Math Prof answers 6÷2(1+2) = ? once and for all ***Viral Math Problem*** 

I thought you explained it well in the video already- I'm honestly baffled that people continue to argue which answer is "correct" 🤷

@@yourmomsfilms he didn't expkian, he blamoved the question for not understanding the answer.

@@NeoiconMintNet he most definitely explained but, maybe you didn't understand his explanation?

@@yourmomsfilms he definitely didn't explain, he simply repeated what he was told, including the acronym to remember the rules, but he didn't explain how the rules work. he's like someone that didn't know how to cook, was given a recipe for instructions to cook one thing, but still doesn't understand how to cook.

@@NeoiconMintNet Are you the same person as R S?

haha right? Computer programmers just don't have this issue:D

Especially with Smalltalk, which I don't think has normal procedural language precedence. I have programmed in C++ for a few decades, and I mostly know the rules, but as you say, when in doubt, write parenthesis, and people will say this in code reviews if they don't think it's intuitively clear.

The problem with all those extra parentheses is readability, especially with inline expressions.

..and that's how we got Lisp.

@@Delirium55 lisp existed before C++ from what I remember, C came before lisp.

It means 1 out of 10.

@@digambarnimbalkar8750 Nah, they gave this video a solid 9.

@@digambarnimbalkar8750 The question is ambiguous and badly written to modern standards so it is both 1 and 9 at the same time (depending on which interpretation you are using - academic or programming) which is the joke 😋. If I wanted 1 I'd write 6÷(2(1+2)). If I wanted 9 I'd write (6÷2)(1+2) or 6÷2×(1+2). These would be unambiguous and the joke wouldn't work then and we wouldn't have the video either as there would be no discussion.

@@JustVezix Schrödinger's rating 🤔😋

In other words 6÷2(1+2)/10...?

It is generally accepted that explicit multiplication and division are both on the same level nowdays. If it makes you feel better though, there was a time, back in the 18th or 19th century, when doing all the multiplication first was the more accepted convention. So you're not wrong per se, just a bit out of date... 😂

Mr Norman you are also correct so 6×3÷2=9

​@@calebfuller4713fairly certain some teachers skip that part, like mine.

There is no left to right convention as the video presenter said. When on one line you have to use brackets to replicate both possible answers that the two line notation shows you. If you do left to right you can only ever get one of the two possible answers. With 2 lines left to right is not needed of course, hence why no left to right convention.

@zakelwe I never said there was. I was saying I could go left to right. My point was that he said it doesn't matter what order the multiplication and division was. My teachers taught me the opposite (outdated way) so therefore there was only one answer with that method vs the current accepted way.

Ya man . Now the tricky thing is identidying questions like this and when its (a+b)

That is correct. And a parenthesis isn't "solved" until you complete the multiplication or division of it. All rules states parenthesis (or brackets) are to be solved first and foremost.

So, according to you, a(b+c) is the same as (a(b+c)). I was taught that only the contents within the parentheses are evaluated. Sure, a(b+c) is the formula used to describe the distributive property but the expression of 6÷2(1+2) is composed of only one term and must be evaluated as such because terms are defined by the presence of addition and subtraction and not multiplication and division. You need to evaluate the entire context of the expression and not just part of it. Also, the obelus (÷) does not imply grouping where what is before the sign is the numerator and what is after it is the denominator. That is the function of a vinculum or horizontal fraction bar where what is above the bar is the numerator and what is below is the denominator. If you desire an answer of 1 for the given expression, you must add an additional set of parentheses. 6÷(2(1+2))=1.

@@JoeNarbaiz a(b+c) is the same as as (a(b+c)) yes. The outside parenthesis is redundant since it is a regular + parenthesis and thus is solved as soon as you solve what is inside. Given there are no terms outside the parenthesis it offers no change. Let's say you want the content to be the 6÷2×3 where 3 is a sum of 2 numbers, you will need to put in those extra parenthesis like (6÷2)x(1+2). Otherwise a multiplicative parenthesis will always take priority. Actually use this quite often in economics, due to the fact that a lot depends on factors.

I was taught that there is no difference between 2(1+2) and 2*(1+2) and that it's just a shorthand way of writing it.

Indeed. Heck, I haven’t even used that symbol in at least 15 years!

@@DrTrefor BTW, thanks for all your great calculus videos! I've used them as supplementary viewing for Calc 1, 2, and 3 this summer and fall with distance learning.

Thanks for mentioning, always like hearing they are being used. Hope your students find them helpful:)

Well, it's wrong. The habit has become to write a number next to a parentheses, but between the '2' and the '(' should be an 'x'. No one uses divisors, but if you use them its... formatting that is only used to teach pemdas and in that -- very specific -- formatting, you are required to use every mathematical operator. This skips one, and thus we don't know what else it decided to skip. It's a "wrong" formula.

