Help me resolve a stupid facebook argument

[TheJim]

6÷2(2+1)

Is this:

a) 1 because 6/2*3 (2*3 resolved first because brackets)
or
b) 9 because 6/2*3 (right to left)
or
c) 3.5 because 6/4+2 (expand brackets)
or
d) all of the above because it's just a horribly written expression

I'm aware that it's badly written, because the author chose to use a division symbol instead of using a numerator and denominator in order to create this ambiguity.

Are they all right? Is one more right than the others? Is there no real right answer because it's been expressed terribly?

Or am I just an idiot? (other than being an idiot for engaging with this nonsense in the first place, of course)

Thanks for indulging this pointlessness!

Jim

 

[Denis]

The way it is shown means 6/2*3 = 3*3 = 9

If shown this way: 6/(2*3), then 6/6 = 1

 

[Dr.Peterson]

6÷2(2+1)

Is this:

a) 1 because 6/2*3 (2*3 resolved first because brackets)
or
b) 9 because 6/2*3 (right to left)
or
c) 3.5 because 6/4+2 (expand brackets)
or
d) all of the above because it's just a horribly written expression

I'm aware that it's badly written, because the author chose to use a division symbol instead of using a numerator and denominator in order to create this ambiguity.

Are they all right? Is one more right than the others? Is there no real right answer because it's been expressed terribly?

Or am I just an idiot? (other than being an idiot for engaging with this nonsense in the first place, of course)

Thanks for indulging this pointlessness!

Jim

Yes, it's pointless. No one should ever write an expression like this, and no one should ever argue about it.

(a) is one way to interpret it, but not for the reason you give; parentheses only force what's inside to be done first. It would be because some textbooks teach that multiplication that is indicated without a symbol is done before other multiplications or divisions. But not everyone teaches that.

(b) is another interpretation, but I hope you meant "left to right". It's what the usual rules imply.

(c) is utterly wrong; in decades of answering this question, I've never seen anyone make this particular claim. If you expand, you get 6÷(4+2), not 6÷4+2, which disregards the order of everything.

So the real issue is that it's ambiguous, and in order to tell what it means, you have to ask its author what rules he goes by.

This has been written about hundreds of times. Here is one I wrote relatively recently.