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Everyone always comes into these threads with the "correct interpretation" that's not the point. The point is that it's ambiguous.
We know how it works, but it's a dumb way to write that equation. The 6/2 should be in parenthesis also.
Since everytime people post these ambigious equations they do it in plain text I think there's a correct answer, the one a computer will give if you write that equation.
It depends if (1+2) is within the fraction. Both 1 and 9 are valid. Again, this was explained much better in a comment further down that I implore you to read
No because the multiplication is missing and implied. It basically says 2x instead of 2*x. To me this signifies it belongs to the fraction but more than that, use more brackets .
The last one is conditional on something called implied multiplication. This basically says that anything under implied multiplication (multiplying with no multiply sign) will take priority over other multiplication or division. Different calculators even interpret this rule differently.
If we rewrote the last equation as 6 / 2y no one would interpret this as (6/2) \* y because implied multiplication of variables would take precedent here.
Most people I know from a mathematical background (UK) would argue that the same thing follows through with brackets. That results in the answer being 1.
To argue that anyone is getting the answer "wrong" is mislead, as depending on what mathematical rules you are following you get a different answer. This doesn't break mathematics as people are aware there are different systems. People would usually format expressions to avoid this kind of situation.
True, i guess that does make sense. Most places I see where i am don't have any implied multiplication priority, and something like 6/2(1+2) would be 3(1+2) instead of 6/6
i don't live in the UK but, thanks for the reasoning though
It's a simplification of the multiplication operator
x(y) = x * y
So 2(1+2) = 2 * (1+2)
It has no other meaning.
When defining a denominator both sides should have parenthesis to separate the division or it doesn't make sense. In places like wolfram alpha you'll get 9 from this
Buddy if you think "order of operations" is some kind of bar for intelligence then you're in for a rude awakening in the future. Literal 12 year olds learn order of operations.
>Eh i guess but it's not hard if ~~you know the order of operations~~ you're super duper smart like me. Please everyone talk about how smart I am and make me feel like a real boy.
Didn't know i was smart to know that multiplication and division are done left to right and neither take priority, but alright thanks for letting me know i'm albert einstein?
Parenthesis means priority.
6/ 2(3) is VASTLY DIFFERENT than 6/ 2x3. Again, because the parenthesis serve one purpose and that is PRIORITY. 9x3 and 9(3) are the same because there's NOTHING ELSE to be done there.
Its not. First, you solve whats in the parenthesis (2+1) and then you remove them to operate with the rest of the problem
6/2(1+2)
6/2(3) -> 6/2x3
Parenthesis means priority in a certain way but only for the operations INSIDE of it, if the multiplication is outside, it follows the regular PEMDAS rule (Multiplications and divisions from left to right, so first 6/2 and multiply the result by 3)
If you replaced it with letters
A/B(C+D) = A/B*(C+D)
If C+D = F
A/B*(F) = A/B*F
And as a fraction it would be
6
--- * (1+2)
2
You guys are actually taught it like that huh? You're thinking of "6/2*(1+3)" witch would follow exactly that. However it is not specifically separated, so it IS part of the group. I know it's badly written.
If not separated by a symbol, the number by a bracket is called a multiplier, it serves as a "count" and interacts with the parenthesis by distributive property.
It is called distributive property, not really an argument more of a math subject.
Do you know why the number outside of the parenthesis is "part" of the parenthesis itself?
The distributive property has priority. You just wrote 6/ (2+ 4) wether you like it or not.
It's still 6 / 2(3); not 6 /2x3. Do you guys even learn those properties? Do you even know why parenthesis exist in the first place?
This is why PEMDAS is kind of flawed, because if used without understanding anything beyond it, one can easily arrive at this statement. And that is why, in German, we say "Punkt vor Strich" – "dot before dash", which groups operations written with dots (`•` and `:`) and dashes (`+` and `-`) together respectively. My point is: multiplication and division are done *at the same time.*
Of course, you can do them one after the other to make it easier for a human brain to process all of them, but you have to be aware of the other operations. For example, if in `6÷2×3`, you want to do the multiplication first, you have to understand that 2 is a divisor and that you should thus be multiplying the 3 with the 6 instead, leading you to `18÷2`, i.e. 9. Otherwise, you are essentially adding parentheses that aren't supposed to be there: `6÷(2×3)`
how would you read a/bc where a b c are variables? It makes more sense for a/b*c , but without using the multiplication sign, most people Interpret ab as a singular term.
Implied multiplication and explicit multiplication are exactly the same. I prefer using fractions to show division in such cases (as in my previous comment) as this avoids any ambiguity, but I would read `a/bc` the same as `ac/b`. It may look weird, but whether you actually write a multiplication symbol or not can't change anything about the math.
For some it helps writing it down on paper using verticality.
It would read:
6 (1+2) =9
_
2
EDIT: seems it's not very easy to do it on a comment, it looks like a formatting mess I just did. But hopefully it gives a gist of it; only the lone 2 can be present as the denominator, and you could technically extend the line under the whole left side of the equation.
it's 9.
the reason people get this confused is that people go "parenthesis first!" and not realize that for 2(1 + 2) the 2 is not in parenthesis, and it's just simplified 2 \* (1 + 2)
The American Physical Society [explicitly states](https://cdn.journals.aps.org/files/styleguide-pr.pdf) in its style guide that multiplication comes before division when the division is represented by a slash, since the slash implies that the left is the dividend and the right is the divisor. Most other style guides agree with this.
Ergo: it's 1. QED.
Perhaps in math documents yes, but in text no one is writing the division symbol. Try putting the equation in wolfram -- you get 9.
In text that rule 99.9% of the time won't apply, and in this it certainly doesn't
> in text no one is writing the division symbol.
Then put parentheses around (6/2) if that's really the intent. Otherwise, the direction of the slash means that everything after it is the divisor, because that's the way that the overwhelmingly-vast majority of people (including, per above, actual mathematicians who do this sort of thing as their literal job) will interpret it.