What about textbooks? I can pull examples from nearly any textbook (math or physics) I own that has a/bc in it, and you're supposed to interpret that as a/(bc). Yes, it's quite obvious in that context to interpret it that way, but I think that definitely casts doubt on the idea that mathematicians and physicists don't use implicit multiplication when writing symbols in-line. This is not to say that one or the other is "correct", but just to cast doubt on your claim.

It’s the same, ÷ should not be used. But in essence ÷ = / = : Yes : is also used for division.. and it’s all the same.

@ Jose: Moreover, when you have implicit multiplication as a result of the 2 being juxtaposed right next to the (1+2) like that, anybody with any knowledge of math -- or at least, algebra and higher -- will treat that as a single, indivisible (no pun intended) expression. It's basically a ÷ bc (or a/bc), where a=6, b=2, and c=(1+2). And everybody knows -- or damn well _oughta_ know -- that a/bc is a/(bc) and *_not_* (a/b) × c.

Then textbooks should STATE that EXPLICITLY in the Order of Operations.

@@Milesco no! a/bc = a/b*c!!!!!!

Shame on you how did you became civil enginner

an analyst? you're a smartie, and you know it. it's always been my exp that folks who hate algebra are good at geometry and vice versa! diff sides of the brain i heard!

@@melissalynn5774 not me, I excel in both

This is actually a great idea and a BIG topic imo

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-eLMccl_z9Xg.html

Viral Math Equation 6÷2(1+2) = ? Watch this video for answer - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-zqXvBLXw5Tc.html

How society views math doesn't solve the problem.

A lot would follow this rule, but it isn't actually a universally accepted rule of math. The problem here is that the mathimatical community hasn't bothered to settle this for a good reason. No matter what rules you make its always possible to poorly communicate a math problem. This is the same as saying when writing a sentence in english I can misscommunicate by using unclear verbs, sentence structure, or grammar. The point of mathimatical expressions is to clearly communicate an idea just like in any other language. Using ambiguous structures that can have multiple inturrputations is just poor math and you wouldn't find any formal math proof submitted for peer review using them. Math papers avoid the old division symbol because it had two different inturrputations over time. They also clearly communicate the term breakdown using brackets. This question and others like it failed to do that and that leads to multiple correct answers depending on inturrputation used.

PEMDAS leaves it out because PEMDAS is a simplified version of the order of operations that is taught to young kids. The real question is why the order of operations isn't revisited in the US after concepts like functions, multiplication by juxtaposition, and unary operators are understood.

The correct answer is 9

@@MrGreensweightHist The 'correct' answer is "fix your notation". 1 and 9 are both right and both wrong depending on if you respect juxtaposition. 1 ÷ 2x vs 1 ÷ 2 * x are two different operations.

I 100% agree! AND....the most important thing is bringing PEJMDAS to primary teachers/education authorities' attention. It is here that most people learn and take PEMDAS as being the correct rule without any other consideration. Even calculator companies need to be consistent. For example, using a CASIO Scientific calculator [Model fx 82AU] gives an answer 9 for this problem. While a CASIO Scientific calculator [Model fx-83GT PLUS], gives an answer 1. The first calculator obviously is programmed to use PEMDAS and the second [same company different model] uses PEJMDAS. So, this means one person in an exam is getting the 'right' answer and the other the 'wrong' answer depending on a teacher's preferred answer/interpretation. This doesn't mean more than that for two students of equal ability (but with different calculators) one gets a mark or two more/less in the test. A little unfair, but this I can cope with. BUT....what if two nurses are in a hospital (with the two calculators I mentioned above), and each calculates (via the formula given by the drug company re the dosage) a medicine dose. They both type in the exact same information, and one (even if she/he checks two or three times) calculates the dosage as 9 units, while the other that 1 unit is required. This is not trivial anymore. Whether they learnt PEMDAS (or know of PEJMDAS) their trust in the calculator is sort of 'Russian Roulette' for their patient. We all need to become consistent. This is not a trivial misinterpretation of one way of looking at expressions compared to another, but an extremely important issue that needs attention.

100%

My exact thought process thank you

As a mechanical engineer, I 100% agree.

As the son of an electrical engineer, I agree, too. 😊 It troubles me that *_so many_* people think otherwise!

You can't factor a denominator without maintaining all operations of that factorization WITHIN a grouping symbol... 6÷(1x+2x)= 6÷(x(1+2)) NOT 6÷x(1+2) 6÷x*1+6÷x*2+6÷x*3-6÷x*4= 6÷x(1+2+3-4) as the LIKE TERM 6÷x was factored out of the expanded expression.... 6÷(1x+2x+3x-4x)= 6÷(x(1+2+3-4) as x was factored out of the expression WITHIN the grouping symbol... You can't factor a denominator without maintaining all operations of that factorization WITHIN a grouping symbol....

WRONG

Definitely wrong, there are a bunch of questions like this in my text book. Here in Australia.

