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I found a strange question on Internet and I am curious about the right answer,

On facebook people have bee asked a mathematical question and now I don't know what is the right answer since it is hard to tell.

And there is the equation. 6/2(1+2) = ?

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marked as duplicate by MJD, Dominic Michaelis, JSchlather, Cameron Buie, dtldarek Mar 12 '13 at 13:58

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

do you mean 6/(2(1+2)) or (6/2)(1+2) ? the point is that it is ambiguous. the correct answer it to tell them to be more clear –  user66419 Mar 12 '13 at 13:37
@MJD you mean n-plicate ? –  Dominic Michaelis Mar 12 '13 at 13:47
I have another really hard problem: "Is Blahblah blah blablablah?" 100% of the population don't know the correct answer. Are you a genius? Those problems are equivalent. –  Godot Mar 12 '13 at 13:51
Also, I nominate this as the worst post title ever. –  MJD Mar 12 '13 at 15:24

3 Answers 3

Old question, a FB meme, seen also on G+.

I believe the question originated from the fact that if you use different calculators, you get different answers

enter image description here

(Photo credit)

This has to do with a convention on some Casio calculators (it's written in the manual, see page E-30, Order of operations), that juxtaposition (called abbreviated multiplication in the manual) takes precedence over division.

So on a Casio the expression

$$6 / 2 (2 + 1)$$

is parsed as

$$6/(2 \cdot (2 + 1)) = 6/6 = 1$$

But if you type

$$6 / 2 * (2 + 1)$$

instead on a Casio, you will get $9$ as a result, as this is parsed as $$(6/2) \cdot ( 2 + 1 )$$

PS I have now seen the previous post mentioned by @MJD in a comment. So this confirms my suspicion about the origin of the problem, but I do not think any of the answers to the other question mentioned this difference between multiplication and abbreviated multiplication.

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Nice answer and nice picture too :-) +1 –  user1551 Mar 12 '13 at 16:27
@user1551, which reminds me that I had forgotten the photo credit, just fixed. –  Andreas Caranti Mar 12 '13 at 16:32

We see this (usually unintentionally) here with some frequency. $6/2(1+2)$ could be meant as $\frac 6{2(1+2)}=1$ or as $\frac 62(2+1)=9$. Often one can guess from the problem, but sometimes not. The solution is to add parentheses as $6/(2(1+2))$ or $(6/2)(2+1)$, to write $(2+1)6/2$ if that is what you mean, or to typeset in $\LaTeX$ to get properly stacked fractions.

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It's not really hard, just a little bit ambiguous; when taking it completely rigorously, the division and multiplication operations are performed without inner order or precedence from left to right, so $$6/2(1+2)=6/2\cdot3=3\cdot3=9$$

However, when people write $6/2(1+2)$ they often mean $\frac{6}{2(1+2)}$, in which case $\frac{6}{2(1+2)}=\frac{6}{2\cdot3}=\frac{6}{6}=1$

This is a 'trick question' (I assume the writing says that 99% of the people get it wrong), but I'm not sure which way the trick is. If I had to guess I'd say that they expect $9$ and "99% of the people" say $1$.

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