To determine which of the given fractions is less than one-third, we can compare each fraction to \(\frac{1}{3}\) by finding a common denominator. 

The least common multiple of 3 and the denominators of the given fractions is 1386.

So, we can rewrite each fraction with a denominator of 1386:

A. \(\frac{22}{63}\) = \(\frac{22 * 22}{63 * 22}\) = \(\frac{484}{1386}\)

B. \(\frac{4}{11}\) = \(\frac{4 * 126}{11 * 126}\) = \(\frac{504}{1386}\)

C. \(\frac{15}{46}\) = \(\frac{15 * 30}{46 * 30}\) = \(\frac{450}{1386}\)

D. \(\frac{33}{98}\) = \(\frac{33 * 14}{98 * 14}\) = \(\frac{462}{1386}\)

E. \(\frac{122}{303}\) = \(\frac{122 * 4.57}{303 * 4.57}\) = \(\frac{557.94}{1386}\)

One-third can be written as \(\frac{1 * 462}{3 * 462}\) = \(\frac{462}{1386}\).

Comparing each fraction to this value, we see that the only fraction that is less than one-third is option \(\frac{15}{46}\).