6/2(1+2) = ?

It's 9. PE(MD)(AS) then when you can do multiple things at once you go from left to right.

^This.
Rewrite in unambiguous RPN and no one will disagree on the answer.

6/2(1+2)
6/2(3)
3(3)
9

Its not vague, its 3 as a coefficient of 3. If you arent in 6th grade, its very clear.

en.wikipedia.org/wiki/Order_of_operations
>Similarly, there can be ambiguity in the use of the slash symbol / in expressions such as 1/2x.[6] If one rewrites this expression as 1 ÷ 2x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:
>1 ÷ 2 × x = 1 × ½ × x = ½ × x.
>With this interpretation 1 ÷ 2x is equal to (1 ÷ 2)x.[1][7] However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2x equals 1 ÷ (2x), not (1 ÷ 2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[8] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[nb 1]

>physics
not math

>However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division

So some fringe academic literature uses a more complicated version of PEMDAS? That's why its vague to you?

Any mathematician will read this as 6/(2(1+2)) = 1. That is because juxtaposition is taken as having higher precedence than explicit multiplication and division, despite representing the same operation as multiplication. This makes it unambiguous.

6/2(1+2)
6/2(3)
6/6 = 1

t. layperson living vicariously as his fantasy idea of a mathematician

...

Why would you multiply by the denominator of a fraction and not the numerator?

Well shit, reading it like this nigga did instead of OP's image does make more sense, so yeah its 9.

This is the reulsts we get on the science and math board? Really? Why even come here? Are yiu from /pol and got baited into this while looking fir an IQ or "race realism" thread? I really dont get it.

Forgive me for not taking that seriously from someone who takes the behavior of Mathematica as evidence of anything.

Misleading, not vague.
It preys upon people lack of understanding on eve the most basic math.

>Are yiu from /pol and got baited into this while looking fir an IQ or "race realism" thread?
that and high school kids who are looking for homework help

I do come from excuse my vague Mathematical knowledge, I don't have much time to study the field since I spend most of my time on Meme research studies. I tip my fedora to you fellow 4channer, may Kek be with you.

>That is because juxtaposition is taken as having higher precedence than explicit multiplication and division
According to who? Thats not at all a standard practice, dont pass it off as such.

>fringe
It's not "fringe," Physical Review is pretty fucking mainstream.
Just accept infix has ambiguity problems, everyone in these arguments always insists their own version for order of operations is the unambiguously right one.

PE(J*)MDAS
*if you're a physicist

>According to who?
Not him, but:
>Thats not at all a standard practice
It's officially the standard for Physical Review, and again, they're not some "fringe" publication, they've been around since 1893 and are plenty reputable.

Lol this

>According to who?
According to everyone writing math, basically.

>Thats not at all a standard practice, dont pass it off as such.
Yes it is. It's rarely written about, but most textbooks and articles implicitly follow this notation.

PEMDAS is fundamentally wrong beyond sixth grade, because in real life disambiguation of expressions is based on syntactic cues, not semantic cues. [math]a \times b[/math] is not equivalent to [math]ab[/math] in regards to expression parsing, and similarly [math]\frac{a}{b}[/math] is not parsing-equivalent to [math]a/b[/math]. Which means that [math]a / b \times c[/math], [math]a / bc[/math], [math]\frac{a}{b} \times c[/math], and [math]\frac{a}{b} c[/math] are all syntactically different, and are disambiguated differently. The operation of multiplication may (and does) have a different disambiguation behavior depending on whether it has the syntactic form of a [math]\times[/math] symbol or a juxtaposition, causing [math]a / b \times c[/math] to disambiguate to [math](a / b) \times c[/math] but [math]a / bc[/math] to disambiguate to [math]a / (bc)[/math]. There is not actually an order of *operations* to parsing expressions -- there is an order of binary-operator *syntactic constructs*.

You know that this problem is not in that context though so why would you use a non standard order of operations? Again, it doesnt make sense to arbitraily use a diffrent set of rules than those that would be standard practoce in this context.

>>According to who?
>According to everyone writing math, basically.
Thats bullshit though.

when would you ever write a/bc? you'd use a horizontal division bar

>It's rarely written about, but its the standard

No its not.

or parentheses like a/(b*c)

Exactly.

>context
This is an anime website, there is no meaningful context to speak of here
The point you should be getting out of threads like these is that infix notation is ambiguous garbage built around the retarded idea that mathematical expressions should be parsed based on an arbitrary list of operator precedence rules.

>arbitrary

>This is an anime website, there is no meaningful context to speak of here
Its an underwater knitting forum and the lack of context is explicitly my point, the previous claim was that in a certain context youd do it diffrently, we are not operating under that diffrent context though.

See
The vague or ambiguous argument has been defeated already.

Yes. But if for some reason you can't (maybe you are writing in a line-height-restricted context) and you need to write a/bc anyway, you DO need to worry about the different syntactical behavior.

Say you want to write [math]\frac{1}{2}c[/math] in an expression. If you are height restricted and can't use proper fraction notation, you would write this as [math](1/2)c[/math], NOT [math]1/2c[/math], for that would be interpreted as [math]1/(2c)[/math].

(Yes, you could just write c/2 and avoid the whole issue. But that's besides the point.)

We can argue about whether this convention is a good one. But it is a brute fact that [math]1/2c[/math] will be interpreted as [math]1/(2c)[/math], so are clearly the rules that actual people using math notation are implicitly following.

Operator precedence rules are definitely arbitrary, the fact more than one set of these rules exist should've tipped you off to that. There is no actual reason why you should perform one given operation before another as a default behavior in an otherwise ambiguous collection of operations. They're all just arbitrary conventions, not mathematical truths. And if you write your expressions in unambiguous RPN you can make it clear what you mean without needing to define any sort of operator precedence rules in the first place.

That doesn't "defeat" shit, infix being ambiguous is a well established known problem.

interactivepython.org/runestone/static/pythonds/BasicDS/InfixPrefixandPostfixExpressions.html

Here ya go buddy

>In fact, you have been reading and writing these types of expressions for a long time and they do not cause you any problem. The reason for this is that you know something about the operators + and *. Each operator has aprecedencelevel. Operators of higher precedence are used before operators of lower precedence. The only thing that can change that order is the presence of parentheses. The precedence order for arithmetic operators places multiplication and division above addition and subtraction. If two operators of equal precedence appear, then a left-to-right ordering or associativity is used.

How is that an argument for anything?
Also guess what happens to your infix expressions when you execute them in a Python script (or through any other programming language)? They get converted to RPN. Hmmmmmm, I wonder why?

obviously 1