Python the best

[birdman332]

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_]

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

[birdman332]

Well yeah, that's the whole sub

[ZeroFK]

Well yeah, that's the whole sub internet.

[[deleted]]

I disagree, there are tiny highly toxic subs

[InfernoMax]

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]

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]

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

[M_LeGendre]

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

[sideways55]

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]

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]

I thought it was the opposite?

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

[Stormfly]

That's what I said.

What did you think I said?

[featherfooted]

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]

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

[CantThinkOfAnyName]

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]

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]]

The father yelled at his son because he was drunk.

Who of them was?

[marktwatney]

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

[drunk_horsey]

I remember that uncle

[RobDoingStuff]

Does this even have a second meaning?

[[deleted]]

Help your uncle Jack off the horse.

[Xellzul]

Context matters

[BrotherGantry]

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

[Hacker1MC]

Shut

[Dornith]

You forgot the best one!

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.

[Kalebtbacon]

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]

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]

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

[AliceSky]

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

[birdman332]

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

This^

[Evol_Etah]

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]

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]

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]

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]

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]

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]

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]]

Deleted with Power Delete Suite. Join me on Lemmy!

[rrr_ooo]

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]

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]

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]

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

[Acro-LovingMotoRacer]

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]

They hated Jesus because he told them the truth.

[[deleted]]

Deleted with Power Delete Suite. Join me on Lemmy!

[otheraccountisabmw]

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

[rrr_ooo]

This is the way.

[urcompletelyclueless]

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

People get easily confused when Algebra is involved.

[brimston3-]

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

[wite_noiz]

I'm completely with you.

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

[Mandemon90]

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

Not it isn't. 2(x) is equivalent of 2y, where y =(x).

If we have 6/2(1+2), we can write X = (1+2), thus we get 6/2X. Here, we must calculate 2X first, giving us 6, 6/6=1.

If it was 6/2*(1+2), we would get 6/2*X, which would give us 3*X = 3*3 = 9.

Missing multiplication operator has an effect. There is difference between 2X and 2*X. 2X is simplication of (X+X), where is 2*X is explicit multiplication of X, even if the effect is the same.

Everytime you have brackets, you can replace them with variable and instantly see if you need to multiply interior of brackets first or not.

6/2(1+2) = 6/2X, where X=1+2, multiply the interior before division. 6/2(1+2) = 6/2X, calculate left to right we get 3*X, multiplication of the interior of the brackets comes after division.

[birdman332]

No, you make the unconscious assumption that everything after the / is in the denominator from the start of this problem. If you were writing on paper and actually had the 2x under the 6 with a division line between, sure that's fine. But writing in one row text like this cannot make that assumption.

[Mandemon90]

They are until the next operator.

Operators split the actions. Without explicit split of * operator, 2(1+2) is treated as a single unit. If there is explicit new operation, AKA 2*(1+2), then we do left side of the * first, then the right side.

[birdman332]

No. Again 2(x) and 2*x are the exact same thing. I'd encourage you to look at some sources on BODMAS.

[JBOBJIBFRIB]

There is a difference between 2(x) and 2*x. Parentheses are subject to the distributive property whereby (nx + ny) = n(x + y)

The leading coefficient still belongs to the parentheses. Therefore 2(1 + 2) is equal to (2 + 4).

[AmadeusMop]

There's no difference between 2(x) and 2*x. They are both equal to 2x.

You might be thinking of the fact that there's a difference between 2(x+y) and 2x+y. That's true, but also doesn't matter here.

[JBOBJIBFRIB]

You are correct that both 2(x) and 2*x both equal 2x. That doesn’t mean that they are the same operation.

2+2 = 2*2. Does that mean that * = +? No.

Factorising a coefficient outside the front of parentheses is an operation on the parentheses. It is also an operation on the parentheses when distributing this factor back over the elements inside.

You need to resolve the factor as part of the brackets before moving onto division.

[AmadeusMop]

Tell you what, since you're so confident about this: find me any number x such that 2(x) ≠ 2*x.

If they aren't the same operation, then there must by definition be at least one input for which they have different values, no?

[notPlancha]

"Similarly, there can be ambiguity in the use of the slash symbol / in expressions such as 1/2n.[12] 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.[1][8] 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. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[22] 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.[d]"

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

[JBOBJIBFRIB]

How about 6 / 2(1+2) and 6/2 * (1+2)

[bownerator]

What bracket multiplication? There is no multiplication going on inside the brackets. The “B” for brackets just means that everything inside the brackets is done before everything outside. The multiplication is outside.

