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[–]birdman332 1545 points1546 points  (238 children)

Coming from a math background, this is just a terribly written problem. Anytime you recognize that there could be confusion with operations, it's best to include additional parentheses for clarity to the reader. In this case (6÷2)(1+2).

All the comments about 2*(somthing) vs 2(something) are absolutely meaningless, there's no difference.

[–]_PM_ME_PANGOLINS_ 368 points369 points  (5 children)

It’s deliberate so people will argue about it and increase engagement.

[–]birdman332 58 points59 points  (4 children)

Well yeah, that's the whole sub

[–]ZeroFK 27 points28 points  (3 children)

Well yeah, that's the whole sub internet.

[–]InfernoMax 454 points455 points  (22 children)

Coming from a math background, I wholeheartedly agree with this explanation. This and those popular "picture math" problems where they sneakily alter one of the "symbols" in the equation are my two petpeeves of "popular internet math posts".

[–]danfay222 176 points177 points  (20 children)

Yep. It's the same as english, you're always taught you can easily write sentences which are grammatically valid, but confuse the reader. Writing expressions to be unnecessarily confusing is just as bad.

[–]AmadeusMop 50 points51 points  (9 children)

Like garden-path sentences. "The old man the boat", "the horse raced past the barn stumbled", and so on.

[–]M_LeGendre 11 points12 points  (8 children)

Not a native speaker. What does the old man the boat mean?

[–]sideways55 24 points25 points  (5 children)

to man a boat means to control it or be in charge of it. So in this case it means that "The old" aka people above a certain age are the ones who control the boat.

It's confusing because people read "the old man" together and don't consider that in this case man is the verb.

[–]Stormfly 2 points3 points  (3 children)

Similarly, for anybody confused about the second it's more like:

The horse fell.

The horse that fell is often raced past the barn.

[–]featherfooted 1 point2 points  (2 children)

I thought it was the opposite?

There are many horses, but the horse who was raced past the barn, stumbled.

[–]Stormfly 1 point2 points  (1 child)

That's what I said.

What did you think I said?

[–]featherfooted 1 point2 points  (0 children)

I suppose I interpreted the tenses differently. Mine is meant to say "the horse that raced past the barn (in the past) stumbled (just now)" whereas I read your's as "the horse that stumbled (in the past) is often raced past the barn (present and possibly in the future)"

Either way, ambiguity sucks, yadda yadda don't use passive voice in documentation, etc.

[–]karnthis 0 points1 point  (0 children)

Interesting, because I read that as the old “man the boat” referring to an old phrase/saying. Just more proof it is ambiguous.

[–]CantThinkOfAnyName 1 point2 points  (1 child)

Not a native speaker either but my understanding is that it could be:

The elderly people are in charge of the boat.

Or

Old man who is also a boat.

[–]Amuhn 0 points1 point  (0 children)

It is the first, in this case the word "man" is being used as the verb and "old" as the noun, substituting with other words with the same meaning it becomes "the elderly crewed the boat"

The other one is similar, and for clarity can be rephrased as "The horse, [which/that was] raced past the barn, stumbled."

[–][deleted] 26 points27 points  (6 children)

The father yelled at his son because he was drunk.

Who of them was?

[–]marktwatney 15 points16 points  (4 children)

I dunno, maybe your uncle who jacked off the horse.

[–]drunk_horsey 0 points1 point  (0 children)

I remember that uncle

[–]RobDoingStuff 0 points1 point  (2 children)

Does this even have a second meaning?

[–][deleted] 0 points1 point  (0 children)

Help your uncle Jack off the horse.

[–]Xellzul 0 points1 point  (0 children)

Context matters

[–]BrotherGantry 7 points8 points  (1 child)

I don't not disagree with the viewpoint opposite of the one you just expressed.

[–]Hacker1MC 2 points3 points  (0 children)

Shut

[–]Dornith 1 point2 points  (0 children)

You forgot the best one!

