...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