$\displaystyle -1 - \frac{1}{3}$

$\displaystyle - \frac{1 * 3}{1 * 3} - \frac{1}{3} = - \frac{3}{3} - \frac{1}{3} = - \frac{-3 - 1}{3} = - \frac{-4}{3} = ??$

does the negative sign on the faction mean that both the numerator and the denomanator shoud be treated as negative numbers when used in cross multiplication?