You can use p-add to add up n fractions to m<n output fractions (partial sums).
./p-add [number of parallel threads]
The number of parallel threads will also be the number of output fractions. p-add reads from and writes to stdin in the same file format, so you could invoke it like that:
cat millions-of-fractions.txt | ./p-add 10000 | ./p-add 40 | ./p-add 1 > result.txt
After this chain has finished (probably within a few seconds), you will end up with a single big fraction that is, while not having lost any of its initial precision, the sum of all fractions in the original file. That's great division of labor! You cannot fulfill this task faster on normal hardware.
Numerator of first fraction Denominator of first fraction Numerator of second fraction Denominator of second fraction Numerator of third fraction Denominator of third fraction ...
1 2 3 5 8 9 11 17 22 23
We invoke p-add:
$ cat test.txt | ./p-add 1 126419 35190
Your local mathematician will confirm that 1/2+3/5+8/9+11/17+22/23 equals 126419/35190 (≈ 3.5925).