Here's something you could get working very quickly, without a lot of coding. Use bigrat to work with fractions, and let perl itself parse the math. You will have to break up the parts into stages, though, so it doesn't do all the simplifications at once. Here is an example:

use strict;
use bigrat;
my ($x, $y);
 
$x = 5/3 + 7/13;
print $x,"\n";
$y = 5/2 - 3/7;
print $y,"\n";
print $x/$y,"\n";
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This prints:

86/39
29/14
1204/1131
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With a loop to read expressions from input and an eval statement, you could get a perl fractional calculator going in no time.