Comments
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@Invisigoth, Currently a PhD candidate for electrical engineering myself, and I couldn't agree more. Its ambiguously written, and a shame that associativity isn't better emphasized in grade school.
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@Invisigoth, Schrodinger's equation #2
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@Invisigoth, Correct me if I'm wrong, but the confusion stems primary from the presence of the division symbol in an equation that also requires implicit multiplication, right?
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@Myredhulk, The division and multiplication with no defining parentheses causes the confusion. Dr. Oliver Knill from Harvard has a great comprehensive study/analysis on the topic if you want more. I don't think I'm allowed to give links in the comments, but it shouldn't be difficult to locate.
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@Berzerker, from what i always understood it was always parenthesis, exponents, then left to right multiplication and division, then left to right addition and subtraction. Or its just been so long that i just dont remember how to do meth.
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@MMSieBreeze, Yes, it is taught this way in grade school for some* folks. Doesn't mean it's correct. I encourage you to check out Dr. Oliver Knill's analysis on the topic, it's very thorough. For my take, from your perspective you would get 9, I on the other hand lean towards 1, as do most graduates. Many expressions in scientific documents and journals will give "multiplication by juxtaposition" higher priority than "division". But again this is an assumption, doesn't mean it's necessarily correct or not ambiguous. However, literature I've encountered, when stating an expression in this manner, will unambiguously show how the fraction really looks before short-handing it like that. Take the time constant for resistive capacitive circuits. If written: 1 --- RC I would see in plain text, written as 1/RC, where the multiplication by juxtaposition takes precedence over the division. It really should be 1/(RC) to ensure no confusion, though with the fraction present, it clears it up.
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@MMSieBreeze, I'm not sure where in time multiplication by juxtaposition took precedence over division, but it might've been a cultural thing, or maybe there's some utility in thinking this way. In other words, anecdotally, most scientists and engineers will follow something like PEMJDAS instead of the typical PEDMAS most public school systems seem to use, perhaps it's easier to teach children this way, as they already understand reading left to right, so it's a simple extension. Doesn't mean either is right, because obviously there's no consensus. So best to be clear with parentheses when you can.
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No we did this already
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@orion55, how many times do we have to teach you this lesson old man
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Its 9
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@Fencingfiend93, Great. Now I have an obligation to reply that it is 1.
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@Fencingfiend93, People who still think its 1 “NEIN NEIN NEIN NEIN NEIN NEIN!”
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@Xandie, it IS 1
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@Gattsu, hey fücking Gattsu, go back to fücking school ya fük. You too JiggleMyPuffs and ThirdNipple, don't be mad 10 year Olds are better at math
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@Fencingfiend93, distributive property
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@BigJohnson86, Math was my worst subject but I’m pretty sure it was 1. Whats distributive property?
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@Uncut Bandito, ab + ac =a(b+c) Distribute the number outside the parenthesis. Then perform order of operations.
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@twopotatoes, "oh no, someone disagreed with me on a meme app! I better call them out so everyone knows who these slanderous people are!" You're the 10 year old
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@JiggleMyPuffs, glad I could elicit a reaction from you, that was my only goal, I'll keep doing it until your dvs are worth it *edit: I've been having an unusually shítty 3 days so I genuinely apologize if I've been taking it out on you, things just can't seem to get darker and they do edit again, fvck off downvoters @UncutBandito, way to jump on the downvote wagon over a week later, you're a real trailblazer
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I recently tried to nail down where, culturally, we break down on this seemingly arbitrarily simple question by asking around my laughably, embarrassingly small social group. Being nearly 30 and from the west coast USA, I believe it's unambiguously 9 - the order of operations I was taught is best shown as P-E-MD-AS, where multiplication and division share the same importance in the hierarchy and are tackled by simply sweeping left-to-right, then the same happens to addition and subtraction. There's a pocket of people, all of whom are between 22 and 25, and whom were educated in the central USA and the rust belt, who get 1, as they were specifically taught an OoO that gave division a lower priority than multiplication. Interestingly, the youngest individual I was able to ask gets 9 as well, who, being 12, learned under Common Core. edit for clarity
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@Needless Contrarian, I'm actually from the Rust Belt and I get one, explicitly because I prioritize multiplication over division, not the other way round
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@Needless Contrarian, I feel like the confusion around this problem isn’t around PEMDAS, it’s around factoring. The equation 6/(2+4)=6/2(1+2) the 2 is part of the parentheses it has just been factored out. If you don’t believe me just set the 1=x No one would argue that 6/(2x+4)=6/2(x+2) the problem creators just added an extra step in there to confuse people.
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@Sven and Otar, very right, I misspoke. Apologies for that - though that does somewhat reinforce the idea that there's a geographic through line.
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@Needless Contrarian, to be fair, I first learned PEMDAS from my dad who was a bio and calc double major from Colorado, so I think while there may be a general geographic trend, it may not be explicitly definite
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@Sven and Otar, the only definite thing in this world is the lack of clear definition. The question has simply engaged my internet-brand autism.
