For the 2-fractions puzzle, the unique result (up to symmetry) is:

8    9
-- + -- == 1
26   13

Similarly, the 3-fractions puzzle has a unique result up to symmetry:

5    7    9
-- + -- + -- == 1
34   68   12

Some of the many solutions to the 4-fractions puzzle are:

1    3    8    9
-- + -- + -- + -- == 1
24   56   14   27
1    5    7    8
-- + -- + -- + -- == 1
39   26   42   13
1    3    6    9
-- + -- + -- + -- == 1
52   78   24   13

Some of the many solutions to the 5-fractions puzzle are:

1    5    8    9    9
-- + -- + -- + -- + -- == 1
12   45   36   27   36
1    6    7    8    9
-- + -- + -- + -- + -- == 1
12   45   35   24   36
1    7    8    9    9
-- + -- + -- + -- + -- == 1
12   56   48   24   36

Some of the many solutions to the 6-fractions puzzle are:

1    2    4    5    8    9
-- + -- + -- + -- + -- + -- == 1
12   33   45   77   68   69
1    2    4    5    7    8
-- + -- + -- + -- + -- + -- == 1
12   33   45   78   69   69
1    2    5    5    6    6
-- + -- + -- + -- + -- + -- == 1
12   33   49   79   78   84