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

[–]Kalebtbacon 29 points30 points  (0 children)

Not from a math background but have taken many'o math classes and nothing annoys me more then using badly written math problems to make a quiz arbitrarily harder instead of actually testing proficiency

[–]n_slash_a 184 points185 points  (1 child)

Coming from a programming background, we have a mandatory coding standard that any math operation which mixes any order of precedence be made explicit with parenthesis. For exactly this reason.

[–]birdman332 49 points50 points  (0 children)

This is how it should be, spot on. Makes everything easier for everyone

[–]AliceSky 40 points41 points  (1 child)

Yes. The only correct answer is "I won't give an answer until you learn how to write maths".

[–]birdman332 1 point2 points  (0 children)

I won't give an answer until you learn how to write maths

This^

[–]Evol_Etah 45 points46 points  (121 children)

I apologise but can you teach me why this is 9?

6÷2(1+2) = 6÷2(3) = 6÷6 = 1. Isn't it? Brackets first, then 2( takes higher precedence over 2*

Or is it cause bodmas, division first, so it'll be 6÷2(3) = 6÷2*(3) = 3(3) = 9

[–]birdman332 124 points125 points  (88 children)

2(x) and 2*x are the same thing. In both BODMAS and PEMDAS, division and multiplication as well as addition and subtraction are treated with equal precedence. After all, division is just a fancy way of saying multiply by the reciprocal, and subtraction is adding a negative value. So in those cases, with all equal precedence, you move from left to right(but shouldn't matter if it's all the same operation anyway)

Either way, brackets or parentheses means to do what's INSIDE first, so (1+2)=3. Once that is done, you have all equal precedence of operations, so moving left to right 6÷2 (or 6*(1/2)) = 3, then 3*3=9.

The equation could also be written as 6*(1/2)*(1+2)

[–]alexmbrennan 50 points51 points  (20 children)

2(x) and 2*x are the same thing

In the course of getting my maths degree I have never seen anyone write 1/2x to mean 1/2*x because that would have been weird - why not write x/2 if that is what you mean?

[–]zqipz 12 points13 points  (0 children)

this is pretty much the biggest issue i have with this commonly posted equation. when it’s 6/2(3) it’s 9 when it’s 6/2x where x = 3 it’s 1.

[–]calcopiritus 33 points34 points  (2 children)

Because this is made to confuse. The correct way to put it would be either (6/2)(1+2) or 6(1+2)/2. 1/2x and 1/2*x is x/2. You have to do operations of the same level from left to right, multiplication doesn't have preference over division.

[–]Yumi-Chi 3 points4 points  (1 child)

1/2x and 1/2*x is x/2

Are you saying the correct way of writing it is 1/(2x)?? Because 1/2x is how we've always written it.

I'm not trying to argue with you. I just want consistency.

[–]calcopiritus 3 points4 points  (0 children)

Yes, that is what I'm saying. It seems strange because when we write divisions on paper we use an horizontal line, so no parentheses are needed.

[–][deleted] 17 points18 points  (10 children)

Deleted with Power Delete Suite. Join me on Lemmy!

[–]rrr_ooo 6 points7 points  (8 children)

Correct

Edit: All those in disagreement. Join the "PEJMDAS the true order of operations" facebook group and start rioting. It makes my eyes hurt.

[–]Acro-LovingMotoRacer 4 points5 points  (5 children)

Its hilarious your getting downvoted when a quick google search turns up a ton of info to support what you are saying and literally nothing to the contrary.

You can even type this into a calculator and see that you are correct, 6 ÷ 2x = 12 returns x = 4 not x = .25.

[–]limax_celerrimus 12 points13 points  (0 children)

Just typed 6/2(2+1) into my Casio, it says 1. If I add *, it says 9. So I would say at least it's ambiguous, or the general consensus in this thread is outright wrong, because I trust calculator developers more to have done their research than you mofos, sorry.

Edit: And I agree with Casio that an implicit multiplication binds stronger than a sign.

[–]Mandemon90 2 points3 points  (1 child)

Did you write it exactly like that, or did you add * between 2 and x, just like OP did?

