Facebook's Trickiest Viral Math Problem Explained! [6/2(1+2)]

Our take on this tricky viral Facebook math problem! This video is intended to outline the main reason why people arrive at different answers for a seemingly simple problem. Is it a sign convention issue...or is it cut and dry? Find out our opinion on the matter here!

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[AFMathandEngineering]

This video is intended to outline the main reason why people arrive at different answers for seemingly simple problem, and the one we feel may be considered more correct in a test situation. Do you agree that this question's sign convention can be interpreted two ways, or do you think it's clear that there's one way of solving it? Let us know down below!

[sarahchattha]

When I learned bedmas in grade school, I was taught that D and M both hold the same priority and we just do whatever operation comes first when reading the equation from left to right. Same with A and S so according to that as well, 9 would be correct but when I first looked at this, I immediately thought the answer was 1.

[relikuscreates]

The solution really depends on what the question is actually asking.Each math equality can be interpreted as a sentence and based on that is written out in mathematical notation.If the question is asking to divide 6 by the product of 2 and 1 + 2 then the answer is 1. If the question is asking to divide 6 by 2 and then multiply that by 1 + 2 the answer 9. It all really just depends on what you interpret the notation written down to mean but if the question is formulated as a sentence then no confusion can truly occur. In order to avoid such confusion with notation you simply write down each division as a fraction which makes it obvious as to what is really being asked, as notation like this is rather vague.Otherwise use brackets to clearly state what is being asked.Something like :

( 6 ) / ( 2 * ( 1 + 2 ) ) is not saying the same as ( ( 6 ) / ( 2 ) ) * ( 1 + 2 )

It is important to remember that in math formulas are simply ways of writing down sentences and it is important to express those sentences in a way which can not cause confusion based on the agreed upon rules for writing them down.It's also important to remember that the rules we use are just arbitrarily made up and that somebody else's rules are just as valid as long as they are interpreting the same sentence. As long as they interpret the same sentence they will yield the same result. Here we have one notation with two different sentence interpretations based on which system of rules is used. If you use one system you get one answer, if you use the other system you get another answer.Both answer are equally correct within that system, but do not correspond to the same problem being asked by sentence and therefore cannot be equalized.

In short, both are correct if you change what the problem is asking in sentence based on the system.

If we agree on only one sentence being asked then we can write it down using both notations in a way which will yield the same result.

[ms.guanajaylover]

Im even more confused now and I was good at math.

[guilesivann]

Observe the equation as a fraction.
Ignore for a moment the integer numerator 6 and solve integer denominator (bellow the fraction line) a(b+c) = ab + ac i.e. 2 (1+2) or 2*1 + 2*2 = 2+ 4 = 6 .
So, integer denominator is 6.
Now insert it into the fraction using numerator 6 i.e.  6 /6 = 1

[swethathouta]

The correct answer to this seemingly impossible yet simple problem is 1. If you follow the laws of claculus, algebra and pemdas/bodmas you will arrive at the answer 1. But the most popular response to this problem seems to be 9 and that's due to the fact that people think6÷2(3) is the same as 6÷2*3 . However that's not at all true . 2(3) is ONE SINGLE term and has to be evaluated first. We cannot write it as 6÷2*3=3*3 because that would SEPARATE the term 2(3) which is totally wrong.Let us replace 3 with π. We get 6÷2π. We first evaluate 2π. We don't write it as 6÷2π=6÷2*π=3π do we? People assume 2(3) = 2*3 just to put that multiplication sign. But the correct equation using multiplication sign would be 2(3)=(2*3) so we get

[Renegadereadingsrecovery]

The way I was taught it’s one.
The distributive property is applicable.

6/2(2+1)
6/2(3)
Still a parenthesis here so it isn’t gone yet
6/6
1

Or

6/2(2+1)
6/[2(2+1)]
6/[4 + 2]
6/6
1

[petepalmere]

Yes, we understand why many come to different answers but BEDMAS and PEMDAS are misunderstood and misapplied. If the order of operations starts with resolving the brackets or parentheses first then they must be fully resolved. Just, as in this case, summing the 1+2 doesn't eliminate the brackets. As written at 2:47 you still have the parentheses yet you decide to go onto division when, in fact, you haven't eliminated them. You are viewing the two outside the parens as a standalone item, when, in fact, it is the coefficient/GCF of the group and as such is either a multiplier or a multiplicand of the factors in the group. I will not even get into factored expressions or the properties of real numbers now. Here's what a Ph.D. has to say: "Look at the expression 6÷2(1+2). What does it say in words using the left-to-right convention. Take the number 6 and divide it by the "result" of the number 2 times the "quantity" of the number 1 plus 2. What is implied is 6÷(2(1+2)). The bottom line is you can't perform mathematical operations involving "quantities" until you first resolve the quantities"! The sub-expression 2(1+2) has a real value and if viewed in its non-factored, expanded form is really (2*1+2*2) and in either form, it has a real value of 6. Yes, if the subject expression was written as 6÷2 x 3 it could solve to one as there is no grouping. The 2 in the subject expression which you use as the divider/denominator has a bond with the group and is integral to its inherent value. Though some people call this implied multiplication where a number is juxtaposed to either a variable or in this case a group, it is bonded to the group and cannot be ripped away to be used in another operation regardless of the widely taught interpretation of PEMDAS. Just saying.

