1. The problem is to simplify the expression $\frac{1}{7} \div 2$.\n\n2. The formula for division of fractions is: $\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}$.\n\n3. Applying this rule, we rewrite the division as multiplication by the reciprocal:\n$$\frac{1}{7} \div 2 = \frac{1}{7} \times \frac{1}{2}$$\n\n4. Multiply the numerators and denominators:\n$$\frac{1 \times 1}{7 \times 2} = \frac{1}{14}$$\n\n5. The fraction $\frac{1}{14}$ is already in simplest form.\n\nTherefore, the simplified result of $\frac{1}{7} \div 2$ is $\frac{1}{14}$.