  The q-deformed Clebsch-Gordan coefficients corresponding to the
$\lrpy{3}\times\lrpy{21}$ reduction of the $SU_q(3)$ quantum algebra are
computed. From these results and using the quantum Clebsch-Gordan coefficients
for the $\lrpy{21}\times\lrpy{21}$ reduction found by Zhong Qi Ma, the
q-deformed Gell-Mann-Okubo mass relations for octet and decuplet baryons are
determined by generalizing the procedure used for the SU(3) algebra. We also
determine the Coleman-Glashow relations for octet and decuplet baryons in the
$SU_q(3)$ algebra. Finally, by using the experimental particle masses of the
octet and decuplet baryons, two values of the $q$-parameter are found and
adjusted for the predicted masses expressions (one for the Gell-Mann-Okubo mass
relations and the other for the Coleman-Glashow relations) and a possible
physical interpretation is given.
