Originally Posted by alostpacket
You're basically saying because there are parenthesis, you can do the multiplication of 2 * (a+b) before c/2 even though that's not how the order of operations work. After the parenthesis, you're supposed to go back to division/multiplication and left->right. x(y) is just another way of writing x*y, it doesnt change the rules
Well there's debate on how order of operations work as it pertains to M and D. But I was trying to eliminate that debate entirely by focusing on the OP's statement in one of his posts:
You have to make a decision simply based on the equation given in the title
And in the title, it was written as: 6÷2(1+2)
And my point was: there are two popular answers: 9 and 1, depending on whether (1+2) was considered to be part of the numerator or denominator of the division operation. We all agree that (1+2) has to be evaluated first, but as written, does it belong on the top or bottom of the fraction?
And my argument was that if it belongs on the numerator, you get 9. But if it was INTENDED to be part of the numerator, the equation would have been written as 6(1+2)÷2.
If it was INTENDED to be part of the denominator, the equation would look pretty much as it was originally written, with the (1+2) associated with the 2 in a multiplication operation.
So, yes, I AM saying that the 2 multiplies (1+2) first because, as written, the equation implies this MORE than it implies "treat division and multiplication equal and just go left to right."
BTW, I can easily argue against this viewpoint, but this justification satisfies me more.
I re-read your post and see what your argument is. You think my numerator trick is not the same as (6÷2) * (1+2). But it is, because multiplication is associative and distributive.