From Förberedande kurs i matematik 1

Multiply top and bottom of the double fraction by the reciprocal of the denominator.

\displaystyle \frac{\frac{2}{7}}{\frac{3}{8}}=\frac{\frac{2}{7}\centerdot \frac{8}{3}}{\frac{3}{8}\centerdot \frac{8}{3}}=\frac{2}{7}\centerdot \frac{8}{3}

The numerator and denominator on the right-hand side do not have a common factor, so the answer is:

\displaystyle \frac{2}{7}\centerdot \frac{8}{3}=\frac{2\centerdot 8}{7\centerdot 3}=\frac{16}{21}

NOTE: It is also possible to learn a quick formula for double fractions which says that when the expression is rewritten with just one fraction sign, the denominators in the partial fractions change place:

\displaystyle \frac{\frac{2}{7}}{\frac{3}{8}}=\frac{2\centerdot 8}{3\centerdot 7}