Implied multiplication is simply a method for displaying multiplication sans the explicit multiplication sign, and was originally adopted to prevent the mistaking of the x multiplication symbol with the x variable. There is no inherent priority of multiplication displayed in this fashion over division or explicit multiplication. It was simply a preferable typesetting choice at the time it was adopted. It does not follow the PEMDAS BODMAS rules which is why it should not be used in arithmetic. The form a/bc actually simplifies to ac/b. However,so for those stuck on the distributive property, this expression is a/b(c+d) which by distribution simplifies to ac+ad/b. So this means 6/2(2+1) simplifies to 6*2+6*1 / 2=9 which makes a lot more sense than 6/6=1.