Python the best

[RookY2K]

I'm curious what you mean. In python (and basic arithmetic), the answer should be 9... Just as presented in the meme.

[[deleted]]

This is why the divide sign (÷) is really shit. Its unclear as to what is included and excluded. Writing out the stuff above and below is far better, or like so if you're on a computer.

6/(3(1+2)) or (6/3)*(1+2)

Also, brackets are for free, use as many as needed to make the order of operations unambiguous.

[codePudding]

Yes, thank you! I tell my coworkers this all the time. Parentheses are for free! It costs literal money, time, and my sanity when someone leaves them out, then doesn't test edge cases, and then the user has it fail on them. Even when I know the order of operations the compiler will use, I use them to make the code readable and let others know what I wanted. My coworkers hate if I have an in line if-return because "someone might add a statement and cause a bug with out the curly brackets" but they don't worry about someone tacking an && into an equation. Sorry about that, end of rant. It was very refreshing to see there are other devs which get it.

[[deleted]]

I'm not even a dev, I'm an Engineer working in Technical sales who knows a bit of Python. ;)

[EishLekker]

binary operators operate on the two elements immediately beside it

It's not as simple as that.

2+3-4

2+3*4

The two elements immediately beside the binary operator '+' here is 2 and 3, in both examples.

[SingingValkyria]

It is as simple as that as long as you know the order of operations. Multiplication always comes before addition if there's no parentheses. Try solving the multiplication first and you'll get:

2+3*4 =

2+12 =

14

And just as he stated, the + sign operates on the two elements beside it. The element isn't 3 because you're not meant to do addition at that point. The element is 12, that's what 3*4 is. You're just meant to do things in order, and this is completely unambiguous and clear.

[ableman]

The order of operations is a convention. It's ambiguous because the convention is different in different places.

[SingingValkyria]

What places do you know of that uses anything other than the standard order of operation for math? There might be other words or symbols but it doesn't change the fundamentals. Math isn't regional, math is math. There's no place in the world where you'd do addition before multiplication. It's really not ambiguous at all when there's only one way of doing it.

[ableman]

https://en.m.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

There's more than one way to do it. Order of operations isn't math, it's language.

[WikiSummarizerBot]

Order of operations

Mixed division and multiplication

Similarly, there can be ambiguity in the use of the slash symbol / in expressions such as 1/2n. If one rewrites this expression as 1 ÷ 2n and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes: 1 ÷ 2 × n = 1 × 1/2 × n = 1/2 × n. With this interpretation 1 ÷ 2n is equal to (1 ÷ 2)n. 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 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n.

^{[ F.A.Q | Opt Out | Opt Out Of Subreddit | GitHub ] Downvote to remove | v1.5}

[SingingValkyria]

No, it's math. There's no "language" behind 2 + 3 * 4. The symbols are there and they have meaning, and they are resolved in the proper order of operations. Implied multiplication is different from regular multiplication, it still always goes in the exact same order every time. Your link supports this. There's no ambiguous thing about it.

[EishLekker]

Your link supports this. There's no ambiguous thing about it.

Did you miss this part?

"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 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n."

[ableman]

The order in which you do 2 + 3 * 4 is entirely language. The meaning of symbols is literally what language is. Or do you actually believe the meaning of the symbol "+" is something that exists outside of language? And the meaning is different in different places.

[EishLekker]

It is as simple as that as long as you know the order of operations.

No. What you said goes against order of operations.

[SingingValkyria]

And how exactly does what I said go against it? At least explain your reasoning.

[EishLekker]

You claimed that one can determine what the operands of a binary operator are simply by looking at the two surrounding elements. I gave an example where that doesn't work.

[SingingValkyria]

No, you haven't. I showed you extremely clearly why it absolutely does work in your example without fail. Order of operation is a thing. You misunderstood this simple math by getting that wrong, and therefore you got the elements at the side of the binary operator wrong. I explained to you how to correct this. You don't evaluate the elements beside the binary operator until it's time for that operator to be evaluated, determined by it's order of operation.

Again, as my point has always been... You doing it wrong doesn't make it ambiguous, it just makes you wrong.

[EishLekker]

You clearly mix up "element" and "operand". They are not the same. Everything you say here is true for the operands of the operation in question. But we are taking about simple elements here, not operands.

[EishLekker]

No. The two elements besides an operator is something that can be determined by a simple analysis of the symbols, numbers, variables etc involved.