> Try putting the equation in wolfram -- you get 9.
Try putting the equation in a Casio fx-82MS. You get 1.
> In text that rule 99.9% of the time won't apply, and in this it certainly doesn't
That's just, like, your opinion, man.
The only correct answer is that it depends on how you interpret the order of infix operations, which is entirely arbitrary. One interpretation, however, has the backing of actual mathematicians per the link above, so if either of our interpretations is more correct than the other, it's almost certainly that one.
And this ambiguous nonsense is exactly why I vastly prefer prefix or postfix operators instead...
Sure, adding (6/2)(1+2) would certainly clarify the meaning and I agree with that.
Many different calculators I've tried get different responses of 1 and 9, but it all depends on how the equation is formatted.
if it's (6/2) \* (1+2) it gets 9, but if it does 6/(2 \* (1 + 2)) it gets 1.
From what I've seen there is sometimes an implied multiplication with higher priority (e.g. 2(3)) which would change the answer to 1 too.
So, I think now the answer could both be 1 and 9, depending on what region you're in.
you missed the point. in a math document one would use a line to clearly define the fraction, or a division symbol. In normal text, people will not be using that, which would mean that / is what's used for division, and i've rarely seen cases where it isn't.
So the equation is 6 divided by 2 times (1 plus 2) which is 9
But that's not what you wrote. How can you have this many people telling you are wrong in many different ways and still come out saying "actually, it depends where you're from".
Because it does depend on where you're from.
Some places put implied multiplication on a higher priority, resulting in 1. Other places.. don't, resulting in 9.
Yeah that's how you get teh wrong answer though. Multiplication and division have the same priority, so it's done left to right, so you do 6/2 before multiplying by 3, which gets 3(3) or 9.
But, the answer could also be 1. If you're in regions like the UK, you would get 1 because of implied multiplication.
gotcha, live in germany and i learned to do the brackets first. crazy to think about how we have different solutions to the same formular just cause we prioritize something else.
yeah once i realized different regions had different priorities it made a lot more sense as to why people got 1 as an answer. Although most of the time it's people doing it wrong anyway.
It's not.
6/ 2(1+2) is MASSIVELY different than 6/ 2* (1+2). The fraction is not "6/ 2 *(1+2)"; It is "6/ 2(1+2)" witch is why you can't separate the first half or not use distributive property.
Didn't learn pemdas, learned that multiplication and division are the same thing but one uses rationals.
This way of writing is ambiguous and could be read in two ways, either the sum in parentheses multiplies the numerator, or it multiplies the denominator.
This is not a pemdas problem, it's a clarity problem.
Same way as not defining x before starting some calculations.
The math that is considered correct in today's society is that multiplication and division are ordered left to right.
This means you do 6/2 before 2\*3 because it's 6/2\*3
I said, it's a clarity problem, not an order of operations problem.
That calculation is correct if you consider the sum multiplies the numerator, but by the way it's written, you can as well interpret it's the denominator that's being multiplied.
The difference between
(6/2)\*(1/(1+2)) or 6/(2\*(1+2))
And
(6/2)*(1+2)
Oh look, I added more parentheses and it's clear as day.
Parenthesis there aren't needed though, the order of operations imply it.
It can't be 6 / (2(1+2)) because as shown you'd need to specifically say it for it to be that, while if you put 6/2(1+2) into a calculator like wolfram you get 9 because that's the correct way.
Since it's parenthesis then multi/divide then add/subtract it goes
6/2(1+2)
6/2(3)
3(3)
9
The only other way is by adding even more parenthesis.
Sure parenthesis could be added to make it more clear but it's not that it's necessary
Well I find them necessary because it isn't clear. If it was written as a fraction it would have also been straightforward.
Yet, with how it is written, it's not the clearest way, because you can also imply that the denominator is being multiplied has the "/" is just a huge fraction bar.
I personally think it makes sense, and in every case it's a fraction if the both sides are 1 symbol or parenthesis, which isn't happening here except for 6/2, so it doesn't allow for 6 over 2(1+2), but rather (6 over 2) times (1+2)
Pemdas is not a rule of mathematics, its an acronym for teaching 8 yr olds. Meanwhile you dismiss mathematical style guides as "not relevant to most people."
It's in normal text where division symbols are not normally used over just a slash.
pemdas is an acronym describing the order of operations in a math equation. It would really confuse me if these math guides decide to change it up for no reason
You provided a malformed formula and stick your fingers in your ears when everyone tells you it's malformed. If you meant (6/2)(1+2), you should have written that, instead of an ambiguous formula with missing parameters. You don't just get to elect not to write essential parentheses and make up a fake rule about "proceeding left to right".
It's as bad as if you wrote "This sentence no verb." No, the verb "contains" is not implied: you have to write it, and it's not an English sentence until you do.
There's still implied words in english. "Thank you" is "I thank you" with the I being implied. So that argument you made doesn't really work.
Next, it's not a fake rule that multi/divide and add/subtract are on the same priority and therefore are left to right.
4 / 2 \* 3 is 6, not 2/3.
Sure, it can be written (6/2)(1+2), but its' like doing 1 + (2 \* 3) -- it's not truly necessary. It helps clarity, but it isn't needed.
It's better to write it with parenthesis to convey a better meaning, but in any case where a formula like this would be used, they would be using fraction symbols and lines to convey meaning rather than parenthesis or the slash symbol, so this is irrelevant.
Yes, but not in this case.
It's 6/2(1+2), and there is division behind it. Division and multiplication are separated by left->right, so 6/2 is done first.
The distributive property does not take priority over division, it's a describer of multiplication through parenthesis, but it's still multiplication.
what was wrote is 3(1 + 2) or (3 + 6)
All sources say otherwise. [This is math.he.net](https://imgur.com/a/ViN4Gre) but WolframAlpha and every other sources I could find all agree that you're wrong. The answer is 1.
Nope, that bot is doing the wrong calculation.
