PHP is confused when adding and concatenating

Both operators the addition + operator and the concatenation . operator have the same operator precedence, but since they are left associative they get evaluated like the following:

echo (("sum:" . $a) + $b);
echo ("sum:" . ($a + $b));

So your first line does the concatenation first and ends up with:

"sum: 1" + 2

(Now since this is a numeric context your string gets converted to an integer and thus you end up with 0 + 2, which then gives you the result 2.)

If you look at the page listing PHP operator precedence, you'll see that the concatenation operator . and the addition operator + have equal precedence, with left associativity. This means that the operations are done left to right, exactly as the code shows. Let's look at that:

$output = "sum: " . $a;
echo $output, "\n";
$output = $output + $b;
echo $output, "\n";

This gives the following output:

sum: 1
2

The concatenation works, but you then try to add the string sum: 1 to the number 2. Strings that don't start with a number evaluate to 0, so this is equivalent to 0 + 2, which results in 2.

The solution, as you suggest in your question, is to enclose the addition operations in brackets, so they are executed together, and then the result of those operations is concatenated.

echo "sum: " . ($a + $b);