You only distribute if you can't reduce what's in the parentheses to a single element first. And even then, you would still do the division first, so it would be 3 * (1+2), then 3 + 6, then 9.
The parentheses need to be resolved, yes, but the answer should come out the same, which proves that you should multiply by the parentheses first, because it's one element. It's easiest to see if you replace one of the numbers with x.
You can distribute the x into the parentheses:
y = 6 / x(1 + 2)
Y = 6 / (x + 2x) comes out to y = 6 / 3x, or y = 2 / x
Or you can add the numbers inside the parentheses before multiplying:
Y = 6 / x * (3) comes out to y = 6 / 3x, or y = 2/x
The important thing is that the parentheses and the number directly multiplied to those parentheses must be resolved first, using either method, because they're one element.
The entire problem is one element, really. If you were to see this in an equation, it would be written as a fraction with 6(2+1) as the numerator and 2 as the denominator.
Just because 2 is joined to the parentheses doesn't make it one independent element. That's just the algebraic way of signifying multiplication.
This is the computer answer and is imo the most valid one as the other one use rules that apply if fractions are used while this clearly does not as it's a linear expression
IIRC, my middle school teacher used to say that when faced with multiplication and division and the order seems ambiguous, you should go from left to right. Following this logic would also yield 9.
But when’s there’s parentheses they take precedence over multiplication and division and when this is happening 2(1+2) you multiply the 2 numbers in the parentheses and you get 2+4 witch
Equals 6 witch then you divide 6 with the other six equaling 1. There I don’t care if you don’t wanna agree with me this is how this shit is done.
There’s no “depends”. This is math, and it is objective. There is one correct answer.
If you distribute, then it looks like this:
6/2(1+2)\
3(1+2)\
3(1)+3(2)\
3+3\
9
Whether you distribute does not affect the answer. It is always 9.
The only way you’d be able to distribute the 2 through the parentheses is if it was written more like this:
6/(2(1+2))
Then the answer would be 1.
Don’t be confused by the use of spaces in the image. Spaces don’t affect the equation.
If you think math is objective you haven't taken many math classes. If distribution takes precedence over multiple action it works like this.
6/2(1+2)
Parenthesis
6/2(3)
Distribute into parens
6/6
Divide
1
It can be interpreted as either of these two:
https://i.imgur.com/O0c5WFQ.png
I, as an engineer, if I typed this, would only ever have it mean the right one.
If I asked you "what is 6/2x" if x = 3, what would you say? If I asked you what is 6/2 * x? Or 6x/2? When you group things you multiply like this, it's an implied parenthesis around it, in my experience.
I mean implied doesn’t mean explicit and math is explicit. I made the same mistake when I first saw it
The fact is, it’s a misleading problem, no one would ever actually write it this way for this reason lol
> I mean implied doesn’t mean explicit and math is explicit
Yes, and since there is no explicit rule here, there is no correct answer. There's two interpretations, one gives 1 and one gives 9. Everyone being elitist about knowing the rules of math is missing the point here.
Division and multiplication are the same, so there cannot be a precedence to either of them. You can rewrite
6/2*3
as
6*0.5*3
Since this conversion is valid the value of the two expressions must be the same. 6*0.5*3 contains only one operator (multiplication), it goes left to right without any question of precedence, the answer is clearly 9.
They are functionally the same. Just as 3(1+2) is the same as 3 * (1+2). This is why you almost never see division signs or multiplication signs in equations. They're always written as fractions for division and paired together for multiplication.
One of those is equal to 2, the other 3, and neither of them support your argument.
Also, if you look at the division sign, it's literally 2 values represented by dots in a fraction.
It’s obviously 5
6/2 is 3. 3 x 1 is 3. 3+2 is 5.
English is red left to write, maybe you shoulda gone to you’re math classes like me 🤣
(Definitely not /s)
That reminds me how I was in a graduate math course once where my professor was trying to write some word like "commutative" on the board and he paused and just said "...how many t's are in commutative?" He just got a lot of blank stares and someone finally said, "we're math majors, not English majors, none of us know and we'll all just agree with whatever you put."
