...41

(I checked my work 3 times because if I mess this one up I will never live this down)

Yay?

Detailed Solution

$\mathrm{Line\:up\:the\:numbers}$

$\begin{matrix}\:\:&2&7\\ +&1&4\end{matrix}$

$\mathrm{Add\:each\:column\:of\:digits,\:starting\:on\:the\:right\:and\:working\:left.}$

$If\:the\:sum\:of\:a\:column\:is\:more\:than\:ten,\:'carry'\:digits\:to\:the\:next\:column\:on\:the\:left.$

$\mathrm{Add\:the\:digits\:of\:the\:bolded\:column}:\quad \:7+4=11$

$\begin{matrix}\:\:&2&\textbf{7}\\ +&1&\textbf{4}\end{matrix}$

$\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:bolded\:column}$

$\frac{\begin{matrix}\:\:&1&\textbf{\:\:}\\ \:\:&2&\textbf{7}\\ +&1&\textbf{4}\end{matrix}}{\begin{matrix}\:\:&\:\:&\textbf{1}\end{matrix}}$

$\mathrm{Add\:the\:digits\:of\:the\:bolded\:column}:\quad \:1+2+1=4$

$\frac{\begin{matrix}\:\:&\textbf{1}&\:\:\\ \:\:&\textbf{2}&7\\ +&\textbf{1}&4\end{matrix}}{\begin{matrix}\:\:&\textbf{4}&1\end{matrix}}$

= 41