In rare-earth (R) ferroborates, RFe3(BO3)(4) with R = Eu, Gd, and Tb, the magnetoelectric (ME) responses appear to stem from both the antiferromagnetic order of the iron (Fe) spins and the magnetic moments on the R ions. We measured the electric polarization (P) along the a axis while rotating a magnetic field (H) around the a axis and found that the target compounds show mutually distinctive H-direction dependencies. EuFe3(BO3) (4) (R = Eu) shows an almost constant spontaneous P with a slight modulation when H is slanted from the c axis. The H-angle (theta(H)) dependence of the P can be described by a formula P = P-0 - Lambda sin(2) theta(H). As for GdFe3(BO3)(4) and TbFe3(BO3)(4), they show highly anisotropic theta(H) dependence of P, which characterizes the respective ME responses from their R magnetic moments. In certain regions of theta(H), the P can be described by P = P-0 - K sin 2 theta(H) and P = P-0 -/+ Gamma sin theta(H) for R = Gd and Tb, respectively. We devised a theory for the ME response of the individual magnetic ions in a RFe3(BO3)(4) crystal and applied it to these compounds focusing on their local symmetry and their ground-state multiplet structures. The above formulas successfully reproduce the observed results as the summation of P from each magnetic subsystem, which in turn enables us to assign the first and second terms to the spontaneous P due to a collinear antiferromagnetic ordering of the Fe spins and the ME response of the R ion under H, respectively. The thermal and H -induced evolutions of the magnetic-ion resolved P quantitatively agree with the theoretical predictions, ensuring the relevant microscopic ME mechanism for each magnetic ion. The measurement of angular dependence of P is particularly useful to decompose the overlapped ME responses into the respective origins in the system with multiple magnetic subsystems.