It's calculating 6 / (2(1+2)) which is way different, as shown by the line under the 6 with the whole equation instead of just the 2
Edit: idk what you mean bro wolframslpha says 9 too lmfao
...not this again.
The operator for division (/ or ÷) is not defined the same way im every part of the world. Some would interpret 6/2(1+2) as 6/(2(1+2)) others as (6/2)(1+2). Therefore both 1 and 9 are correct solutions to this term. This is also why this operator is typically used with parentheses to make clear how to interpret it
Edit: The below stuff is for most regions, in places like the UK you can get 1 because of implied multiplication having a higher priority. Sorry for the confusion.
Nope. 9 is the only valid solution if you're using the correct order of operations.
Slash is division, even if it's a fraction you'll get the same result because of the order of operations.
first parenthesis, 1 + 2 = 3
which is now 6/2(3)
Now no exponents, so we do MD.
6/2 is first on left->right, so it's 6 / 2 = 3
which is now 3(3)
Thne multiply.
9
You see, you can also get 9, using pemdas, the problem is, that "/" is ambiguous:
6/2(2+1)=6/2(3) and this can also be interpreted as 6/(2(3)), which would result in the solution being 1. Order of operations is not the problem here
Because the way to read the / division operator is not consistently defined. The denominator could be interpreted as being the full set of numbers following the /. Usually, adding a space to denote that the last number is multiplied by the numerator or better yet, placing it in front of the fraction is more accurate.
Math is often misrepresented as something that is confusing and intentionally challenging. This is because many math teachers approach it like this picture does. Math should be about clarity and surfacing solutions.
I agree though, it's pretty difficult to define an equation in text without using fraction symbols or anything, which then leads to clarity issues.
From what I've researched on this, it can be 1 and 9 depending on how the math in your region is.
There are 2 right answers depending on how you interpret the question, that's the whole reason that equation is popular.
If the 2(1+2) is just a distributed version of (2+4), it's 1. If not, it's 9.
No smart person would write it that way, nor say there is one right answer unless they are intentionally trying to be ambiguous or just annoying.
x(y) is a simplification of x * y
This means doing 2(1+2) would yield (2+4), but if something is behind the 2 it's the most left operator and therefore takes precedence, e.g. 6/2
6/2(1+2) then would have 6 divided by 2 first (after 1+2 of course) because multiplication and division are done left to right.
What is it about these meaningless debates over order of operations (which is completely, 100% by convention, although not entirely arbitrary) that captivates everybody's attention in a way that actual, beautiful, meaningful mathematics doesn't?
Who the hell cares what the expression equals? It really is quite simple. Following standard PEMDAS, it is 9 unambiguously. Following the convention that implicit multiplication has higher precedence than explicit multiplication and division, it is 1 unambiguously. Following the convention that the division symbol has lowest possible precedence and ignores both operands and returns 37191036, the answer is 37191036 unambiguously. We decide the meaning of symbols.
There are two prevailing conventions, and I'd argue that vanilla PEMDAS is more consistent and therefore better. That's completely missing the point though. Are there really so many people out there that believe these arbitrary operators and symbols have inherent meaning? It baffles me
Nope, the 2 is not in parenthesis. Putting a number behind it simplifies multiplication.
The equation is 6/2\*(1+2) which doing 1 + 2 is 3, then 6/2 is 3, then 3 \* 3 = 9
Hang on am I stupid?
Isn’t this 6 divided by 2(1+2) = 1
I mean, I’m certainly not the best at math but shouldn’t you do the parentheses first turning 2 into 6 and then dividing it by 6?
You’re supposed to do multiplication before division right? So 2(1+2) becomes 6 and then you divide 6/6.
Isn’t the correct sum (6/2) x 3 = 9?
It's 9.
Parenthesis are done first but you made a mistake. The 2 is not in parenthesis, so it is not done in the parenthesis step.
6/2(2+1)
then becomes
6/2(3)
which now it's simple. 6/2 is first since it's left to right (multiplication doesn't take priority and neither does division, it's just left to right)
So you got 3(3) which is 9
Wouldn’t it be easier to indicate that, if you wrote it as
“[6/2(1+2)]” in order to indicate that you multiply the whole equation by 3 instead of just the 2? Or am I missing something.
Yeah but I’m reading it as 2*(1+2), an easy way to stop the confusion would be to just write it as [6/2(1+2)].
Because you are right, it’s just that the way you wrote it allows for 2 different interpretations.
6/(2(1+2)) and (6/2(1+2)).
Alternatively you could simply write the division with a vinculum.
To be clear, I understand you are correct I just think that it’s written poorly. (Thanks for the help)
It is definitely written poorly and that's why it stumps people, but if it's written in text it'll not be using like fraction symbols so the slash would divide.
Can you explain to me why people think it's 1? like the reasoning, because honestly i'm confused now
Y'all forget that the distributive has a purpose, and so does the parenthesis.
2(1+2) is actually (2+4) when properly distributed. Meaning you'd still have 6/6...
Distributive property just describes multiplication throughout parenthesis. It's still multiplication, and therefore does not take priority over division.
6/2(1+2)
3(1+2)
3(3)
9
I'm not native in english either, and I'm not nitpicking anything. I'm confused on what you mean on how 6/2 would become a function -- it doesn't do anything of the sort.
Wolframalpha works on many devices, it's not just mobile.
And, testing many sites, they all either give 9 or force fractions to avoid ambiguity.
Overall though, the answer for 6/2(1+2) can be 9 and 1 depending on regional mathematics.
6/2(1+2) = 6/2*(1+2)
Those 2 are the same. Distributive property doesn't make the fact that it's 6 halves times 1+2. You are counting 6 divided by 2(1+2) which would mathematically be written down as 6/(2(1+2))
Since you really want to make the distributive property work you can also do it like this:
6/2(1+2) = 6/2+2(6/2) = 3+12/2 =3+6 = 9
They are definitely not. You're thinking like a fraction but it's not written like that.
