Yes, she votes, as do millions just like her
(media.scored.co)
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To the equation itself, and at the risk of starting controversy, I think it's somewhat ambiguous. I've seen even mathematicians debate it, and I've seen a good way of describing it is that this is a language problem, not a math problem. It's intentionally written in a way that's somewhat open to interpretation. It's pretty much disingenuous from the start, since it's not written to be legible. It's a troll, and not good math. There are arguments to be made for either order, and they produce different outcomes.
This could reasonably be interpreted as 6/(2*(1+2)), and that is in fact how a ton of people were taught. It could also be interpreted as the "correct" version of 6/2*(1+2). Which version you'd use also changes if you substitute variables in place of an integer. It's just unclear, and that's why it confuses people. There are dumb people who get everything wrong, like this person (if she's not trolling), but I don't think everyone who gets this "wrong" is stupid. The whole thing is designed to output two different answers based on slight differences in methodology.
I find myself agreeing with the argument that the issue is with the statement itself, not which particular answer you output.
EDIT: For those interested, below are my favorite videos on the issue.
Also, "6/2(2+1)=1" master race!
The Problem with PEMDAS: Why Calculators Disagree
How School Made You Worse at Math
The Order of Operations is Wrong
How? There's no extra parenthesis in the original equation, which would change the final answer.
BTW here's the original image since the guy who tweeted it deleted it: https://i.ytimg.com/vi/URcUvFIUIhQ/maxresdefault.jpg
You could argue that they should've included the multiplication symbol, but that's still perfectly valid math syntax.
I could just be wrong. In fact I think I am. Although, again, I've seen mathematicians argue for that answer as well. So, although I think I'm wrong, and have now confused myself, I do still think the best answer is just that this is an intentionally confusing statement made to troll people.
I think where some of the confusion for people is coming from is distribution, too. Because if it was, for example, 6/2(x+2), a lot of people would end up with 6/2x+4, right? 6/2x+4 is actually a completely different answer to either the 1 or 9 method. I believe that's actually in line with the "7" method the person in the picture bungled. But I think here you'd actually want to first solve outside the parentheses, so you'd actually end up with 3(x+2) = 3x+6, which would be the correct "9" answer.
Regardless, it is a very messy statement. But I think I have now talked myself back around to there being one correct answer, and that answer being 9...mostly. But it's still all fucked.
TL;DR: Who the heck knows, this shit is intentionally confusing.
No one's gonna cast judgement for getting it wrong so long as you realized where you screwed up because mistakes happen and the lack of multiplication symbol can throw people off.
I just hope we can all agree that anyone who arrived at 6 / 6 = 0 should not be allowed to vote lol.
Yup, that is certainly incorrect.
I'm now doubting myself on the main question, again, though.
To my example of 6/2(x+2), there's also still an argument to be made for reading it as 6/(2(x+2)), which is back to the "1" answer. In written form like that, "/" often denotes that it's treated as the preceding divided by the solution to the multiplication/division that comes after.
This video someone else linked goes into that pretty well:
https://www.youtube.com/watch?v=lLCDca6dYpA
I think I have to switch my answer back to "this question intentionally sucks, and that in itself is the answer." The "actual" mathematical answer doesn't really matter, since even math experts won't agree, despite the seeming simplicity. I was almost convinced of "9," but I'm back to "1" or "9" having strong arguments.
This is why it's a troll. Apparently somewhere along the way--possibly a generational change or a widespread math-teaching policy change--what constitutes "resolving the parenthetical" involves.
I'm going to guess I'm older than you, because that is how this usually goes. To me, resolving the parenthetical (which is PEMDAS priority numero uno) means resolving that chunk together, which includes the 2 stuck to the outside of the parenthesis. That "clause" becomes "2 * 1 + 2 * 2." PEMDAS again, and that portion becomes "2 + 4." Solve, "=6."
YM obviously MV, but I find it very odd to not treat the parenthetical as a whole clause, in the absence of an operator between the 2 and the parenthesis.
Now, I'm no slouch. SAT/GMAT scores with math in the top 1%, back in the day, and having tutored statistics at the graduate level. So I don't think this is me remembering it wrong. Somehow at one point I managed to not get these questions wrong on standardized testing, relying on this method.
My best guess is some time between scenes, what was considered SOP, or at least was taught by primary school math teachers, changed. Maybe it wasn't even a universal change, leaving some people to know it one way, and some people to know it another. What you're left with is a "Gif/Jif" fight where people are largely just so used to their certainty, that the other guy's usage causes them frustration and discomfort.
I mean, any explanation of PEMDAS is clear about the parentheses
https://pemdas.info/
And the the 2 outside the parenthesis signifies to multiply with the result of the parenthesis, so there should be no debate about that.
LOL, we're using different definitions of "clear," I think. It twice says that Parentheses come first, but then declines to show an example, or to address the conundrum that is the equation at the heart of this forum.
Yes. 2(1+2) is read either as "1+2, * 2, which gets you 6, or "2 * 1 + 2 * 2," which is also 6. That's not where we're stuck. We're stuck at the "6 / 2(" beforehand. Some people's (and my) view is that even though there's a division sign between 6 and 2, which would make that a priority over addition and subtraction, that the 2 is stuck to the parenthetical without an operation between makes the 2( part of the parenthetical equation that must be resolved before the "6 / " can be addressed. "Six divided by the product of 2 times the sum of one plus two." Is how I read it.
Kiernan called this a matter of language, and I concur (and mathematics is symbolic language). It is clear to me that 2(1+2) is a symbolic chunk, a "clause" that constitutes a parenthetical. The more modern view, which I think is more unclear in intent (thus making a poor linguistic choice) says that 2( is irrelevant, the parenthetical is only what is contained inside the parentheses, concluding that 6 / 2 is a "clause" and "(1 + 2)" is another.
Doesn't make sense to me, as it introduces this ambiguity, that could easily have been avoided by presenting the equation as: 6 / 2 * (1 + 2). "Six divided by two, times the sum of one plus two." Bada bing, bada boom. The modern view considers this clarification extraneous and unnecessary. I think the resulting confusion and agitation demonstrate that it's not.
I've seen people claim pre-1917 methods would give you the "1" answer, but it - assuming we're not all crazy - went on well past that. Pretty sure I was also taught what you're talking about and, and I think I was like top 3% in SAT mathematics too, although it's been ages. No graduate level stuff, but I'd say I'm decent (if now rusty) at math concepts.
To be fair, I'm not sure there were these kind of weird questions; it's just an odd layout, a trick.
I'm thinking something like that too. That said, I do think "9" is largely correct here, but I absolutely see the other angle too, and think it's just a bizarre equation anyway, and that's the real issue.
I think I can best describe the split as what I came up with responding to user20461. The two ways of reading it are:
A)"Six divided by the product of 2 times the sum of one plus two."
B)"Six divided by two, times the sum of one plus two."
Which of these does "6 / 2(1+2)" really say? B), what seems to be the most common modern view, invents a comma not indicated by the symbology. A) doesn't require it to be understood clearly and simply. I tie my horse to A) for clarity's sake.
WELL THEN MOTHERFUCKING PISTOLS AT DAWN SIR