Poll: 6÷2(1+2)

6/2(1+2) = ?

  • 9

    Votes: 516 68.9%
  • 1

    Votes: 233 31.1%

  • Total voters
    749
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Just seen this on Facebook questions.

6÷2(1+2)

1 or 9?

The majority of people have put 9. How can it possibly be 9?
Reading justifications for why it is 9 is infuriating so I was just wondering if any maths experts on here can clarify.

EDIT
There is no right or wrong answer. It's all in the interpretation of the expression which is inherently unclear.
 
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Bidmas is clearly fallible if people are justifying an answer of nine with it.

6÷2(1+2)

6 is ONE term.
2(1+2) is ANOTHER term.


In order to achieve a result of 9 you would need:
6(1+2)÷2

It is entirely possible this problem was introduced to highlight the flaws of the BIDMAS rule.
 
Can anyone doing a PhD or MSc in mathematics or a related degree give an opinion.

I appreciate some people are using order of operations rules to justify various answers however I have an inkling this problem is a special case used to highlights the flaws of the procedure.
 
It's a misunderstanding based on the fact that there is no explicit multiplication sign between the 2 and the (1+2) and therefore people are making the assumption that they should treat them as one term IMO.

Similarly, you could have the equation x / 1 * x and ask it is equal to x^2 or 1.
Applying the order of operations correctly the answer is x^2, but I would imagine lots of people who are saying the answer to your original question is 1 would pick 1 here as well, even though there is nothing in the equation that says I need to calculate 1 * x first.

Thanks for this answer.

Actually in the case of x / 1 * x I would go for x^2.

The issue I have is that 2(1+2) implies you expand out the contents of the bracket first.

Now IF It said 6 / 2 * (1+2) then I would answer 9.

2(1+2) is NOT strictly the same as 2 * (1+2).
 
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Ok for those that think their calculators are giving them 1. Plug in 6/2 * (1+2) (don't forget the multiplication sign) in and report the answer back.

That would be 9.

It's not 6/2*(1+2)

It's 6/2(1+2).

They're not the same.

Bodmas interprets 6/2(1+2) AS 6/2*(1+2)
 
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It is unclear and poorly expressed.

It should be written as one of the following two, and this is also how it is percieved by both sides:

First side for it equalling 9:
(6/2) * (1+3) = 9

and the second for it equalling 1:
6/(2(1+3))

you don't know whether what is contained in the brackets is in the denominator or in the numerator/separate.

Also whether division is higher order than multiplication is risky, they are taught as being the same as any division can be represented by a multiplication and vice versa.

I think this is the best answer I can hope to find, where we can agree that Bodmas takes one of the two possible interpretations.
 
There is no right answer.

If I said to you lot:

A = 6
B = 2(1+2)

What is A ÷ B?

... It is unambiguously equal to 1 as we treat A and B as separate terms.

The argument I failed to comprehend before this thread is that the expression can actually be interpreted in two ways:

(6÷2) * (1+2) which gives an answer of 9 - The same you would get using BODMAS.

(OR)

6÷(2(1+2)) which gives 1 - and IMO makes more sense given practical mathematical application.
 
Like stated above people are confusing the calculation as a fraction in which case 1 would be correct. The lack of brackets around (2(1+2)) to create a single expression means the answer is 9.

2(1+2) implies (2(1)+2(2)) as one term.

Otherwise it would be written as 2 * (1+2).

I just don't see how (2(1+2)) is necessary and I don't think I've ever seen it written in that form.
 
2(1+2)

is meaningless without a * there.

In fact as mentioned, excel, c# and c++ won't let you leave it at just that.

Yes, I agree.

My point is in practical application of maths you usually take:

2(1+2) = (2(1)+2(2))

In the absence of the multiplication symbol you would expand out the brackets. My degree is heavily maths intensive and that is how I would interpret the expression in solving various problems.
 
Would not agree with you.

a / b(c+b) is =/= a / b * (c+b) in a practical sense. It is too open to interpretation.

This is also where you'll get the difference between pure mathematicians and engineers/physicists who use and apply maths.

Could not agree more. This is the key point I have been trying to make.

In the mathematical models I'm working with at the moment failing to read the original equation to yield an answer of 1 would result in an incorrect result.

In a general sense, it is inherently unclear.
 
Step 3: laugh at others who think it is one.

Those with a rigorous academic understanding into Mathematics or other academic subjects involving practical or theoretical application of maths are virtually all agreeing that there expression is inherently unclear and as such an answer of 9 is no better or worse than an answer of 1.

So poking fun at either those who answered 9 or 1 is retarded in itself.
 
Just a message for some of those who are poking fun at others.

There are two solutions, differing in interpretation of the ambiguous expression.

If you can't understand this then refrain from accusing others of lacking intelligence. Any spastic can apply some Kindergarten mathematical operating rule without really having a grasp on the subject. The argument being put fourth by those who are qualified to debate this is that in practical application of mathematics either interpretation may be more appropriate given the context of the problem at hand, although the expression is still irrefutably ambiguous.
 
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