@@Kage-jk4pj can you post pics of your textbook so we can see what it says...

@@filename1674 No you can't. 🙄🙄🙄

@@RS-fg5mf Argue with a maths professor on this one? You are unbelievably up your own rear end

Yup bingo

100%

Except it's not ambiguous to anyone competent in maths. The answer is 1, and that's it. All other answers are wrong.

@@peterthomas5792ion see your PHD so ur wrong

With no multiplication sign, the only indication that (1 + 2) is multiplied comes from its being grouped with 2.

agreed, I'm currently trying to explain this to a friend and he's still refusing to believe that it's a language problem. and that onyone who views it the other way is simply wrong.

After all, math is a language, too.

There is still an objectively correct answer. It can be shown here: "6 / 2(1 + 2) = 6 / 2(3) = 6 / 6 = 1" because "6 / (1 + 2) = 6 / 1(1 + 2) ≠ (6 / 1) * (1 + 2)", therefore "6 / 2(1 + 2) ≠ (6 / 2) * (1 + 2)". There is no ambiguity because "n(m)" always implies "(n(m))" just like "m" implies "1m" or "1(m)".

Carl, I agree it is a language problem but maybe more..... For example, I just took my CASIO Scientific calculator [Model fx 82AU] and typed in the problem and it gave me the answer 9. I then took another calculator, CASIO Scientific calculator [Model fx-83GT PLUS], and it gave the answer 1. The first calculator obviously is programmed to use PEMDAS and the second [same company different model] uses 'implied multiplication precedence over division 'Juxtaposition' (PEJMDAS)'. So, this means one person in an exam is getting the 'right' answer and the other the 'wrong' answer depending on the teacher's preferred answer/interpretation. This doesn't mean more than that, for two students of equal ability (but with different calculators) one gets a mark or two more/less in a test. A little unfair but I can cope with that. BUT....Now I have two nurses in a hospital, (with the two calculators I mentioned above) they calculate, via the formula given by the drug company, the dosage for a medicine. They both type in the exact same information, and one (even if she/he checks two or three times) calculates the dosage as 9 units, and the other that 1 unit is required. This is not trivial anymore. EVERYONE needs to be taught orders of operations in a consistent way that gives the 'right' answer. As a scientist I use PEJMDAS, but primary students are usually taught PEMDAS, and brackets are often not used if there is a chance of ambiguity. This, I feel, is the main reason why there is a problem - two (or more) ways of interpreting the same 'piece of language'. When does this first come up? In primary school So.... I feel it is very important that primary teachers are trained 'correctly', because it is here that this/these problem(s) are first encountered and can be tackled. Also, by doing this hopefully trust in our health practitioners, and calculator/computer company can be restored.

@@wrrsean_alt so this has been a very long ongoing and thoughtful discussion. What I find most interesting is that some people still believe there is an objectively right answer. With the calculator issue you've expressed there is to me an obvious time when people believed one way to be right and excepted it. Then some evolution happened and a new algorithm was accepted. What makes the version now right and the previous wrong? Also, usually I view math as an explanation for some process in the universe that the series or expression represents. And I'm not saying I disagree with anything or any ones point of view here. But objectively something seems to be changing in the foundations of math.

I'm with the 2nd argument as well. Since it makes more sense when you think about algebra. Along with distributive property of Multiplication

@@manzanajoemerj.9849 distributive property doesn’t apply here.. 6/(2(1+2)) is distributive property which equals 1.. 6/2(1+2) isn’t distributive so the answer is 9

@@jshad1074 always do parenthesis first and open them... Its argument 2

@@jshad1074 when you start to use / , I'd say any numbers come after that would be as one denominator

@@jshad1074 2(2+1)/6 = 1 do you know what does it mean when a result of division is 1? that the operators before and after the division sign are equal. so 6/2(2+1) = 1, not 9. I don't have to add any futile brackets. I don't have to write 6/(2(2+1)) to get 1. I didn't write (6/2)(2+1) to get your stupid 9. could you fix your stupidity please?

I agree that the problem is just that there is no context. a/(bc) is probably the more useful interpretation for a/bc but these textbooks kinda suck then as our textbooks were unambiguous and wrote fractions vertically when grouped together. When using standard text signs I always Parenthesis in abundance. I also agree that maybe a debate could be interesting but fundamentally the point of the video is that the equation isn't written correctly or consistently which is why there is no need to come to a conclusion when the input is the problem.

There was an explicit choice to NOT include a multiplication sign but they included the division sign in the original problem so it strongly suggests that the right side is the denominator and the answer is 1.

The problem is what if this actual problem shows us on the test. We all know test are there to be tricky

@@Jry088 I have seen problems like this written in text books although with a / instead of a ÷. In those cases it's usually to save space because they are trying to get the whole thing on one line and then in that case the right side is the denominator. I would not expect a trick. Also if I saw this in a notebook found somewhere I would guess the author left out the multiplication sign because they want the whole right side to be solved first otherwise they would have written X or * just like the wrote ÷ on the other side. Not writing X or * would be inconsistent with the style unless they meant it to be a denominator so if found in a notebook it would be very safe to assume the right side is solved first.

