Much better, but a little refactoring improves things even more:

#!/user/bin/perl
use strict;
use warnings;

print "Welcome to the math program\n";
while (1) {
    print "Enter a number (or q to quit)\n";
    my $first_number = <STDIN>;
    chomp ($first_number);
    die "Goodbye!\n" if $first_number eq 'q';

    print "Enter a second number";
    my $second_number = <STDIN>;
    chomp ($second_number);
    my $add = $first_number + $second_number;
    my $subtract = $first_number - $second_number;
    my $times = $first_number * $second_number;

    print "$first_number + $second_number =  $add\n";
    print "$first_number - $second_number = $subtract\n";
    print "$first_number x $second_number = $times\n";

    if ($second_number !=0) {
        my $divide = $first_number / $second_number;
        print "$first_number / $second_number = $divide\n";
    }
}
[download]

Of course there is another way to do it. Consider:

#!/user/bin/perl
use strict;
use warnings;

print "Welcome to the math program\n";
while (1) {
    print "Enter a number (or q to quit)\n";
    my $first_number = <STDIN>;
    chomp ($first_number);
    die "Goodbye!\n" if $first_number eq 'q';

    print "Enter a second number\n";
    my $second_number = <STDIN>;
    chomp ($second_number);
    
    print "$first_number $_ $second_number = ", eval "$first_number $_
+ $second_number", "\n"
        for $second_number != 0 ? qw(+ - * /) : qw(+ - *);
}
[download]