### Overloaded addition operator
sub _add {
    my ( $x, $y ) = @_;
    my ( $n_sum, $sum_str );
    my ( $n1,    $n2 ) = ( $x->{NUMER}, $y->{NUMER} );
    my ( $d1,    $d2 ) = ( $x->{DENOM}, $y->{DENOM} );
    my $com_denom = ( $d1 == $d2 ) ? $d1 : $d1 * $d2;
    $n_sum =
      ( $d1 == $d2 )
        ? $n1 + $n2
        : do {
            $n1 = $n1 * ( $com_denom / $d1 );
            $n2 = $n2 * ( $com_denom / $d2 );
            $n1 + $n2;
          };
    my $gcd = _simplify( $n_sum, $com_denom );
    ( $n_sum, $com_denom ) = map { $_ /= $gcd } ( $n_sum, $com_denom );
    $sum_str =
        ($com_denom)
          ? ( $n_sum == $com_denom )
            ? "1"
            : "${n_sum}/${com_denom}"
          : "0";
    return $sum_str;
}
### Overloaded subtraction operator
sub _sub {
    my ( $x, $y, ) = @_;
    my ( $n_diff, $diff_str );
    my ( $n1, $n2 ) = ( $x->{NUMER}, $y->{NUMER} );
    my ( $d1, $d2 ) = ( $x->{DENOM}, $y->{DENOM} );
    my $com_denom = ( $d1 == $d2 ) ? $d1 : $d1 * $d2;
    $n_diff =
      ( $d1 == $d2 )
        ? $n1 - $n2
        : do {
            $n1 = $n1 * ( $com_denom / $d1 );
            $n2 = $n2 * ( $com_denom / $d2 );
            $n1 - $n2;
          };
    my $gcd = _simplify( abs($n_diff), $com_denom );
    ( $n_diff, $com_denom ) = map { $_ /= $gcd } ( $n_diff, $com_denom );
    $diff_str =
        ($com_denom)
          ? ( $n_diff == $com_denom )
            ? "1"
            : "${n_diff}/${com_denom}"
          : "0";
    return $diff_str;
}