Comments

@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 shorthanding 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.

@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.

@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

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 PEMDAS, where multiplication and division share the same importance in the hierarchy and are tackled by simply sweeping lefttoright, 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

@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.

@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

@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.

@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 postsecondary 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

@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.

@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

@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

@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.

@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.

@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

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.

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

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.
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.