What is 6÷2(1+2) = ? The Correct Answer Explained


Hey, this is Presh Talwalkar. What is the value of this mathematical expression? This math problem has gone viral and it has received millions of comments on Facebook, Twitter, Youtube, and other social media sites. In this video, I’m going to present the correct answer. The problem is an example of the order of operations. These are commonly refered to as PEMDAS or BODMAS. This refers to evaluating the parentheses/brackets, then the exponents/orders, Then multiplication and division And finally, addition-subtraction. You have two operations of the same precedence, you want to evaluate them from left to right. The first of the problem has no controversy. This expression contains a parenthetical expression which must be evaluated first. 1+2 is inside the parentheses, so we’ll evaluate 1+2 to get 3. Now, the question is what to do next. If you this into google, wolfram alpha, or pretty much any scientific calculator, the thing that’s going to happen next is all of these will interpret the parentheses as an implicit multiplication. So this two parenthesis three will be converted into 2 times 3. Now we continue the order of operations. This expression only contains multiplication and division, These are operators of equal precedence, so we’ll evaluate them from left to right. Starting on the left, we have 6 divided by 2 6 divided by 2 is equal to 3 We then have 3 multiplied by 3 – one final multiplication. And that gets us to the correct answer of 9. This is, without a doubt, the correct answer to this expression as written according to the modern usage of the order of operations. So why did this problem cause so much controversy? Well, there is another answer that you could argue from a historical perspective, so I actually found some documentation that the order of operations did have a slightly different understanding in certain texts in 1917 or before. So the first part of the equation is the same as before: we have a parenthetical expression and this should be evaluated first we have 1 plus 2 and that becomes 3. The debate then centers around this division symbol. So what does it mean that we have 6 divided by 2 parentheses 3? While there were textbooks and there was a lot of usage that if you had this division symbol where you had something on the left divided by something on the right, this was understood to mean you want to divide the entire product on the left by the entire product on the right. So, for example, if a textbook wrote “x divided by 2y” with this division symbol they actually did mean x divided by parentheses 2y. You wanted to take 2y as the entire product and have that as your denominator. So under this historical usage – which is a special exception to the order of operations (and we don’t use it anymore) – you would want to take this product on the right as your divisor. So applying this rule would then lead to the expression 6 over 2 x 3. We will now convert the multiplication in the denominator so that 2 times 3 is equal to 6 and we now have one division which is 6/6 and that’s equal to 1. So, many people argue that one is a correct answer, and there is some historical justification of this because of the way that texts used to use the division symbol. I would suggest this is probably because of some historical artifact about typesetting: it would have been much easier to write the division symbol and have the understanding you want to divide everything on the left by everything on the right; you wouldn’t need to have an expression where you write a numerator over a denominator that would take a lot more vertical space and you also would need to keep putting parentheses everywhere. This would be just something that would be understood. Today we don’t use this practice, because it can be confusing. Instead, we follow the order of operations. If we want to have a fraction, we will put it as an expression like 6 over 6 which is written here. So the correct answer to this problem is 9, but there is some historical justification for the answer 1, but it’s not how we’d interpret the problem today. Did you get to the correct answer of 9? Thanks for watching this video. Please subscribe to my channel. I make videos on math and game theory. You can catch me on my blog “Mind Your Decisions” which you can follow on Facebook, Google+ and Patreon; you can catch me on social media at Presh Talwalkar and if you like this video, please check out my books! Links in description!

Comments 100

  • 10 million views!

  • The modern order of operations is based on the idea of the supremacy of the addition operation (e.g. how computers and calculators resolve the problem). Notice the problem is gradually reduced to a simple addition operation, since 3×3 = 3+3+3 = 9.

  • If you distribute, you get a different answer. So your answer is broken.

  • Wrong answer, I use caculator equal 9

  • You are breaking the commutative LAW which, one would think, takes precedence over this Common Core “all’s you need to do is remember an acronym” drivel. By the commutative law:

    a*b = b*a

    We all agree? Good. Then,

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

    We should still be in agreement; anything that is multiplied MUST obey the law.

    Then there should be no problem obeying the commutative law using this asinine “new” way of solving the equation…right…? Per the strict application of PEMDAS, we should ALWAYS give division precedence [implied by the brackets]. Let’s see:

    6/(1+2)*2 = 6/2*(1+2)
    [6/(1+2)]*2 = [6/2]*(1+2)
    [6/(3)]*2 = [3]*(3)
    [2]*2 = 9
    4 != 9

    WRONG. This method just invalidated itself.