@@nickjunes that's why 1 seemed so obvious to me also. At least the way I learned a(b+c) is all included in the P in pemdas. Otherwise it would be easily separated.

You are most welcome!

Everybody agrees what the result would be if we were to take PEMDAS literally. The question is if we should break with tradition, rewrite the text books and start taking PEMDAS literally. Who died and made PEMDAS king, suddenly? PEMDAS is a simplified mnemonic for teaching the order of operations to children.

pemdas vs the bs

the problem is indeed the implicit * sign

No bodmas says it is 1. B is for brackets, so in 6÷2(3) you have to calculate brackets first, aka you get 6÷6. Now all of your reversals works aswell.

@@kimf.wendel9113 The 2 is outside the bracket. If it was 6÷(2*3) no confusion would arise.

@@manzerm7805 yes, and that means the contents of the parenthesis is shortened by a factor. And to remove the parenthesis you need to multiply is expression inside. All logic in maths says you solve the parenthesis first, that is why the first letter in those order of operations starts with a that. It doesn't matter what is inside, you solve it first until there are no parenthesis

Well bring it

What is 77 + 33

@@skiddadleskidoodle4585 "What is 77 + 33" Easy, it's 7733.

However, we still understand 1/2x as 1/(2x), since if we meant it the PODMAS way, we would have written x/2. And if there is ambiguity, there is context to clear that up. Six letter acronyms are for children!

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-lLCDca6dYpA.html

No, the problem appeared because there are different calculators that take this exact formula input and output different results. Because some calculators follow strict PEMDAS, the others don't (they give implied precedence). And the "strict PEMDAS" calculators only exist because North American Math teachers (below university/college level) asked for them. And all those calculators claim "textbook entry" as selling point.

The problem is that if you ask to any professional mathematician about the problem in the video, the answer would be something like "I refuse to answer, let's talk about topological algebra instead".

Yuck.

You are not the only one. It's sad that most of the people don't have any clue about the wonderful mathematical universes that unravel, once these stupid problems disappear.

Exactly! I should hire you to be my script writer:D

@@DrTrefor lol 🤣🤣🤣

For most people, mathematics is a set of numerical expressions or questions, each of which (usually) has 1 right answer & many wrong answers (most of which, fortunately, are highly implausible). The goal is to find the right answer-or answers, for those comparatively rare cases in which there are 2 or more correct answers.

Math is a science how you use it as a function is an art but you can't change the scientific elements of the math. Smh!!

I indeed see Math as a complex machine with very specific rules, maybe because of my background (Software Engineer). So that makes me always see "6 ÷ 2(3)" as "6 ÷ 2 × 3", which is unequivocally 9. I can see the confusion on this being interpreted as "a ÷ bc" which, for what I understand, would be 1. HOWEVER, if you, the guys who really know this stuff, say it's ambiguos, then I believe you and I'm ok with that.

Still doesn't answer the question of what he answer is. Please don't ever work in payroll.

@@popeyelegs Because the answer doesn't matter anyway if the question is wrong in the first place, it's ambigous.

thata numbers right there

Im in 8th grade and that’s the exact same thing I thought but with other examples, I finally found someone that knows his stuffq

On this operation

That last sentence is exactly my argument against the answer 9. a(b+c) implicates the entirety as a factor that needs to be resolved first. Otherwise order it as a×(b+c) to separate the functions to 6/2 × 2+1.

Too much wordas for 1 math problem my friend

You said it all and so few likes

but us folks for whom math has always made me feel stupid, i i need rules!

​@@melissalynn5774The rule is called "#PEJMDAS": Parenthèses - Exponentiation - Juxtaposition - explicit mult/div - addition/subtraction.

Not only that, but following some rules and conventions over others breaks some of the arguments, imo at least. It's easy to confuse people with this type of notation because the results are usually integers... But, if you apply juxtaposition before Order Of Operations then a decimal value can never be represented as its fractional equal without being inserted in brackets because the juxtaposition will enter in effect without applying it to the entire fraction, but the other part of the expression is already inserted in brackets. Eg. 0.25(2+2)=x. You can, according to the concept of equality, replace the 0.25 for 1/4 or, since "/" is equally representative to ":" , as 1/4(2+2) or 1:4(2+2) . However, in any of the latter two, by applying juxtaposition before OOO you will not get x=1 but x=1/16 if the fraction isn't in brackets. But following OOO instead of juxtaposition 0.25(2+2) can be represented as 1/4(2+2) or 1:4(2+2) without any confusion. That example can be replaced with anything similar, like 0.x(a+b)=y being replaced with 1/z(a+b)=y . But we can't forget that 1 is also 2/2, 3/3, 4/4, 5/5, or x/x , and any (a+b) can be written as 1(a+b) or x/x(a+b) . That is how I look at it, I don't know if my argument is valid or invalid since I'm not a mathematician though.