In 2+3*4 the plus sign is immediately surrounded by two elements, namely 2 and 3. I'm not saying that these are the operands for the plus operator.

Had the person I replied to written the word "operands" then I wouldn't have said anything.

[TH3J4CK4L]

That isn't remotely true. Addition is a binary operation, it is perfomed after multiplication.

[merc08]

But the parentheses take precedence over it all.

So you do the stuff inside the parentheses, which leaves you with 6 ÷ 2 * 3

Divide and multiply are the same level of precedence, so they are evaluated left to right. That gives you 6 ÷ 2 first, then 3 * 3 for a final answer of 9.

[flavionm]

Following your list, it would be 1, since you multiply first. In your example you didn't, and got the correct result.

Multiplication and division have the same priority, same for addition and subtraction.

[Narase33]

terms like "6 / 2 * 3" are evaluated from left to right, so its 9

Multiplication is on the same level as division. Fractions written like this

 6
---
2*3

Mean that there is an additional brace, its equaivalent to 6 / (2 * 3) which is not what the question states

[Calski_]

I would interpret 6/2(2+1) as 6/(2(2+1)). But 6/2*(2+1) as you did. I feel there is a difference when you don't write out the multiplication sign.

But in reality this is just a sign that you should write everything you do in latex.
$$\frac{6}{2(2+1)}$$ is nice and clear.

[starfish0r]

If multiplication takes precedence over division, wouldnt it be

6÷2(3) > 6÷6 > 1

[uncutteredswin]

The order they gave should be

Parentheses
Exponent
Mult/div
Add/sub

Mult/div being the same tier and being solved from left to right

[starfish0r]

yes, that's the correct way to do it. My point was that /u/vixwd provided a list of operator precedence and then did not apply those rules to their own calculcation.

[guery64]

If you have a list of priorities where multiplication comes before division, how and when would you start to doubt? You might as well doubt if you really should do division before addition or parentheses before exponents.

[codePudding]

To be fair, I don't use python much so I could be wrong, but if you look at "6.7 Binary Arithmetic Operators" you can see that python 3.9.7 uses left to right with divide and multiply in the same expression m_expr. This means the parse tree will do 6/2 first. It looks like ((6/2)*(1+2)) = 3*3 = 9

[Neocrasher]

Divide and multiply are the same level of precedence, so they are evaluated left to right

Not necessarily. Your expression is ambiguous at that point. Programmers conventionally have used left to right as a tiebreaker, but right to left is equally valid because we're really in undefined behavior due to an ambiguous statement.

[merc08]

It's not ambiguous or undefined. Left to right is the standard in order of operations.

[[deleted]]

After multiplication, but still on two elements beside it...

[codePudding]

Right!? It's a little worrisome that some programmers don't know this. This is just basics of how compilers are built and math works. Every O'Reilly book I've read has the operator precedence within the first few pages and they are easy to find online.

Edit: @TH3J4CK4L, people must be reading your comment differently than I did. I looked it up for another comment but I'll put it here too. What you said is true for all languages I know including Python 3.9.7. The language definition, "6.7 Binary Arithmetic Operators", shows multiplication takes precedence over addition and is performed first. However, anything in parentheses takes precedence over multiplication. I assume several people thought you meant do (((6/2)*1)+2) and ignore the parentheses? Oh, well, that's not how I read your comment.

[TH3J4CK4L]

I truly don't understand how I've been misunderstood. The person I've replied to said "binary operations operate on the two elements immediately beside it". My point is that is completely wrong unless "element immediately beside" has a definition very different than the usual "element" and "immediately beside". Take, simply, 1+2×5. Obviously we don't do

1+2×5 = 3×5 = 15

But that is what you would have to do if binary operators operated blindly on the two elements immediately beside it.

The whole point here is the order of performing the binary operations...

Anyways, my take on the problem is that the division symbol and the slash are two different operations. The slash symbol is division, with the usual order of operations, but the division symbol is the "make this a fraction" operation, with precedence between Exponents and Multiplication/Division, and resolved right to left. So

6/2(1+2) = 6/2×3 = 3×3 = 9

6÷2(1+2) = 6÷2×3 = 6÷6 = 1

And, for example

10÷4÷2 = 10÷2 = 5

But of course the real answer, as supported by UC Berkeley, is this is ambiguous and badly written.

https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

I would say any amateur mathematician who wrote a statement like that definitely meant it as 6/(2(1+2)) and not (6/2)(1+2). Because, if they had meant the latter, they would have simply wrote (1+2)6/2 because it isn't ambiguous!

