Sunday, 1 May 2011

6/2(1+2) = 1 or 9 ?

Recently, I found that there are a lot of people argue about this mathematics calculation.

6/2(1+2) = ??

Is it equal to 1 or 9?

The people, who argue the answer is 1, calculate this question in this way.

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

On the other hand, those who argue the answer is 9 calculate this question in this way.

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

The argument happen because of the second step, whether should we do the division first or multiple fist.

Actually the scenarios maybe two.


If it's scenario 1, then the answer should be 1.
And if it's scenario 2, then the answer should be 9.

I seriously support that it should be scenario 1.

If it's scenario 2, it suppose written as (6/2)(1+2).
A bracket should be put on 6/2.

Just like 2/3^2.

You may say that it should be

2/3^2
= 2/6
= 1/3

or

2/3^2
= 0.666666666 ^ 2
= 4/9

But......

If you it's the second case, we write it as below, correct?

We put a bracket there.

So, it's the same with 6/2(1+2) case.
If it's the scenario 2, we should write it as (6/2) (1+2).

So, for this question, 6/2(1+2), I still on the side with the answer of 1.

34 comments:

  1. LOL the answer is definately 1

    6/2(1+2) means

    6/ [2(1+2)] where u calculate the denonimator first

    unless the question is [6/2](1+2) then the answer is 9

    haha

    ReplyDelete
    Replies
    1. 6 / 2 ( 1 + 2 )
      6 / 2 * 3
      3 * 3 = 9

      On the other hand
      6 / 2 ( 1 + 2 )
      6 / 2 * 3 <- why are we multiplying first?
      6 / 6 = 1

      BIDMAS, people, BIDMAS

      Delete
    2. Also why do you put square bracket on 2(1+2)
      Just write it as it is.
      If your method is correct you wouldn't have to add anything extra.

      Delete
  2. 嗨学弟,this question is sharing fast at FB leh...

    ReplyDelete
  3. lolx.. so funny la.. like that also can.. XD
    hey.. is been a while since dropping msg here.. XD
    how are you..?? =)

    ReplyDelete
  4. Wa.. i cannot think of maths at this hour! :D
    Long time no visit.. hope all is well :)

    ReplyDelete
  5. from what i understand, all this symbols(+,-,*,/,(),etc) have certain priority. And we always interpret the symbols of the same priority from left to right. So, I am more agree with your eqn 2. :)

    my humble opinion as a mathematics student.

    ReplyDelete
  6. Please solve using the order of PEMDAS. International method of solving. The way you trying to prove the use of bracket for 2/3^2 is misleading as it involves exponential. It is different from multiplication.

    ReplyDelete
  7. This comment has been removed by the author.

    ReplyDelete
  8. lol i just checked it out now...i got 1 when i first calculated it...

    ReplyDelete
  9. ACTUALLY YOU WILL USE PEMDAS ON THIS ONE. I LOVE PEMDAS SO I STUDY IT UNTIL NOW.

    So...

    6/2(1+2)
    So you will solve the numbers inside the parenthesis...

    6/2(3)

    So here you will apply the pemdas..

    6 / 2 x 3

    3 x 3

    9 :)

    ReplyDelete
    Replies
    1. Now you're just using PEDMAS instead of PEMDAS ...

      Delete
  10. There isn't any variable involved so communicative property is unnecessary. Therefore, you are wrong for even suggesting the scenario where the result is 1. This is basic math and all that requires is simple order of operation. The answer, as anyone who passed elementary in America said, is 9.

    ReplyDelete
  11. I learned from my elementary days that we should perform operations inside parenthesis first so just like Anonymous above, I think no special property is needed. Then simply perform the operation using MDAS, thus multiplication then division after. I think the answer is 1. But whoever made that very simple mathematical problem should have made it clearer by using appropriate symbol, signs just like how you presented it. ☺

    Have a great week ahead!

    ReplyDelete
  12. You should non have written this. The correct answer is 9!!!!

    http://en.wikipedia.org/wiki/Order_of_operations#The_standard_order_of_operations

    Multiplications and divisions have the same priority and they must have been resolved from left to right.

    ReplyDelete
  13. "If you it's the second case, we write it as below, correct?"

    Answer : 2/3^2 not egual at 2/6 but at 2/9 (3^2 = 3*3 = 9).
    Besides PEMDAS --> Exponential are more important than division. So, whithout brackets, exponential first. It's the rule.
    Epic fail ?!

    Try in any calculator 6/2*3. The only answer is 9. With every calculator. Because 6/2*3 = (6/2)*3 and not egual at 6/(2*3), consequence of rules of PEMDAS.

    you said "If it's scenario 2, it suppose written as (6/2)(1+2).
    A bracket should be put on 6/2.".

    Just a rule (PEMDAS consequence yet), when sign are egual, priority is for the first which appear.

    So, to change the order, use brackets. Then, if you want 2(2+1) at denominator you must write [2(2+1)].

    At the end 6/2(2+1) =/= 6/[2(2+1)].

    ReplyDelete
  14. you can't rise (2+1) like this..you need to separate the fraction 6/2*1/(2+1)

    ReplyDelete
  15. How the hell did you manage in school with such a twisted way of logic?

    ReplyDelete
  16. For me 1 Forever I trust in my knownledge, LoL

    ReplyDelete
  17. Dude, you even dont know how to square it... and u think u know math...
    2/3^2
    = 2/6
    = 1/3

    --> 2/9

    Method where you get 1 is mathematical invalid, operations are LEFT TO RIGHT. On other hand, that operation IS used in computer programing, i know it, and i use it, but what i know about it, IT IS MATHEMATICAL WRONG, BUT SAVES SPACE AND RESOURCES, you must place extra notes when you use it in your product.