You are incorrect.

I don’t know the exact answer to your question, you’d probably need to ask someone specialized in the history of mathematics, but I do know that in general terms, it was a very, very slow journey (I’ll be focusing in Europe/the western world). For example, before Leonardo de Pisa (Fibonacci) we didn’t even use numbers like 16 or 184, we used roman numbers. Can you imagine the pain that it was to do something like XVII multiplied by XI? We didn’t always use the “=“ symbol, I think we used to write “is equal”, but then summarized it with “=“ because it represents to *equal* lines. I’m sure similar stuff happened to the other symbols like +×÷, etc, they each must have their own story, and the only reason we use them is because they were the most intuitive symbols to use. For the rules of the order of operations, it probably comes from the idea that exponents are repeated multiplication, which are repeated additions. So it makes intuitive sense to give them priority in that order. And we do divisions with the same priority of multiplications because they’re very similar operations, likewise with adding and subtracting. So we probably just chose the order that was the easiest to remember

@@AndresFirte Thanks for this response and I do appreciate the reasoning you have used. I think that we developed math to help us count the things we see like the books on a book shelve, bottles of wine, and hot wheels cars. I say this because it seems more reasonable to attach math to what we consider tangible not intangible as in count the non-fiction and not the fiction. So, if we view from this perspective then we get a very precise math with the limitations that are currently expressed in problem solving.

She is right. The question is badly written to modern standards. ISO-80000-1 mentions about fractions on one line and how brackets are needed to remove the ambiguity now. Back in the early 1900s this would not have been an ambiguous question but with modern programming it now is.

You can't factor a denominator without maintaining all operations of that factorization WITHIN a grouping symbol... You fail to understand the Distributive Property correctly. It amazes me how otherwise very intelligent people fail to understand and apply very basic rules and principles of math... The Distributive Property is a PROPERTY of Multiplication, NOT Parenthetical Implicit Multiplication, and as such has the same priority as Multiplication... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication.... Multiplication does not have priority over Division they share equal priority and can be evaluated equally from left to right.... The Distributive Property is an act of eliminating the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in. The Distributive Property REQUIRES you to multiply all the TERMS inside the parentheses with the TERM not just the factor outside the parentheses... TERMS are separated by addition and subtraction not multiplication or division... 6÷2 is part of a single TERM... FURTHERMORE people misunderstand Parenthetical Priority... The rule is to evaluate OPERATIONS INSIDE the symbol as a priority before joining the rest of the expression outside the symbol. It does NOT literally mean that the parentheses have to be evaluated BEFORE anything else in the expression can be done... A(B+C)= AB+AC where A is equal to the TERM VALUE i.e. monomial factor outside the parentheses not just the factor next to it... A=6÷2 B= 1 C= 2 6÷2(1+2)= 6÷2×1+6÷2×2= 3×1+3×2= 3+6= 9

@@RS-fg5mf stop spamming your stupidity

@@RS-fg5mf 6÷2 is not a single term like (1+2) is. By juxtaposition, it is the 2 which is multiplied by the bracket. "The How and Why of Mathematics" has a couple of videos on this topic where she looks at periodicals to see how professionals would approach it; they all use juxtaposition and get the answer to be 1.

@@shaunpatrick8345 you're wrong and so is she. Every example she gives is in the form of a/bc NOT a/b(c) There is a distinct mathematical difference between 6÷2y and 6÷2(y) despite your misguided beliefs and subjective opinions... 6÷2(1+2) is a single TERM EXPRESSION with two SUB-EXPRESSIONS. 6÷2 is a single TERM sub-expression juxtaposed outside the parentheses as a whole to the two TERM sub-expression inside the parentheses 1+2 There are two types of implicit multiplication and they are not mathematically the same.... Type 1... Implicit Multiplication between a coefficient and variable... A special relationship given to coefficients and variables that are directly prefixed (NO DELIMITER) and forms a composite quantity by Algebraic Convention... Example 2y Type 2... Implicit Multiplication between a TERM and a Parenthetical value or across each TERM within the parenthetical sub-expression... Terms are separated by addition and subtraction not multiplication or division.... 6/2(1+2) is a single TERM expression with two sub-expressions. The single TERM sub-expression juxtaposed outside the parentheses as a whole 6÷2 and the two TERM sub-expression inside the parentheses (1+2) In the axiom A(B+C)= AB+AC the A represents the TERM or TERM outside the parentheses not just the numeral next to it. The biggest mistake that people make is incorrectly comparing 6÷2(1+2) as 6÷2y. This is an inaccurate comparison... These two expressions utilize two DIFFERENT types of Implicit multiplication... 6÷2y = 6÷(2y)= 3/y by Algebraic Convention 6÷2(a+b)= (6÷2)(a+b)= 3a+3b by the Distributive Property... All variables have a coefficient written or not. Constants can be coefficients but constants do not have coefficients. There are no coefficients in the expression 6÷2(1+2)... 6÷2y the coefficient of y is 2 BUT 6÷2(a+b) the coefficient of a and b after simplification is 3 not 2 Correlation does not imply Causation. Just because both expressions utilize implicit multiplication doesn't inherently mean they are treated in the same manner... The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. For people who argue 6÷2(1+2) and 6÷2y should be evaluated the same way, their argument is circular and is an informal fallacy that is flawed in the substance of their argument...