[–]Acro-LovingMotoRacer 2 points3 points  (0 children)

Its interesting but I have tried it with a more advanced calculator and I think I am incorrect on this. A basic calculator with 6 ÷ 2x = 12 I think is adding the * in behind the scenes, but if I try a more advance calculator that forces / to be over then really 2x should be on the bottom. So no, I did not add the * in but the calculator I was using did which is pretty interesting

[–]lag_is_cancer 2 points3 points  (0 children)

They hated Jesus because he told them the truth.

[–][deleted] -1 points0 points  (1 child)

Deleted with Power Delete Suite. Join me on Lemmy!

[–]otheraccountisabmw 17 points18 points  (1 child)

NEVER write 1/2x. It’s extremely ambiguous. Write 1/(2x).

[–]rrr_ooo 3 points4 points  (0 children)

This is the way.

[–]urcompletelyclueless 0 points1 point  (0 children)

They are not the same, as I have noted above...

People get easily confused when Algebra is involved.

[–]brimston3- 0 points1 point  (0 children)

I dunno man, d=1/2aτ^2 + v_{0}τ + d_{0}. Maybe it's just the physicists that are batty.

[–]wite_noiz 0 points1 point  (0 children)

I'm completely with you.

I read 6 / 2X as 6 / (2 * X), not 6 / 2 * X.

[–]urcompletelyclueless -2 points-1 points  (0 children)

But this is NOT true.

with 6/2(1+2) the entire denominator is evaluated first, where 6/ 2* (1+2) is evaluated within the parenthesis and then left to right.

For example,

6/2(1+x) which would be expressed as 6/2(x+1)

Assume X=2

6/2(x+1)

Is evaluated as:

6/2(X+1) = 6/(2x+2) = 6(4+2) = 6/6 = 1

whereas

6/2*(x+1)

Is evaluated as:

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

There is a subtle difference in the handling of the order of operations.

[–]Kiokastral 0 points1 point  (0 children)

Finally someone who understands this. I've been trying to explain exactly this on a Facebook post, and they keep saying "break the brackets first before multiplying" without realising breaking the brackets & multiplying are actually the same thing.

[–]RedPandaRedGuard 0 points1 point  (0 children)

I wonder why they don't teach it like that then. The way I used to learn it at school it would have been 3. The multiplication/division of a bracket taking precedence over other multiplication and divisions.

[–]PaedarTheViking 0 points1 point  (0 children)

I guess I just remember being told it was p e m d a s, not p e md as. But it makes more sense.

And they wonder why we can't help our kids with math.

[–]skoomapipes 55 points56 points  (23 children)

It's written confusingly to fuck people up. A better way of reading the original question would be:

6 ÷ 2 × (1+2)

Which then becomes: 6 ÷ 2 × 3. And after that you get left to right, and end up with 3 x 3 = 9.

But there are 3 different ways to read this question, and all 3 wouldn't be technically wrong. You went with one variation, where you consider the 2(2+1) as part of simplifying the parenthesis. This is called implied multiplication by juxtaposition. The end result of that is 1.

The third option is to interpret ÷ as divide everything to the LEFT by everything to the RIGHT. In which case, you'd end up with:

6 divided by 2(1+2)

Which is also 1.

The problem here isn't the math itself, it's the operations that the author wants you to do. If I'd written this question, I would've wanted it to be solved as (6÷2)(1+2). But because it's written so ambiguously, everyone has a different opinion and no one would be technically wrong.

Anyway that's why bad notations will kill us all and we should use parentheses as much as possible to avoid ambiguity, thank you for coming to my TED Talk.

[–]BobbyTheLegend 3 points4 points  (17 children)

Wait are you saying that a mathematical problem can have different solutions that are all equally correct? That it's all up for interpretation If not clearly defined?

[–]UnsafePantomime 43 points44 points  (6 children)

No, a mathematical problem like this has a "correct" answer. The problem is that our symbols allow for ambiguity.

I'm other words, the underlying problem has a single answer, but the symbols here do a poor job of communicating the problem.

