Just for fun.

Just for fun.

Didn't find your answer?

Not sure if this has been posted yet (sorry if it has), but a maths riddle is doing the rounds and causing a huge debate.

Solve the following equation.

6/2(1+2)=?

Have fun.

Replies (44)

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By mrme89
01st Jul 2015 11:23

Easy...

9

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Stepurhan
By stepurhan
01st Jul 2015 11:26

Agreed

What is the debate?

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By JCresswellTax
01st Jul 2015 11:29

Perhaps

Reading it as 6 divided by 6?

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Universe
By SteveOH
01st Jul 2015 11:30

42

Or is that the answer to a different question?

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By NHGlos
01st Jul 2015 11:32

Order of operations...

...BEDMAS

Brackets
Exponentials
Divisions
Multiplications
Additions
Subtractions

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By Lee11_1989
01st Jul 2015 11:35

9 or 1?

Excel will interpret the formula to be:

6 / 2 x (1+2) = 9

A scientific calculator will interpet differently, as:

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

I was always taught that maths is factual and that there can only be one answer. I've seen about 200 comments on Facebook regarding this, and there is a fairly even split on the answer.

I personally calculated the answer to be 9. Someone else is my office is positive that the answer is 1.

 

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By rorydowney
01st Jul 2015 11:39

Definitely 9

I don't see any issue

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By mrme89
01st Jul 2015 11:41

The answer is 9. NHGlos has given the reason.

 

Facebook users are not known for the excellency in mathematics.

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By andy.partridge
01st Jul 2015 11:43

Yes, easy

1

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By Lee11_1989
01st Jul 2015 11:45

Make it real

Like I said, I answered 9. But I tried to think of a real life situation where this formula might actually occur. I managed to think of a situation where the answer is 1, but not 9.

Let's say I'm on a daytrip with my parents, a friend and his parents. I have a six cookies (because I like cookies) and because I'm a generous fellow, I decide to share them. There are two groups of people, my family and my friends family. In each group, there is one offspring and two parents. The mathematical formula for this would be:

6 cookies / 2 groups of (1 offspring + 2 parents)
OR
6/2(1+2)

Of course, there are six cookies and six people so the answer is 1 each.

Can you think of a real life situation where the answer is 9? I would genuinely like to hear it, as I want to prove my answer of 9 as correct.

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Replying to whitevanman:
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By andy.partridge
01st Jul 2015 11:57

You've lost me now . . .

Lee11_1989 wrote:

I have a six cookies (because I like cookies)

Do you mean biscuits?

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By Lee11_1989
01st Jul 2015 11:47

NHGlos...

I agree with the order of operations. BEDMAS (or BODMAS as I was taught). But is the first '2' treated as part of the brackets or as outside the brackets.

Excel believes that there is hidden multiplication symbol between the '2' and the opening bracket.

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pic
By jndavs
01st Jul 2015 11:55

6/2(1+2) or 6(1+2)/2
By convention the answer is 9.

Otherwise you need to be more explicit: 6/(2(1+2))

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By justsotax
01st Jul 2015 12:05

1 according

to the excel process...but the fact that different people are getting different answers is more of a reflection on the poor way in which the 'sum' is shown....if you wrote it down it would be obvious if the (1+2) was meant to be multiplying the 6/2 or just the 2...but hey where would the 'fun' be in that.

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Portia profile image
By Portia Nina Levin
01st Jul 2015 12:07

@ Andy

Cookies are naturally occurring internet phenomena.

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Replying to WorkingFromHome:
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By andy.partridge
01st Jul 2015 12:20

Thanks, that helps

Portia Nina Levin wrote:

Cookies are naturally occurring internet phenomena.

I particularly like choc-chip naturally occurring internet phenomena

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James Reeves
By James Reeves
01st Jul 2015 12:07

BODMAS confuses people because, like anything that tries to simplify something already fairly simple, it over-complicates it. I was never taught it at school and had never heard of it until my kids were in school. They managed to get some fairly simple sums wrong by following it blindly. Luckily, I was able to catch it in time, teach them properly, and at least one of my kids subsequently went on to earn a maths degree, but it was a close run thing.

The DM does indeed specify Divide and Multipy, but these two operations carry equal weight - it is NOT division first, they are equal precedence and taken from left to right. Many many teachers in schools do not seem to grasp this.

So 6/2(1+2) = 6/2 x 3 = 3 x 3 = 9.

Thanks (2)
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By jndavs
01st Jul 2015 12:52

Does that mean
mass (weight) = information (cookies transfer both)
Can information be converted into energy (E = IC^2)?
Cookie powered reactors?

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By Sperethiel
01st Jul 2015 13:18

I disagree about the problem.  It is how the division bracket is drawn - i.e. is it:

       6 x (2+1)
       2

or:

             6     
        2(2+1)

as the horizontal line is also a bracket for this purpose.