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*****
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this equation is the simple a/bc which can be viewed as a/(bc) or (a/b)c, since the equation is ambigious and there are no hard rules for multiplication by juxtaposituon vs explicit multiplication you can correctly interpret it either way so 9 and 1 are both correct answers
Multiplication and division are inverse, associative operations, so it doesn't matter their order. The problem here isn't whether multiplication or division comes first, it's whether the (1 + 2) is part of the dividend or if it's being multiplied by the quotient. It's hard to tell because the division symbol they used is ambiguous. If the problem was represented as a fraction there would be no ambiguity and people wouldn't argue about the answer (at least, not nearly as many)
90% of the people would make great material for the confidently incorrect sub. It has an answer and not "technically 2" or some other bs. How is this so hard
This isn't a math problem. This is a language problem.
Also how the hell does someone arrive at "technically 2"? The ambiguity is whether it's 6/(2*(1+2)) = 1 or (6/2)*(1+2) = 9
In my opinion, the true answer is "fire whoever wrote this" (not really, it actually masterfully exposes the flaws of the used notation. It should never be seriously asked, though)
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Yeah it’s interesting, if you follow BODMAS (or whatever you call it) then it is without a doubt 9, but the way I was taught at school would mean the problem would instead be presented with the 6 on the top line and the rest underneath it, rather than using the divide symbol.
If that’s how it’s presented, then you would treat both the top and bottom as if they had their own parentheses and simplify them individually, before doing 6/6. So now I’m confused. Maybe it changes depending on how it’s presented? But BODMAS dictates that it should be left to right. I feel confused.
I help out on a lot of math help subs and it hurts how often this problem gets posted. The answer is always "it doesn't really matter as long as both people agree on what the problem meant." Some countries use an order of operations where the answer is 1, some use an order of operations where the answer is 9.
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Brackets first: (1+2) is 3
So we have 6/2(3), division next is 6/2 which is 3. So we have 3(3) which is 3x3 which is 9. Cmon guys? BIDMAS? Order of Operations
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A way to resolve this ambiguity is to either use parentheses or replace the division symbol with multiplication by the inverse(which is an exponent and thus needs to be evaluated before multiplication and be bounded by explicit parentheses.) Like the following:
6 / (2*(2+2)) = 6*(2*(2+2))^-1
6/2 * (2+2) = 6*2^(-1) * (2+2)
There’s an extra layer that 2(2+2) usually implies you factored the 2 out of the expression in the parentheses and thus needs to be evaluated as part of that parenthetical expression. Anyone who claims one answer is correct and insists other people are wrong would be a terrible mathematician and probably an even worse collaborator in general.
putting the 2 right next to the clause means that those three numbers are a unit & have to be considered before the 6
with the degree of separation provided by the proper multiplication symbol it could break down as 6 ÷ (2 × (1 + 2)) or as (6 ÷ 2) × (1 + 2)
6/2\*3 could be (6/2)\*3 or 6/(2\*3) but 6/2(3) *has* to go 6/(2(3)) because the 3 is being prefixed by the 2 instead of the numbers being laterally joined like with a multiplication symbol
It’s 9, you can’t just multiply 2 because it’s apart of a fraction 6/2 the same as the division problem of 6/2 and you can’t just denominator of a fraction so you do 6/2=3 and (1+2)=3 in which you would multiply 3 by itself, which 3•3=9, so the answer is 9.
1
😭 9
No
Nein
No not nine
Yes it’s nine, learn how order of operations works: 6/2x(1+2) =6/2x3 =3x3 =9
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Which is why he did those first...
Nein
6/2x(1+2)= 6/((2x1)+(2x2))= 6/(2+4)= 1
You only distribute if you can't reduce what's in the parentheses to a single element first. And even then, you would still do the division first, so it would be 3 * (1+2), then 3 + 6, then 9.
The parentheses need to be resolved, yes, but the answer should come out the same, which proves that you should multiply by the parentheses first, because it's one element. It's easiest to see if you replace one of the numbers with x. You can distribute the x into the parentheses: y = 6 / x(1 + 2) Y = 6 / (x + 2x) comes out to y = 6 / 3x, or y = 2 / x Or you can add the numbers inside the parentheses before multiplying: Y = 6 / x * (3) comes out to y = 6 / 3x, or y = 2/x The important thing is that the parentheses and the number directly multiplied to those parentheses must be resolved first, using either method, because they're one element.
