I was taught to do

• Brackets
• Division and multiplication left to right
• Addition and subtraction left to right

There should be a fucking ISO for this shit tbh

The real answer is "what's the fucking context for how these numbers are being used?"

If it's "just as written on a test" I think asking for clarification on order would be accepted.

If it's an actual context of some kind then that alone dictactes the way you solve it.

Can't quickly come up with a word problem for this one though.

The P in PEMDAS just means resolve what's inside the parentheses first. After that, it's just simple multiplication with adjacent terms, and multiplication and division happen together left to right.

6÷2(1+2)

6÷2(3)

3(3)

9

Use unambiguous notation

Oh christ the math memes are leaking from facebook

I was taught not to write like this so we dont have to deal with this shit 😊

It's 9 if you actually understand PEMDAS

I don’t think I ever used a divide symbol like that beyond elementary school. In practice always use fraction style notation for division because it’s not ambiguous or a gotcha.

The ÷ symbol is a bane of mankind

it's ambiguous

We discovered mathematics, the unflinching language of reality itself, and then managed to make it ambiguous.

If i was an alien id give humanity a big hair-tussle like a dog.

Well, Patrick IS an idiot ... so it checks out?

6 2 ÷ 1 2 + ×

Or 6 2 1 2 + × ÷ for Patrick

No mathematician would write an ambiguous equation like that.

People who argued over these are displaying an incorrect memory of a math education that is simply not a good look.

Division and multiplication have the same precedence, equations are evaluated left to right, so equation is divide then multiple. Division and subtraction are syntactic sugar for multiplication and addition.

These are fun little experiments showing how social media makes people more stupider and how proud the ignorant behave amongst themselves.

Uh oh, here we go! Before the Fediverse's favourite mathematical charlatan comes to play, let's lay out a few facts:

• This is an unusual way of writing down this expression: you would not normally mix in-line division (written with ÷) and multiplication written without a symbol. It's written this way on social media to for engagement bait.
• Because of this, a perfectly valid reply is to ask "can you put in some brackets to make it clear" :)
• A strict, standard reading of the order-of-operations as abbreviated by PEMDAS, BODMAS, etc, is to perform multiplication and division in the order that they occur. This would mean the evaluation goes like this:
  1. 6÷2(1+2)
  2. Perform addition inside the brackets: 6÷2(3)
  3. Perform the first multiplication or division: 3(3)
  4. Perform the remaining multiplication: 9
• Occasionally, PEMDAS is interpreted as indicating that multiplication must be done first because the M occurs before the D. This is not usually how it is taught, but rarely it happens. This would give you 1 but, to be clear, in most places this is wrong. I myself was taught BODMAS and, in fact, do division first in all circumstances.
• Much more commonly, though, the actual practical order in which mathematicians, teachers and students all evaluate expressions is a little different, in that it evaluates symbol-less multiplication (also known as "juxtaposition" which just means "writing two things next to each other" or, in discussions about this topic in particular, "implicit multiplication") before anything else. This is done because writing two things next to each other creates a tightly-bound visual unit.

It's rare for this last point to be mentioned explicitly as a violation of the order-of-operations. It usually only becomes relevant well after those conventions are spelled out (which is typically done in late primary school or early high school) after children start learning algebra and how to write algebraic expressions: using letters to represent unknown quantities, omitting the × symbol. Exam boards and textbooks are usually quite careful to avoid writing problems in which this unstated rule actually matters.

It's important to realise that the order in which we evaluate a mathematical expression is a matter of convention. After establishing how to add, multiply, subtract or divide two numbers, it is a separate question which operations should happen first when more than one is written together. This is why we need to teach students the order of operations - they can't just work it out themselves. Having said that, it certainly makes a lot more sense to do multiplication before addition, and exponentiation before multiplication, because each of these operations is (typically: you can define them in different ways if you're a masochist) defined in terms of the previous one. This means that if you have an expression involving all three, and you first turn all the exponentiation into multiplications, you are left with a simpler expression that means the same thing. This only happens if evaluating exponentiation is the first thing you're supposed to do. However, it would be a mistake to think this means that there is any mathematical necessity about this: what a sequence of squiggles on paper means is entirely up to the people reading and writing the squiggles; as long as they agree, the person reading the squiggles will get the same answer as intended by the person writing them. There's a good, lengthy write-up here

This means that while what I was taught is "wrong" according to how it is usually taught (including today in the same country), this wrongness is better understood mathematically as "unusual" - something that needs to be worked out by communication and consensus rather than by dictating one right and another wrong.

You do get some people with very strong opinions about this, which is not always correlated with their actual knowledge. If the aforementioned charlatan turns up, I'll explain...

BODMAS

• Brackets
• Of
• Division
• Multiplication
• Addition
• Subtraction

my calculator disagrees.

and i would too, this is basically
6÷2(1+2) = 6÷2×(1+2) = 6÷2×3

while you resolve brackets first, you still go left to right. you would get 1 if you did
6÷(2×(1+2))

the issue is the missing multiplication sign between the 2 and the brackets, thats why i always write them even if it is not strictly required

It’s ambiguous either this resolves to 6 / (2(1+2)) or (6/2) * (1+2), and therefore both answers must be accepted.

By convention, the division sign is not to be used in equations. It is not a standard operation.

It is may be used for representing the operation of division as a symbol, but never as an operator itself.

Anyone using the division sign is using it entirely for trolling purposes.

I guess the joke is that it wasn't an ambiguous expression in the first place and that pedmas/bedmas wasn't the issue, or rather using just it here is the problem?

When you have multiplication expressed as numbers joined without a symbol, that takes precedence at the current layer, where layers are created using brackets, fraction symbols, superscript exponents and concatenated multiplies.

I'm not sure this resolves all ambiguity, but it simplifies the rule to just doing multiplication/division before addition/subtraction. It seems simple enough in my mind, so I'd need to see a counter example if it does break down.

Though I hate how mainstream math problems/puzzles always end up being an order of operations problem, which I'd argue isn't even math but more of a metamath thing. If you're using math to solve a real problem, the correct order of operations will be determined by logic, not any conventions.

Like if it takes you 5 seconds to get in your car and 12 seconds per km traveled, and 5 seconds to get out of your car, if you multiply the 10 seconds to get in or out by the distance, you'll have a wrong answer. It'll always be distance traveled in km times 12 seconds/km plus the 10 seconds, and the math works on the units as well as the numbers to show you did it in a way that makes sense.