The procedure for decomposing the symmetric three-quark SU(6) x O(3) basis states of baryons into vector products of the two-quark SU(G) x O(3) basis states and the one-quark states is elaborated and the relevant ”coefficients of fractional parentage” in the decompositions are listed. Some applications of the decomposition to the evaluation of the matrix elements of the matrix elements of one-body and two-body quark operators are illustrated.