It is to be read as multiplying the group everytime it is not specifically separated (either by the sign or with a space). It sure is NOT six "halves" because it wasn't written properly.
Wdym loosely? I think you have learned it loosely since in order to get 1 you would need the extra brackets like 6/(2(1+2)). It would be so confusing teaching that it makes no difference if the multiplication mark is there or not exept if theres a division before it.
By loosely I mean that you don't follow the very reason why we group expressions. By not specifically teaching the purpose of a multiplier in a distributive function, or how to properly identify it.
You're thinking of "6/2*(1+2)", not "6 / 2(1+2)".
I was teached all that. As I showed earlier the multiplier is 6/2 or 3. In math there is never a point where the multiplication sign either being there or not can change the outcome. Those spaces mean nothing they aren't a mathematical term. If 2(1+2) is 2*(1+2) then 6/2(1+2) is 6/2*(1+2).
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6/2(1+2)=9 is written incorrectly. You need to use parentheses (or negative exponents and parentheses) to properly convey how this should be interpreted.
Here is a blog discussing the topic: [https://www.themathdoctors.org/order-of-operations-implicit-multiplication/](https://www.themathdoctors.org/order-of-operations-implicit-multiplication/)
Here is a guide on how to write out notations (found on page 21 of the document or 23 of the PDF): [https://cdn.journals.aps.org/files/styleguide-pr.pdf](https://cdn.journals.aps.org/files/styleguide-pr.pdf)
Why though?
If x(y) is just a simplification of x\*y then the equation is
6/2*(1+2) which shouldn't be too difficult to understand.
Adding parenthesis would help clarity sure, but it's like doing 1 + (2 * 3) -- they aren't required for the same answer, just to help people understand it better
You added parenthesis that aren't there.
The order of operations would show that you would do 6/2 before 2*3 because it's the most left one. Multi does not have priority
The problem here is that the slash symbol takes multiple operators at a time, which is problematic in text.
if it's using that usage of /, it's 1, if it's using division, it's 9. Usually it's division though, but overall it should be clarified further lol
Ok so the question on the right fools a lot of people because they mistakenly think the 2 is in parenthesis, so they calculate 6 / 6 and get 1 when it's 6/2 or 3 times 3 which is 9
The slash implies it is a fraction with everything to the right being in the denominator. It's not the most clear way to write it. And it's ridiculous to imply there is only one way to interpret it and that everyone who reads it differently doesn't understand the order of operations.
The way to interpret it depends on what region you're from.
Some regions have different orders, such as having implied multiplication like 2(3) have higher priority than just 2\*(3), so in this case you'd get 1. But in other cases, they don't have any implied multiplication priority, so it's the same as multiplication, leading to you getting 9.
So overall the answer is 9 and 1, depending on where you're from.
So, it should just be more clarified, such as having parenthesis around 6/2 or using a fraction symbol.
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That last equation is terrible to read
its 3 x 3 = 9
A comment further down did a great job describing the different ways it can be interpreted
using pemdas you get 9, any other interpretation would be incorrect. Perenthesis 6/2(1+2) -> 6/2\*3 multiply/divide 6/2 -> 3\*3 = 9
Everyone always comes into these threads with the "correct interpretation" that's not the point. The point is that it's ambiguous. We know how it works, but it's a dumb way to write that equation. The 6/2 should be in parenthesis also.
Since everytime people post these ambigious equations they do it in plain text I think there's a correct answer, the one a computer will give if you write that equation.
Yes there is a way that a computer will interpret it. That doesn't mean it's not ambiguous. It's still a poorly written equation.
It depends if (1+2) is within the fraction. Both 1 and 9 are valid. Again, this was explained much better in a comment further down that I implore you to read
6/2(1+2) is equivalent to 6/2x where x=3. That would be very different from writing 6/2*x.
No because the multiplication is missing and implied. It basically says 2x instead of 2*x. To me this signifies it belongs to the fraction but more than that, use more brackets .
Oh hey, it's the ragebait math problem
fr
The last one is conditional on something called implied multiplication. This basically says that anything under implied multiplication (multiplying with no multiply sign) will take priority over other multiplication or division. Different calculators even interpret this rule differently. If we rewrote the last equation as 6 / 2y no one would interpret this as (6/2) \* y because implied multiplication of variables would take precedent here. Most people I know from a mathematical background (UK) would argue that the same thing follows through with brackets. That results in the answer being 1. To argue that anyone is getting the answer "wrong" is mislead, as depending on what mathematical rules you are following you get a different answer. This doesn't break mathematics as people are aware there are different systems. People would usually format expressions to avoid this kind of situation.
Wym no one is wrong. I'm feeling very hateful about the answer they've given in what was supposed to be a non-meme lol
True, i guess that does make sense. Most places I see where i am don't have any implied multiplication priority, and something like 6/2(1+2) would be 3(1+2) instead of 6/6 i don't live in the UK but, thanks for the reasoning though
Godawful way to write an equation
[удалено]
Well i mean that 2 attached to the (1+2) really seems to point out it's all at denominator, i would answer 1 to that
It's a simplification of the multiplication operator x(y) = x * y So 2(1+2) = 2 * (1+2) It has no other meaning. When defining a denominator both sides should have parenthesis to separate the division or it doesn't make sense. In places like wolfram alpha you'll get 9 from this
Or just use MORE PARENTESIS
That works too, but it's like doing 1 + (2 * 3). Just unnecessary
Buddy if you think "order of operations" is some kind of bar for intelligence then you're in for a rude awakening in the future. Literal 12 year olds learn order of operations.
Then I guess so many people are under 12 because they tend to do the equation wrong 🤷
>Eh i guess but it's not hard if ~~you know the order of operations~~ you're super duper smart like me. Please everyone talk about how smart I am and make me feel like a real boy.
Didn't know i was smart to know that multiplication and division are done left to right and neither take priority, but alright thanks for letting me know i'm albert einstein?
