From Förberedande kurs i matematik 1

We calculate the double fraction by multiplying top and bottom by the reciprocal of the denominator,

\displaystyle \frac{\displaystyle\ \frac{3}{5}\vphantom{\Biggl(}\ }{\displaystyle\ \frac{7}{10}\vphantom{\Biggl(}\ } = \frac{\displaystyle\frac{3}{5}\cdot\frac{10}{7}\vphantom{\Biggl(}}{\displaystyle \frac{\rlap{/}7}{\rlap{\,/}10}\cdot \frac{\rlap{\,/}10}{\rlap{/}7}\vphantom{\Biggl(}} = \frac{3}{5}\cdot \frac{10}{7}\,.

The expression can now be simplified further by removing the common factor 5,

\displaystyle \frac{3}{5}\cdot \frac{10}{7} = \frac{3}{\rlap{/}5}\cdot \frac{2\cdot {}\rlap{/}5}{7} = \frac{3\cdot 2}{7} = \frac{6}{7}\,.