How to make table less cramped

Experiment with Mico's solution: The fractions can be made less ragged, if the fraction bars have equal lengths. All numerators and denominators have one or two digits. The macro \mytwofrac extends the numerator and/or denominator, if there is only one digit. The following example assumes non-proportional widths for the digits and that the width of a digit is 0.5em (for simplicity).

\documentclass{article}
\usepackage{calculator,pgffor,etoolbox}
\usepackage{array} % <-- new
\begin{document}

\newcommand*{\mytwofrac}[2]{%
  \frac
  {\ifnum#1<10 \kern.25em#1\kern.25em\else#1\fi}%
  {\ifnum#2<10 \kern.25em#2\kern.25em\else#2\fi}%
}

\newcommand*\mytable{}
\foreach \i in {1,...,6}{
    \foreach \j in {1,...,6}{
        \ADD{\i}{\j}\sum
        \FRACTIONSIMPLIFY{\sum}{35}\num\div
        \xappto\mytable{
            (\i,\j)\to\mytwofrac{\num}{\div}&
        }
    }
    \gappto\mytable{\\}
}

\[
\renewcommand\arraystretch{2.25}
\setlength\arraycolsep{4pt} % default: 5pt
\begin{array}{@{} *{6}{>{\displaystyle}l} l @{}}
    \mytable
\end{array}
\]
\end{document}

Here's a solution that uses an array environment instead of a tabular environment and creates 6 separate left-aligned columns whose contents are automatically in display-math mode.

\documentclass{article}
\usepackage{calculator,pgffor,etoolbox}
\usepackage{array} % <-- new
\begin{document}
\newcommand*\mytable{}
\foreach \i in {1,...,6}{
    \foreach \j in {1,...,6}{
        \ADD{\i}{\j}\sum
        \FRACTIONSIMPLIFY{\sum}{35}\num\div
        \xappto\mytable{
            (\i,\j)\to\frac{\num}{\div}& % note: no $-symbols necessary
        }
    }
    \gappto\mytable{\\}
}

\[
\renewcommand\arraystretch{2.25}
\setlength\arraycolsep{4pt} % default: 5pt
\begin{array}{@{} *{6}{>{\displaystyle}l} l @{}}
    \mytable
\end{array}
\]
\end{document}

Some explanations:

• The opening and closing @{} particles mean, "no whitespace padding" (at the left- and right-hand edges). (These particles are, strictly speaking, optional. However, I think it's nice to provide them.)

• *{6}{>{\displaystyle}l} means, "create 6 columns of type >{\displaystyle}l", i.e., left-aligned columns whose cells are automatically in display-style math mode. This is useful because \frac will then generate "large" fractions.

• The final l-type column is a "dummy" column. Its contents are always going to be empty; it's necessary, though, to specify a 7th column, as the (\i,\j)\to\frac{\num}{\div}& directive inserts a column divider, &, at the end of each output string. Since there are 6 instances of &, one must set up 7 (not 6) columns.

Here is a solution with cellspace, which lets you define minimal vertical spacing at the top and bottom of cells in columns with sprefixezd with the letter S (or C if you load siunitx):

\documentclass{article}
\usepackage{calculator}
\usepackage{nccmath}
\usepackage{pgffor,etoolbox}
\usepackage{cellspace}
\setlength{\cellspacetoplimit}{6pt}
\setlength{\cellspacebottomlimit}{6pt}

\begin{document}

\newcommand*\mytable{}
\foreach \i in {1,...,6}{
    \foreach \j in {1,...,6}{
        \ADD{\i}{\j}\sum
        \FRACTIONSIMPLIFY{\sum}{35}\num\div
        \xappto\mytable{
            $(\i,\j)\rightarrow\frac\num\div$
        }
    }
    \gappto\mytable{\\}
}

\begin{tabular}{Sc}
    \mytable
\end{tabular}

\end{document}