I know some places use BIDMAS as well. Overall though, to someone who knows little about mathematics, why is this the correct order? What’s the exact logic behind it
In: 6
The same logic behind grammar and spelling rules. To be consistent and prevent ambiguity and misunderstanding when communicating with others.
Math is just like any other language we use to describe the world around us, with it’s own set of “grammar” rules.
You even have an equivalent of PEMDAS in the English language, the order of adjectives. It goes:
Opinion->Size->Age->Shape->Colour->origin->material->purpose + noun.
Here are 2 examples:
“My neighbour drives a beautiful little old red Italian sports car”
Vs.
“My neighbour drives a little beautiful red sports Italian old car”
Or:
“The big old brown cat shat on the sofa”
Vs.
“The old brown big cat shat on the sofa”
Although both sentences can be used to convey information, you intuitively know one is correct and the other is not. Why is one more correct than the other? Just because we agreed it is, nothing more.
Similarly, deviating from PEMDAS doesn’t result in mathematical impossibilities, or causes math to implode in on itself, but it yields results that just don’t feel quite right…
Take the equation 4*5+3
If we add before we multiply we just get:
4×5+3 = 4×8 = 32 instead of 4×5+3 = 20+3 = 23.
If both yield valid, real answers, why is one correct over the other? Just because we all agreed it is.
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