If you were doing something complicated (eg. your precedence problem), my first inclination would be to use eval, but only after validating that the input was sane.  For example:

#!/usr/bin/perl -w

use strict;
use warnings;

# Test data
my $string = "1 + 9 * ( 60 / 5 )";

# Validate
if ($string !~ m:^[-+*/()0-9.\s]+$:) {
    die "Bad input '$string'\n";
}

my $result = eval $string;
print "Result of '$string' = $result\n";
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But I don't know offhand if that's the best way to do it, or what other caveats you might run into.

Update:  Fixed the regexp.