Weyl semimetals such as the TaAs family (TaAs, TaP, NbAs, NbP) host quasiparticle excitations resemblingthe long-sought-after Weyl fermions at special band-crossing points in the band structure denoted as Weylnodes. They are predicted to exhibit a negative longitudinal magnetoresistance (LMR) due to the chiralanomaly if the Fermi energy is sufficiently close to the Weyl points. However, current jetting effects, i.e.,current inhomogeneities caused by a strong, field-induced conductivity anisotropy in semimetals, have a similarexperimental signature and therefore have hindered a determination of the intrinsic LMR in the TaAs familyso far. This work investigates the longitudinal magnetoresistance of all four members of this family along thecrystallographicaandcdirections. Our samples are of similar quality as those previously studied in the literatureand have a similar chemical potential, as indicated by matching quantum-oscillation frequencies. Care was takento ensure homogeneous currents in all measurements. As opposed to previous studies where this was not done,we find a positive LMR that saturates in fields above 4 T in TaP, NbP, and NbAs forB||c. Using Fermi-surfacegeometries from band-structure calculations that had been confirmed by experiment, we show that this is thebehavior expected from a classical purely orbital effect, independent of the distance of the Weyl node to theFermi energy. The TaAs family of compounds is the first to show such a simple LMR without apparent influencesof scattering anisotropy. In configurations where the orbital effect is small, i.e., forB||ain NbAs and NbP, wefind a nonmonotonous LMR, including regions of negative LMR. We discuss a weak antilocalization scenarioas an alternative interpretation to the chiral anomaly for these results, since it can fully account for the overallfield dependence.