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I want to calculate some numbers, basically for some layout stuff. However, I am stuck a this point because it seems you can not write something like this in latex:
\newcommand{\MyNewWidthValueA}{{0.6666 + 0.075} \textwidth}
\newcommand{\MyNewWidthValueB}{\MyNewWidthValueA + 2cm}
Is there a way to do these quite basic things? I assume this is a very standard function that should work as I need this for defining position of frames and boxes for some specific layout things.
Latex cannot directly handle expressions or calculations. I am far from an expert but I believe there are ways to achieve what you want.
You can keep numbers as dimensions and use \dimexpr in calculations: e.g. \the\dimexpr12pt + 13.5pt to get 25.5pt. This works in both macros and new length names. In this case, the \the is used if you want to extract and print a dimension.
You can also calculate expressions directly inside \fpeval{<expression>}, which returns a number (without units), has access to mathematical functions, and allows formatting the results, s.a. rounding (requires xfp package before 2022/01/06)
Similarly to \fpeval{}, pgfmath package adds the following macros (among many others): \pgfmathparse{expression} and \pgfmathresult. The latter returns the last expression parsed by \pgfmathparse{}.
Finally, there's calc but I have the least experience with this one.
Here's one example based on your code:
\documentclass{article}
\usepackage{pgfmath}
% \usepackage{xfp} % Required before 2022/01/06 of latex
\newlength{\MyNewWidthValueA}
\newlength{\MyNewWidthValueB}
\setlength{\MyNewWidthValueA}{\dimexpr0.6666\textwidth + 0.075\textwidth}
\setlength{\MyNewWidthValueB}{\dimexpr\MyNewWidthValueA+2cm}
\newcommand{\Vala}{\dimexpr0.6666\textwidth + 0.075\textwidth}
\newcommand{\Valb}{\dimexpr\MyNewWidthValueA + 2cm}
\begin{document}
\the\dimexpr12pt +13.5pt
Length names:
\the\MyNewWidthValueA, \the\MyNewWidthValueB
\bigskip
Macros expanding to lengths:
\the\Vala, \the\Valb
\bigskip
A macro to print a formatted result from an expression:
\fpeval{round((0.6666 + 0.075)\textwidth,1)}
\end{document}
You may use \fpeval.
\documentclass{article}
\newcommand{\MyNewWidthValueA}{}
\newcommand{\MyNewWidthValueB}{}
\begin{document}
\edef\MyNewWidthValueA{\fpeval{(0.6666 + 0.075)*\textwidth}pt}
\MyNewWidthValueA
\edef\MyNewWidthValueB{\fpeval{\MyNewWidthValueA+2cm}pt}
\MyNewWidthValueB
\end{document}
You may want to do
\fpeval{round(<expression>,5)}
but TeX will not bother if you use many decimal digits and will ignore the surplus ones.
\dimexrto calculate with lengths, e.g.,\newlength{\MyNewWidthValueA}\setlength{\MyNewWidthValueA}{\dimexpr 0.6666\textwidth+0.075\textwidth}. You can also use packagecalcfor calculations like this without need of using\dimexpr. See a good LaTeX introduction about the distinction of lengths/skips/dimensions and commands/macros. Another alternative for experienced users would be to useexpl3.