Math: 6÷2(1+2) = ?

To be fair to the OP, there IS an old precedence of using '÷' the way he does (signifying an implicit denominator expression to the end of the line, without needing parentheses). It's not been used that way in a looong time, but when you really dig into it, you'll find there was an old German algebra book where it happened:

"The obelus (÷) was first used as a division symbol by Johann Rahn (or Rhonius) (1622-1676) in 1659 in Teutsche Algebra (Cajori vol. 2, page 211)."

[link to jeff560.tripod.com]


So one could perhaps claim the oldest known use for the obelus symbol should have precedence over how it's commonly used today, so that


6÷2(1+2)

implies

6÷[2(1+2)] = 9


Just as the OP likes it. Unfortunately, this is only the oldest known use of the obelus AS DIVISION, as we see further down:

"The division symbol (the obelus) was used by many writers before Rahn as a minus sign."

OK, if we think the oldest known usage should take precedence over more contemporary usage, we must therefore read


6÷2(1+2)

as being equal to

6-2(1+2) = 0


But then, it turns out the obelus was commonly used even before that, to mean A TYPOGRAPHICAL ERROR, so the absolute oldest meaning of


6÷2(1+2)

is

6 <TYPOGRAPHICAL ERROR!> 2(1+2)


Which sums it up pretty nicely, in that the common symbol for division is '/', and putting a '÷' there instead, just to try and be clever, is a bad typographic choice. If we do the right thing, and write


6/2(1+2)


then there's no problem, the result is of course 9, as per standard algebraic rules.

For all the wrong people saying it is 1:

[link to en.wikipedia.org]

Please go read that page, all of it, and learn proper steps of algebra/mathematics. Then try again.

The correct/logical/true answer, is 9.

btw. this question is on facebook:

1: 1,534,946 votes
9: 1,978,015 votes

lol

but i still say it's 1

9

Actually, I have already:

In proper mathematics:
6÷2(1+2)
the bracketed operation MUST be done first
(in a calculator, you would enter those first)
6÷2(3)
then you do multiplication and division, in order as they appear
6÷2(3) can also be written correctly as
6÷2*3 since both operations are forms of multiplication
therefore
3*3
9
Quod Erat Demonstrandum

Please listen to your intellectual superiors. Thank you.

But then you'd be wrong, wouldn't you? ;)

[link to en.wikipedia.org]

You are wrong. The 2 outside is not part of a bracketed operation. Therefore, it is 2*3, which must come after the 6 divided by 2. Therefore, it is 3 * 3, which equals 9. Pure and perfect mathematical logic truth.
9

I agree, but what about the difference between

÷

and

/

?

if ÷ represents a fraction, the answer is 1
if ÷ represents division, the answer is 9

so it all boils down to how ÷ should be interpreted...

Well OP?

And we come full circle. Because among those people for whom mathematics is a language, the given expression would be somewhat of a typographical error, requiring clarification.

9

Please listen to your intellectual superiors.