The theory of the order-$\ensuremath{\alpha}$ radiative correction to the $\ensuremath{\beta}$ decay of baryons is briefly reviewed. An effective procedure for the calculation of the real-photonic part of the order-$\ensuremath{\alpha}$ correction is outlined. Numerical results are tabulated for the radiative corrections to the branching ratio, the electron-antineutrino correlation parameter, the electron-energy (${E}_{e}$) spectrum, the final-baryon-energy (${E}_{f}$) spectrum, and the electron-antineutrino angular-correlation (${E}_{e}$) distribution, and to the (${E}_{f}$, ${E}_{f}$) and the (${E}_{e}$, $cos{\ensuremath{\theta}}_{e\ensuremath{\nu}}$) two-variable distributions in the cases of the decays ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{ne}\overline{\ensuremath{\nu}}$, ${\ensuremath{\Sigma}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}e\overline{\ensuremath{\nu}}$, ${\ensuremath{\Xi}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}e\overline{\ensuremath{\nu}}$, and $\ensuremath{\Lambda}\ensuremath{\rightarrow}\mathrm{pe}\overline{\ensuremath{\nu}}$.