1. **State the problem:** We need to divide $-7$ by $-1 \frac{3}{4}$ and express the answer as a whole number. 2. **Convert the mixed number to an improper fraction:** $$-1 \frac{3}{4} = -\left(1 + \frac{3}{4}\right) = -\frac{7}{4}$$ 3. **Rewrite the division problem:** $$-7 \div \left(-\frac{7}{4}\right)$$ 4. **Use the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. $$-7 \times \left(-\frac{4}{7}\right)$$ 5. **Multiply the numbers:** $$-7 \times -\frac{4}{7} = \frac{\cancel{-7}}{1} \times \frac{\cancel{-4}}{\cancel{7}} = \frac{4}{1} = 4$$ 6. **Interpret the result:** The negatives cancel out, and the answer is the whole number $4$. **Final answer:** $4$