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Yeah, differentiating between multiplications vs. divisions and additions vs. subtractions doesn't make sense, because they're the same thing respectively, just written differently.
When you divide by 3, you can also multiply by β
.
When you subtract 7, you can also add -7.
There is one quirk to be aware of, though. When people notate a division with a long horizontal line, that implies parentheses around both of the expressions, top and bottom.
Something I haven't seen mentioned yet is how we remember it as either BEDMAS or PEMDAS, but not PEDMAS or BEMDAS. The order of M and D are tied to whether we use the term brackets or parentheses. BEMDAS sounds very wrong to me
Why? Why would this be important?
It's not important, just an observation of spoken language. Similar to the order of adjectives or how there's usually a "correct" sounding way to list two names
FWIW they all sound equally ok to me. I never learned any of these acronyms, tho I've come across them on occasion, and if someone had presented any of the 4 as THE acronym for this I'd have believed them.
I think because I read about this riddle in the past, I might have built up some associations myself. So maybe there's actually nothing there π
Its PEMDAS and nothing else
I think the question is whether you interpret that acronym as P E M D A S or P E MD AS (i.e., whether multiplication has higher precedence than division or whether they are the same).
The latter is correct, the former is an unfortunately common misunderstanding.
Until now, it did not occur to me that there are some who believe multiplication and addition come before division and subtraction, respectively.
Please excuse my dear aunt sally. I always assumed this was sequential.
Exponents are typically highest exponent first.
10^10^10 implies 10^(10^10) not (10^10)^10 which is astronomically different.
PEMDAS
Parentheses, exponents, multiplication, division, addition, and subtraction.
Never met multiple exponents in a row at the same size and level, always saw them as ~a^~b^^c^, or a^(b^(c)) , so I didn't even think about that case.
Have a PhD in physics and this is the first time that I hear of some kind of "order" here. May be I forgot but I only remember that I used associative, distributiveand commutative properties of mathematical objects.
Itβs because in any higher level math these rules arenβt needed. Everyone just uses brackets(and mathematical notation) to clearly define an order of operations. Thereβs no confusion as youβll never see something potentially ambiguous like βx * y / z / aβ .
And even if you did, the division operators would likely be horizontal lines to make it clear what is being divided.
And I think writing "3x" implies the precedence in a way that "3 * x" doesn't.
Right the brackets .. and functional notation..
Just had a quick read on wikipedia s order of operations an now I know why I can not remember any more.. Every peace of software does its own Thing so one can not relay on conventions.
The people spouting the first one didn't learn it correctly.
Most of those are mindlessly parroting the mnemonic device without getting that a few of them are swappable.
What we were taught and what I've seen a lot in the German speaking world was "punkt for strich", "dot before line" since the addition and subtraction symbols are written with lines and the mult/div with dots (β and :).
The fact that parentheses/brackets are always top priority was taught separately (even before multiplication iirc) and once we got to powers/roots it was just quickly mentioned that they have higher prio than mult/div/add/sub.
I learned, "Please excuse my dear aunt Sally."
Parentheses Exponents Multiplication Division Addition Subtraction
If there is confusion, you wrote it wrong. Don't inline it, use a proper equation in whatever software you're using. If you need to inline it, go heavy on parentheses.
When you get to doing division and multiplication, it can make sense to look at what is being done to what and see if operations cancel out or simplify. E.g. if you are multiplying by 6 and dividing by 2 and bother operations are going to affect the same number/group/etc. there is no need to do both operations, you just multiply by 3 since that's ultimately what you are doing. Really, any place you can simplify operations, do that. Same goes for addition/subtraction. The Commutative Property is really handy for making hard math easier.
This are equivalent because the order of multiplications/divisions and the order of additions/subtractions doesnβt affect the end result.
Also in general if the order of operations in your equation isnβt clear without thinking about it you are doing it wrong and need to add some parenthesis.
Also caveat: on a computer the order of operations can matter in more detail due to floating point errors, and you may want to add extra parenthesis to control it.
BOPS
Brackets Orders Products Sums
In order, left to right
I only write math in the context of programming languages. I prefer ones without order of operations. Rebol, (Polish notation), Factor/Forth (Postfix notation), smalltalk, (left-to-right) apl (right-to-left), etc.
In short, it doesn't matter as long as your audience understands you.
Please Excuse My Dear Aunt Sally
BEDMAS cuz all y'all "parentheses" people are way too hoity toity and they're called Brackets, y'all
Edit: this is a shitpost. The downvotes are deserved.
Brackets are squared [ ]
Parentheses are round ( )
Apparently, that's American English. And for whatever reason, it's the British that are less hoity toity about it: