Quote:
Originally Posted by storymilo
So should we just not solve any equations that don't get the same answer using all orders of operations? The equations I'm presented with at school were written with the order of operations that I'm used to in mind, so that's the one I use. I assumed this one was too, which may or may not have been a mistake, but I went ahead and solved it the way I've been taught too. I suppose the best thing to do when one comes across an equation would be to somehow find out what order the person who wrote it had in mind, but in many cases that's impossible.
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a) Parentheses. Exist. For a reason. That differential in terms of order exists for that exact reason, to specify the order of operations
for that specific equation. Nowhere in the base axioms of multiplication does it say "by the way, if you have an ambiguous statement, do them in the order they come up. It's fine, for addition and multiplication on their own, as on the domain of natural numbers, rational numbers and real numbers, both are associative (the order in which the equation is evaluated doesn't matter) but when you start mixing operations, associativity isn't proven. Thus, you need parentheses in order to specify the order. Like I've been saying.
I know that you went ahead and solved it the way you'd been taught, but if you noticed, in my original post, which I then quoted as it was ignored, I stated that such "order conventions" shouldn't really be taught, as they lead to such ambiguities, where people assume they're both right, when the problem is that they've both been taught a convention that a) isn't standard and b) is a nasty shortcut in the first place. If people were taught to use parentheses properly from the start, we could avoid situations like this.
I agree that in a situation like that, you kinda have to guess for an answer. That, however, doesn't instantly mean that your guess is right.
That's my point. I'm not saying sit on your hands and do nothing because you can't make a definite conclusion, I'm just saying that multiple answers can technically be correct as the statement is ambiguous, which you will note I stated at the start
and and of my first post.