1. **Problem Statement:** Divide $\frac{3}{4}$ by $\frac{4}{7}$. Find the correct answer from the options. 2. **Formula Used:** To divide fractions, multiply the first fraction by the reciprocal of the second fraction. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the formula:** $$\frac{3}{4} \div \frac{4}{7} = \frac{3}{4} \times \frac{7}{4}$$ 4. **Multiply numerators and denominators:** $$= \frac{3 \times 7}{4 \times 4} = \frac{21}{16}$$ 5. **Convert to mixed number:** $$\frac{21}{16} = 1 \frac{5}{16}$$ 6. **Conclusion:** The correct answer is $1 \frac{5}{16}$.