    The “old”, correct way, using your brain and assuming the term left of the division sign is the numerator, and right term the denominator [illustrated with implied square brackets]:

    6/(1+2)*2 = 6/2*(1+2)
    6/[(1+2)*2] = 6/[2*(1+2)]
    6/[(3)*2] = 6/[2*(3)]
    6/[6] = 6/[6]

    1 = 1

    Oh look, it obeys commutative law…

  • When I pulled up the scientific calculator I got 1. Standard I got 9. So the scientific one is bull?

  • I'm in India & if i start solving like this, I would end up getting negative marks in the quantitave section of every exam..

  • I am an Asian. I know Asians do better math ! So I would say the answer is 1.

  • 2(1+2) has to be solved first.. First inside brackets then whatever is attached.. Otherwise don't attach it to brackets.. Why not just write 6/2 x. 3 ..maths is a language and when you say divide something. It has to be divided by what comes after the divide symbol. The old way made sense

  • Calculators get this wrong because they are made and programmed by humans getting it wrong

  • For me the confusion relays on wether 2(3) is exactly the same than 2×3 or not, not on the division.
    2(3) for me it shows that they are grouped together and it cannot be separated, for me 2(1+2) would be (2x(1+2)) not simply 2x(1+2)

  • Finally wht is d answer 1 or 9

  • Why caused so much controversy?

    Bcos everyone skipped school

  • Done in 3 sec

  • Does 6 = 2(1+2). Using PEMDAS, it does. 6 divided by 2(1+2) is therefore equivalent to 6 divided by 6. 6 divided by 6 equals 1. Sorry if you got something different.

  • Yo sombody needs to re educate the math teachers in america cuz i swear they taught us something else if so many people are getting 1. 🤦🤦🤦

  • Division first, no need to complicate stuff….

  • There are two ways to interpret the problem, but labeling one of them as "historical" and implying it went out of use generations ago is false and dishonest. Both methods are indeed current, though one may be favored in parts of the world.

  • Ahhhhhhhhhhhh!!,!!!, math

  • Do we interpret
    6/2(1+2)
    as (6/2)(1+2) = 9 or
    as 6/(2(1+2)) = 1?

    The people who get 9 seem to be more vehement than the people who get 1.

    But what about the commutative law of multiplication? It says
    ab = ba. which means
    2(1+2) = (1+2)(2).

    There is no commutative law of division. Hence, the commutative law of multiplication argues for
    6/(2(1+2)) = 1.

  • I got 1

    Edit: I've been reading the comments and some of these niggas dont know how to use PEMDAS.

    6÷2(1+2)
    6÷2(3)
    6÷6
    1
    Do parenthesis first. Then multiplication and then division

  • Fake news

  • Tom Lehrer said, "The idea is the important thing rather than to get the right answers" so i am answering 3

  • 6÷(2+4) is undoubtedly = 1, and if i want to, I can factor out a 2 from the parentheses and write 6÷2(1+2) and it doesn't change the answer and I don't have to put additional parentheses to make 6÷(2(1+2)) because they are implied (look at any factoring videos on YouTube). If I asked someone to write down the equation for 6 divided by the circumference of a circle, they would write 6 ÷ 2πr. Now who is going to perform (6 ÷ 2) X πr

  • In a historical perspective, since true facts are used for history then the true answer 1 is a fact

  • The distributive property is a property of multiplication where a * (b + c) = a*b + a*c.

    It is unnecessary to solve this problem with the distributive property, and those of you who bring it up to defend your answer have no clue what you're talking about.

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

    This is the correct way to solve the problem, whether in 1917 or today. There is no "historical" way. The method yielding 1 was wrong in 1917, and it's still wrong today.

    People could be wrong back then too, doncha know?

  • Solve for x in the 2 expressions. X÷2(1+2)=1 and X÷2(1+2)=6. Simplify X÷2(3)=1 and X÷2(3)=6 Simplify X÷6=1 and X÷6=6. Multiply by 6 to both sides. X=6 and X=36 That means 1 is right. 36÷2(1÷2)=16.

  • Got the answer one, when using my calculator.

  • So you can solve now the new viral problem: 8 / 2 (2+2) = ?

  • At 2:01, you pronounced nine as like that of dyne .HOWEVER, question
    was wonderful.

