In terms of your fraction problem, given that
this is HackerNews I'm surprised that no one
claimed that the answer should be zero. :)
$ python
>>> 12/13 + 7/8
0 $ python
>>> 12/13 + 7/8
0 $ irb
>> 12/13 + 7/8
=> 0[1]> (+ (/ 12 13) (/ 7 8))
187/104