Originally Posted by jhawkkw
I'm am not disputing at all that 6/(2x) where x = 2+1 isn't 1 at all; it is absolutely equal to 1.
I think there was a typo in there
As for your example, they are actually two different questions that are trying to be posed as the same. In fact, there is an inconsistency that causes a contradiction. In the left picture, the width is 2ft, but in the right picture it is 3. The left picture calculates the area beforehand and poses the question and asks how many times the area can be divided by itself. The right picture asks to calculate the area of a new rectangle. The logic of the first question is correct, but the notation is wrong. Even though the problem does require the multiplication to occur before the division, the notation signals that the division must occur before the multiplication. The correct equation should be written as 6 ÷ [2(2+1)].
The picture I showed you is 2 different problems. I was only trying to show how different the equations really mean. I didn't mean for you to try and understand them as the same. Sorry about that.
So then, what I gather, from your post, is 6/2(2+1) = (6/2)(2+1) ??
I have a REALLY hard time wrapping my head around that. Every reference I have seen, and I mean every, uses parentheses for a fractional coefficient.
And... if n = 1n, then n/1n = n^2. Just because we do not write "1" as a coefficient, does not mean it is not there. Therefore 1n/1n SHOULD = n/n = 1, but, according to 'order of operations' 1n/1n = n^2 ?? This is why I cannot get my head to accept 6/2n = 3n. To me it is 3/n. Just as 6/2(2+1) is 6/6. Why would anyone write this: 6/2(2+1) to mean 9, when it would be written either
1 - (6÷2)(2+1) = 9
2 - 6(2+1)÷2 = 9
Those are clear as the day is long , just as 6÷2(2+1) is one is clear to me.
I look forward to you response on:
6 ÷ 3x = ?
a/a or 1a/1a; and
the rectangle problem with respect to the "multiplication" required to be first. The question I have is: Isn't it already computed ? 2(2+1) square feet?