Question

Which rule would make all of these input-output pairs true?
Finally, think about the rule, 'Divide by 2, then add 1.' If we take each input and divide by 2, then add 1, do we get each corresponding output?
input
Input Output Arrow
rule
Input Output Arrow
output


Input Output
6 4
44 23
9 5.5
4 3


If we apply the rule, 'Divide by 2, then add 1', to each input, we
get each corresponding output.

Answer 1

Let's first check the proposed rule 'Divide by 2, then add 1' with each of the input-output pairs:

1. For the input **6**:
\[
\text{Divide by 2: } 6 \div 2 = 3
\]
\[
\text{Add 1: } 3 + 1 = 4
\]
The output is **4** (this matches).

2. For the input **44**:
\[
\text{Divide by 2: } 44 \div 2 = 22
\]
\[
\text{Add 1: } 22 + 1 = 23
\]
The output is **23** (this matches).

3. For the input **9**:
\[
\text{Divide by 2: } 9 \div 2 = 4.5
\]
\[
\text{Add 1: } 4.5 + 1 = 5.5
\]
The output is **5.5** (this matches).

4. For the input **4**:
\[
\text{Divide by 2: } 4 \div 2 = 2
\]
\[
\text{Add 1: } 2 + 1 = 3
\]
The output is **3** (this matches).

Since applying the rule 'Divide by 2, then add 1' results in the corresponding outputs for all the given inputs, we conclude:

The rule that makes all of these input-output pairs true is:
**"Divide by 2, then add 1."**