Study of the semileptonic charm decays $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, $D^0\to K^{-}{e}^{+}{\nu }_e$, and $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$

Using a sample of 1.8 million $D\overline{D}$ mesons collected at the $\psi (3770)$ with the CLEO-c detector, we study the semileptonic decays $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, $D^0\to K^{-}{e}^{+}{\nu }_e$, and $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$. For the total branching fractions we find $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)=0.299(11)(9)\%$, $\mathcal{B}(D^{+}\to {\pi }^0{e}^{+}{\nu }_e)=0.373(22)(13)\%$, $\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e)=3.56(3)(9)\%$, and $\mathcal{B}(D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e)=8.53(13)(23)\%$, where the first error is statistical and the second systematic. In addition, form factors are studied through fits to the partial branching fractions obtained in five $q^2$ ranges. By combining our results with recent unquenched lattice calculations, we obtain $|V_{cd}|=0.217(9)(4)(23)$ and $|V_{cs}|=1.015(10)(11)(106)$, where the final error is theoretical.