1. The problem is to convert the mixed number $-14\frac{1}{2}$ into an improper fraction. 2. Recall that a mixed number consists of a whole number and a fraction. To convert it to an improper fraction, use the formula: $$\text{Improper fraction} = \left|\text{whole number}\right| \times \text{denominator} + \text{numerator}$$ 3. Here, the whole number is $14$, the numerator is $1$, and the denominator is $2$. 4. Calculate the numerator of the improper fraction: $$14 \times 2 + 1 = 28 + 1 = 29$$ 5. So the improper fraction is $\frac{29}{2}$. 6. Since the original mixed number is negative, the improper fraction is also negative: $$-\frac{29}{2}$$ 7. Therefore, the mixed number $-14\frac{1}{2}$ as an improper fraction is $-\frac{29}{2}$.