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@Needless Contrarian, I grew up in the Pacific Northwest, and I got 1. I always have given multiplication a higher priority than division. As someone else pointed out, it’s wrote weird
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Guys don't fall for i- DAMMIT I'm too late
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6 ÷ 2(1+2) 6 ÷ 2(3) 6 ÷ 2 x 3 3 x 3 = 9
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Parenthesis, then multiplication, then division, so actually 1
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@Zincarlo, 6 / (2+4) = 6 / 2(1+2) The 2 is just factored out but is still part of the parentheses
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@Zincarlo, 6 ÷ 2(1 + 2) 6 ÷ 2(3) 6 ÷ 6 1
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@Sven and Otar, Order of operations has multiplication and division simultaneously, not separate
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@dshira, no, it's in that specific order explicitly for the purpose of correct ordering and to ensure mistakes in professions where errors in math which can result in critical failures do not occur. For example, in my medical math courses I've had to take as a nursing student I've been told multiple times by my prof that this is how we order things to ensure no med errors occur. If this problem were regarding a dosage for a med for a given patient (obviously not the case), the difference of 8 between 1 and 9 is extremely drastic and could easily result in patient death. By ensuring everyone follows the exact same procedure of multiplication before division, we can help prevent med errors which result in injury or death of patients
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@Sven and Otar, The six divided by two should be written as a fraction. This can, and should, be read as six halves times three, as 6/2 x 3, which would be 9. Despite my assertion, which I will certainly not hold as a pure truth but a verifiable fact, to avoid critical errors of the kind you are referring to, there are clearer ways to write the expression so as to leave no ambiguity.
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@riidii, But as also mentioned elsewhere numerous times in this thread, the 2 is actually part of the parenthesis, so even if Multiplication doesn't inherently go before Division (which is what I've been taught in my post-secondary education as well as primary and secondary education and therefore, I reasonably consider it to be true), it still needs to occur before the division because it is a factored out portion of the parenthesis. Therefore regardless of order between the M and D in PEMDAS, the answer *is* 1
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@riidii, Yes! That’s why I was taught to use parentheses to make absolutely sure there can be no mistakes. So I’d write it as either 6/(2(1+2))=1 or (6/2)*(1+2)=9, depending on what the problem was.
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@Sven and Otar, the two is outside the parenthesis, not inside them. It's the same as 2 x ( 1 + 2 )
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@riidii, 6 (2+4) 2*(1+2) But ultimately the problem is incomplete because there is no why to the origin of the values. Someone else said it should have been written as a fraction. But it wasn't. So you have to respect the origin of the equation and what it's trying to find. The most likely answer is 1 while you could stretch it to 9.
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It's 1. Parentheses comes first, then multiplication, division comes last PEMDAS
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@Kangaroo Jacked, hey to be the bearer of bad news broski but they changed the rules once you do all that pe part then you do left to right then you do the as part
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@gokiser, whoever changed the rules is a dick. Pulling a switcheroo mid generation
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@Kangaroo Jacked, multiplication doesn't actually come before division. It's whichever comes first because those operations are equivalent just like addition doesn't actually come before subtraction. That answer is 9
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@Kangaroo Jacked, they switched math so much it made me say meh no to math that's new
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@gokiser, Mr Incredible: "why would they change math? MATH IS MATH"
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@gokiser, They didn't change anything... it has always been that multiplication and division have the same priority...
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@Kangaroo Jacked, lol, memer switched it
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Here we go again an intentionally ambiguous equation. I will die on the hill that it’s 1. There is no separation between the 2 and the parentheses. That makes the 2 part of the parentheses.
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@Jfosh, I 100% agree with you. No doubt in my mind that the real answer is 1. However, from what I have looked up and tested, not everybody agrees that X(Y) is different than X×Y Also, if you write it as numerator/denominator you get 1.
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@Petersquatch, XY, X x Y, and X(Y) are all the same. I have a Masters in Engineering. No operation sign always implies multiplication. The answer is 9
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@dshira, x(y) is different though, because x is what has been factored out of the parentheses (2x+4)=2(x+2) so while you would have to multiply the 2 into the parentheses to get back the original equation, it is slightly different in terms of PEMDAS because the x in x(y) is actually a part of the parentheses but has just been factored out
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@dshira, alright, who mentioned engineering. X=6÷2(1+2) Becomes X=6÷(2+4) or X=6÷2(3) This means that X=6÷6 either way Therefore X=1 both the parenthetical and multiplicative operations always occur before division. Even if the thing happening inside the parenthesis happens to be addition.
