1 by the rules I was taught (multiplication and division in order from left to right).
Which gives 9 here, not 1.
6 ÷ 2 (1 + 2) =
6 ÷ 2 (3) =
3 (3) =
9
Now if you do multiplications before you do divisions, you get 1, but that's not the usual PEMDAS order of operations.
Shouldn't you distribute the 2, since it's in from of a parenthese? The inverse of a factorisation, sort of?
6 ÷ 2 (1 + 2) =
6 ÷ (2 + 4) =
6 ÷ (6) =
1
I was always taught that the parentheses only grouped what was inside them and not any implied multiplication outside them.
Thus
6 ÷ 2 (1 + 2) =
6 ÷ 2 x (1 + 2) =
6 ÷ 2 x 3 =
3 x 3 =
9
Now obviously, there's no reason why it couldn't also bind the implied multiplication, but as I said, it isn't what I was taught.
If we truly wanted a context free notation, we'd drop infix and use either prefix or postfix.
x ÷ 6 2 + 1 2
or
6 2 ÷ 1 2 + x
are both unambiguously 9.
÷ 6 x 2 + 1 2
or
6 2 1 2 + x ÷
are both unambiguously 1.
Poll
