PEMDAS / BODMAS / whatever is just wrong...

You don't have to do brackets first, you can leave them for later. You just can't do much with them until you solve them, or for example use the distribution rule.

Same with exponents. They are separate units of the problem and cannot interact with other parts of the problem. In most cases the best plan of attack simply is brackets, exponents, etc.

Also, addition does not take precedence over subtraction (it is the same thing) and multiplication does not take precedence over division (same thing). Subtraction is just adding a negated number and division is multiplying an inverted number.

So it should be PEMA, but better yet nothing and just an understanding of what parts of a problem can interact with each other and how.

It is LEFT TO RIGHT otherwise the meaning of subtract and divide changes. If you don't have subtract/divide the order doesn't matter either!

Addition/subtraction is on a higher level than multiply/divide simply by convention so we save on the number of brackets we need to use.

So... if you want to do the distributive thing you need to do 6/2 first:

3*(1+2) = 3 + 6 = 9 !

The problem is a trick because it intuitively (for me at least, at first glance) made me see 6/(2(1+2))=1. Somehow the omission of the * operator glues the 2 tighter to the (1+2) than it should... or perhaps that is a very valid convention too.. implicit brackets around a multiply without the * operator...?

These are CONVENTIONS to allow for single line equations. If you work with multi line equations there is no confusion:

6

------- = 1

2*(1+2)

6

- * (1 + 2) = 9

2

Of course if you use a different convention then you are also right!