The Modular Neutron Array (MoNA) and 4 Tm Sweeper magnet were used to measure the free neutrons and heavy charged particles from the radioactive ion beam induced ${}^{32}$Mg+${}^9$Be reaction. The fragmentation reaction was simulated with the constrained molecular dynamics model (CoMD), which demonstrated that the $⟨N/Z⟩$ of the heavy fragments and free neutron multiplicities were observables sensitive to the density dependence of the symmetry energy at subsaturation densities. Through comparison of these simulations with the experimental data, constraints on the density dependence of the symmetry energy were extracted. The advantage of radioactive ion beams as a probe of the symmetry energy is demonstrated through examination of CoMD calculations for stable and radioactive-beam-induced reactions.