  • I put this into wolfram alpha and desmos scientific calculator and the answer I got was 1. I also tried the web 2.0 scientific calculator and the answer was 9. So this is confusing. You said the scientific calculators would solve this problem the right way but it seems that they don't.

    Back in school they taught me to always solve the parentheses first. Means an a(b+c) = ab+ac. And after that calculate from left to right.

  • Who else answered it after looking at the thumbnail a few seconds, yet still clicked to see the answer?

  • It seems as though I was just slightly late to the party

  • Dummy You don't divide before you multiply. You didn't follow the order of operations correctly the answer is 1. Order of operations is not PEDMAS. The parenthesis does not disappear prior to multiplication either. Completely and utterly incorrect.

  • Please excuse my dear aunt Sally…this isn't rocket surgery.

  • It's 1.. Why? Hmmm well the answer is simple.. We can do distributive property wish means we can multplay 2 and 1 +2 and 2.. So it would go like this 6÷ (2×1+2×2) = 6÷(2+4)=6÷6=1… First learn distributive property and then only then make a video like this.. This is the only right way how people should calculate this.. Using math rules.. First u need to get rid of parenthesis and u can do that by using distributive property…

  • Which is right answer?

  • The reason the whole internet and even the New York Times is a-buzz with this seemingly simple math expression is rooted in a catastrophe called PEMDAS or more precisely a part of that mess called the left-to-right rule. Students worldwide are subjected to this ridiculous "anti-mathematical" activity and in my humble opinion it is the primary reason students start to hate math as early as 6th grade.

    The confusion about this expression comes from whether to apply this left-to-right rule or not:

    everyone agrees that parentheses go first:

    If we use the left-to-right rule we divide first and get 4 x 4=16, but if we go with the multiplication first and do not use the left-to-right rule (tempting because of the way it is written close to the parentheses) we get 8/8=1.

    Here's an excerpt about this from my upcoming book "Why Everyone Hates Math":

    "The left-to-right rule is the main reason parents are often humiliatingly forced to give up on helping their child in math around 6th grade. Obviously, most adults have forgotten all about this since 7th grade (the rule disappears in 8th grade), so they are actually incapable of doing their child's 6th grade homework!

    After making up a confusing, if not incorrect, acronym (PEMDAS) for something 3rd, 4th, and 5th graders thought they understood (and probably did until PEMDAS happened and exponents suddenly magically appeared), 6th grade school-math with the left-to-right rule now refuses to follow the one piece of actual solid advice contained in PEMDAS, parentheses.

    The left-to-right rule is necessary because PEMDAS does not tell us whether to multiply or divide first , even though it sure looks like it does! This should be resolved by using parentheses as is always later the case in mathematics. There is no good reason not to. And yet, for some unknown reason, and despite the prominence afforded the concept of parentheses in PEMDAS, 6/7th grade school-math does not use parentheses to clear this up. Instead the left-to-right rule creates a clumsy, anti-mathematical mess and confusion that often lasts a life-time.

    Finally, in 7/8th grade as a grand finale, school-math abruptly and silently abandons the left-to-right rule with absolutely no further explanation, as if it never happened. It becomes a fleeting memory, remaining stuck somewhere in the students' math sub-conscience like a scalpel a doctor forgot in a patient after an operation. Search deeply enough and you too will probably vaguely remember something about reading math left-to-right? What happened to that?”

    What happened was that the left-to-right rule was not math in the first place, and so it had to be abandoned in 8th grade because it contradicts actual mathematical notation.

    Even mathematicians (and now the whole internet) I have spoken with don't recall this absurd made-up school-math rule, and are puzzled by 6th grade homework.
    This really is a great way to start things off and get on the right foot with the students and their natural interest in math."

    The real kicker is that this expression everyone is discussing is even not the worst of it. There are actually expression that defy PEMDAS completely!

    Depending on what exponent you do first you get two different answers. PEMDAS and the left-to-right rule both utterly fail here, and do not tell you what you should do first! This is an actual mistake in school-math not just an ambiguous confusion like the expression above everyone is discussing!

    The poor kids!

    Here is the link to the (almost) full chapter from "Why Everyone Hates Math": http://whyeveryonehatesmath.com/pemdas/

    The (dis-) Order of Operations

  • Again, just a simple algebra test…polynomial fraction 6 over 2(1+2) or 6 over 6. answer is 1.

  • I just do the inside bracket first, then outside bracket, and the last i open the bracket to multiply and the answer is 9.
    Is that wrong?
    I don't watch the video, just leave my comment, thanks.

