To address the claim "Dividing a number by 2 always results in a smaller number," we need to find a counterexample. A counterexample is a specific case where the claim does not hold true. In this context, it would be a number that, when divided by 2, does not result in a smaller number.
Let's examine each option:
- Option A: The number is 8.
- Dividing 8 by 2: [tex]\( \frac{8}{2} = 4 \)[/tex]
- Since 4 is smaller than 8, this does not serve as a counterexample.
- Option B: The number is 5.
- Dividing 5 by 2: [tex]\( \frac{5}{2} = 2.5 \)[/tex]
- Since 2.5 is smaller than 5, this does not serve as a counterexample.
- Option C: The number is 2.
- Dividing 2 by 2: [tex]\( \frac{2}{2} = 1 \)[/tex]
- Since 1 is smaller than 2, this does not serve as a counterexample.
- Option D: The number is 1.
- Dividing 1 by 2: [tex]\( \frac{1}{2} = 0.5 \)[/tex]
- Since 0.5 is smaller than 1, this does not serve as a counterexample.
- Option E: The number is -1.
- Dividing -1 by 2: [tex]\( \frac{-1}{2} = -0.5 \)[/tex]
- Since -0.5 is greater than -1, this serves as a counterexample.
Based on this analysis, the correct counterexample to the claim "Dividing a number by 2 always results in a smaller number" is:
O E. The number is -1.