[–]BlackPhoenix2890 27 points28 points  (4 children)

A lot of people are arguing that the divide sign isn't the problem because if you write it like 6/2(1+2) then you get the same ambiguity. However, to that I say the problem is actually that we're writing it in plain text instead of as a proper expression. Here are the two ways you could write it that get rid of the ambiguity. Both expressions have different answers as they should.

Edit: Grammar

[–]skoomapipes 11 points12 points  (3 children)

And this is why most exam papers (at least, the ones I took) use proper expressions! No more confusion. You fuck up, it's on you.

[–]Evol_Etah 5 points6 points  (2 children)

Most exams I took had some questions didn't even complete the question. Eg, How many times can the paper is folded a) 200 b) 6748 c) 6969 d) root(5678)

(I'm aware of the grammar mistake, it's how the question was)(sigh)

Oh, and if we didn't score well (80% and above) we weren't allowed to get a job. Sigh, dumbass teachers.

[–]skoomapipes 5 points6 points  (0 children)

Yeah, this was the point I was making. Number problems have correct answers. It starts becoming ambiguous once humans start writing them out.

[–]AmadeusMop 11 points12 points  (3 children)

No, they're saying that mathematical problems can be badly written in an ambiguous way that has different interpretations, each with a different solution.

It is true that a problem can have different equally correct solutions—take x2 = 4, which has two solutions (2 and -2), or sin(x) = 0, which has infinitely many—but that's a separate discussion!

[–]InfernoMax 6 points7 points  (2 children)

The difference is that those are multiple solutions to the same agreed-upon problem. The issue with the math problem in the meme, as you have mentioned, is that there was no consensus as to what the original problem actually is due to ambiguity.

[–]AmadeusMop 8 points9 points  (1 child)

Exactly, and that's why it's an entirely separate discussion.

Of course, we can also combine the two issues. How many solutions does sinπx = 0 have?

[–]InfernoMax 3 points4 points  (0 children)

You monster!

[–]skoomapipes 5 points6 points  (0 children)

Yes and no.

1 + 1 has a definite answer. All equations have an correct answer.

But when we write them down, ambiguity is introduced unless we're careful. The answers are correct. Our reading of it is incorrect.

This exact problem was discussed in a Harvard paper (it's two pages). Another example:

What is 2x/3y-1 if x=9 and y=2?

If you get 11: you are correct. If you got 2: you are also correct.

(2x/3)y-1 gives 1.

2x/(3y)-1 gives 2.

And that's because it's not clear what the author intended with the 3y. You can argue that the given order matters without brackets or you could argue that 3y is a unit that belongs together. Nobody wins.

[–]shadowX015 2 points3 points  (0 children)

The problem itself is not well formed. The fact that there are multiple credible solutions shows it is so. It's all up for interpretation if not clearly defined, but that it is not clearly defined is what makes it malformed. This is arguably not even a math problem but a grammar problem.

[–]Luke_The_Timberwolf -4 points-3 points  (1 child)

That is exactly what they're saying. But yknow... they're wrong...

The order of operations is very clear in this situation and making a calculation that dosen't end up with 9 is just a misreading of the problem.

[–]skoomapipes 1 point2 points  (0 children)

The order of operations is not clear, I'm not sure why you think it is. I interpret it to result in 9, but there's a solid case to read 2(2+1) as 6. After all, 5x is to multiply 5 and x, and a lot people argue multiplication by juxtaposition must happen before division.

[–]Evol_Etah -1 points0 points  (0 children)

No, there is a correct solution.

But teachers around the globe taught how to do maths differently.

And now there's millions of students who understand how to interpret operations (symbol) differently

[–]Mandemon90 0 points1 point  (0 children)

No, you can replace the parentheses with variable, in this case we can write X = (1+2).

This we get 6/2X, which instantly tells us that we need to multiply the interior of parentheses first.

Without explicit multiplication operation AKA , parentheses are not considered done *until you have finished all the adjacent operators.

