In actuality, it’s because of fundamental properties of operations
Commutation
a + b = b + a
a×b = b×a
Association
(a + b) + c = a + (b + c)
(a×b)×c = a×(b×c)
Identity
a + 0 = a
a×1 = a
If you know that, then PEMDAS and such are useless because they’re derived from those properties but do not fully encompass them.
Eg.
3×2×(2+2) = 3×(4+4) = 12+12 = 24
This is a correct solution that is improper if you’re strictly adhering to PEMDAS rule as I’ve done multiplication before parenthesis from right to left.
I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct
The “why” goes a little further than that.
In actuality, it’s because of fundamental properties of operations
a + b = b + a
a×b = b×a
(a + b) + c = a + (b + c)
(a×b)×c = a×(b×c)
a + 0 = a
a×1 = a
If you know that, then PEMDAS and such are useless because they’re derived from those properties but do not fully encompass them.
Eg.
3×2×(2+2) = 3×(4+4) = 12+12 = 24
This is a correct solution that is improper if you’re strictly adhering to PEMDAS rule as I’ve done multiplication before parenthesis from right to left.
I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct