1. **State the problem:** Simplify the expression $1 \div \frac{7}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. 3. **Apply the rule:** $$1 \div \frac{7}{2} = 1 \times \frac{2}{7}$$ 4. **Multiply:** $$1 \times \frac{2}{7} = \frac{2}{7}$$ 5. **Final answer:** $$\boxed{\frac{2}{7}}$$ This means that dividing 1 by $\frac{7}{2}$ results in $\frac{2}{7}$.