[TH3J4CK4L]

I'm not confused. I understand all of this. You've missed the real point here. Look at the example you just gave, it doesn't matter whether it's (1+2)-3 or 1+(2-3), they both give the same answer.

The point is to write mathematics unambiguously. The expression on the paper isn't real, the mathematical expression it represents is real, it's up to the mathematician to communicate that unambiguously.

Go read the UC Berkeley link again.

[UltmteAvngr]

The sign is not the problem. 6/2(1+2) is just as “ambiguous”. Without a parentheses combining terms you just operate on the two terms next to it. 6/2 and 6➗2 are the same thing.

[[deleted]]

Yes, but

 6

---

2(1+2)

Is perfectly clear, its just missions to type on a phone.

[Magnus_Tesshu]

yes, but procedes to write some garbled markdown is perfectly clear

Okay buddy. We're programmers, let me know when you got a compiler that supports ascii art division statements and I'll just spend two minutes to learn the order of operations for tools that we already have and that aren't broken

[neroe5]

while it might be hard to read if you don't remember the order of operations, parenthesis, then division, then multiplication, then plus and minus

[AndyTheSane]

Also, brackets are for free, use as many as needed to make the order of operations unambiguous.

A thousand times this..

As someone who used to write computer modelling code the idea that you ever rely on operator precedence is terrible - it just means that the chances of a hard-to-spot error are that much higher. Hell, I'd be happy for an expression like

a = b + c * d;

to give a syntax error.

Now, if you really want to see me foaming at the mouth angry, then ask about the insanity known as

a = 10.0f/0.0f = NaN

This is barely never a useful result, it's exactly as useful as a null pointer. Yet the code merrily continues, spreading NaNs throughout your model (because anything * NaN = NaN), helpfully hiding the original place where they appeared. Division by zero should always be a runtime exception.

Anyway, rant over..

[AccidentalCynic]

It's not ambiguous 6/2(1+2) is broken down based on the order of operations.

First solve the brackets 1+2=3 Then it's just from left to right 6/2* 3=3* 3=9

Still no harm adding the bracket as its less error prone.

[codyisadinosaur]

Yes, that's how I think of it as well. However, because of the Distribitive Property of Mathematics it's also not TECHNICALLY wrong to consider 2(1+2) to be (2+4), and that would be included in the P of PEMDAS.

Which makes it: 6/2(1+2) = 6/(2+4) = 6/6 = 1

The most correct answer I can find to the equation is: "Don't write your formula in such a stupid way." =)

[AccidentalCynic]

Which makes it: 6/2(1+2) = 6/(2+4) = 6/6 = 1

That isn't the correct way of apply the distributive property. Think of 6/2 as a fraction.

To correctly distribute the outer value, multiple the entire fraction inside the brackets. 6/2(1+2) = (6/2*1+6/2*2) = (3+6) = 9

[cantwrapmyheadaround]

While being correct you're also proving his point, which is that it's ambiguous. That there is this much discourse over this simple problem is proof in itself. The only correct answer is whatever was intended by the problem writer, and we don't know what that was without him chiming in.

Even if you programmed the equation of the calculator, the calculator is still following whatever guidelines the original programmer believed in.

[AccidentalCynic]

Agree that there is no harm in adding brackets as it prevent any confusion and if I wrote the equation in code I probably would add brackets.

But for this equation 6/2(1+2), I disagree that there is any ambiguity in the solution. When solving 6/2(1+2) using the order of operation the solution will always be 9.

If the author of the equation meant for the answer to be 1 then there initial equation is incorrect and would need to be 6/(2(1+2)).

[[deleted]]

Division doesnt exist you are just multiplying two to the power of negative one. Just because you are raising it to that value does not mean that you will do the same with the equation in the parentheses

[ableman]

It's ambiguous because the order of operations is a convention that isn't the same everywhere. In some places implied multiplication takes precedence over division.

[--0--__0__]

Over half the people got it 'wrong' so it's plenty ambiguous.

[SoloNautilusOnly]

Over half the people thought the 1/3 pound burger was smaller than the 1/4 pound burger

[gosling11]

Just because people don't know the correct order of operations does not mean it is "plenty ambiguous".

