The behavior is the correct one if you supress the warnings flag:

p2@nereida:~/src/perl/testing$ cat precedence1.pl
my $n1 = 2;
my $n2 = 4;
print "$n1 plus $n2 is " . $n1 + $n2 . "\n";
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When you run this program there are no warnings:

pp2@nereida:~/src/perl/testing$ perl precedence1.pl
6
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However:

pp2@nereida:~/src/perl/testing$ cat precedence2.pl
use warnings;
my $n1 =2;
my $n2 = 4;
print "$n1 plus $n2 is " . $n1 + $n2 . "\n";
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Issues the warning:

pp2@nereida:~/src/perl/testing$ perl precedence2.pl
Argument "2 plus 4 is 2" isn't numeric in addition (+) at precedence2.
+pl line 6.
6
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The warning flag and the Warnings module are full of heuristics that helps you most of the time.

Whenever you have problems with operator priorities use the p option of Deparse like this:

pp2@nereida:~/src/perl/testing$ perl -MO=Deparse,-p precedence2.pl
use warnings;
use strict 'refs';
(my $n1 = 2);
(my $n2 = 4);
print(((("$n1 plus $n2 is " . $n1) + $n2) . "\n"));
precedence2.pl syntax OK
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It will tell you the execution order of the involved operations.

Observe that the extraordinary thing is that the operation

(((("$n1 plus $n2 is " . $n1) + $n2) . "\n"))
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still gives 6!. This is because the phrase starts with 4 plus .... There is some irony here.

The first time I stomped in this sort of "Perl priority problems" I was puzzled. But if you live with it time enough you start to appreciate the fun of it

Hope it helps

Casiano