The answer is that the PEMDAS convention was created from its use by compsci niggers, being too retarded to understand what the obelus meant and was designed to represent.
The obelus (÷) represents a fraction, a fraction is universally the representation of rational numbers. the upper tiny dot represents a placeholder for the numerator, the symbol on its left, while the bottom tiny dot is a placeholder for the denominator.
When you write 6÷2(1+2) you are essentially writing the fraction 6((2(2+1))^-1). However since compsci niggers need to read shit from left to right, they decided that any division symbol represents multiplication by the recyprocal of the number that follows thus 6(2^-1)(1+2).
tldr compsci faggots are niggers.