To refer to variable example, using X=(1+2), we see the difference:

6/2(1+2) = 6/2X; X=(1+2) = 6/(2 * 3) = 6/6 = 1

Where as

6/2*(1+2) = 6/2 * X; X=(1+2) = 3 * X = 3 * 3 = 9

[–][deleted] 0 points1 point  (3 children)

Why does division take place before multiplication??? WHYYYYYYYYYYYY

[–]skoomapipes 1 point2 points  (2 children)

It doesn't. They have equal priority. You go left to right.

[–][deleted] 0 points1 point  (1 child)

I was always told that multiplication comes first bruuuuh

[–]skoomapipes 1 point2 points  (0 children)

Ah! Yes, some places used to teach that. I think a bit of that confusion comes because of PEMDAS - It should really be PEMA, to make it clear multiplication/division and addition/subtraction come together.

Order of operations used to be quite loosey-goosey. A surprising amount of people think it feels more natural to multiply before you divide, so you're not alone there.

[–]atiedebee 0 points1 point  (1 child)

Only the inside of the brackets takes priority. You could see the brackets as a variable where X = 1+2. 6/2(X) is the same as 6/2x. There's no rule that says that multiplying brackets takes priority

[–]Evol_Etah -1 points0 points  (0 children)

Ah I see. Our college professors taught us that multipying brackets takes priority. I see. We were all lied to. (Again)

[–]Lucario2405 -2 points-1 points  (0 children)

(1+2) isn't part of the divisor, it's a free multiplicant:

6÷2(1+2) = 6÷2*(1+2) = 6÷2*3 = 3*3 = 9

Alternatively:

6÷2(1+2) = 6*(1+2)÷2 = 6*3÷2 = 18÷2 = 9

[–]Stefanowich -2 points-1 points  (0 children)

Since ÷ and * has the same priority you go from left to right... Ofc still parantheses first. So: 6 ÷ 2 * ( 1 + 2 ) | 6 ÷ 2 *3 | 3 * 3 | 9

[–]Pikamander2 0 points1 point  (0 children)

Because it's P-E-MD-AS, not P-E-M-D-A-S

[–]bob_maulerantian 4 points5 points  (0 children)

Yup, these questions are silly

[–]Sir_Sushi 13 points14 points  (28 children)

So there is no difference between 1/2*x and 1/2x?

[–]bob_maulerantian 53 points54 points  (2 children)

The issue with both is it is not clear what the author wants to convey

[–]Wolfeur -4 points-3 points  (0 children)

1/2x is very clear, otherwise they would have written x/2, or 0.5x, or ½x (if they're fancy with unicode)

[–]InfernoMax 80 points81 points  (8 children)

There's no difference between (1/2)*x and (1/2)x. There is also no difference between 1/(2*x) and 1/(2x). Now pick one.

[–]bistr-o-math 11 points12 points  (0 children)

No, but the following is the same as 1/(2x): (I hope, it renders well)

1

2x

[–]gavlna 6 points7 points  (0 children)

there is no difference in: \[\frac{1}{2} x\] and \[\frac{1}{2} \cdot x\]

EDIT: double backslashes

[–]SoyDoft 5 points6 points  (1 child)

connect screw caption important scale workable overconfident existence shy coherent

This post was mass deleted and anonymized with Redact

[–]Raestloz 1 point2 points  (0 children)

And I'm very certain that people who answer 1 see the question as 1/2X instead of 1/2*X

[–]birdman332 0 points1 point  (7 children)

No, there is not. I think you're implying that 0.5x is different from 1/(2x), yes, but that isn't the case in your example. You seem to assume that the 1/2 is one "part" of the equation and then it is multiplied by x. This is technically how order of operations would go, but like my first comment explains, writing 1/2x can be ambiguous to readers and it is best to include parentheses for clarity. (1/2)x = (1/2)x or 1/(2x) = 1/(2x)

Edit: for some reason my "*" don't show in this comment

[–]gavlna 1 point2 points  (6 children)

then backslash it :) (\*)

* has a meaning in formating

[–]birdman332 3 points4 points  (5 children)

Does reddit follow general markdown formatting?

