1. The problem asks to convert the mixed number $1 \frac{1}{2}$ 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 $1 \frac{1}{2}$, the whole number is 1, the numerator is 1, and the denominator is 2. 4. Substitute these values into the formula: $$\frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$$ 5. Therefore, the mixed number $1 \frac{1}{2}$ as an improper fraction is $\frac{3}{2}$. Final answer: $\frac{3}{2}$