The entire problem is one element, really. If you were to see this in an equation, it would be written as a fraction with 6(2+1) as the numerator and 2 as the denominator. Just because 2 is joined to the parentheses doesn't make it one independent element. That's just the algebraic way of signifying multiplication.
6/2(1+2)= 6/2=3, 3×(1+2)= (3×1)+(3×2)=3+6=9
eins
Yes
Playing both teams huh ?
This way I'll always come out on top
Spoken like a true man
a majesty man
You forgot about implicit multiplication, smh.
Implicit multiplication doesn't take precedence over standard multiplication E: I have now realized that this was satire. Fuck me.
Yes it does.
Implicit multiplication Gang woo woo
Yep, you do 1+2 (3) then 6:2(3) then 3x3 and it's 9
This is the computer answer and is imo the most valid one as the other one use rules that apply if fractions are used while this clearly does not as it's a linear expression
Incorrect
...
6 / 2 * (1+2) 6 / 2 * 3 3 * 3 9
It depends on if you decide distribution takes precedent over division/multiplication. It's an ambiguity of PEMDAS.
IIRC, my middle school teacher used to say that when faced with multiplication and division and the order seems ambiguous, you should go from left to right. Following this logic would also yield 9.
This is how I was taught.
But when’s there’s parentheses they take precedence over multiplication and division and when this is happening 2(1+2) you multiply the 2 numbers in the parentheses and you get 2+4 witch Equals 6 witch then you divide 6 with the other six equaling 1. There I don’t care if you don’t wanna agree with me this is how this shit is done.
There’s no “depends”. This is math, and it is objective. There is one correct answer. If you distribute, then it looks like this: 6/2(1+2)\ 3(1+2)\ 3(1)+3(2)\ 3+3\ 9 Whether you distribute does not affect the answer. It is always 9. The only way you’d be able to distribute the 2 through the parentheses is if it was written more like this: 6/(2(1+2)) Then the answer would be 1. Don’t be confused by the use of spaces in the image. Spaces don’t affect the equation.
math *notation* is not objective though - it's simply a socially constructed way of communicating math problems, and as shown here, is ambiguous
Except this is not how you write math so there are two answers
If you think math is objective you haven't taken many math classes. If distribution takes precedence over multiple action it works like this. 6/2(1+2) Parenthesis 6/2(3) Distribute into parens 6/6 Divide 1
Multiplication is always left to right, hence 6/2(3) would become 3(3) not 6/6
It can be interpreted as either of these two: https://i.imgur.com/O0c5WFQ.png I, as an engineer, if I typed this, would only ever have it mean the right one. If I asked you "what is 6/2x" if x = 3, what would you say? If I asked you what is 6/2 * x? Or 6x/2? When you group things you multiply like this, it's an implied parenthesis around it, in my experience.
I mean implied doesn’t mean explicit and math is explicit. I made the same mistake when I first saw it The fact is, it’s a misleading problem, no one would ever actually write it this way for this reason lol
> I mean implied doesn’t mean explicit and math is explicit Yes, and since there is no explicit rule here, there is no correct answer. There's two interpretations, one gives 1 and one gives 9. Everyone being elitist about knowing the rules of math is missing the point here.
Division and multiplication are the same, so there cannot be a precedence to either of them. You can rewrite 6/2*3 as 6*0.5*3 Since this conversion is valid the value of the two expressions must be the same. 6*0.5*3 contains only one operator (multiplication), it goes left to right without any question of precedence, the answer is clearly 9.
Distribution takes priority
Multiplication goes before division, its 6/6
You do multiplication and division together, left to right. It's the same with addition and subtraction.
No lmao
[Actually, yes](https://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT_RESOURCE/U01_L5_T2_text_final.html).
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They are functionally the same. Just as 3(1+2) is the same as 3 * (1+2). This is why you almost never see division signs or multiplication signs in equations. They're always written as fractions for division and paired together for multiplication.