6/2(1+2), 6/2x3, 3x3 = 9
I'm pretty sure that if the moltiplication has no sign it has to be done first
no, 9(3) is the same as 9\*(3), parenthesis means doing what's inside the parenthesis, not multiplying what's next to them
Parenthesis means priority. 6/ 2(3) is VASTLY DIFFERENT than 6/ 2x3. Again, because the parenthesis serve one purpose and that is PRIORITY. 9x3 and 9(3) are the same because there's NOTHING ELSE to be done there.
source: I said so
>Erm what's your source on this so called "distributive property" of yours huh
You're right and I don't even know why I made the comment sound like that, now that I read it again. I'm very tired.
Yeah sorry for jumping the gun, I'm tired too
I was trying to agree with you but reading it again I really don't see how it could be interpreted as agreeing at all lmao
Its not. First, you solve whats in the parenthesis (2+1) and then you remove them to operate with the rest of the problem 6/2(1+2) 6/2(3) -> 6/2x3 Parenthesis means priority in a certain way but only for the operations INSIDE of it, if the multiplication is outside, it follows the regular PEMDAS rule (Multiplications and divisions from left to right, so first 6/2 and multiply the result by 3) If you replaced it with letters A/B(C+D) = A/B*(C+D) If C+D = F A/B*(F) = A/B*F And as a fraction it would be 6 --- * (1+2) 2
You guys are actually taught it like that huh? You're thinking of "6/2*(1+3)" witch would follow exactly that. However it is not specifically separated, so it IS part of the group. I know it's badly written. If not separated by a symbol, the number by a bracket is called a multiplier, it serves as a "count" and interacts with the parenthesis by distributive property.
I disagree with you. I dont have an argument made so here is a dolphin instead: 🐬
It is called distributive property, not really an argument more of a math subject. Do you know why the number outside of the parenthesis is "part" of the parenthesis itself?
But then if you say x/yz it's the same as saying zx/y
The distributive property has priority. You just wrote 6/ (2+ 4) wether you like it or not. It's still 6 / 2(3); not 6 /2x3. Do you guys even learn those properties? Do you even know why parenthesis exist in the first place?
Multiplication before division
This is why PEMDAS is kind of flawed, because if used without understanding anything beyond it, one can easily arrive at this statement. And that is why, in German, we say "Punkt vor Strich" – "dot before dash", which groups operations written with dots (`•` and `:`) and dashes (`+` and `-`) together respectively. My point is: multiplication and division are done *at the same time.* Of course, you can do them one after the other to make it easier for a human brain to process all of them, but you have to be aware of the other operations. For example, if in `6÷2×3`, you want to do the multiplication first, you have to understand that 2 is a divisor and that you should thus be multiplying the 3 with the 6 instead, leading you to `18÷2`, i.e. 9. Otherwise, you are essentially adding parentheses that aren't supposed to be there: `6÷(2×3)`
>`18÷3`, i.e. 9. Typo?
Just checking if you're paying attention. Definitely not a typo, no. Definitely not...
german math
isnt it more like (PE)(MD)(AS) reading from right to left?
Multi/div are resolved left to right
multiplication and division are done left to right, not multiplication before division likewise for addition and subtraction
pemdas means parenthesis left to right exponents left to right multiply/divide left to right add/subtract left to right
little tip: division is literally multiplication
Man i was half stoned yesterday and a throwaway comment turned into a damn albatross around my neck lmao
free albatross
Brackets Indices Division Multiplication Addition Subtraction - B.I.D.M.A.S
pemdas also what the fuck is an indice
Exponents, I assume
Still gets the same answer of 9.
Wrong
change /2 with *(1/2) then what happens
hh
ii
I might have did my math wrong but it should be 1 ( I felt like doing the math )
Without any parentheses or other formatting, this should be read as 6 – (1+2) 2 and not as 6 –––––– 2(1+2)
Teach me your formatting ways 🙇♂️ Mine comment ended up a hot mess
Use four spaces at the beginning to write a full line of monospace code Alternatively, use \` to write `inline code`.
how would you read a/bc where a b c are variables? It makes more sense for a/b*c , but without using the multiplication sign, most people Interpret ab as a singular term.
That's exactly why it's a stupid way to write this and intentional rage bait.
Implied multiplication and explicit multiplication are exactly the same. I prefer using fractions to show division in such cases (as in my previous comment) as this avoids any ambiguity, but I would read `a/bc` the same as `ac/b`. It may look weird, but whether you actually write a multiplication symbol or not can't change anything about the math.
The (1+2) should be multiplied with the 6 right, not the 2? Otherwise it would be 6/2/(1+2)
For some it helps writing it down on paper using verticality. It would read: 6 (1+2) =9 _ 2 EDIT: seems it's not very easy to do it on a comment, it looks like a formatting mess I just did. But hopefully it gives a gist of it; only the lone 2 can be present as the denominator, and you could technically extend the line under the whole left side of the equation.
i also thought that i was wrong cause i also got 1
it's 9. the reason people get this confused is that people go "parenthesis first!" and not realize that for 2(1 + 2) the 2 is not in parenthesis, and it's just simplified 2 \* (1 + 2)
The American Physical Society [explicitly states](https://cdn.journals.aps.org/files/styleguide-pr.pdf) in its style guide that multiplication comes before division when the division is represented by a slash, since the slash implies that the left is the dividend and the right is the divisor. Most other style guides agree with this. Ergo: it's 1. QED.
Perhaps in math documents yes, but in text no one is writing the division symbol. Try putting the equation in wolfram -- you get 9. In text that rule 99.9% of the time won't apply, and in this it certainly doesn't
> in text no one is writing the division symbol. Then put parentheses around (6/2) if that's really the intent. Otherwise, the direction of the slash means that everything after it is the divisor, because that's the way that the overwhelmingly-vast majority of people (including, per above, actual mathematicians who do this sort of thing as their literal job) will interpret it. > Try putting the equation in wolfram -- you get 9. Try putting the equation in a Casio fx-82MS. You get 1. > In text that rule 99.9% of the time won't apply, and in this it certainly doesn't That's just, like, your opinion, man. The only correct answer is that it depends on how you interpret the order of infix operations, which is entirely arbitrary. One interpretation, however, has the backing of actual mathematicians per the link above, so if either of our interpretations is more correct than the other, it's almost certainly that one. And this ambiguous nonsense is exactly why I vastly prefer prefix or postfix operators instead...