  • I'm going to explain this in a different way, hopefully making things clearer. The 2 outside of the parentheses is the coefficient of the term inside the parentheses, (1+2). So, if you do the first step of adding together what is inside the parentheses, you get 6÷2(3). Again, the 2 is the coefficient of the 3, which links them together. If you then divide the 6 by 2, you are separating the coefficient 2 from its expression 3. You can't do that. Your second step would be to reunite the coefficient with its expression, giving you 6÷6. Imagine the 3 was a variable instead of a number. 6÷2(X) would give you 6÷2X, which would be the same as 6/2X, not (6/2)X.

  • Multiplication comes before division. 6÷2(3)=6÷6

  • https://www.wolframalpha.com/input/?i=6:2(1%2B2)

    Wolframalpha does not agree.

  • 9

  • “And that gets us to the correct answer of nine”
    Yeah no kidding Sherlock

  • I was always taught the second way you showed. If the parentheses was attached to a number, multiply those two and then go from left to right to finish the order of operations.

  • 9

  • That's easy

  • The confusion doesn't stem from a bunch of rogue teachers forcing everyone to learn early 19th century order of operations. The reason everyone is so confused is they are using the PEMDAS acronym in it's literal order.
    Parentheses
    Exponents
    Multiplication
    *Then Division
    Addition
    *Then subtraction
    They forget that multiplication and division are to be figured left right same with addition and subtraction. which is a common problem when you use an acronym that doesn't include the additional left to right rule.
    It was a wonderful history lesson, but essentially a waste of research and time…. Who am I kidding you probably had the history memorized to begin with.

  • The answer is 1:
    Please Excuse My Dear Aunt Sally (PEMDAS)
    Parenthesis first: 1+2=3
    Then, you cannot separate the multiplication by the distributive property, so: 2(1+2 already done) is 2(1+2) = 2(3) = 6
    Then 6 / 6 = 1 QED

    The distributive property is a mathematical property. You cannot avoid it. If you wanted to specific it another way, that is why you could put parenthesis (notice that the P in Please Excuse My Dear Aunt Sally or PEMDAS is for Parenthesis) around whatever the expression is, such as: (6÷2)(1+2). Also notice that ()() is implied multiplication. Nowhere in the expression does it say to multiply those 2 numbers together (× sign is nowhere to be seen). However, in algebra, the convention of distributing, such as: 2(1+2) = 2(1)+2(2) or 2×1+2×2=2+4=6=2(3) or 2×3=2(1+2). Hence, it all makes sense. Also, even if you were to use a fraction bar instead of the ÷ sign, it would be: 6/2(1+2)=6/(2(1+2))=6/2(3)=6/6=1.
    But anyway you look at it, the answer is 1.
    If you were taking a test in school (and this would be in primary school, there are no variables, hence no algebra), is you answered the question with 9 you would be incorrect since the answer is 1.

  • 3 second.

  • ES 1 https://www.youtube.com/watch?v=zKGiyN3qp68

  • Well in pemdas, multiplication and devision are equivalent but opposite operations so they are solved left to right

  • 6÷2÷(2+1) isn't it curious if you do this one correctly you get 1 but if you do it incorrectly you get 9, 6/1//2/3 = 9 fantastic.

  • 6÷2(1+2) can be expressed as 6÷(2+4), which can also be expressed as :
    1) 6÷1(2+4) or
    2) 6÷4(0.5+1) or
    3) 6÷8(0.25+0.5) or
    4) 6÷16(0.125+0.25) and so on and so forth ………..
    All these will have a common expansion of 6÷(2+4)
    If we insist on PEMDAS/BODMAS way, we'll have 4 different answers, namely
    1) 36
    2) 2.25
    3) 0.5625
    4) 0.140625
    There can only be one common answer of 1,
    if and only if 2(1+2) is treated as a whole.
    Maths statements should be expressed without ambiguity. Using PEMDAS/BODMAS method has made this maths statement ambiguous.
    Therefore, I suggest 2(1+2) be first entirely resolved and then divisible by 6.
    That way, we always get the answer 1, no matter how the statement is expressed.
    My 2 cents ……………………….

  • 'if you input this into a device that will add operational symbols so that the device can understand, which will modify the formula into something new, you get this:'

    I am sorry, wish you would stop teaching/reinforcing this bad math.

    Wish you would instead see it (as it was intended, when written that way) as a word problem.