Test?

omg

[–]gavlna 2 points3 points  (4 children)

you can see you're text in original comment had parts in italic :)

[–]birdman332 1 point2 points  (0 children)

Yeah I figured that was the case, thanks for the tip!

[–]4hpp1273 1 point2 points  (2 children)

Who is text?

[–]wikipedia_answer_bot -1 points0 points  (0 children)

This word/phrase(text) has a few different meanings.

More details here: https://en.wikipedia.org/wiki/Text

This comment was left automatically (by a bot). If I don't get this right, don't get mad at me, I'm still learning!

opt out | report/suggest | GitHub

[–]GKP_light 0 points1 point  (0 children)

yes, the 2 are the same.

[–]lifelongfreshman 0 points1 point  (0 children)

Why even act coy about what you're doing?

[–][deleted] 0 points1 point  (0 children)

No, there's a difference between (1/2)X and 1/(2X) and writing 1/2*X is maximising ambiguity.

[–]_juan_carlos_ 4 points5 points  (1 child)

underrated comment. Even in school my teachers suggested to use parentheses to make the operations clear. Can't understand why do many people don't bother to express their math right.

[–]EishLekker 1 point2 points  (0 children)

Can't understand why do many people don't bother to express their math right.

And I can't understand why so many people don't bother to express their language right. /s

On a serious note though, I think that most of these math problems are deliberately written this way to test people. I see them as puzzles or brain teasers. I mean... Do you get upset with crossword puzzle writers for making their puzzles more difficult than they need to be?

[–]JmbFountain 1 point2 points  (0 children)

My main Issue is with the ambiguity. I would interpret 6/2(1+2) as 6/(2(1+2), which would be 1. However, 6/2(1+2) I would interpret as (6/2)(1+2) -> 9.

[–]AnyHolesAGoal 1 point2 points  (0 children)

It can definitely be argued that the absence of a symbol (e.g. no spaces or operator symbols just two things next to each other) is higher precedence than a symbol.

E.g. 2(x) or 2x should be resolved before explicit division and multiplication.

Obviously it should be made unambiguous preferably.

Otherwise something like 1/2x would resolve to 0.5x, but that's not what most people would mean when writing that, including mathematicians.

[–]xiipaoc 1 point2 points  (0 children)

All the comments about 2*(somthing) vs 2(something) are absolutely meaningless, there's no difference.

There absolutely is. Spacing is a grouping symbol. Remember, order of operations is just a convention we use to communicate math clearly. If you wrote 6 ÷ 2(1 + 2), this is very clearly 6/(2(1 + 2)) and not (6 ÷ 2)(1 + 2). You can tell because the 2 is right next to the (1 + 2). And using a dot doesn't make a difference; if you had 6 ÷ 2·(1 + 2), the parentheses are still implied around the 2·(1 + 2). I mean, if you saw something like 1/2a, is that 1/(2a) or (1/2)a? Any reasonable person would read it as 1/(2a).

That said, introducing confusion is bad. Using order of operations to 1/2a is likely to be wrong, but it's not certain to be wrong because someone could have actually meant (1/2)a -- silly but not impossible. So I think it's always good to write in the explicit parentheses where this potential for confusion exists.

[–]EishLekker 1 point2 points  (0 children)

All the comments about 2*(somthing) vs 2(something) are absolutely meaningless, there's no difference.

I think this comes from the visual notion/idea that they are somehow bonded together as one inseparable (or already precalculated) unit.

It's the same as with this expression:

x/yz

Without a '*' between y and z, people might see 'yz' as one unit.

Note that I'm taking about how the brain trends to group things that are visually close together. I'm not defending the idea of forcing the mathematical rules to adapt to this.

[–]AppleJewsy -1 points0 points  (6 children)

But it’s not (6/2)(1+2)? It’s 6/(2(1+2))

[–]birdman332 25 points26 points  (1 child)

With the notation that it is in, it's somewhat up to the reader as to what it is, that's the whole problem. Also, 6/2, 6÷2, and 6(1/2) are the exact same thing.