It's more insidious than that. It was created not to edify, but to explicitly be ambiguous and to drive "interactions" on a given FB page or Tweet. The idea is not to arrive at a "correct answer" [none is given, and no winners declared]. The idea is simply to create drama and dissent, which leads to more clicks, more page views, more comments, and arguably more reputation for the page, and thus possibly more monetization, etc., in some form or other. They're not here altruistically to teach people anything, but to sow discord and make money off of it, whether driving clicks to other pages / sites / videos, or growing some subscriber base and then selling the page to some new chump willing actually pay something for it for some unknown reason, with a built-in subscriber/liker/follower base that can then be advertised to or whatever.

@@MGmirkin Exactly right, the authors of the videos saying the answer is 9 are doing it for money, despite the harm that they do to society. It is shameful.

No some people just forgot what they learned i school and got confused. As such they turned to social medias to verify they weren't the only ones to forget how math works. Then more fot confused becuase they were in doubt aswell, and then a confusion spread.

​@@kimf.wendel9113sometimes that's the case, but different people have been taught differently as well. Some people have been taught that multiplication by juxtaposition has priority over other multiplication and division and some were taught that it's bo different than any other multiplication.

@@Andrew-it7fb that doesn't mean the latter group is right. If they were taught that + was "divide by" there would not be an additional right answer, they would just be wrong.

I couldn’t find the exact one, but check out the description I put one similar in my Amazon store

@@DrTrefor Thank you

The issue is with the notation, not the order of operations. It comes down to how do you interpret multiplication by juxtaposition? Academically, it implies grouping so 6/2(1+2) means 6/(2×(1+2)) Using whatever order of operations you like gives 1 Literally/programming-wise, multiplication by juxtaposition implies only multiplication so 6/2(1+2) means 6/2×(1+2) So using the same order of operations gives 9 now. It's just bad writing. 1 and 9 are correct. The expression is wrong.

That’s correct too the answer is 9 so there is nothing wrong you solve it correct

Thank you!!

Except that P is for inside parentheses only. Juxtaposition is either a separate step after Exponents, like in PEJMDAS, or it's a notation convention that needs to be interpreted and written explicitly before you start to simplify at all. Easy to show with 3²(4) If the P step is still present, how can you do P before E here? What's the next step? It's bad teaching to say outside parentheses is part of the parentheses step.

@@GanonTEK this might actually be hard to understand because the answer to 3²×4 and 3²(4) are the same but the way they are calculated is different. 3²×4 = (3×3)×4 = 9×4 = 36 3²(4) = ((3²)(4)) = ((3×3)(4)) = ((9)(4)) = (9×4) = (36) = 36 This becomes more obvious if you begin with 3²(2+2) instead of 3²(4). 3²(2+2) = (((3²)(2))+((3²)(2))) = (((3×3)(2))+((3x3)(2))) = (((9)(2))+((9)(2))) = ((9×2)+(9×2)) ((18)+(18)) = (18+18) = (36) = 36 The thing is 3²(4) can be calculated as 3²×4 = 9×4=36 but if it were to be part of a bigger equation 3²(4) doesn't become 3²×4 but (3²×4).

wow you really didn't get the video you just watched start to finish huh

I went to a birthday party with the strippers, JFK and Stalin

PHD in WHAT, you clown?

There is a slight argument that scalar multiples may be interpreted that way but even then it's ambiguous. But when all symbols are in the same general realm (being variables or numbers, but all the same) - that argument goes away. And even then, it's just bad form to create ambiguity and virtually all math people... scratch that, people that use math to communicate e.g. +physicists etc. - would write it in an unambiguous way

@@ibarskiy Exactly. I have a Bachelor's degree in Mathematics and what I usually tell people is that if I had written a formula like that on a test paper where I was showing my work, I would have gotten points off for writing something so ambiguous

@@ibarskiy Just repeat 5th grade, and this time, stay awake.

It is NOT an equation, it is merely an EXPRESSION.

