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    3    6    7    9    9 
 -- + -- + -- + -- + -- + -- == 1
 18   27   45   28   36   45
 2    4    5    5    7    7 
 -- + -- + -- + -- + -- + -- == 1
 99   18   12   33   66   84
 6    6    8    8    9    9 
 -- + -- + -- + -- + -- + -- == 1
 72   72   34   51   34   51