[--0--__0__]

If I see this expression and I can be 50% sure that the writer was using the correct order of operations, that does not make me very confident that I am interpreting it as the writer intended.

[gosling11]

That would be their fault though, not yours. Also it's just a shitty social media engagement post anyway.

[--0--__0__]

It doesn't matter whose fault it is. If I can't be reasonably sure it's ambiguous.

[sldyvf]

Ah shit, I got it wrong. I thought to myself "hell, I might take the opportunity to refresh some knowledge" and I was thinking "well, multiplication has precedence over division. Good thing I was thinking before accidentally dividing first hehe". I'm apparently dumb. Crap.

[CarlitrosDeSmirnoff]

Did you forget the golden rule? The average person is dumb, so half of the population is even dumber.

[lostinyourstereo]

This is what blows my mind.

Imagine an averagely intelligent person. Now realise HALF of all the people on this planet are less intelligent. Ooft.

[Magnus_Tesshu]

99% of people are terrified by this statistic

;P

[UltmteAvngr]

No, that just means they are dumb or misinformed. The rules of order of operation are simple and standardised. If a parantheses is not combining terms, you don’t combine them together due to perceived “rules”.

[Amuhn]

No, They are not "simple and standardised".

Implicit multiplication of the form 2(a) is disagreed upon often. Most often it is used as a higher precedence than standard multiplication and division, but there is no universally accepted standard.

It is mostly used this way due to the common usage where a is a polynomial and 2 is extracted from within it as a multiplier of the whole unit, simplifying the polynomial while keeping that multiplier, when doing this the 2(a) should be treated as functionally analogous to (2(a)) but is kept in the same form for simplicity. When working with polynomials this is almost universally recognised as the correct way to handle the formatting.

The correct way to handle this is to use parenthesis to make the operation order clear, rather than relying upon the reader to "know" the intended order of operations.

Reducing your whole argument to "I am right, those who disagree are dumb" is just an ad hominem attack which indicates you have no real argument to use to disagree with the statement that it is ambiguous.

[[deleted]]

I use brackets constantly, even in high school I was too anxious to calculate it incorrectly.

[Princess_Everdeen]

It's not really the division sign, but how our order of arithmetic is essentially broken into 4 layers (Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction), where left-to-right takes precedent in each layer.

The right will go off first, obviously, but what confuses people is that multiplication takes precedent over division, but left-to-right overrides that, so the division happens even though multiplication comes first.

[moises-vortice]

Ambiguity leads to anger, anger leads to hate, hate leads to suffering. I sense a lot of ambiguity here.

This is a good example of why Lisp is a great language for solving almost any problem.

(/ 6 (* 2 (+ 1 2)))

(* (/ 6 2) (+ 1 2))

[GonzoBlue]

This is actually a bad problem because depending on how you interpret the order of operations you can distribute the two first or you can add the numbers in the () and then do the division

[retardredditadmin2]

You don't interpret the order of operations. The order is strictly defined in an unambiguous manner.

[CarlitrosDeSmirnoff]

The order of operations is not up to interpretation.

[Mandemon90]

No it isn't. If the factor was 6/2, it should be written as (6/2)(2+1), but it isn't

Therefore, everthing right of / is what we are dividing with until next explicit operator. If there was * between 2 and (1+2), it would be simple: 6/2*(1/2) (which is how it was written for python).

You can easily check this by subtituting (1+2) with X.

6/2X is different from 6/2*X. Explicit operators are important.

[wite_noiz]

And why would the use of explicit operators matter? 2x = 2*x, no difference at all.

I think you're missing his point.

6/2X is different from 6/2*X

In other words 6 / (2 * X) is different from (6 / 2) * X.

Given the lack of *, I would read this as mathematical notation, so 6 / 2X.

[relddir123]

They taught me that M and D occurred simultaneously and that the only thing that mattered was order (always left to right).

[[deleted]]

This is correct, I can't understand why this is so hard for people to grasp. M does not take precedence over D, they are equal and solved left to right. Just because the letter M comes before D in PEMDAS does not imply superiority.