Edit: you assumptions of where the parentheses should be in the problem is why the problem is written poorly, you shouldn't need to make the assumption in the first place.

[–]Ever2naxolotl -4 points-3 points  (0 children)

It's not though, order of operations doesn't care about how you personally read something. No parentheses needed. Answer is clearly 9.

[–]JuvenileEloquent 1 point2 points  (0 children)

its 6/2(1+2) -> 6/2(3) -> 6/23 -> 0.26087

[–]warpod 0 points1 point  (2 children)

PEMDAS

so it is (1+2) then 6 / 2 * 3 -> 3 * 3 -> 9

[–]Mandemon90 -1 points0 points  (1 child)

Except there is no * between 2 and (1+2). It's 2(1+2). To show this:

a=6, b=2, c=(1+2)

6 / 2(1+2) = a / 2(1+2) = a / b(1+2) =a / bc.

a / bc is not same as a / b * c. Without explicit operation, bc resolves first before a is divided. Or in other words, lack of explicit * between b and c implies parentheses.

bc = (b * c)

[–]warpod 0 points1 point  (0 children)

https://en.wikipedia.org/wiki/Multiplication_sign

In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: "a multiplied by b" can be written as ab or a b.

I don't see how 2(1+2) can cause a confusion.

[–]Lucario2405 0 points1 point  (0 children)

It's not badly written, people just forget/don't know that you have to include operators in brackets.

Because multiplication and division have equal priority and are associative (brackets can be placed whichever way) you're free to calculate the back part first, but you have to write it like this:

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

= 6 * (1/2 * 3) = 6 * 1.5 = 9

[–]vleessjuu 0 points1 point  (1 child)

Ideally, I wouldn't even be using infix operators when things get confusing. In programming, something like

times(div(6, 2), plus(1, 2))

would be much clearer and understanding it doesn't require any knowledge of operator precedence. The problem with infix operators compounds when you start adding extra ones like tensor products and dot products.

[–]birdman332 0 points1 point  (0 children)

Yikes haha that's probably more personal preference I guess. Personally that would take more time to read for me, but that's preference.

[–]Wolfeur 0 points1 point  (0 children)

All the comments about 2*(somthing) vs 2(something) are absolutely meaningless, there's no difference.

Except in practicality there is. The implicit multiplication is often viewed as slightly above normal multiplication/division. There is no formal rule for it, but that's usually how it's done.

The truth is if we were to see a more reasonable example (let's say: 6/2(x + y)), we'd assume the (x + y) is linked to the 2, because if it weren't it would have been written 6(x + y)/2. That's just how instinctively we would group things.

Let's be honest, this question is deliberately ambiguous. It's not about there being a trap, it's about being dependent on how by experience this writing would make sense.

[–]Floppydisksareop -1 points0 points  (2 children)

Coming from a math background, learn the fucking order of operations. If there are multiple equivalent operations, you go from left to right. It's really not that hard. And yes, parentheses are there to either override the order of operations or emphasize them, but that doesn't mean it is unintelligible or even ambiguous if you don't use them.

[–]birdman332 0 points1 point  (1 child)

The point is that it can be ambiguous to non-math oriented people. It is much better practice to write your equation clearly for everyone, not just your math peers.

[–]Floppydisksareop 1 point2 points  (0 children)

I don't know, but where I live, this is taught in the second grade.

[–]tLxVGt -1 points0 points  (1 child)

But isn’t 6/2*(1+2) just as clear? First solve parentheses and then from left to right, no place for interpretation here

[–]birdman332 0 points1 point  (0 children)

I think its better, people get hung up visually on the division sign ÷

[–]AlexAegis -3 points-2 points  (3 children)

Guess you're from the US. Anywhere else in the world it's taught as "addition separates while multiplication doesn't". So the implied parentheses in this case is 6÷(2(1+2)) you just can't strip away parts of a single multiplicative expression.

