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\cdot 5}{6\cdot 5}-\frac{2\cdot 6}{5\cdot 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}\,.