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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Order of operations...
...BEDMAS
Brackets
Exponentials
Divisions
Multiplications
Additions
Subtractions
The answer is 9. NHGlos has given the reason.
Facebook users are not known for the excellency in mathematics.
You've lost me now . . .
I have a six cookies (because I like cookies)
Do you mean biscuits?
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))
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.
Thanks, that helps
Cookies are naturally occurring internet phenomena.
I particularly like choc-chip naturally occurring internet phenomena
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.
Does that mean
mass (weight) = information (cookies transfer both)
Can information be converted into energy (E = IC^2)?
Cookie powered reactors?
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.
Surely it's the first one?
If it was the second one it would be 6/(2(2+1))? And if not...why not?
Surely it's the second one?
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
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!
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).
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
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?
Well
÷
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?
Fractions
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
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!
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
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! :)
Where is the fun in that?
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)
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.
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!)
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.
the question
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?
Yep but...
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?
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.
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?
Extra bracket and reduction of initial fraction
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)