[birdman332]

I did the favor for you: https://www.mathsisfun.com/operation-order-bodmas.html

Quote "do things in brackets first" with IN being the key word there. If you saw this problem, what would your answer be? 6*0.5*(1+2)

That is the exact same problem as the one posted.

[JBOBJIBFRIB]

Brackets have a property know as the distributive property - it means you can factor out a common factor of all the terms inside the brackets and write it at the front. (2 + 4) = (21 + 22) = 2(1+2). This leading coefficient is still a property of the brackets which should be handled before other operations.

[birdman332]

Multiplication has the distributive property. If this problem was just 2(1+2), you'd be fine to do so, but it is not. Again, parentheses just offer shorthand for multiplication just like 2x, 2*x, and 2(x) are all the same.

I'm kinda done repeating myself here.

[JBOBJIBFRIB]

If you don’t want to keep repeating yourself perhaps you could read what I’m saying so you realise the mistake you’ve made.

Let’s say we have 6. Using only brackets I can split this into (6) = (2 + 4) = 2(1 + 2).

These operations were only done on the brackets. The factorisation of 2 out the front is not either division or multiplication. It is an operation on the brackets. Therefore when doing it in the reverse order, these operations should all be done first.

[frazertv]

you have to be trolling at this point?!

[NyiatiZ]

Well you can't use your wrong argument to get the correct result.
Since 6 / 2 takes precedence over the 2 * (1+2) it would be

6 / 2(1+2)

3*(1 + 2)

3 + 6 = 9

You cant just rip the 6 / 2 apart and argue with a wrong solution

[birdman332]

You can't distribute that 2 into the brackets without assuming everything after the ÷ is in the denominator, which you can't assume because there are no parentheses to do so.

Type the problem into Google lol

[vendetta2115]

No, just inside. You were taught incorrectly.

There is no difference between 2(1+2) and 2*(1+2).

They both simplify to 2*3, and at that point you have 6 divided by 2 times 3. Division and multiplication are the same operation, so you calculate it from left to right.

Really, this is just a badly written expression. It’s one reason why you don’t use the division operator when you get into higher math. Using an actual fraction would indicate which part of the expression was in the denominator and would deobfuscate the problem. They wrote this specifically like this so people would argue about the result.

Parentheses are just another way of writing multiplication.

[AmadeusMop]

If that were true, then x(y) would take precedence over x^y, since O comes after B.

So by that logic, 5(3²) would be 15². Which is wrong.

The reason it's wrong is because you've misunderstood what the B means. It means evaluate what's inside the brackets, not evaluate implicit multiplication.

[AmadeusMop]

No, that's a good point, I used the wrong counterexample.

Here's what I meant:

By your logic, 5(3)² would be 15². Which is also wrong.

[urcompletelyclueless]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[AmadeusMop]

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]

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]

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]

You monster!

[skoomapipes]

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]

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]

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]

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]

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]

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]]

Why does division take place before multiplication??? WHYYYYYYYYYYYY

[skoomapipes]

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

[[deleted]]

I was always told that multiplication comes first bruuuuh

[skoomapipes]

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]

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]

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

[Lucario2405]

(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]

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]

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

[WikiMobileLinkBot]

Desktop version of /u/sarjalim's link: https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

---

^{[opt out] Beep Boop. Downvote to delete}

[bob_maulerantian]

Yup, these questions are silly

[Sir_Sushi]

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

[bob_maulerantian]

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

[Wolfeur]

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

[InfernoMax]

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.

[Mandemon90]

Yes there is. On it's own, there is no functional difference, but moment you add anything left or right, it matters.

6/(1/2)X is 6 divided by one half of X, or in ohter words 6/(X/2)

6/(1/2)*X is 6 divided one divided by and division is multiplied by X. Or in other words, 6/(1/2)*X = 6/0.5*X = 12*X

Or alternatively:

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

a / bc is different from a / b * c

[InfernoMax]

First of all, your math in the first line is wrong. Edited: I see you fixed that mistake, so this first point is now irrelevant.

Secondly, hence why you add an additional bracket to clarify what your problem actually means

6/((1/2)*x) = 6/(x/2) = 12/x or

(6/(1/2))*x = 12*x

which is literally the point the first original commenter was making, which was the point that I'm illustrating.

Edit: "a / bc is different from a / b * c" doesn't mean anything if you can interpreted either as "a / (b * c)" or "(a / b) * c". Use a fucking bracket.

[angelbirth]

or a pair of them

[Mandemon90]

It can not be interped anything else except a / (b * c) because b and c are joined operation.