The answer is in the basic rules and principles of math when understood and applied correctly as intended... When you actually understand that GROUPING SYMBOLS only group and give priority to operations WITHIN the symbol of INCLUSION as a priority and that the 2 is not WITHIN the symbol of INCLUSION and there is no math book that states "with the exception of " then you will understand the only correct answer is 9 6 -----(1+2) = 6÷2(1+2)=9 2 6 -------- = 6÷(2(1+2))=1 2(1+2) A vinculum (fraction bar) is a grouping symbol and groups operations within the denominator and when written in an inline infix format extra parentheses are required to maintain the grouping of operations within the denominator... ________ 2(1+2) and (2(1+2)) both have two grouping symbols ________ __________ 2(1+2) = 2×1+2×2. Distributive Property. Parentheses REMOVED. One grouping symbol... (2(1+2))= (2×1+2×2) Distributive Property. Inner parentheses REMOVED. One grouping symbol 6÷2(1+2) does not equal 6÷(2×1+2×2) as you have not REMOVED any parentheses and you still have the same number of grouping symbols.... 6. 6. 6 -------(1+2) = ------- ×1 + ----------×2 2. 2. 2 The same as 6÷2(1+2)= 6÷2×1+6÷2×2

You can evaluate this expression at least 6 different ways but you still get the only correct answer 9

RS can get his head dropped 1 or 9 times as a baby and he’d never graduate elementary school

A curious person like you would be amazed from the mathematical universes that unravel, after these stupid problems, equation, and expression disappear

Well, if this trend is to be considered it seems to just be confusing people.

@@andrewboyer7544 many people confuse and conflate an Algebraic Convention (special relationship) between a variable and its coefficient that are directly prefixed (juxstaposed) and forms a composite quantity by this convention to Parenthetical Implicit Multiplication... They are not the same thing...

It is a lack of understanding of the Order of Operations and the various properties and axioms of math... BODMAS/PEMDAS and any other acronym that is a memory tool for the Order of Operations 6÷2(1+2)= 6÷2(3)= 3(3)= 9 2(3) is not a bracketed priority and is exactly the same as 2×3 M not B or O in BODMAS. Brackets/Parentheses only GROUP and GIVE priority to operations (INSIDE) the symbol not outside .... There is no rule in math that says you have to open, clear, remove or take off parentheses. The rule is to evaluate operations (INSIDE) the parentheses and nothing more. Commutative Property 6÷2(1+2)= 6(1+2)÷2= 6(3)÷2= 18÷2= 9 Distributive Property 6÷2(1+2)= 6÷2×1+6÷2×2= 3×1+3×2= 3+6= 9 The Distributive Property is an act of removing the need for parentheses by multiplying all the TERMS inside the parentheses with the TERM outside the parentheses... TERMS are seperated by addition and subtraction. 6÷2 is one TERM attached to and multiplied with the two TERMS inside the parentheses 1 and 2 Operational inverse of division by the reciprocal 6÷2(1+2) 6(1/2)(1+2)= 6(1/2)(3)=? Multiply in any order you want you still get 9 Proper use of grouping symbols 6 -----(1+2) = 6÷2(1+2)=9 2 6 -------- = 6÷(2(1+2))=1 2(1+2) A vinculum (fraction bar) is a grouping symbol and groups operations within the denominator and when written in an inline infix format extra parentheses are required to maintain the grouping of operations within the denominator... Another argument people tend to use incorrectly is factoring.... 6 = 2+4 No parentheses required BUT 6÷(2+4) parentheses required 2+4= 2(1+2) only one set of parentheses required. 6÷(2+4) we already have a set of parentheses and the factoring must take place within that first set of parentheses. You can NOT just dismiss the first set of parentheses out of hand in favor of the second set... The 2(1+2) must be placed within the first set of parentheses containing the (2+4) 6÷(2+4) = 6÷(2(1+2)) NOT 6÷2(1+2) Let y = 0.5 6y(1+2)=? 6y*1+6y*2= ? 6/y⁻¹*1+6/y⁻¹*2= ? If you answered 9 to all three algebraic expressions then it would be ILLOGICAL and INCONSISTENT as well as hypocritical to say that 6/y⁻¹(1+2) doesn't also equal 9 The rules of math have to remain logical and consistent across the board... THESE ARE THE FACTS....

It is confusion over the lack of explicit parentheses unambiguously stating which things are grouped together in what way **AND** conflation with the manner in which "distribution" or "factoring" is typically written **in short-hand* when factoring out polynomials and such. For instance x^3+x^2y+xz is often factored / simplified to x(x^2+xy+z). So, one can be **somewhat forgiven** for seeing an **implicit** distributive grouping in 2(1+2) analogous to something like x(x^2+xy+z) and thinking there **should be** an extra **implied** parenthesis (2(1+2)) whereby the 2 is distributed over the contents of the parenthesis, just as one would reconstitute the original x^3+x^2y+xz by distributing that x(...) over the parenthesis' contents. It is this ambiguity that these click-bait @r$3h0l3$ use to create these intentionally ambiguous memes.Not for any clarity or edification but explicitly to drive misunderstandings, arguments, and inevitable more clicks / views / follows / likes and hopefully more $$ through whatever monetization system the page / video / etc. uses. It's not about edifying anyone, it's about driving interactions to make the page money. It's insidious, and should pretty much be banned, IMO. It's a waste of our collective time and attention as a society / species. Just saying. ;)

We are going to agree a lot then!

