide by 6.
- If odd, subtract 9. If even, write 3.