Informally, length calculation are done using factor multiplication as there is no division notation. Since any division can be represented as some multiplication, this shouldn't be a problem. So, .5\textwidth refers to half (1/2) of \textwidth, while 2\wd0 refers to twice the width of box 0. In your case it suffices to use
\includegraphics[width=0.3333\textwidth]{<img>}
You can perform all kinds of calculations using calc or even LaTeX3:

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\cs_new_eq:NN \calc \fp_eval:n
\ExplSyntaxOff
\begin{document}
\newlength{\mylen}
\setlength{\mylen}{\textwidth}
\verb|\mylen|: \the\mylen
\setlength{\mylen}{\calc{1/3}\textwidth}
\verb|1/3\mylen|: \the\mylen
\end{document}
The LaTeX3 syntax above makes \calc an new control sequence (or macro) that is equivalent to \fp_eval:n - a floating point function that evaluates it's argument using the regular programming arithmetic (like +, -, *, /, ^, ...) taking a single argument.
0.33333\textwidth. – Werner Jun 20 '16 at 23:36\dimexpr<calculation>\relaxwhile invoking thecalcpackage. – azetina Jun 20 '16 at 23:48\newlengthhere in TeX.SX – azetina Jun 20 '16 at 23:55