1. The problem asks to convert the mixed number $2 \frac{1}{2}$ into an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, use the formula: $$\text{Improper fraction} = \frac{(\text{whole number} \times \text{denominator}) + \text{numerator}}{\text{denominator}}$$ 3. For $2 \frac{1}{2}$, the whole number is 2, the numerator is 1, and the denominator is 2. 4. Substitute these values into the formula: $$\frac{(2 \times 2) + 1}{2}$$ 5. Calculate the numerator: $$\frac{\cancel{(2 \times 2)} + 1}{2} = \frac{4 + 1}{2}$$ 6. Simplify the numerator: $$\frac{5}{2}$$ 7. Therefore, the mixed number $2 \frac{1}{2}$ as an improper fraction is $\boxed{\frac{5}{2}}$. This fraction is greater than one because the numerator (5) is greater than the denominator (2).