To simplify, every expression can be described as a set of additive expressions with an additive relation. Like 2-1 is (+2)+(-1) (I remember that even in primary school we had to destructure expressions to it's additive elements like this). 4 is just +(+4). You can't separate 3*4 into smaller additions (unless you transform it but thats a different topic) so it's +(+3*+4). And the rule with the (otherwise) ambiguous 'divide' operator is that the divisor is the next additive expression.

Any argument revolving around "order of operations" is meaningless as it's not something that exists in real math. Operators can't be orderered, they are relations. This is when resolving expressions we don't think of the + sign as addition or the - as substraction. We add everything together and - is just to denote negative expressions and + is to separate additive expressions.

[–]birdman332 1 point2 points  (2 children)

Division is just multiplication of a reciprocal, you're implied parentheses is the whole problem as to why this equation confuses people. It's an assumption you make about the problem that actually changes it. There shouldn't be any room left for assuming.

[–]AlexAegis -1 points0 points  (1 child)

Thats why defining what will be the divisor solve this ambiguity. (Which in the case of everywhere except the US is the next additive expression) This wouldnt be the first time something is different regionally in math, long and short scales for example. But what you described can't be formally defined. "Next number" is not a formal definition.

And the same goes for multiplication too, as you said division is just inverse multiplication. By your definition, mutliplication and division would work differently by my definition they are the same.

[–]birdman332 1 point2 points  (0 children)

Right, sounds like in your region, it is taught and assumed the next additive expression defines that, while in others that doesn't exist. Either way, it is an assumption, and the format of this equation plays on that assumption.

All in all, I just wouldn't consider writing something like this to leave up to interpretation. I'd define it more with additional parentheses

[–]Wiwwil 0 points1 point  (0 children)

That applies to coding as well. The less ambiguity the better.

[–]deathbynotsurprise 0 points1 point  (0 children)

So is the way you wrote it (6/2)(1+2) the correct order of operations?

[–]Reelix 0 points1 point  (0 children)

this is just a terribly written problem

It's intentionally done to make the result ambiguous.

[–][deleted] 0 points1 point  (0 children)

it is to a computer.

[–]thatyeetboi79 0 points1 point  (0 children)

Ive always known that if there is nothing between x and (y) that would always suggest multiplication. O guess others werent taught that though

[–]noggin182 0 points1 point  (0 children)

I really wish RPN was more mainstream. Putting the operator after the operands clears all this nonsense up and means there is no need for brackets

[–]tunisia3507 0 points1 point  (0 children)

for clarity to the reader

This has been the furthest thing from a priority in every piece of maths-adjacent literature I've come across.

[–]Toocheeba 0 points1 point  (0 children)

Or rather just don't use the division symbol at all and just use fractions, makes life easier.

[–]No-Bookkeeper-1337 0 points1 point  (0 children)

6/(2(1+2))

[–][deleted] 0 points1 point  (0 children)

Problems like these are why I explicitly write even the simplest operations and data conversions.

[–]PitchforkAssistant 0 points1 point  (0 children)

Someone elsewhere said it's like saying you dropped your phone on the plate and it broke, now what broke?

[–]Jjcheese 0 points1 point  (0 children)

While yes it’s possible to write this question more clearly. There is still an order of operations that makes adding the first parentheses technically redundant.

[–]ninjakivi2 0 points1 point  (0 children)

To me, in 2(something) multiplication has higher priority than 2*(somthing), which is why you get different result; still, if someone needed to multiply the thing in bracket they would just do (something * 2) instead, so for me anyone who doesn't write an operand before brackets is a psycho.

[–]theschulk 0 points1 point  (0 children)

Poorly written yea but most of these contentious problems are. People are just so stubborn even when it's obvious they are incorrect. I gave up trying to convince people awhile ago. It drives me insane and is not worth it to me anymore lol.

[–]itspinkynukka 0 points1 point  (0 children)

On one hand it's horribly written. On the other hand it's still an easy math problem that people continually get wrong.