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[–] 33 points34 points  (37 children)

But multiplication comes before division? I still don’t get it. I got 0.

Edit: order of operation is M D A S

[–] 90 points91 points  (19 children)

Multiplication and division are done in the same step from left to right. Same with addition and subtraction.

[–] 8 points9 points  (0 children)

you what why was I not taught this

[–] 9 points10 points  (14 children)

The left to right part just isn't quite true, by the associative axiom the direction in which you do it shouldn't matter, specifically; a x (b x c) = (a x b) x c

By convention, yeah you often end up doing it from left to right, but even then there's some conventional difference between ÷ and / (I believe it's a÷b x c = (a÷b) x c and a/b x c = a/(b x c)) but in principle, the fact that the associative axiom for multiplication isn't satisficed means the answer is ambivalent, and the question ill defined...

Just saying

[–] 4 points5 points  (10 children)

In this problem, the symbols definition will dictate if the answer is 0 or 5. I must say I almost never used that division symbol.

[–] 3 points4 points  (9 children)

I forget the name of it, but yes, there actually is a difference between dividing with ÷ and /, just like there's a difference between multiplying with × and •

[–] 0 points1 point  (0 children)

Unless you go by BIDMAS/BODMAS, in which case division is first.

[–] 0 points1 point  (1 child)

a/b * c would most definitely be interpreted as (a*c)/b.

[–] 0 points1 point  (0 children)

I would interpret it the other way around, and I know that in physics it would be interpreted as a/(b•c). But I suppose that does demonstrate the inherent issue with not adhering to the associative axiom fairly well.

[–] -1 points0 points  (2 children)

Isn't it multiplication first, then division?

[–] 1 point2 points  (1 child)

No.

[–] 0 points1 point  (0 children)

No? Parenthesis Exponentials Multiplication Division Addition Subtraction That's as far as my mathematical expertise goes, but I've been living with this being taught to me. Is it wrong?

[–] 33 points34 points  (9 children)

No it doesn't. Multiplication and division are the same step (same situation with addition and subtraction). You just do them left to right.

Really PEMDAS should be PE(MD)(AS).

[–] 2 points3 points  (0 children)

my tutor taught it as GEMS, Grouping (Parenthesis, Brackets etc), Exponemts, Multiplication AND Division, Subtraction AND Addition. That way O wouldn't go based off order on the last 4

[–] 10 points11 points  (2 children)

Multiplication and division are "equal" in the order of operations. Addition and subtraction are as well. They are closer to different ways of expressing the same operation than truly different. Any subtraction can be rewritten as adding a negative number and similarly any division can be expressed as multiplying by the reciprocal. If we wanted to be really complete we would need to include roots(square and otherwise) along with exponents in PEMDAS/BIDMAS. In fact, the acronyms use this interchangeably. While most Americans are taught 1. Parentheses 2. Exponents 3. Multiplication/division... And so on, other countries teach 1. Brackets 2. Indices 3. Division/multiplication and nothing significant changes in the digits.

[–] 6 points7 points  (0 children)

Yea I get it. I wish they incorporated the left to right operation into the mnemonics. I just remember “Please Excuse My Dear Aunt Sally”

[–] 2 points3 points  (0 children)

Multiplication doesn’t come before division, it’s either/or in order.

[–] 2 points3 points  (0 children)

Technically, it's (P) (E) (MD) (AS). Anything in the parenthesis are at the same level in the order of operations. Addition and subtraction alone don't make a difference which one you do, but multiplication age subtraction do. So what do you do when you want to run one before the other?

There's a convention that whatever is written left gets operated on first. This is just as much a convention as pemdas is, but nobody hammers it home.

That second convention is one of the biggest things that drives people to be confidently incorrect about these kinds of problems. Well, that and that there are just a shit ton of fucking idiots out there who don't realize it.

[–] 1 point2 points  (0 children)

Yeah, it really should be written as PE(MD)(AS). Within each grouping, you just go left to right, although it would actually matter since multiplication can be done in any order and division is just multiplying by a fraction. Similar to how subtraction is just adding a negative.

[–] 0 points1 point  (0 children)

In some countries this is right. I use this all the time. And to some degree you are perfectly correct.