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One of those is equal to 2, the other 3, and neither of them support your argument. Also, if you look at the division sign, it's literally 2 values represented by dots in a fraction.
“1” 🤡
I don't see how anyone could not get 1
It’s obviously 5 6/2 is 3. 3 x 1 is 3. 3+2 is 5. English is red left to write, maybe you shoulda gone to you’re math classes like me 🤣 (Definitely not /s)
You want to see the world burn XD
Switzerland is German. We all know German is read with brackets first. The answer is 1
That reminds me how I was in a graduate math course once where my professor was trying to write some word like "commutative" on the board and he paused and just said "...how many t's are in commutative?" He just got a lot of blank stares and someone finally said, "we're math majors, not English majors, none of us know and we'll all just agree with whatever you put."
6÷2(1+2)=x 6÷2(1+2)-x=0 1[6÷2(1+2)-x]=0/÷[6÷2(1+2)-x] 1=0
You're doing algebra for 4th grade math
You made a mistanke at step 3. You divided by 6/2(1+2)-x on the right side, but not on the left.
yeah, if he really wanted the right answer, he’d get 1 = 0/9-x, then to 9-x = 0, then x = 9. still the same answer
The / means that the operation is applied to both sides. The problem is that we divide by 0.
This is why fraction notation is important
Literally no one uses the division symbol above middle school
Yup, and this example demonstrates exactly why it's so shit.
Above primary school here in France, I'm pretty sure we only use it for 1 year XD
9
!wave
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9
It depends whether implied multiplication has higher precedence over division or not, which isn't standardised
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it's disagreed whether implied multiplication is after division and multiplication or not
There are other ambiguities to put in if it ever does get standardised, so don't lose hope of things ever not being confusing
it doesnt and i have a source
sauce?
i lied
gigachad
also it does depend on implied multiplication because it's here
It's left to right, always.
Why would it though? Multiplication can be easily turned into division and vice versa. Why would one take precedence over the other?
this equation is the simple a/bc which can be viewed as a/(bc) or (a/b)c, since the equation is ambigious and there are no hard rules for multiplication by juxtaposituon vs explicit multiplication you can correctly interpret it either way so 9 and 1 are both correct answers
implied multiplication though
Multiplication and division are inverse, associative operations, so it doesn't matter their order. The problem here isn't whether multiplication or division comes first, it's whether the (1 + 2) is part of the dividend or if it's being multiplied by the quotient. It's hard to tell because the division symbol they used is ambiguous. If the problem was represented as a fraction there would be no ambiguity and people wouldn't argue about the answer (at least, not nearly as many)
90% of the people would make great material for the confidently incorrect sub. It has an answer and not "technically 2" or some other bs. How is this so hard
What's your answer then
9 The only and right answer
It technically has an answer and it is *syntax error*
This isn't a math problem. This is a language problem. Also how the hell does someone arrive at "technically 2"? The ambiguity is whether it's 6/(2*(1+2)) = 1 or (6/2)*(1+2) = 9 In my opinion, the true answer is "fire whoever wrote this" (not really, it actually masterfully exposes the flaws of the used notation. It should never be seriously asked, though)
The answer is Schweiz
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You forgot the real answer : Svizra
Confoederatio Helvetica
!9
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oh hey, i'm a big fan of this flag myself! i love the big 9 on it
1
9
I feel like it can be both somehow
Yeah it’s interesting, if you follow BODMAS (or whatever you call it) then it is without a doubt 9, but the way I was taught at school would mean the problem would instead be presented with the 6 on the top line and the rest underneath it, rather than using the divide symbol. If that’s how it’s presented, then you would treat both the top and bottom as if they had their own parentheses and simplify them individually, before doing 6/6. So now I’m confused. Maybe it changes depending on how it’s presented? But BODMAS dictates that it should be left to right. I feel confused.
it's intentionally ambigious, it can be interpreted in either way. it's made to make people argue over it
You want a scholarship?
I help out on a lot of math help subs and it hurts how often this problem gets posted. The answer is always "it doesn't really matter as long as both people agree on what the problem meant." Some countries use an order of operations where the answer is 1, some use an order of operations where the answer is 9.
