1. **State the problem:** Simplify the expression $\frac{41}{49} \div \frac{1}{2}$. 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:** $$\frac{41}{49} \div \frac{1}{2} = \frac{41}{49} \times \frac{2}{1}$$ 4. **Multiply the numerators and denominators:** $$\frac{41 \times 2}{49 \times 1} = \frac{82}{49}$$ 5. **Check for simplification:** 82 and 49 have no common factors other than 1, so the fraction is already in simplest form. **Final answer:** $$\frac{82}{49}$$