What makes non-PEMDAS answers invalid?
It seems to me that even the non-PEMDAS answer to an equation is logical since it fits together either way. If someone could show a non-PEMDAS answer being mathematically invalid then I’d appreciate it.
My teachers never really explained why, they just told us “This is how you do it” and never elaborated.
In: 834
>If someone could show a non-PEMDAS answer being mathematically invalid then I’d appreciate it.
Try forming it as a word puzzle. If you have two lots of six apples, plus another two apples, what do you have? How do you write it? Well, there are a bunch of ways:
* (2 × 6) + 2
* 2 × 6 + 2
* (6 × 2) + 2
* 6 × 2 + 2
(There are others, but let’s just go with that for the moment.)
If we calculate those out using PEMDAS, we get:
* (2 × 6) + 2 = 14
* 2 × 6 + 2 = 14
* (6 × 2) + 2 = 14
* 6 × 2 + 2 = 14
If we calculate those same expressions out using a different system — for example, PESADM — we’d get:
* (2 × 6) + 2 = (12) + 2 = 14
* 2 × 6 + 2 = 2 × (8) = 16
* (6 × 2) + 2 = (12) + 2 = 14
* 6 × 2 + 2 = 6 × (4) = 24
But we’re talking about real, concrete things here: two packages of six apples, plus another two apples. You can take those apples out of the packages, line them up, and count them. There are 14 apples. That’s just a fact.
PEMDAS allows us to minimise the number of parentheses we need to use in order to get a consistent answer. (You’ll notice that in the last batch of answers, the two expressions that ‘worked’ both had parentheses right from the start.) Basically we use that order because it’s a way of both simplifying an expression and getting a consistent answer that everyone — if they follow the rules — can agree on.
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