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. $$1/\frac{3}{7}=\frac{1}{1}/\frac{3}{7}=\frac{1\cdot 7}{1\cdot 3}=\frac{7}{3}$$