Since Perl 6 has good handling of rational numbers, perhaps looking at its guts would help.

Using Perl 6 one could use the OP's arrays to do this:

#!/usr/bin/env perl6

my @a = <1 4 6 2 7 87 5 6 4 32>;
my @b = <86 50 62 41 32>;

my $a = [*] @a;
my $b = [*] @b;

say "Product of array \@a = $a";
say "Product of array \@b = $b";

# generate an arbitrary precision rational number:
my $c = FatRat.new($a, $b);
say "Real \$c: $c";
say "Rational \$c: { $c.numerator } / { $c.denominator }";
[download]

Output

Product of array @a = 112250880
Product of array @b = 349779200
Real $c: 0.3209193
Rational $c: 87696 / 273265
[download]