Yes, she votes, as do millions just like her
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Honestly I can't decide what the answer is 1 or 9 or for all I know neither. When I did math I learned to write things such that order of operations was less ambiguous for lack of mistake sake. What I do know is how the hell is 6/6 = 0
P|E|MD|AS
How are you getting to 9?Never mind, I'm an idiot.
Once I figured it out, it seemed obvious - but then again, 1 seemed obvious every time before that.
So I thought it was 1 because I eliminated the parentheses and did the multiplication.
Of course, that's pretty dumb, because once you eliminate the parentheses, you have to consider that '/' and '*' have equal precedence, so they have to be executed in the order that they're written.
So you end up with:
6 / 2 * 3
Which then becomes:
3 * 3 = 9
Is this wrong? That's be awesome. You wouldn't expect such a dumbass as the tweeter to post anything interesting...
It is still somewhat ambiguous, I believe. Many people were taught the way that gives you 1, not 9. Which leads me to agree with the argument that the issue is the equation itself, not which answer you get. It's just a troll statement that doesn't use sensible notation, and is thus useless for everything outside of trolling people. At least it does that exceptionally well, though.
I'm responding to my own comment, since whoever responded to me saying it wasn't ambiguous deleted the comment as I replied.
I've been breaking it down in various ways myself, as well as watching different people explain and talk about it. There's plenty of ambiguity. Mathematicians don't agree.
There are methods that imply 6/(2(1+2)) as how to read that, and that comes up with 1.
Another way of explaining it is the slash often ends up with...
6
───────
2 (2+1)
Which is 6/6, which is 1.
The statement is intentionally confusing, meant to be solved different ways by different people.
I think the best way I've heard it described is that this is a grammar problem, not a math problem.
How could it lead to a 1 though? I thought it was 1 initially, but that was because I made a mistake in the precedence.
EDIT: I see your other comment. But who was 'taught' the first form? And what is that even? Is it that multiplication precedes division?
How does such a simple not-even-an-equation cause so much trouble?
You should be forced to pass a test before voting. Democracy doesn't work because everyone can vote.
Implying that 'democracies' are democratic. They're not.
Small problem: who writes the test?
For sure, and who grades it, as well?
I'm just venting, tbh, but I do think democracy is fatally flawed because everyone is allowed to vote.
Its fatally flawed because anyone is allowed to vote in matters that do not effect them. The fact that voters in a metropolis on one side of country can dictated life for the residents in a farming town on the opposite end without even meeting them is completely retarded.
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
I'll have to decline, for I have once again changed my mind because this equation is intentionally retarded and I keep talking myself around in circles.
The issue is this is not made to be read clearly or unambiguously, and so is worthless.
Indeed. I even went another step and found this unhelpful thing, on the wiki regarding multiplication:
"In algebra, multiplication involving variables is often written as a juxtaposition (e.g., xy for x times y or 5x for five times x), also called implied multiplication. The notation can also be used for quantities that are surrounded by parentheses (e.g., 5(2) or (5)(2) for five times two). This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations."
Then it says "CITATION NEEDED," meaning THEY'RE FIGHTING ABOUT IT THERE TOO.
I'm quitting it before I develop an eye-twitch.
Watch this before you go, though. My favorite video I've seen on the topic. If the conclusions are to be believed, the confusion comes about because specifically North American teachers are retards.
PEMDAS is an oversimplified teaching tool, and not a hard and fast rule. It seemingly gets broken by juxtaposition/implied multiplication, as you mention. NA teachers actually petitioned calculator companies to switch from "PEJMDAS" (J = Juxtaposition, and moved higher in the order of operations), to PEMDAS...because they're obsessed with it. Which leads to different calculators giving different answers. The PEMDAS answers make less sense.
So I think you're correct that the most logical answer is probably "1."
???
Where the heck did she pull "2 + 4" from?
I get what she did, sort of, but that just looks fucked since now the answer is 7?
"6 / 2 + 4" is completely different than "6 / 2(1+2)" and neither one is the same as " 6 / 6". AJGKLJSD.
I hope this is bait, because almost every single statement along the way is incorrect.
She multiplied the 2 on the outside of the parenthetical by each of the digits on the inside, ie 2(1+2) = 21+22=2+4
That was the wrong order of operations, but that's how she got there.
Edit: Or maybe it isn't the wrong order of operations, going by what some other commenters are saying. I like the notion that this is a language problem, not a math problem.
I know what she did, it's just bizarre. Also, it's ironic, since she's compounding the issue with the problem itself; she herself is poorly notating as well, changing the meaning and answer.
Yeah, it is fascinating. Funny thing is, I think she's actually more on the right path than the "correct" answer...she just unfortunately fucks up on really basic things along the way, leading to a completely wrong answer.
This is a grammar problem rather than a math problem and grammatically the form "x(y)" is more useful if it is short hand for "(x * (y))" rather than "x * (y)". I don't think there's any situation where the latter would be more useful.
e: This video https://www.youtube.com/watch?v=lLCDca6dYpA has an alternative interpretation as to why it would be 1. 6/2(1+2) should be (6)/(2(1+2)) because if you wanted the PEMDAS compliant version you'd write 6(1+2)/2 so this shorthand makes sense. She finds many examples in textbooks and lectures that support this usage. One example was mn/rs being used for (n/s)(m/r) because if you wanted ((mn)/r)*s)) you would just mns/r which is much clearer. This isn't math; it's notation; and useful notation wins; PEDMAS is an oversimplification taught to school children. The formalization of this more useful rule is that multiplication by juxtaposition has a higher precedence than division.
I found this odd thing that helps show why this provokes disagreement:
https://www.autodidacts.io/disorder-of-operations/
In this fellow's view, following "always left to right" as an imperative second only to PEMDAS, he would state firmly that the answer to this equation is 9.