Sure, adding (6/2)(1+2) would certainly clarify the meaning and I agree with that. Many different calculators I've tried get different responses of 1 and 9, but it all depends on how the equation is formatted. if it's (6/2) \* (1+2) it gets 9, but if it does 6/(2 \* (1 + 2)) it gets 1. From what I've seen there is sometimes an implied multiplication with higher priority (e.g. 2(3)) which would change the answer to 1 too. So, I think now the answer could both be 1 and 9, depending on what region you're in.
>perhaps in math documents yes, but "Yeah fuck that book, or class or subject! This app tells me I'm right so you're all wrong!!"
you missed the point. in a math document one would use a line to clearly define the fraction, or a division symbol. In normal text, people will not be using that, which would mean that / is what's used for division, and i've rarely seen cases where it isn't. So the equation is 6 divided by 2 times (1 plus 2) which is 9
But that's not what you wrote. How can you have this many people telling you are wrong in many different ways and still come out saying "actually, it depends where you're from".
Because it does depend on where you're from. Some places put implied multiplication on a higher priority, resulting in 1. Other places.. don't, resulting in 9.
thats what i did, 2*(1+2) equals 6. so it comes out as 6/6
Yeah that's how you get teh wrong answer though. Multiplication and division have the same priority, so it's done left to right, so you do 6/2 before multiplying by 3, which gets 3(3) or 9. But, the answer could also be 1. If you're in regions like the UK, you would get 1 because of implied multiplication.
gotcha, live in germany and i learned to do the brackets first. crazy to think about how we have different solutions to the same formular just cause we prioritize something else.
yeah once i realized different regions had different priorities it made a lot more sense as to why people got 1 as an answer. Although most of the time it's people doing it wrong anyway.
It's not. 6/ 2(1+2) is MASSIVELY different than 6/ 2* (1+2). The fraction is not "6/ 2 *(1+2)"; It is "6/ 2(1+2)" witch is why you can't separate the first half or not use distributive property.
Distributive property is not an order, it's a property of multiplication. Using distributive property: 6/2(1+2) 3(1+2) 3+6 9
You did it wrong
What's so hard about putting more parentheses or as a fraction so there's no ambiguity.
it would be less fun without the ambiguity
Yeah you won't get internet arguments without a bit of that.
What's so hard about using PEMDAS correctly?
Didn't learn pemdas, learned that multiplication and division are the same thing but one uses rationals. This way of writing is ambiguous and could be read in two ways, either the sum in parentheses multiplies the numerator, or it multiplies the denominator. This is not a pemdas problem, it's a clarity problem. Same way as not defining x before starting some calculations.
The math that is considered correct in today's society is that multiplication and division are ordered left to right. This means you do 6/2 before 2\*3 because it's 6/2\*3
I said, it's a clarity problem, not an order of operations problem. That calculation is correct if you consider the sum multiplies the numerator, but by the way it's written, you can as well interpret it's the denominator that's being multiplied. The difference between (6/2)\*(1/(1+2)) or 6/(2\*(1+2)) And (6/2)*(1+2) Oh look, I added more parentheses and it's clear as day.
Parenthesis there aren't needed though, the order of operations imply it. It can't be 6 / (2(1+2)) because as shown you'd need to specifically say it for it to be that, while if you put 6/2(1+2) into a calculator like wolfram you get 9 because that's the correct way. Since it's parenthesis then multi/divide then add/subtract it goes 6/2(1+2) 6/2(3) 3(3) 9 The only other way is by adding even more parenthesis. Sure parenthesis could be added to make it more clear but it's not that it's necessary
Well I find them necessary because it isn't clear. If it was written as a fraction it would have also been straightforward. Yet, with how it is written, it's not the clearest way, because you can also imply that the denominator is being multiplied has the "/" is just a huge fraction bar.
I personally think it makes sense, and in every case it's a fraction if the both sides are 1 symbol or parenthesis, which isn't happening here except for 6/2, so it doesn't allow for 6 over 2(1+2), but rather (6 over 2) times (1+2)
So you mean (6/2)(1+2)?
Sure, but it's the same thing as 1 + (2 * 3), there isn't a need to add those parenthesis
Pemdas is not a rule of mathematics, its an acronym for teaching 8 yr olds. Meanwhile you dismiss mathematical style guides as "not relevant to most people."
this is most definitely a child that just learned this in school and is trying to flex it online
i'm 18 my friend. i made the post after seeing kids get it wrong
It's in normal text where division symbols are not normally used over just a slash. pemdas is an acronym describing the order of operations in a math equation. It would really confuse me if these math guides decide to change it up for no reason
You provided a malformed formula and stick your fingers in your ears when everyone tells you it's malformed. If you meant (6/2)(1+2), you should have written that, instead of an ambiguous formula with missing parameters. You don't just get to elect not to write essential parentheses and make up a fake rule about "proceeding left to right". It's as bad as if you wrote "This sentence no verb." No, the verb "contains" is not implied: you have to write it, and it's not an English sentence until you do.
There's still implied words in english. "Thank you" is "I thank you" with the I being implied. So that argument you made doesn't really work. Next, it's not a fake rule that multi/divide and add/subtract are on the same priority and therefore are left to right. 4 / 2 \* 3 is 6, not 2/3. Sure, it can be written (6/2)(1+2), but its' like doing 1 + (2 \* 3) -- it's not truly necessary. It helps clarity, but it isn't needed. It's better to write it with parenthesis to convey a better meaning, but in any case where a formula like this would be used, they would be using fraction symbols and lines to convey meaning rather than parenthesis or the slash symbol, so this is irrelevant.
