If you are not allowed to use map then it is unlikely that you would be allowed to use modules in this assignment. However, you should be aware that they exist and can be useful even in very small programs. Here I have used List::Util and List::MoreUtils. One big advantage of using these is that the names of the functions suggest what they do.

use strict;
use warnings;
use List::Util qw(sum);
use List::MoreUtils qw(apply);
my @nums = qw( 5 10 15 20 25 );
my $totalSum = sum @nums;
my @array = apply {$_ /= $totalSum} @nums;
printf "Fractional Parts:\n" . "%8.6f\n" x scalar @array, @array;
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OUTPUT:

Fractional Parts:
0.066667
0.133333
0.200000
0.266667
0.333333
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