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@dshira, The reason this is 1 is because you have to write it as it would actually be written, which is 6 / 2(1+2) meaning 6 OVER 2(1+2) which when dealing with fractions you always simplify first. This could be done the way everyone is saying or by factoring out the 2 first, making the equation 3 / (1+2) which still equals 1
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@HELLUVA ENGINEER, both of you are high. Parentheses to imply multiplication does not imply priority by parentheses for that operation. And division and multiplication happen simultaneously in the absence of parentheses (default by left to right, not multiply and then divide)
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@The nOly One, if you’re going with factoring you have to do 6/2 first so it reduces to 3(1+2) which implies 3*(1+2)…becomes 3*1+3*2…9
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@dshira, they are dumb. Having the x(y) just means to multiply x by whatever is inside the parentheses, AFTER having solved any equation INSIDE the parentheses first. And then order of operations is left to right for the 2 groups (multiplication and division; addition and subtraction). Multiplying by the value inside parentheses does not mean it is part of the parenthetical operation. So the answer is indeed 9.
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@dshira, dude, the 2 is part of the factorization. You could rewrite the equation as: X=6/(2+4) Parentheses are absolute. You cant just decide when they group things together and when they don't. The parenthesis portion of Pemdas implies that you deal with the numbers inside, but also the numbers immediately outside as a whole. The equation you are trying to make would have to be written as: X=(6/2)(1+2) In order to perform the division first and then multiply, the 6÷2 would have to also be grouped with parenthesis.
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@dshira, the 6 was never factored out, hence it being in a different part of the equation, if you were to right it out completely it would look like 6 ———- 2(1+2) Or 6 ———- (2+4) If you could pull a factor out of a parentheses and then just decide to use another number to multiply to it whenever you want, then you are breaking literally the first rule of PEMDAS which is to complete the parentheses first
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@dshira, distributive property.
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@dshira, You’re fighting the good fight. Keep team 9 alive brother
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@Petersquatch, not having everyone agree is not your problem. In with parentheses, it is supposed to be what’s inside and the “immediately next to”, that all counts as the “P” then the rest of pemdas takes effect. 1 is the answer. It’s not an opinion. People just forget that part.
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It’s 9. Number(parentheses) is shorthand for and identical to number*(parentheses).
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@DeepwaterJew, true, buy number(parentheses) is also just the number factored out of the original parentheses equation. (2x+4)=2(x+2) and the same is true when x=1
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@DeepwaterJew, it's 1. PEMDAS means *Parenthesis* (therefore resolve the parenthesis first), then exponents (not applicable), then *multiplication* (so multiply the 2 into the resolved parentheses), then *division*, divide 6 by 6. Result? 1
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I feel like the confusion around this problem isn’t around PEMDAS, it’s around factoring. The equation 6/(2+4)=6/2(1+2) the 2 is part of the parentheses it has just been factored out. If you don’t believe me just set the 1=x No one would argue that 6/(2x+4)=6/2(x+2) the problem creators just added an extra step in there to confuse people.
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First, inside, outside, last Thank you Mr.Pizzalato
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I’m sorry I’m advance, but I feel I need to be that person. 6/2(1+2) PeMDas Parentheses first so 6/2x3 Multiplication next 6/6 And last division =1
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9 is the correct answer if you strictly follow PEMDAS, and if you were to find this problem on the ACT, SAT, or GRE. However this is not a universally agreed upon convention, and that is where the mixed answers come from.
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@MrJojo, it’s universally agreed upon in STEM. Gender Studies majors may have a different interpretation…doesn’t mean it’s the least bit correct
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@dshira, I agree, just trying to find common ground with the other side lol
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The reason this is 1 is because you have to write it as it would actually be written, which is 6 / 2(1+2) meaning 6 OVER 2(1+2) which when dealing with fractions you always simplify first. This could be done the way everyone is saying or by factoring out the 2 first, making the equation 3 / (1+2) which still equals 1
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@EVILdrPORKCHOP3, you need brackets to assume everything after 6 is in the denominator. If you want to factor the 2, you have to do 6/2 first, making it 3*(1+2)…reduces to 3*1+3*2…9
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…Where’s the cat?
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The way my teachers taught PEMDAS was to go left to right, doing parentheses, then exponents, and that multiplication and division, as well as addition and subtraction respective to each pair, are done by whatever comes first. So the order of operations could end up being PEMDAS, PEMDSA, PEDMAS, or PEDMSA. And due to being taught this way, I will also take the side of the answer being 9. Also after putting in the equation on 4 different calculators, 3 gave the answer as 9, while only one gave the answer as 1, due to the calculator automatically turning the division symbol into a fraction, therefore changing the equation as a whole.
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You gotta remember PEMDAS people!
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It feels weird seeing everyone arguing about PEMDAS and implying it's that way because the multiplication has to come first. When I went through school, we were taught BEDMAS (Brackets rather than Parentheses, still the same operation) which has division ordered first.
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No wonder the world is fvcked. When it was 1 we went to the moon. Now that it is 9 we have 51 genders.
As a PhD in math and engineering, I can confidently say the answer is both and neither. The failure is the ambiguity in this expression. It’s only purpose is to start a bar fight.