1. **State the problem:** Calculate the value of $\frac{4}{7} \div \frac{1}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the rule:** $$\frac{4}{7} \div \frac{1}{2} = \frac{4}{7} \times \frac{2}{1}$$ 4. **Multiply the numerators and denominators:** $$= \frac{4 \times 2}{7 \times 1} = \frac{8}{7}$$ 5. **Simplify or convert to mixed number:** $$\frac{8}{7} = 1 \frac{1}{7}$$ 6. **Explain the boxed answers:** The boxed 1 is the whole number part of the mixed fraction, and the boxed $\frac{4}{5}$ does not relate to this problem's correct answer. The correct fractional part is $\frac{1}{7}$, not $\frac{4}{5}$. **Final answer:** $$\frac{4}{7} \div \frac{1}{2} = 1 \frac{1}{7}$$