(background - Pure Maths, Cambridge)

S.

 

 

Thanks (3)
Replying to Mallock:
By mwngiol
01st Jul 2015 13:36

Surely it's the first one?

If it was the second one it would be 6/(2(2+1))? And if not...why not?

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Replying to lionofludesch:
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By nogammonsinanundoubledgame
02nd Jul 2015 07:51

Surely it's the second one?

mwngiol wrote:

If it was the second one it would be 6/(2(2+1))? And if not...why not?

If it was the first one it would be (6/2)(2+1)? And if not.. why not?

With kind regards

Clint Westwood

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By Melody
02nd Jul 2015 02:39

I agree with Sperethiel

even though my background is Pure Maths - Oxford!

Sometimes the light and dark blue do agree!

The main problem is that most of us don't know how to type the horizontal line of a fractional formula in a posting, so are quite likely to write both versions the same way when typing on just one line. Although the extra brackets shown by mwngiol would clarify this.

I now feel tempted to combine the two answers with 1 person (me) eating 9 cookies!

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By jndavs
02nd Jul 2015 14:09

Convention
How would you write 'half of x' as opposed to 'one divided by 2x'.

To make it obvious, the '2x' should be enclosed in brackets to ensure prioity in evaluation in the second case. Ergo lack of brackets implies the first case, ie x/2 not 1/(2x).

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Replying to DJKL:
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By Lee11_1989
02nd Jul 2015 09:39

Told you it was fun

I love a good debate! ;)

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By nogammonsinanundoubledgame
02nd Jul 2015 10:32

I put it in Excel

=6/2*(1+2)

Returns 9

Rather than returning an error message on the grounds that the format is ambiguous, it applies a "left to right" priority in respect of operations that otherwise rank equally.  But that of course is just Excel policy.

With kind regards

Clint Westwood

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By Gone Sailing
02nd Jul 2015 11:09

BODMAS
Brackets Off
Definitely 1

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The triggle is a distant cousin of the squonk (pictured)
By Triggle
02nd Jul 2015 11:15

The answer is 10.

I am using base 9 though.

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Replying to accountantccole:
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By jndavs
02nd Jul 2015 14:57

.
Withdrawn

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By mwngiol
02nd Jul 2015 11:18

Only got C at GCSE Maths so no expert!

Would this debate be solved if the old style 'divided by' sign was on keyboards as it is on calculators?  This would negate any confusion between Sperethiel's two possibilities?

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Portia profile image
By Portia Nina Levin
02nd Jul 2015 11:24

÷

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Replying to ComanCo:
By mwngiol
02nd Jul 2015 11:33

Well

Portia Nina Levin wrote:
÷

Well it's not on mine! I'm guessing it's an option hidden away somewhere?

Wouldn't using that for division and only using the 'slash' to denote fractions simplify things? Or is there some mathematical reason which I'm not aware of?

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Replying to bettybobbymeggie:
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By Ben Lauritson
02nd Jul 2015 14:46

Fractions

mwngiol wrote:

Wouldn't using that for division and only using the 'slash' to denote fractions simplify things? Or is there some mathematical reason which I'm not aware of?

Fractions are divisions :) e.g. representing "one half" as 1/2 is the same as saying "one divided by two".

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Replying to lionofludesch:
By mwngiol
02nd Jul 2015 14:59

Yes but

Ben Lauritson wrote:

mwngiol wrote:

Wouldn't using that for division and only using the 'slash' to denote fractions simplify things? Or is there some mathematical reason which I'm not aware of?

Fractions are divisions :) e.g. representing "one half" as 1/2 is the same as saying "one divided by two".

Yes but in the two examples above, having a distinct sign for showing fractions differently when typed in one line would show that the 6/2 is a fraction as in the first example. Whereas a 'divided by' sign would be more indicative of the second example?

Or perhaps more indicative that I'm out of my depth in a discussion about mathematical equations and symbols!

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By Democratus
02nd Jul 2015 14:09

Settled

Wolfram Alpha gets 9 and so do I so that's settled then.

 

http://www.wolframalpha.com/input/?i=6%2F2%281%2B2%29%3D

 

 

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By Ben Lauritson
02nd Jul 2015 15:12

Hmm..

If I'm interpreting your question correctly I would guess that what you're after could be resolved just by adding brackets, i.e. (6/2), if you're wanting the 6/2 to be calculated first before using it elsewhere in the equation?

To be fair I'm not an expert either, despite having an interest in the subject! :)

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Replying to johngroganjga:
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By jndavs
02nd Jul 2015 15:59

Where is the fun in that?

Ben Lauritson wrote:

If I'm interpreting your question correctly I would guess that what you're after could be resolved just by adding brackets, i.e. (6/2), if you're wanting the 6/2 to be calculated first before using it elsewhere in the equation?