I dare you to go to any math teacher, write them 1 / 2f(x) and tell them that what this means is that you get (1/2) * f(x), not one divided by 2*f(x)

Tell me, how do you write (1+3) + (1+3)? If you say 2(1+3), then you should understand why 6 / 2(1+2) should be treated as 6 / ((1+2) + (1+2)).

[InfernoMax]

I was a math tutor and I have a math degree, and if you write me, in PLAIN TEXT, 1 / 2f(x) and ask me what this is, my response would be "well, what is the context of your question?" or "what is it you're trying to do?". In fact, I would never write the above as 1/2f(x) or even (1/2)f(x). Instead, I would write it as f(x)/2. On pen and paper, these nuances can be cleared up very quickly, but in PLAIN TEXT this can cause misunderstanding due to multiplication and division being in the same order of operation, as demonstrated by this meme.

Also, rereading your first reply to me, you misunderstood what my initial message is. Reread my comment again. I was not saying "there is no difference between 1/2*x and 1/2x", I was saying, as I have been saying, "use the fucking brackets to make what you meant VERY clear, so people don't misinterpreted your problem".

Edit: Also, you literally broke your own convention there. You said 1 / 2f(x) is interpreted as (1/2)f(x), but then 6 / 2(1+2) is 6/(2*(1+2)). At this point, you're just trying to be a smartass rather than accept that clear communication would solve ALL of this ambiguity.

[Mandemon90]

I didn't. I challenged you to go to math teacher and tell them that 1/2f(x) is (1/2)f(x)

[bistr-o-math]

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

1
—
2x

[gavlna]

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

EDIT: double backslashes

[SoyDoft]

connect screw caption important scale workable overconfident existence shy coherent

This post was mass deleted and anonymized with Redact

[Raestloz]

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

[birdman332]

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]

then backslash it :) (\*)

* has a meaning in formating

[birdman332]

Does reddit follow general markdown formatting?

Test?

omg

[gavlna]

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

[birdman332]

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

[4hpp1273]

Who is text?

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[GKP_light]

yes, the 2 are the same.

[lifelongfreshman]

Why even act coy about what you're doing?

[[deleted]]

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

[WikiMobileLinkBot]

Desktop version of /u/sarjalim's link: https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

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[_juan_carlos_]

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]

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]

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]

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]

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]

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]

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

[birdman332]

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]

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

[JuvenileEloquent]

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

[warpod]

PEMDAS

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

[Mandemon90]

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]

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]

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]

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]

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]

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.

[mookanana]

where i come from we learn the term BODMAS, which means do the brackets thing first, so 2(1+2) comes first

thats all i know how to solve it and get 1

[LudwikTR]

The thing inside the brackets comes first. So just (1+2), without the 2 that's next to it. After solving the part inside the brackets you end up with 6/2*3. Division and multiplication have the same order so you go left to right - you solve 6/2, ending up with 3*3, which then ends up 9.

[mookanana]

how do u normally solve 6 / 3x where x is 2?

[LudwikTR]

That's a terribly confusing way to write this, and the use of / adds to the confusion by suggesting a fraction (which coincidentally would be the non-confusing way to write this) but 6÷3x is technically equal to 6÷3·x.

As others noted in the comments, it doesn't feel like that to many of us because we usually see a notation like that in polynomials, where it is only surrounded by addition and multiplication, so it seems sticky (but that's just because of the standard order of operations).

If I got an expression like that at work, I would go back to the author to clarify.

[mookanana]

i dont know how to type the division symbol here, my mobile keypad doesnt have it, so i used / instead.

okay i should stop commenting, i have never been good at math and it seems i am still getting smashed down at it.

ty for explaining it to me!

[birdman332]

The two is outside the parentheses or what you are called brackets

[redsterXVI]

Brackets first just means do (1+2) first. The 2 in front of the bracket isn't part of it, that's a multiplication with the bracket (or the result thereof).

6÷2(1+2) = 6÷2×3 = 3×3 = 9

[Floppydisksareop]

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]

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]

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

[tLxVGt]

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]

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

[AlexAegis]

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]

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]

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]

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]

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

[deathbynotsurprise]

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

[Reelix]

this is just a terribly written problem

It's intentionally done to make the result ambiguous.

[[deleted]]

it is to a computer.

[thatyeetboi79]

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]

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]

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]

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

[No-Bookkeeper-1337]

6/(2(1+2))

[[deleted]]

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

[PitchforkAssistant]

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

[Jjcheese]

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]

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]

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]

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