Apparently I fail at the order of operations.

[tsukikage]

Guys, I'm so very lost, and about something that should be sooo simple.

[00:48] 月影: Ano ne, I have this weird question about order of operations
[00:49] 月影: 6÷2(1+2)... That *is* 9, right, not 1?
[00:52] 茜ちゃん: buuuuuh
[00:52] 茜ちゃん: Isn't it 1?
[00:52] 月影: I'm so confuuuuzed
[00:52] 茜ちゃん: Stuff in parentheses is usually first
[00:52] 月影: Like, I know parens come first, but I don't know if that applies to what happens outside the parens
[00:53] 月影: like, is 6÷2(1+2) = 6÷2*(1+2), or 6÷(2(1+2))
[00:53] 茜ちゃん: multiplication when shown by parentheses is usually given a higher priority than other operations, too.
[00:53] 茜ちゃん: 6(n) has the same priority as 6n, I think.
[00:54] 月影: and 6/6(n) would be 1/n, not n?
[00:54] 茜ちゃん: hmmm, don't use the slash there if the previous notation was with a proper division sign
[00:56] 茜ちゃん: 6 ÷ 2(1+2) = 6 ÷ 2n where n = (1+2)
[00:56] 茜ちゃん: so 6 ÷ 2n = 3 ÷ n
[00:56] 茜ちゃん: n = 3, so
[00:57] 茜ちゃん: it ends up being 3 ÷ 3
[00:57] 茜ちゃん: = 1
[00:57] 月影: hmm
[00:57] 月影: yeah
[00:57] 月影: that makese some weird sense
[00:57] 月影: sdfjasdlfkjasdfjlkdj
[00:57] 月影: I DON"T KNOOOOOOOW

[00:54] 月影: Mike, how strong is your order of operations?
[00:54] Mike: ... huh?
[00:54] Mike: ... i ... exercise it daily... yeah
[00:54] Mike: tried to use steroid son it... but
[00:55] 月影: 6÷2(1+2)... That *is* 9, right, not 1?
[00:55] Mike: the parenthesis are done first
[00:56] Mike: so 6/2*3
[00:56] Mike: yes, so 9
[00:56] 月影: okay
[00:56] 月影: for some reason my brain was trying to tell me that the "power of the parens" extended to the implied multiplication as well

So, my imaginary internet friends, WHICH IS IT?!

Comments

[kelglitter.livejournal.com]

Um... if it's written 6÷2(1+2) the answer is 1. When you reduced it to 6/2*3 you screwed it up. You made it into (6÷2)*(1+2), which it is not. You should have simplified it to 6/(2*3) - that was the mistake. That said, it's a really poor way to write a problem - my guess is that there are other things (like, this is an applied math problem) that aren't stated which influence the outcome. Where did you actually find it, and in what context?

[tsukikage85.livejournal.com]

See, I was talking with an ex-math major and he agreed with me that there's no reason that the implied multiplication would be bumped up in priority just because it's directly outside parentheses. He (and I) think 6÷2(1+2) = 6÷2*(1+2)= 9

[kelglitter.livejournal.com]

Technically that could be true, but people use different nomenclature under different assumptions so the context is really the most important question. In my experience getting my economics degree and taking engineering & physics classes later I'd guess that nobody would have notated it like that if they meant 9 to be the answer.

Are you plugging numbers into some kind of formula, or working on a rudimentary math test for some reason?

[tsukikage85.livejournal.com]

It's a question on Facebook. That's literally all the context there is.

[kelglitter.livejournal.com]

It's of note that if this is a simple math question you encountered somewhere, the way to think of it is 6*(1/2)*(1+2). Nobody with any kind of mathematical sense would have written in the division sign as a division sign and not a slash though, and then failed to include the multiplication sign, which is why I'm asking about the larger context and suspicious that the answer is really 1.

[tsukikage85.livejournal.com]

Yeah, maybe you got to the heart of the problem - regardless of what PERMDAS strictly dictates, whoever wrote that used crappy style, perhaps deliberately.