To be fair I'm not an expert either, despite having an interest in the subject! :)

The question is 6/2(1+2)=?
Without adding any more brackets.

Mooted answers are 9 (correct in my opinion) or 1
The general convention is to use arithmetic presidence (BEDMAS etc above) and evaluate left to right, so the answer is
6/2(1+2)= 6/2*3 (Brackets first)= 3*3 (left to right) = 9 (or 1001 for the techies)

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By mwngiol
02nd Jul 2015 15:31

Yep

That's what Mr Westwood pointed out above when I tried experimenting with brackets. So I thought perhaps the use of the 'divided by' sign would remove the need for bracketish manipulations.

Totally out of my depth here lol.

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By Alan Davies
02nd Jul 2015 16:04

is it?

Does the missing x between the 2 and the bracket not imply that this is still the same number?

So the you are dividing 6 by 2(1+2) as opposed to multiplying 6/2 by (1+2)?

 

 

(I did think 9 was the answer to start with, the above is due to doubts about my maths knowledge!)

 

 

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By mwngiol
02nd Jul 2015 16:17

Missing x

I was taught that if there was no symbol between a number and the bracket, then convention was that an x was implied.

Assuming that the 'slash' means division then I can't see how the answer can't be 9.

But if, as per Sperethiel's illustration, the 'slash' is a horizontal line with the 6 above it and the rest of the formula below it, then the answer is 1.

Hence my obsession with the 'divided by' sign. Purely to differentiate between a division and a horizontal line.

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Replying to frankie3:
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By Alan Davies
02nd Jul 2015 16:44

the question

mwngiol wrote:

I was taught that if there was no symbol between a number and the bracket, then convention was that an x was implied.

Assuming that the 'slash' means division then I can't see how the answer can't be 9.

But if, as per Sperethiel's illustration, the 'slash' is a horizontal line with the 6 above it and the rest of the formula below it, then the answer is 1.

Hence my obsession with the 'divided by' sign. Purely to differentiate between a division and a horizontal line.

 

The / is a division and the x is implied in both examples - the difference is where the multiplication is applied to the numbers around it. 

Is the final sum 6 divided by 6 or 3 multiplied by 3?

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Replying to Southwestbeancounter:
By mwngiol
02nd Jul 2015 16:51

Yep but...

Alan Davies wrote:

mwngiol wrote:

I was taught that if there was no symbol between a number and the bracket, then convention was that an x was implied.

Assuming that the 'slash' means division then I can't see how the answer can't be 9.

But if, as per Sperethiel's illustration, the 'slash' is a horizontal line with the 6 above it and the rest of the formula below it, then the answer is 1.

Hence my obsession with the 'divided by' sign. Purely to differentiate between a division and a horizontal line.

 

The / is a division and the x is implied in both examples - the difference is where the multiplication is applied to the numbers around it. 

Is the final sum 6 divided by 6 or 3 multiplied by 3?

Yes the / is a division in both. But in one it's a division with the 2, and in the other it's a division with the rest of the equation. That difference is key, seeing that we're not allowed to introduce extra brackets. So the critical question is how do you show the difference between Sperethiel's two examples if you're typing the equation in one line?

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By cheekychappy
02nd Jul 2015 16:55

If you add up all the numbers you get 11. I get the same result if I add them up left to right or right to left.

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By cparker87
02nd Jul 2015 18:26

One

I think the answer is 1 and read it as:

6 / ( 2 (2 + 1) )

I didn't take maths any further than GCSE but I can't see anyone giving an example of where BODMAS/BEDMAS/PEDMAS is incorrect?

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Replying to lionofludesch:
paddle steamer
By DJKL
02nd Jul 2015 19:36

Extra bracket and reduction of initial fraction

cparker87 wrote:

I think the answer is 1 and read it as:

6 / ( 2 (2 + 1) )

I didn't take maths any further than GCSE but I can't see anyone giving an example of where BODMAS/BEDMAS/PEDMAS is incorrect?

Surely that is only the case if the extra bracket is actually added, but it is not  per the original stated question, surely 6/2 is merely an unresolved fraction.

If it were 5/4(2+1)= 15/4  would you believe that was 5/(4(2+1))= 5/12  The brain here does not need to ask itself why is the opening fraction not reduced, so is not misled.

To me the trick to the original question is having a starting fraction that is readily reduced, 6/2 being capable of being reduced to  3, it is this that leads the mind to the  answer as 1, the brain thinks as it has not been reduced  that maybe the 3 is a part of the denominator, however  where that first fraction cannot be reduced the temptation is removed.

I am a 9 sort of person, I am only a 1 if you give me the extra brackets, after all if you led with 2 there would be no argument. In my counter example if you led with 1.25 there would be no discussion., you would not say 1.25 is 5/4 etc. and then calculate to 5/12.

 

p.s( I did Maths 1 at university (a long time ago, and very badly) but I did the one for idiots (Non Maths students)

 

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