1. **State the problem:** Evaluate the division of fractions $\frac{4}{3} \div \frac{7}{8}$. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its reciprocal. The reciprocal of $\frac{7}{8}$ is $\frac{8}{7}$. 3. **Apply the rule:** $$\frac{4}{3} \div \frac{7}{8} = \frac{4}{3} \times \frac{8}{7}$$ 4. **Multiply the numerators and denominators:** $$= \frac{4 \times 8}{3 \times 7} = \frac{32}{21}$$ 5. **Simplify if possible:** $32$ and $21$ have no common factors other than $1$, so the fraction is already in simplest form. 6. **Final answer:** $$\frac{4}{3} \div \frac{7}{8} = \frac{32}{21}$$ This is an improper fraction as requested.