"Math is about more than getting the right answer" I hope you never change your mind, even when your employer pays you less than you are owed.

You are right, but unfortunately, notational conventions still exist, and they have to exist. No amount of thinking is going to eliminate the necessity in using symbols with the agreed upon rules. Even in natural languages, this is true. This is why dictionaries exist.

Never in my life would I have thought I'd agree so much with someone whose name is literally "Vaginal arthritis", yet here we are,

@@angelmendez-rivera351 To (mis-)quote a well known adage about standards: "The great thing about notational conventions is that there are so many of them to choose from."

And yet, so many people still couldn't get it.

100%

-🤓

boy...bet you're fun...just reading your comment made me feel stupid!

i'm just extremely jealous of folks like you. intimidated i guess.

The typical algebraic calculator mixes "infix" notation and "postfix" notation whereas an RPN calculator is always postfix. Once you get used to it you no longer have to wonder if operators always immediately execute (in RPN they do). But in a Texas Instruments calculator, some operations expect another operand, some execute immediately and if you forget, you usually have to start over. Infix: 2 + 3 = 5. you press 2, then plus; nothing happens yet. Then press 3 then either another operator and the = tells it that no more operators are offered; complete the formula. But some calculators will execute immediately such as the square root or sin/cos keys. Others if you push sine key will display sin() Postfix: Press 2, then ENTER, press 3 then plus. That's it! Operators execute immediately; so whatever is on the stack is added. If you then type more digits, it goes on the stack; the calculator does not know or care what you are going to DO with those digits.

i am moko and think it could be written better however it is correct in it definition the answer is 1

The context and notation should match... If the notation doesn't match the context then it's wrong... 6÷2(1+2)=9 and if there were context that says otherwise then the notation needs to be changed.. 6÷(2(1+2))=1

@@RS-fg5mf you're right but I don't think the (1+2) in both first and second equation has different answer therefore I put it as "3" rather than "(1+2)" to shorten the context. But if you're going with the consistency, you can still find alot of context that match the notation. Great analysis mate

It is NOT an equation, it is merely an expression.

@@trwent True

The vinculum is a grouping symbol. It's not implied grouping, it's actually grouped within the denominator... 6 -----(1+2)= 6÷2(1+2)= 9 2 6 ----------- = 6÷(2(1+2))= 1 2(1+2) A vinculum (horizontal fraction bar) is a grouping symbol and groups operations within the denominator and when written in an inline infix format extra parentheses are required to maintain the grouping of operations within the denominator... _________ 2(1+2) = (2(1+2))

This is something that came from calculators (which is also why the symbol is the way it is -- calculator manufacturers combined the fraction bar and the ":", which was the written division OPERATOR symbol in many countries.) The earliest calculators had only OPERATOR buttons, and on the RPN calculators that actually made sense. Pressing "÷" divided Y by X (on the stack). You also could not use "-" to start a calculation like "-2+5", because "-" was the operator for "subtracting x register from y register", and you mostly had something on the y register that you couldn't see. You had to re-arrange the computation, or use the "+/-" or "CHS" (change sign) button that Hewlett-Packard wisely prepared for you. And actions like A÷B÷C made sense as shortcut entry for A/(B*C). But then the calculators gained algebraic and then textbook entry, and the symbols moved away from being just operators. It's easier to see with the "-". If you have an expression like "2x-x^2", which most would rewrite as "-x^2+2x", the "-" is not an operator anymore, but a modifier for the number following, and "x-y" becomes short for "x+ (-y)". Which leads to modern (non-graphing) calculators having a SECOND minus key (labeled "(-)" on Casios) for the modifier -, which may or may not be used interchangeably with the normal "-" operator key beside the numbers (and yes, this leads to a lot of confusion and lengthy discussions away from maths with students I tutor. Essentially, I must them teach how a calculator works and is used because the regular teachers have no time or inclination to do it.) I also recall that the earliest Casio algebraic calculators retained the "+/-" key from the earlier RPN calcs even though you did not need it. You could enter a calculation like "-2+5" with the normal "-" operator key if you started from a display showing "0". The calc would take pressing "-" as: Take what is currently displayed (0), and subtract the next number entered from that. So 0-2 = -2.

There are many calculators that support implicit grouping. My Casio fx-991ES PLUS for instance, it returns 1 in this case.

Pemdas says it is 1, P stands for Parenthesis. To solve a a(b+c) parenthesis you end up with ab+ac. So 2(3) is not solved, it is shortened, 2x1+2x2 is the solved state which is to be reduced to a 6.