There's a module (I never used) called Math::Fraction which seems to do the trick. It even handles mixed fractions:

use Math::Fraction;
$a = frac("10 3/4");
$b = frac("1/2");
$c = frac("2/5");
$d = $a * $b + $c;
print("$d\n");
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It supports:

+  -  /  *  +  +=  -=  *=  /=  ++  -- abs
<=> == != < <= > >=
** sqrt
[download]

and has some useful conversion methods.