Improving alignment of signed fractions in table

Question

I would like to find a way to better align signed fractions in a table. Take the following example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{booktabs}

\begin{document}

\begin{table}
  \centering
  \begin{tabular}{rr} \toprule
    $\alpha$ & $\beta$ \\ \midrule
    $-\frac{9}{2}$ & $-\frac{1}{6}$ \\[0.8ex] 
    $-\frac{7}{2}$ & $\frac{1}{30}$ \\[0.5ex]                                  
    \bottomrule
  \end{tabular}
\end{table}

\end{document}

This gives:

I don't like the look of the second column, which I think would look better if 1/30 would be centrally aligned with 1/6. By playing around, I noticed that changing the type of the second column to c and adding a \phantom{-} in front of 1/30, i.e.,

\begin{table}
  \centering
  \begin{tabular}{rc} \toprule
    $\alpha$ & $\beta$ \\ \midrule
    $-\frac{9}{2}$ & $-\frac{1}{6}$ \\[0.8ex] 
    $-\frac{7}{2}$ & $\phantom{-}\frac{1}{30}$ \\[0.8ex]                                  
    \bottomrule
  \end{tabular}
\end{table}

I get what I think is a much better looking result:

This, however, requires that I manually add the \phantom{-} command for every positive entry in my tables: I want to avoid this because the tables are large. So I have two questions:

1. Is there a way in LaTeX or through a package which I can automate the addition of \phantom{-}?
2. Do you know of a better way to get the kind of alignment of fractions I'm looking for?

Answer 1

I don't think there's anything wrong with standard center alignment. Consider the case where you have -1/6 and -1/30: if you center align the fractions, the minus signs will be off.

I can offer a new column type for the columns with negative entries.

\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{booktabs,array,calc}

\newcolumntype{n}{@{\hspace{\dimexpr\fontcharwd\textfont2 0+\arraycolsep}}c}
\newcommand{\?}{\mathllap{-}}
\newcommand{\mcn}[1]{%
  \multicolumn{1}{c}{\kern-\fontcharwd\textfont2 0 #1}%
}

\begin{document}

\begin{table}
\centering

$\begin{array}{nnc}
\toprule
\mcn{\alpha} & \mcn{\beta} & \gamma \\
\midrule
\?\frac{9}{2} & \?\frac{1}{6}  & 2 \\[0.8ex]
\?\frac{7}{2} &   \frac{1}{30} & 3 \\[0.5ex]
\bottomrule
\end{array}$

\end{table}

\end{document}