    ReplyDelete
  18. It seems to be simple. Lets try it:
    a/b*c
    its just simplification of the problem. 6/2*(1+2), and (1+2) is our c.
    lets take out the division(write this down on paper, the value in bracket is 1 over b):
    a*[1/b]*c
    so, from that we can easily go to
    a*c*[1/b]
    which will give us
    [a*c*1]/b
    and this is
    [6 * (1+2)*1]
    ----------------
    2
    which is
    18
    ----
    2

    which is 9.

    ReplyDelete
  19. your theory on 2/3^2 just proves that you're a dumb fuck.

    ReplyDelete
  20. Here are some undeniable facts:

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

    6 / 6 = 1.

    Now assuming PEDMAS is correct, we have: 6 / 6 which is also 6 / (1*2)*3 or

    6 / 3*(1*2).

    Now 6 / (1*2)*3 = 9 and 6 / 3*(1*2) = 4.

    PEDMAS convinces us that 6 does not equal to either (1*2)*3 or 3*(1*3) and that 6 / 6 has at least two answers: 4 or 9. The veracity of PEDMAS also tells us that 6 / 6 does not equal 1.

    ReplyDelete
  21. the problem on facebook isn't written as 6/2(1+2) it is written as 6 division symbol 2(1+2) which means 6 Over 2(1+2) You solve the numerator first which is six, denominator next which is 2(1+2)=2(3)=6. Using Numerator over denominator we get 6/6=1

    Even Pedmas gets 1 6/2(1+2)=6/2(3) to get rid of the parenthesis before we can continue we get 6/6 which equals 1. Left to right is for reading not math...

    School teachers, college kids, and laymen get 9
    professionals, engineers, astronomers, chemists, Math Professors get 1

    Which shows you the sad state of American education today.

    ReplyDelete
    Replies
    1. First of all, 6/2 is the same as 6 division symbol 2... See notation for division at the site below:
      http://faculty.wiu.edu/JROlsen/wiu/MathFundamentals/fractions/FractionReview.pdf

      Since there are not parenthesis around what you are calling the denominator, 2(1+2), the 2 and (1+2) should be looked at as separate terms.
      In fact, your rule of numerator over denominator is a no no in this case because it changes order of operations!!!
      You do not need to get rid of the parenthesis because you are not dealing with any variables... 2(3) is the same as 2*3.
      PEMDAS should be used to solve the problem from there. The comment below explains this well.

      Does that make sense genius?

      Delete
    2. I'm a professional engineer. The answer is 9.

      Delete
  22. http://www.mathsisfun.com/operation-order-pemdas.html explains order of operations well!

    Please Excuse My Dear Aunt Sally is an awesome acronym but a little misleading in this case... Here is how we should really think about it.

    P
    Parentheses first
    E
    Exponents (ie Powers and Square Roots, etc.)
    MD
    Multiplication and Division (left-to-right)
    AS
    Addition and Subtraction (left-to-right)

    Since Multiplication and Division are of equal ranking, we do that part of the problem from left to right, resulting in the answer of 9 :)

    ReplyDelete
  23. Order of operations is fine. It is the terms that people can't grasp:

    People are incorrectly separating the 2 from the parentheses. It is a term of the 2 numbers inside it.
    Now, think of the Identity Law: a = 1a = 1(a)
    Ask what is a ÷ a = ?? Ans: 1
    now Identity law says any variable that has no coefficient actually has a 1, whether it is written or not. So,
    a ÷ 1a = 1 ALWAYS. It is NOT a ÷ 1 * a = a² That is ridiculous.
    This proves that 1a = (1a) and and (1 * a) != 1 * a.
    a ÷ 2a ? Ans: 1/2
    6 ÷ 2a ? Ans: 3/a
    let a = 2+1 for All of The Above.
    6 ÷ 2(2+1) ? Ans: 1 Proven with the laws of math.
    6 ÷ (2+1)2 = 1

    (6 ÷ 2)*(2+1) = 9
    6(2+1) ÷ 2 = 9

    Here is an algebra Lesson:
    http://cstl.syr.edu/fipse/Algebra/Unit2/parenth.htm

    ReplyDelete
  24. The original poster is ALSO right on the fact that ALL FRACTIONS that use a '/' instead of a horiztonal line, when used as a coefficient, REQUIRE PARENTHESES. Anyone who has researched this 'equation', has probably opened a book or 2. This is where you see all the fractions with '/' use ( ). Google an algebra or calculus PDF, and download to see for yourself. If the problem is to be done (6/2)(2+1) = 9, that is how is MUST be written. Even google changes the original equation after a user inputs it. There are other arguements that can be made along with this one, and the previous one that I posted about useing the Identity Law to show how the terms are laid out.
    Therefore, it becomes:

    6 ÷ 2(2+1) = 6 ÷ [2(2) + 2(1)] = 6 ÷ (4 + 2) = 1

    Since the (6/2) is not in ( ), the 2 beside the ( ) means it is a factor of the inside terms (it was factored out), and now the reverse must happen: Distributive Property.

    ReplyDelete
  25. Excel, Google and wolfram alpha say it's 9 ;-)

    ReplyDelete
  26. its clear google isn't working the same problem. it even shows you that it has rewritten the problem. (6/2)*(2+1) this isn't what written is it?

    ReplyDelete