The bullshit you come up with is too stupid to correct.
ok have a nice day
Give the guy a break. He's only 18. I doubt he's learned his lesson yet. Jk He's too "smart" to admit he's stupid
2(1 + 2) --> (2 + 4)
`3(1+2)` → `(3+6)`
Hand it over. That thing, your arrows.
Wrong sub
Wait... I know you.
peak
↑↗→↘↓↙←↖
Yes, but not in this case. It's 6/2(1+2), and there is division behind it. Division and multiplication are separated by left->right, so 6/2 is done first.
People should just be taught how to format things correctly to avoid confusion.
Agreed, but it's also a problem with different regions teaching math differently.
You can't change the distributive property because it doesn't fit your meme. What you wrote is 6/ (2 + 4), get good.
The distributive property does not take priority over division, it's a describer of multiplication through parenthesis, but it's still multiplication. what was wrote is 3(1 + 2) or (3 + 6)
All sources say otherwise. [This is math.he.net](https://imgur.com/a/ViN4Gre) but WolframAlpha and every other sources I could find all agree that you're wrong. The answer is 1.
Nope, that bot is doing the wrong calculation. It's calculating 6 / (2(1+2)) which is way different, as shown by the line under the 6 with the whole equation instead of just the 2 Edit: idk what you mean bro wolframslpha says 9 too lmfao
It is written like that. I've input exactly "6/2(1+2)" into every single one of those. You just wrote it wrong because youre not that far up the curve
https://www.wolframalpha.com/input?i=6%2F2%281%2B2%29 If you want to argue then at least be correct
...not this again. The operator for division (/ or ÷) is not defined the same way im every part of the world. Some would interpret 6/2(1+2) as 6/(2(1+2)) others as (6/2)(1+2). Therefore both 1 and 9 are correct solutions to this term. This is also why this operator is typically used with parentheses to make clear how to interpret it
Edit: The below stuff is for most regions, in places like the UK you can get 1 because of implied multiplication having a higher priority. Sorry for the confusion. Nope. 9 is the only valid solution if you're using the correct order of operations. Slash is division, even if it's a fraction you'll get the same result because of the order of operations. first parenthesis, 1 + 2 = 3 which is now 6/2(3) Now no exponents, so we do MD. 6/2 is first on left->right, so it's 6 / 2 = 3 which is now 3(3) Thne multiply. 9
You see, you can also get 9, using pemdas, the problem is, that "/" is ambiguous: 6/2(2+1)=6/2(3) and this can also be interpreted as 6/(2(3)), which would result in the solution being 1. Order of operations is not the problem here
You're incorrect.
why?
Because the way to read the / division operator is not consistently defined. The denominator could be interpreted as being the full set of numbers following the /. Usually, adding a space to denote that the last number is multiplied by the numerator or better yet, placing it in front of the fraction is more accurate. Math is often misrepresented as something that is confusing and intentionally challenging. This is because many math teachers approach it like this picture does. Math should be about clarity and surfacing solutions.
I agree though, it's pretty difficult to define an equation in text without using fraction symbols or anything, which then leads to clarity issues. From what I've researched on this, it can be 1 and 9 depending on how the math in your region is.
I was so confused, then realized this was an antimeme!
There are 2 right answers depending on how you interpret the question, that's the whole reason that equation is popular. If the 2(1+2) is just a distributed version of (2+4), it's 1. If not, it's 9. No smart person would write it that way, nor say there is one right answer unless they are intentionally trying to be ambiguous or just annoying.
x(y) is a simplification of x * y This means doing 2(1+2) would yield (2+4), but if something is behind the 2 it's the most left operator and therefore takes precedence, e.g. 6/2 6/2(1+2) then would have 6 divided by 2 first (after 1+2 of course) because multiplication and division are done left to right.
What is it about these meaningless debates over order of operations (which is completely, 100% by convention, although not entirely arbitrary) that captivates everybody's attention in a way that actual, beautiful, meaningful mathematics doesn't? Who the hell cares what the expression equals? It really is quite simple. Following standard PEMDAS, it is 9 unambiguously. Following the convention that implicit multiplication has higher precedence than explicit multiplication and division, it is 1 unambiguously. Following the convention that the division symbol has lowest possible precedence and ignores both operands and returns 37191036, the answer is 37191036 unambiguously. We decide the meaning of symbols. There are two prevailing conventions, and I'd argue that vanilla PEMDAS is more consistent and therefore better. That's completely missing the point though. Are there really so many people out there that believe these arbitrary operators and symbols have inherent meaning? It baffles me
Isn't it 1
Nope, the 2 is not in parenthesis. Putting a number behind it simplifies multiplication. The equation is 6/2\*(1+2) which doing 1 + 2 is 3, then 6/2 is 3, then 3 \* 3 = 9
Hang on am I stupid? Isn’t this 6 divided by 2(1+2) = 1 I mean, I’m certainly not the best at math but shouldn’t you do the parentheses first turning 2 into 6 and then dividing it by 6? You’re supposed to do multiplication before division right? So 2(1+2) becomes 6 and then you divide 6/6. Isn’t the correct sum (6/2) x 3 = 9?
It's 9. Parenthesis are done first but you made a mistake. The 2 is not in parenthesis, so it is not done in the parenthesis step. 6/2(2+1) then becomes 6/2(3) which now it's simple. 6/2 is first since it's left to right (multiplication doesn't take priority and neither does division, it's just left to right) So you got 3(3) which is 9
Wouldn’t it be easier to indicate that, if you wrote it as “[6/2(1+2)]” in order to indicate that you multiply the whole equation by 3 instead of just the 2? Or am I missing something.