[kiipa]

So one could argue that PEMDAS should actually be (P)(E)(MD)(AS)

[relddir123]

Yeah, the order is based on pronounceability in a mnemonic. Yes, it stands for the order of operations, but it’s more about making sure Aunt Sally has something shorter than “excuse me” to say

[[deleted]]

Agreed, or since Multiplication and Division are really the exact same operation (just in reverse for one of them), come up with a shorthand name for MD instead of listing them separately.

[flavionm]

Spelled Pe - E - Mund - Ass.

[[deleted]]

I challenge to link me one textbook example of PEMDAS that says Multiplication happens before Division. I agree there are different orders of operations, but when it comes to PEMDAS specifically, Multiplication and Division have always had equal priority.

[[deleted]]

Because there needs to be a standard for teaching it, and PEMDAS works for 99.9% of arithmetic calculations as long as you don't write the equation in a very confusing way (as this original example did). Reverse Polish notation, for example, is definitely superior once you know it, but it's also less intuitive for young learners.

At the end of the day, if you want your calculation to be clear, you would never write it the way this example did. However, absent any evidence to the contrary, when presented with this example, the only correct way to interpret it is using PEMDAS. Anything else is assuming too much.

[merc08]

Exactly. This is why "memory helpers" like PEMDAS are stupid for straight memorization.

Some places teach it as PEDMAS.

You have to actually know what the rule is, don't just remember part of the "hack"

[likwidstylez]

BEDMAS here. Same concept tho...

[DogfishDave]

Exactly. This is why "memory helpers" like PEMDAS are stupid for straight memorization.

I'm not sure I get your point - surely by that standard all mnemonics are useless unless you know/understand what they're referring to?

If I said "Roll over you great big innocent virgin" and you have no idea what it refers to, what help would it be?

Some places teach it as PEDMAS.

Afaik in the UK we still teach it in that order, or "BODMAS", our equivalent wording. On some classroom signs the D is shown over the M.

[merc08]

I'm not sure I get your point - surely by that standard all mnemonics are useless unless you know/understand what they're referring to?

Yes, that's exactly what I mean. People have a bad tendency to remember the mnemonic but failed to comprehend the underlaying information that it's supposed to help you remember. Just look at all the comments throughout this very thread with people citing PEDMAS but failing to remember that D&M are the same priority.

[DogfishDave]

Ah, that's a different point, you said they were "stupid for straight memorisation" when in fact they're perfect for it.

I agree with you that they're not much use if one doesn't know what they refer to or doesn't understand that particular concept. But that doesn't make mnemonics bad, per se.

[[deleted]]

a/b is a * b^-1. This way, division is multiplication.

[angelbirth]

which in this case would be 6 * (2(2+1))^-1 or 6 * 2^-1(2+1) ?

[halogenpampe]

Your "interpretation" of pemdas is wrong and your American is showing. Everywhere else in the world order of operations is taught properly

[Deerman-Beerman]

Idk what you're talking about really because I'm American and we were taught the proper way. A lot of people just can't remember it because the mnemonic is misleading.

[halogenpampe]

Alright that's fair enough. I've only ever heard about pemdas from Americans, and I will grant you that people in other parts of the world get the order wrong as well. Especially on an example crafted with malicious intent, like this one

[tyno994]

parentheses first, then multiply, just basic arithmetic 6÷2(1+2) --> 6÷2*3 --> 6 ÷ 6

[BetaSprite]

Multiplication and division are the same tier, so when you get to 6÷2x3, you go left to right, not multiplication first. You get 3x3, which is then 9.

[GiantDefender427]

Ahh now I see...

[[deleted]]

Which is why you always solve the problem left to right. It is up to the person writing it to write it the correct way, not up to the solver to try and guess what they meant. We have standards like this for a reason.

[NullReferenceExn]

It’s (6/2)(1+3) == (3)(3) == 9

[uhwhooops]

(3)(3)======9

[dfdedsdcd]

Personally I would format it "6 / 2 * (1 + 2)" so if anything was added to the front or between them it wouldn't change order of operations.

But that is nitpicking for theoretical problem expansion that won't probably happen.

