# What is 6÷2(1+2)?

#1
30 December, 2016 - 13:06

#### What is 6÷2(1+2)?

What is the answer to the following math problem?

\( 6\div2(1+2)= \)

Give it a try before scrolling down for the discussion. :)

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This video claims to have the correct answer

The video concludes that the correct answer is 9, but many comments on the video still argue that the answer is 1,

More info here: What Is the Answer to That Stupid Math Problem on Facebook?

What do you think? 9 or 1? :)

The problem is that you're not supposed to use the ÷ sign in maths, and that "2(1+2)" is also ambiguous and not the right way to put it. If it was written properly, like for example

___6___

2⋅(1+2)

... then there wouldn't be any confusion :)

Most calculators will still give 9 if written that way:

I can only get Wolfram Alpha to give me what would appear to be the correct answer if I enter \( \frac{6}{2 \cdot (1+2)} \) in LaTeX format:

https://www.wolframalpha.com/input/?i=%5Cfrac%7B6%7D%7B2+%5Ccdot+(1%2B2)%7D

Is \( 6/2 \cdot (1+2) \) different from \( \frac{6}{2 \cdot (1+2)} \)? A calculator will answer 9 for the former and 1 for the latter.

Bear with me if I fail to make any sense here - generally speaking, I don't express myself very clearly when I'm complaining about other people not expressing themselves clearly...

What I was trying to say is that you're supposed to write things like that in such a way that it's clear which parts of the equation you're dividing the 6 by. If everything's under the line, then the answer's 1; if only the first 2 is under the line, the answer's 9. But if you write it like it's written up there, you can basically read it however you want. And maths is meant to be always written in a way that doesn't leave any room for ambiguity...

I blame computers, incidentally. Because it's hard to write mathematical formulas with a standard keyboard, this whole problem has sprung into existence. I think we need to scrap the whole thing and build a new internet that works with moveable type.

I guess that the solution would be to write things with extra brackets like \( 6/(2(1+2)) \). That seems to work correctly.

A bit more reading suggests that some calculators interpret a slash as a division sign and others as a fraction line.

Wolfram Alpha says:

Does that mean that they are using the pre 1917 rule that is mentioned in the video above? Shouldn't everything to the right of the slash be treated as a group?

Wolfram Alpha also suggests removing the ambiguity:

This video suggests at around 2:29 that it's just bad notation.

There are also a few answers on Quora:

https://www.quora.com/What-does-6%C3%B72-1+2-equal

And another opinion that it is ambiguous:

And another video that has a few more ambiguities, like 8-2+1 and 6/3/3.

The correct answer is here: http://www.flyingcoloursmaths.co.uk/new-years-resolution-genius-sic/