[williammarkwick]

The answer is 1. Are you not taught what a number outside a bracket means? Mathematics protocol does not change, a number outside a bracket is there because it has been taken out of the bracket as a common factor, it is part of the bracket. You have changed this problem by separating the 2 from the bracket and this is why you have got 9. And as far as Wolfram goes, if it is programmed the wrong way you will get the wrong answer. I have 3 different Graphics Calculators and all give the answer 1, the mathematically correct answer.

[RostovII]

What do you think of this?
Please note that no matter how you wish to solve the problem, these steps apply, there are no ambiguous steps here!

Transforming this problem into an equation
I'll exchange each value with a variable and assume either of the results 9 or 1, then solve the each equation.
(1o) - assuming the result is 9:
a) exchanging 6 with u we have
u/2(1+2) = 9
1/2(1+2) = 9/u
2(1+2) = u/9
2(1+2)9 = u
6*9 = u, as u = 6 then
54 = 6, contradiction

b) exchanging 2 with u we have
6/u(1+2) = 9
1/u(1+2) = 9/6
u(1+2) = 6/9
u = 6/(3*9), I used parenthesis to avoid this whole confusion, now 3 effectively goes over to the other member and divides the value there; and as u=2
2 = 6/27, contradiction

c) exchanging (1+2) with u we have
6/2u = 9
1/2u = 9/6
2u = 6/9
u = 6/(9*2), as u=(1+2) then
3 = 6/18, contradiction



(2o) - assuming the result is 1:
a) exchanging 6 with u we have
u/2(1+2) = 1
1/2(1+2) = 1/u
2(1+2) = u
2(1+2) = u
6 = u, as u = 6 then
6 = 6, valid proposition

b) exchanging 2 with u we have
6/u(1+2) = 1
1/u(1+2) = 1/6
u(1+2) = 6
u = 6/3, as u=2
2 = 6/3
2 = 2, valid proposition

c) exchanging (1+2) with u we have
6/2u = 1
1/2u = 1/6
2u = 6
u = 6/2, as u=(1+2) then
3 = 6/2
3 = 3, valid proposition

Note that I used only valid math operations, no tricks.

[marcello]

I was taught that if there’s a number outside the brackets 2(1+2) than it’s that number of brackets (1+2) + (1+2)
If it’s 2x(1+2) that’s something different 6/2(1+2) should be 1 and 6/2x(1+2) should be 9

[samiiramirez]

I was taught the distributive property :/ which confuses me because they told me in school since it’s division in the beginning, you can just make it a fraction. 6 over 2(2+1). So you’d distribute on the bottom. 2x2=4 and 2x1=2. 4+2=6. 6 over 6 is one

[LongplayCentral]

This is a question of PEMDAS vs PEJMDAS. Most scientific calculators use PEJMDAS (with the notable exception of TI's, which still use PEMDAS), and will give an answer of 1. I'm given to understand the majority of mathematicians, engineers, and scientists also use PEJMDAS, while only American educators are holdouts for PEMDAS (I guess PEJMDAS would be too confusing for grade schoolers?). Personally (as a scientist) I agree with my peers that the correct answer here is 1, not 9. But I can understand if you disagree, as everyone is taught PEMDAS in 3rd grade.

[david]

6 / 2(1 + 2) =
First expand the brackets 6 / (2 + 4)
Complete the brackets 6 / 6
Answer is 1

[dennishulsman]

incase you wont write it in a fraction, because its not written in a fraction it will be 9 always. Incase written in fraction it could be 9 or 1 depending on how written yes. but in this case its just dividing normally so always will be 9

[Jameswhytho]

Wrong wrong wrong wrong.


6/2(3) is not the same as 6/2*3
You are completing the parenthesis too soon as there are parenthesis there that you don't see. The correct equation is (6/(2(3)))

The algebraic proof as follows:

X/y(z)
Implied multiplication by juxtaposition then donates this as (x/(y(z))) =(6/(2(3))) =1

If it had been written 6/2*(1+2) then this would = ((6/2)*(1*(1+2)))
Or x/y*(u+v)=((x/y)*(1*(u+v))) which would equal 9 only if there was an extra multiplication sign in there, which there is not.

This is the absolute correct answer

[ok-xuti]

The answer is 1.
If the answer is 9 then the equation should be
(6/2)(1+2)
But the original equation shows that the (1+2) is not a separate equation from 6/2. Therefore, it should be multiplied to 2 and not to 6/2.
6/2(1+2)
=6/6
=1
That's my opinion as a student who loves math

[bellmichael]

6/2(1+2)= 6/2(3) = 6/6 = 1 If it was written 6/2 x (1+2)= 6/2 x (3)= 3 x 3= 9 Hint: Change (1+2 or 3) to Y... now it reads 6/ 2Y=? Find the value of 2Y which is 6... now one has 6/6 which equals 1 ...

[sharif]

Alright, Wolfram worshippers, I got a message for you.

Wolfram Alpha is said to be the world's most accurate computer that shows different results for
a/ab and 2/2b.

My message is that you should not use calculators/softwares as a concrete proof for debatable notations because... if the notation is debatable, there is a good possibility that the software suffers from it as well.

[JakeVoorhees]

Nice boys, didn't even know about this. Haha appreciate the help!!