However, in his own bullet point 4, he references "Implied Multiplication" (also known as "Multiplication denoted by juxtaposition," even going so far as to cite it 3 times as an academically strong convention and a common standard practice.
Then...he just sort of discards it. For no clear reason. With "Implied Multiplication," the answer is 1. Without it, 9. The only argument he gives against using the academic standard is that "Most decent calculators have no truck for it, and doggedly follow the left-to-right order for division and multiplication."
Then, he...doggedly follows the left-to-right order himself. Bizarre. By using the word "doggedly," he seems to imply the calculator's method is inappropriately rigid. But that's the horse he backs anyway, giving no other reason for discarding implied multiplication.
And here we are! Absolutely nowhere.
That's my conclusion as well.
That equation is just wrong on SO many levels...
This is the correct answer.
6/2(1+2)
6/2(3)
6/6 = 1
OR
6/2(1+2)
6/2+4
6/6 = 1
The first one is in my opinion correct, juxtaposition first.
But your second one is just wrong.
6/2(1+2) is not the same as 6/2+4. And 6/2+4 is not the same as 6/6, in the case of 6/2+4 you would divide first, for 3+4=7, which is completely wrong. 6/2+4 should have been 6/(2+4) if you're doing it that way.
And, although I don't agree with it, I'll make the other argument for completeness too, which is strict adherence to PEMDAS. This is how people are getting the alleged "correct" answer:
6/2(1+2)
6/2(3)
3(3) = 9
This treats juxtaposition as straight multiplication, and moves left to right. This is how many NA teachers teach, but not how most mathematicians, engineers, and the like do things.
That's where the whole issue comes from. The statement is made to be intentionally misleading, and if you use PEMDAS you'll get 9, but PEMDAS is oversimplified, and only almost always holds up. But if you write a confusing statement made specifically to break PEMDAS, you end up with this mess.
Sure. It has been many years since I was familiar with order of operations (I think that's what the PEDMAS refers to, isn't it?). As an English major undergraduate I got a B in college algebra,. which is pretty good considering my background (math retarded). As I'm sure you know, if you don't use math skills you lose them.
What's most interesting is that you start off with what looks like a math problem, and end up with a completely bizarre human history problem. If I've got this right--and I think I do--this is how it goes:
All math-writing dudes, since basically forever, use implied multiplication (multiplication by juxtaposition). They consider it too obvious to mention. Eventually, but not that long ago (within the last 100-150 years) they debate whether they should make a formalized convention that multiplication (explicit, as opposed to implied) takes precedence over division. This debate is left unresolved, yet in that debate implied multiplication is 100%, still too obvious to mention.
In the 1980s, you get the widespread rollout of calculators to students, which I think hits American schools first. These calculators barf when you try to use implied multiplication, insisting on the consistent use of operators. The next generation of calculators, some have fixed this problem (giving priority to implied multiplication over both division and explicit multiplication, which is up to this point, universally considered correct), some still barf, and some "fixed the glitch" by adhering to strict PEMDAS (which is not correct) and hiding the process, and some use the correct PEJMDAS while adding brackets to your equation, thereby notifying you of how they were treating it.
Somewhere in this mess, a conspiracy of North American teachers, frustrated by these conflicting returns, successfully lobby many calculator-making companies to ditch PEJMDAS (the right one) and only adhere to PEMDAS (the wrong one). Going forward, the majority of calculators (or possibly just the ones sold in America) are PEMDAS. To put it plainly, American teachers bullied calculator companies to only give them calculators that abandon thousands of years of standard notational convention. So now, from this time onward, at least the teachers and the calculators are in agreement. They're wrong, but they're in agreement. Eventually Common Core comes along and exacerbates this problem: All Must Agree, Even in Wrongness.
The American students, taught by this weird Cult of PEMDAS, go on to insist on their ideology. 95% of the world rolls along as they always have, with PEJMDAS, but some notable heavies--such as Google Calculator, which obviously has oversized importance due to widespread availability and usage--continue to spread the cult of PEMDAS.
It's fascinating. A tale of innovation, groupthink, authority, conformity, memetic disease, exceptionalism, midwittery, and dogged insistence.
I don't have a high enough understanding to state any of that definitively, but I'd say your mostly over the target.
Seems like, more or less. That's my least/favorite part. Bruh, teachers should not be writing the rules of math. I get PEMDAS is a nice mnemonic, and mostly works. But if it's not completely clear, it's not the best way. But they seem so obsessed by it that they want calculators to use it because it's what they're teaching. That's moronic.
I think mathematics is a complicated enough subject that maybe high school teachers (maybe even including middle school teachers, not sure who was lobbying) shouldn't be (re)writing the rules. Look, you're technically math professionals, in that you get paid for your math. But you don't use math. You're not in the math field, you're in the teaching field. Are they dumb? No, I think math teachers tend to be cooler than the teachers for plenty of other subjects, even. No hate. But they're certainly not at the level of the field where they should be writing the rules for things they don't even understand.
Weird thing, I think it was at the end of that first video I linked, Wolfram Alpha mostly uses PEMDAS...mostly. But in certain cases ends up using something that looks more like PEJMDAS. It all depends on your input; some phrasing involving variables (correctly) solves juxtaposition first.
The whole thing is pretty crazy.
Also, imagine the sheer fucking arrogance to tell a calculator company to change their methodology because it's what they teach.
6/2(1+2)
6/2+4
3 + 4 = 7
Yeah, he dun goofed on that one; did the exact same thing as the woman on Twitter.
BTW 1 isn't the right answer, I just included that comment because it's hilarious.
I mean, 1 is the answer to 6/6, but that's about it.