    IE:

    you have 6 people, who wish to share 2 boxes of 3 apples among them, how many apples would each person get?

    the fact that the 2(2+1) is not written as 2x(2+1) should be a CLEAR sign that the 2(2+1) is a single variable that has to be solved FIRST, before u can move on with the formula. SO it would be 6÷2(3) = 6÷6 = 1.

    Each person would get one apple.

  • You don't just switch it to a multiplication…. You do that in your mind yes… But not actually on the paper

  • Did your teachers teach you to just switch it out??????????

  • It's 9 if anyone says elsewise you need to go back the 7th grade

  • This is correct by a technicality only as if we were to right this stricty algerbraically as

    a ÷ bc in algerbra in common usage, this would always imply a/bc, nobody would interperat that as ac/b. Using the over sign (i.e. / insted of ÷) eliminates all "confusion" but as I said correct by a technicality only.

  • If 2(3) was a single variable it would be writen (2*3). Having a(b) is the same as having a*b.
    This is the reason the answer is 9, pls stop trying to argue with this in the comments this is BASIC math.

  • Use Casio scientific calculator which use advance calculation

  • Just write the division in the form of fraction, never causes confusion anymore.

  • answer is {1,6}

    if you know

  • This maths is very simple..in uk u use Bodmas. In the usa u use pemdas

  • x / 2y != x / 2(y)
    2 is multiplying y in the second part hence you have to follow bodmas and evaluate the division first, however in the first part 2y shouldnt be considered as 2 multiplying y but rather 2 having already multiplied y. the multiplication has already taken place and hence 2y can be considered a new value, z. hence we have x / z, where z = 2 * y to be simplified before carying out the division.

  • So would it be,
    x÷2y = x/(2y) ? ( I use to think in only that way. )
    Or be,
    x÷2y = xy/2 ? (That's really weird to me !)

  • 6 /2(1+2) = 6/2+4 = 3+4= 7 mind =blown

  • m0dern math =9
    silly

  • Watch this Youtube Video to know the correct answer of this puzzle.
    https://youtu.be/HGxQp2Yf6cg

  • 6/2(1+2)
    6/2+4
    3+4
    7

  • 99.99%

  • Yes, amazing this question I ask some people they can not solve this question . What a wonderful viral question

  • Sorry bro but u re wrong, unfortunetelly if 6/(2*(2+1)) than salvation is 1 but if 6/2(1+2) it means that 6/2*(1+2) which is of course equal to 3 SORRY

  • This is so false🤦🏽‍♂️ try this in chemistry and see what happens😂😂

  • I call BS. A number in front of a term (without a multiplication symbol) is called a numerical coefficient and should follow that term in any operation. Why don't you treat this the same way? There is no such thing as "it is interpreted as multiplication and therefore I can apply the BODMAS rules and rip the coefficient away from the term."

    Quoting Google or Wolfram Alpha is in no shape or form proof of any sort of common understanding how things should be interpreted. Their parser is context driven and will give you different results depending on programmer whim. 2/3xy will hold to your answer (interpreted as 2/3 of something because people often forget to put spaces) while 2/xy will not (interpreted as 2 divided by something). 4m/2s will go down the physics branch and become 2 m/s (not 2*m*s). Wolfram Alpha even gives two answers to this particular question….6:2(1+2)=1 and 6/2(1+2)=9

  • How do you just change math and only tel one generation….. this has Mandela effect written all over it

  • how can this be difficult?

  • Is this like a math class for 2nd graders?

  • This is just sad.

  • The answer is 1

  • im confused how is this viral? are westerners that bad at math? is it a meme? someone confirm pls… this question can be solved by anyone around the age of 8.. am i missing a joke or smtg?

  • Pemdas asks for multiplication first
    6/2*3
    Bodmas asks division first
    6/2*3
    By pemdas it is 1
    By bodmas it is 9.

    I don't understand why you'd refer to 1917. Weird

  • There are two correct answers! 9 and 1! Like this as 8÷2 (2+2)

  • 6÷2 (1+2)
    6÷2 (3)
    3×3
    9
    But: 6÷2 (3) 6÷2×3= 6÷6=1

  • No its wrong, let me TRY to explain why.
    So lets say 6÷2(1+2)= does indeed equal to 9 but if you try to check it by changing one of the numbers by x
    For example: 6÷2(x+2)=9 then x equals to -1,66666 a number that is not given in the problem
    But when its 6÷2(x+2)=1 then x equals to 1.
    Or am i wrong?

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