The relative branching fractions of ${B}^{+}\ensuremath{\rightarrow}{h}^{+}{h}^{\ensuremath{'}+}{h}^{\ensuremath{'}\ensuremath{-}}$ decays, where ${h}^{(\ensuremath{'})}$ is a pion or kaon, are measured. The analysis is performed with a data sample, collected with the LHCb detector, corresponding to an integrated luminosity of $3.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of $pp$ collisions. The results obtained improve significantly on previous measurements of these quantities, and are important for the interpretation of Dalitz plot analyses of three-body charmless hadronic decays of ${B}^{+}$ mesons.