If $1$ is divided by a fraction, the result is the reciprocal of the fraction. The rule can be shown by rewriting $1$ as $1/1$ and use the rules for dividing fractions. $$\frac{1}{3/7}=\frac{1/1}{3/7}=\frac{1\cdot 7}{1\cdot 3}=\frac{7}{3}$$