We report measurements of the branching fractions for ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}{K}^{\ensuremath{-}}$, and ${K}^{0}{\ensuremath{\pi}}^{0}$ and ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, ${K}^{+}{\ensuremath{\pi}}^{0}$, ${K}^{0}{\ensuremath{\pi}}^{+}$, and ${K}^{+}{\overline{K}}^{0}$, based on $10.4{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected on the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector. We find $B({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({0.56}_{\ensuremath{-}0.20\ensuremath{-}0.05}^{+0.23+0.04})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, $B({B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1.93}_{\ensuremath{-}0.32\ensuremath{-}0.06}^{+0.34+0.15})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, $B({B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{0})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1.63}_{\ensuremath{-}0.33\ensuremath{-}0.18}^{+0.35+0.16})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, $B({B}^{+}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{+})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1.37}_{\ensuremath{-}0.48\ensuremath{-}0.18}^{+0.57+0.19})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, and $B({B}^{0}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{0})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({1.60}_{\ensuremath{-}0.59\ensuremath{-}0.27}^{+0.72+0.25})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. We also set upper limits on the branching fractions for ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$, and ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{\overline{K}}^{0}$.