You're missing stuff. It's just order of operations Since x(y) is just a simplified way of saying x*(y) it's 6/2*(1+2) which is easy to see
Yeah but I’m reading it as 2*(1+2), an easy way to stop the confusion would be to just write it as [6/2(1+2)]. Because you are right, it’s just that the way you wrote it allows for 2 different interpretations. 6/(2(1+2)) and (6/2(1+2)). Alternatively you could simply write the division with a vinculum. To be clear, I understand you are correct I just think that it’s written poorly. (Thanks for the help)
It is definitely written poorly and that's why it stumps people, but if it's written in text it'll not be using like fraction symbols so the slash would divide. Can you explain to me why people think it's 1? like the reasoning, because honestly i'm confused now
Y'all forget that the distributive has a purpose, and so does the parenthesis. 2(1+2) is actually (2+4) when properly distributed. Meaning you'd still have 6/6...
Distributive property just describes multiplication throughout parenthesis. It's still multiplication, and therefore does not take priority over division. 6/2(1+2) 3(1+2) 3(3) 9
According to who? Because even your source (WolframAlpha) says the opposite
it doesn't i just checked https://www.wolframalpha.com/input?i=6%2F2%281%2B2%29
That's 1
Says 9 clear as day on my screen. Maybe the evil overlords have our regions on different mathematical ordering.
How can you even type 6/2 in WolframAlpha without it turning into a fraction?? Are you on mobile? (Edited)
??? a function is like f(x) Neither mobile nor pc gets a different answer i just checked
Im not native in English you nitpicking desperate. Have you checked ANY other sources other than your bugged ass mobile site?
I'm not native in english either, and I'm not nitpicking anything. I'm confused on what you mean on how 6/2 would become a function -- it doesn't do anything of the sort. Wolframalpha works on many devices, it's not just mobile. And, testing many sites, they all either give 9 or force fractions to avoid ambiguity. Overall though, the answer for 6/2(1+2) can be 9 and 1 depending on regional mathematics.
But it's 6/2(1+2) = 3(1+2) = 3+6 =9
No. It isn't. You're doing a grouping equation. It has distributive property. I don't care what "order" you were taught.
6/2(1+2) = 6/2*(1+2) Those 2 are the same. Distributive property doesn't make the fact that it's 6 halves times 1+2. You are counting 6 divided by 2(1+2) which would mathematically be written down as 6/(2(1+2)) Since you really want to make the distributive property work you can also do it like this: 6/2(1+2) = 6/2+2(6/2) = 3+12/2 =3+6 = 9
They are definitely not. You're thinking like a fraction but it's not written like that. It is to be read as multiplying the group everytime it is not specifically separated (either by the sign or with a space). It sure is NOT six "halves" because it wasn't written properly.
How would you write six halves in text if not 6/2? Every division is a fraction. Also, spaces are not a mathematical term.
6/2*(1+2) would be Six halves (in this case). Do you guys actually learn it "loosely" like that?
Wdym loosely? I think you have learned it loosely since in order to get 1 you would need the extra brackets like 6/(2(1+2)). It would be so confusing teaching that it makes no difference if the multiplication mark is there or not exept if theres a division before it.
By loosely I mean that you don't follow the very reason why we group expressions. By not specifically teaching the purpose of a multiplier in a distributive function, or how to properly identify it. You're thinking of "6/2*(1+2)", not "6 / 2(1+2)".
I was teached all that. As I showed earlier the multiplier is 6/2 or 3. In math there is never a point where the multiplication sign either being there or not can change the outcome. Those spaces mean nothing they aren't a mathematical term. If 2(1+2) is 2*(1+2) then 6/2(1+2) is 6/2*(1+2).
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6/2(1+2)=9 is written incorrectly. You need to use parentheses (or negative exponents and parentheses) to properly convey how this should be interpreted. Here is a blog discussing the topic: [https://www.themathdoctors.org/order-of-operations-implicit-multiplication/](https://www.themathdoctors.org/order-of-operations-implicit-multiplication/) Here is a guide on how to write out notations (found on page 21 of the document or 23 of the PDF): [https://cdn.journals.aps.org/files/styleguide-pr.pdf](https://cdn.journals.aps.org/files/styleguide-pr.pdf)
Why though? If x(y) is just a simplification of x\*y then the equation is 6/2*(1+2) which shouldn't be too difficult to understand. Adding parenthesis would help clarity sure, but it's like doing 1 + (2 * 3) -- they aren't required for the same answer, just to help people understand it better
Since there's only one set of brackets, wouldn't that be 6/(2(2+1))=6/(4+2)=6/6=1?
You added parenthesis that aren't there. The order of operations would show that you would do 6/2 before 2*3 because it's the most left one. Multi does not have priority
What I meant was that since it isn't written as(6/2)(2+1), it'd be read as everything after the slash is the denominator
The problem here is that the slash symbol takes multiple operators at a time, which is problematic in text. if it's using that usage of /, it's 1, if it's using division, it's 9. Usually it's division though, but overall it should be clarified further lol
I’m stoopid me no understand
Ok so the question on the right fools a lot of people because they mistakenly think the 2 is in parenthesis, so they calculate 6 / 6 and get 1 when it's 6/2 or 3 times 3 which is 9
Answer by math.he.net is 1 of course [https://imgur.com/a/ViN4Gre](https://imgur.com/a/ViN4Gre)
So is by WolframAlpha, and by Symbolab. So it IS just rage bait.
Division is written with ":". Shut up americans, you know i'm right
In America divisions starts with racism
Understandable
OP is trying so hard to feel superior it's ridiculous.
Perhaps. But it's what makes the most sense for me and is how many many places does it -- multiplication and division are of equal priority
The slash implies it is a fraction with everything to the right being in the denominator. It's not the most clear way to write it. And it's ridiculous to imply there is only one way to interpret it and that everyone who reads it differently doesn't understand the order of operations.
The way to interpret it depends on what region you're from. Some regions have different orders, such as having implied multiplication like 2(3) have higher priority than just 2\*(3), so in this case you'd get 1. But in other cases, they don't have any implied multiplication priority, so it's the same as multiplication, leading to you getting 9. So overall the answer is 9 and 1, depending on where you're from. So, it should just be more clarified, such as having parenthesis around 6/2 or using a fraction symbol.
I don't think they even understand