Basically, there are
nine possible cases, because the numerator of the first fraction can
either be larger than, equal to, or smaller than the numerator of the
second fraction, and at the same time the denominator of the first
fraction can either be larger than, equal to, or smaller than the
denominator of the second fraction. However, with respect to
congruency in the sense described in Section 1.1, there are five
different types of items that involve non-equal pairs of fractions
and that differ not only with respect to the order of the fractions