The use of the quark configuration (s+f)4 to represent the states of the atomic f shell calls for a simultaneous transformation of operators. Operator equivalences are developed for z0, a two-electron operator associated with spin-spin interactions, and t11, a scalar three-electron operator appearing in third order in perturbation theory. Both belong to the irreducible representation (IR) (111) of Racah's group SO(7), and can be represented by combinations of the single-quark operators of the types (ftheta Dagger ftheta )(2) and (ftheta Dagger ftheta )(0)-712/stheta Dagger stheta , where theta distinguishes the four quarks. The group SO(7)' (which plays the same role for the f quarks as SO(7) does for the f electrons) is used to establish relations between matrix elements of z0 and those of other electronic operators such as U(2) and W(12), thereby accounting for various unexpected connections and proportionalities that go beyond what would be expected from straightforward applications of the Wigner-Eckart theorem.