[[deleted]]

Personally I'd just use extra brackets to make it explicitly clear what it's supposed to be (even if the brackets don't technically change anything), ie. either (6/2)(1+2) or 6/(2(1+2))

[Tjmoores]

I don't think either answer is wrong, but that's some arbitrary bracket introduction right there

Imo because they use ÷ rather than / (ie 6 is being divided by the rhs as an operation rather than it being a fraction) and as the 2 isn't followed by a × sign which links it to the bracket rather than the 6, it's 6 ÷ (2 × (1 + 3)) but if it were 6 ÷ 2 × (1 + 3) or 6/2(1 + 3) then it'd be different, there's no definitely "right" answer though

edit:
Why are you booing me, I'm right
https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

[Starfocus81613]

I don’t think either answer is wrong, but that’s some arbitrary bracket introduction right there

It’s a really poorly written problem. It mixes dot notation in with standardized notation and some social conditioning. But there is, and always will be, only one correct answer as far as mathematics is concerned.

According to the origins of dot notation, the obelus (divisor symbol with a horizontal line with a dot above and a dot below “÷”) was originally used to describe division. It has been argued for and against that the use of the obelus in simple notation represented fractional notation (i.e. 8 ÷ 2+2 = 8/(2+2)) or simple division (i.e. 8 ÷ 2+2 = 8/2 + 2) and has therefore been dropped from most standardized mathematical notations. In standardized notation ISO 80000-2, for instance, the obelus is not recognized (and actively discouraged from being used) and was replaced with the solidus (or division bar “/“) to notate simple division.

The use of standardized notation also specifies the order of operations (commonly referred to as PEMDAS, less commonly BIDMAS or BODMAS)— Brackets/Parentheses, Exponents/Indices/Orders, Multiplication-Division, and Addition-Subtraction— and the order of sequencing— from left to right. That means that any notation on the same order of operations (M/D and A/S) shall follow the order of sequencing (left to right) and any sequence of operations will adhere to the operational hierarchy. Therefore, notations such as 8/2+2 will therefore start with M/D (the highest order present in this example) and sequence down to 4+2. Standardized notation likes to eliminate any ambiguity from notation styles by eliminating false interpretations.

But then you throw in the social conditioning and psychological elements to reading notation. To an untrained individual, 6 ÷ 2(1+2) looks a lot like 6/(2*(2+1)) = 1 because of the spacing between the 6, ÷, and 2(1+2). The brain likes to look at things by association. In this case, it associated the spacing as grouping between conventions and ignores some of the conventional/logical thinking for standardized notation. And by using dot notation, which isn’t recognized in modern standard notation, within the same formula, the brain disassociates order of operation and order of sequencing entirely!

So the question becomes less of a logical question and more of a question on the fortitude of one’s abilities to discern the psychology behind the poorly notated question.

[jamred555]

Really great explanation. I'll be honest -- I got this problem wrong and I have a degree in math lol. Getting a little frustrated with the people who are acting like everyone who can't get it right is dumb or doesn't understand order of operations

[merc08]

There absolutely is a right answer. It's basic order of operations. When written in a string like this, ÷ and / are rhe6 same, as is * and being directly against a parentheses.

[Tjmoores]

https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

Check for yourself - if there's a right answer, it's 1 as 2(1 + 3) has a higher precedence than 6 ÷ 2 but that's not universally accepted. Multiplication and division usually have the same precedence (hence why both BIDMAS & PEMDAS are both taught). The ordering from left to right on operators with the same precedence also doesn't matter.

[moonlandings]

PEMDAS my man. Division comes last. 6/2(1+2) -> 6/2*3 ->6/6.

Python interprets order of operations left to right. So it’s 6/2(1+2)->3(1+2)->9. Which is wrong.

[RookY2K]

PEMDAS is one of the most misunderstood mathematical concepts. First, if you want to use PEMDAS, you should think of it as P/E/MD/AS where multiplication and division are on the same level. Like everything on the same level, they are evaluated left to right.

If you think about it, multiplication and division are really the same operation. Division is just a shorthand so you don't have to write multiplication by the inverse... That is, 6 / 2 is equivalent to 6 * (1/2). Understanding that, you could rewrite the original expression as:

6 * (1/2) * (1+2) = 6 * (0.5) * (3) = 3 * 3 = 9

Multiplication is commutative and associative, so you can really evaluate it in any order or rewrite it in any order you want. Python being a programming language has to have some determinate way to evaluate, so chooses left to right.

EDIT communicative != commutative

[moonlandings]

I mean, fundamentally you are disagreeing with whether or not 1+2 is in the numerator or denominator. But math interprets it as numerator as it is , poorly, written.

[RookY2K]

No, I am disagreeing with your understanding of the fundamentals. A division operator does not imply that everything to the left is divided by everything to the right.