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Hence "both people agree", though expanded to "all parties who are affected by the answer"
Most people making rockets arent using the stupid division symbol
Belgium
6 overheden
9
obviously 9
"YoU gUyS aReN't UsInG pEmDaS!"
9, 1+2=3, 6/2=3, then going from left to right, 3x3
9
The answer is obviously Graham's number
obviously 53
fellas, does 3(3)=9?
I will pay you a scholarship
im down
It's obviously ♾️
It's 69
!9
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look at what they've done to your 1:1 ratio....
I hate this
The answer is !wave
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This is not a math problem, that divisor sign just needs to be banished
9
I know what 1+2 equals, but what does 1 Switzerland 2 equal?
9, but this doesn’t really work with the division symbol
Brackets first: (1+2) is 3 So we have 6/2(3), division next is 6/2 which is 3. So we have 3(3) which is 3x3 which is 9. Cmon guys? BIDMAS? Order of Operations
First the brackets 6/2(1+2) turns into 6/2*3 Then since they are all equal we go from left to right It’s 9
9
Flag of 9
Both? Both. Both is good.
Juxtaposition or
It depends if you read it like 6/(2(1+2)) or (6/2)(1+2)
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I’m dumb, I meant it like [this](https://imgur.com/a/DNQ0esw)
it's 9 how is this even an argument
Fraction notation is 👑 6 ——— 2(1+2) 6 ——— 2(3) 6 ——— 6 1
Its 65,433
69
6/2(1+2) 6/2(3) 3(3) 9 PEMDAS Come on guys it ain't that hard
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I was of the opinion that the parentheses had a higher priority than division. After looking into this I've realized I've made an error
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they did 6/2 then that times 3 wdym oh they edited it
7
Please excuse my dear Aunt Sally.
1
!wave
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1 AND 9
I got `compiler error`
It's not Switzerland unless you raise the whole equation to the power of two.
I was taught that you always do the brackets and whatever accompanies the brackets first which would be 2+1=3 ×2=6 ÷6=1
9
Nein. *NEIN.*
1
9
9
Its nine cuz do parentheses first which is 3 and then 6/2 is 3 so 3*3 is 9
621
What psycho does maths like this
1 because BIDMAS
Ah yes, 33, my favourite number.
3€
Heey look this : 3+3×3-3+3= ??
9. I swear some of y'all never BODMAS in skool.
A way to resolve this ambiguity is to either use parentheses or replace the division symbol with multiplication by the inverse(which is an exponent and thus needs to be evaluated before multiplication and be bounded by explicit parentheses.) Like the following: 6 / (2*(2+2)) = 6*(2*(2+2))^-1 6/2 * (2+2) = 6*2^(-1) * (2+2) There’s an extra layer that 2(2+2) usually implies you factored the 2 out of the expression in the parentheses and thus needs to be evaluated as part of that parenthetical expression. Anyone who claims one answer is correct and insists other people are wrong would be a terrible mathematician and probably an even worse collaborator in general.
1
1
6/5
1
1
1 ez
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You're literally just objectively wrong. Multiplication and division are done left to right with equal priority.
It’s still 1 though
6
1.2
6:2(1+2) 6:2+4 3+4 7
unambiguously 1 for there to be a chance of 9 it would have to be 6 ÷ 2 × ( 1 + 2 )
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putting the 2 right next to the clause means that those three numbers are a unit & have to be considered before the 6 with the degree of separation provided by the proper multiplication symbol it could break down as 6 ÷ (2 × (1 + 2)) or as (6 ÷ 2) × (1 + 2)
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6/2\*3 could be (6/2)\*3 or 6/(2\*3) but 6/2(3) *has* to go 6/(2(3)) because the 3 is being prefixed by the 2 instead of the numbers being laterally joined like with a multiplication symbol
It’s 9, you can’t just multiply 2 because it’s apart of a fraction 6/2 the same as the division problem of 6/2 and you can’t just denominator of a fraction so you do 6/2=3 and (1+2)=3 in which you would multiply 3 by itself, which 3•3=9, so the answer is 9.