From Förberedande kurs i matematik 1

We multiply the top and bottom of each fraction by the other fraction's denominator so that they have a common denominator,

\displaystyle \frac{1}{6}-\frac{2}{5}=\frac{1\centerdot 5}{6\centerdot 5}-\frac{2\centerdot 6}{5\centerdot 6}=\frac{5}{30}-\frac{12}{30}

Then the numerators can be subtracted:

\displaystyle \frac{5}{30}-\frac{12}{30}=\frac{5-12}{30}=\frac{-7}{30}=-\frac{7}{30}