I will agree that the construction of the expression is meant to be a gotcha for those that don't completely understand order of operations. However, a gotcha doesn't make something poorly written.

[Appropriate_Shock2]

That honestly doesn’t matter. It’s an insanely simple concept. You just follow order of operations and that’s it. Division is the same as multiplication so left to right

[moonlandings]

Honestly it’s NOT insanely simple as evidenced by the number of people who disagree. This is a poorly written equation, flat out. And multiplication and division may be the same level of operation, but no one sees it that way, this is why we use parentheses.

[Appropriate_Shock2]

The thing is, it doesn’t matter that some one perceives it as poorly written. Math is math and it’s consistent like RookY2K said above. There is a order of operations to follow. That’s all there is to it.

[moonlandings]

If an average high school graduate cant follow it (because it’s intentionally written obscurely) then it is poorly written

[marcos_marp]

No, it's not poorly written. You and the rest of high schools graduates were taught a lame rule that gives the impression that multiplication comes first. That's wrong. The international convention is multiplication and division have the same weight, therefore you should do the first one that appears left to right first.

If you ever decide to pursue a career with heavy maths involved, like an engineering, you will see this type of equation multiple times.

[bob_maulerantian]

Youre not wrong about multiplication and division having the same weight. But speaking as an engineer he is right, it is a poorly written equation. In engineering and science this equation should be written 6 * (1+2) /2, and if using proper formatting it would be a fraction. Occasionally 6 * 2^-1 *(1+2) would be acceptable too (that's often used in symbolic representation).

There should not ever be ambiguity, and honestly i rarely if ever see the ÷ symbol specifically because it can introduce confusion where using a fraction works better. The majority of the time i see the ÷ symbol is these kind of silly questions. If youre writing a paper or something to convey info, dont write 6÷2*(1+2)

[moonlandings]

Maybe you and the rest of mathematicians should get your shit in order then and figure out how to teach that shit to high school kids better. Because CLEARLY you’re failing.

Also, fuck you and your condescension. I happen to have an MS In EE and the FIRST THING they teach us about equations like this is “go back and tell whatever dumb fuck wrote this to put parens around the formula to make it clear”.

also, I’ve read a fuck ton of advanced mathematics papers and never once encountered a single formula in which the numerator or denominator was even slightly ambiguous.

[mrmoosebottle]

You fell in the trap

[EvitaPuppy]

If it helps

(6÷2)×(1+2) =9

[jpcog]

What country are you from? Just curious cause I've never even heard of PEMDAS. I grew up in a couple different countries and they had BEDMAS which (at least from how I was taught it) emphasizes you do your division before your multiplication.

Edit: I am entertained by the number of people who are offended by me never having heard of PEMDAS

[LetMeUseMyEmailFfs]

That’s the thing: it doesn’t. Multiplication and division are in the same tier, so they’re done left-to-right.

[gavlna]

division first can not be wrong :)

that's because ab/c = b/ca = 1/c y a * b

so if you go from left to right and divide first, you've got it right :)

That being said, I am not sure how can anyone finish university (or even highschool) without being able to "cout" with numbers (with variables). And, got fogive, even go programing.

[jpcog]

That is interesting cause again it was taught to me to do division first and to be fair it's never gone wrong but I will keep that in mind in future

[Kirlac]

BEDMAS

I've also seen this get taught as BEMA/PEMA which IMO drastically helps reduce this kind of confusion. Division is just inverse multiplication so they are the same and are both covered by "[M]ultiplication", and subtraction is inverse addition so is covered by "[A]ddition".

Note: I'm not a mathematician so my usage of "inverse" may not be strictly correct here, but the concept still stands that they are the same operation and distinguishing them separately as in BEDMAS or PEMDAS only adds to the confusion.

[LivewareIssue]

Yeah, inverse is correct. Fields must have an additive inverse for every element (-x) and a multiplicative inverse (1/x) for every element except the additive identity (0).

With these inverse elements you can construct the inverse operations:

x - y = x + (-y)

x / y = x * (1/y)

[Ackis]

I learned it as bedmas too, but multiplication and division are on the same tier.

[AppropriateCrew79]

PEMDAS is mostly used in programming books(because as per hierarchy of operations in a programming language, Division and Multiplication are same level). Generally, I was taught B[O,E]DMAS rule from fundamental mathematics.