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
Think of a formula as communication.
When I write down a mathematical formula, I’m communicating the numbers involved, the operations that need to happen to those numbers and the order it should be done in.
There’s no universal need to do addition and subtraction after multiplication, but for any given formula, I’m trying to communicate a specific order for operations to be performed in. Having that order be standard means I can communicate in a simple compact way without needing to add in a lot of notes on the order.
The P in PEMDAS is the parentheses which IS more or less a note on how to order thing, and it provides a relatively simple tool to break and shuffle the order when needed.
But at the end of the day, PEMDAS is the grammar the person who wrote the formula is using, and so it’s the grammar needed to decode the formula they wanted to share with you. If you use a different grammar to read the formula, you won’t be reading the same formula they tried to give you, just like you won’t pronounce a word as it was intended if you read the letters out of order.
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