It has millions of views because the problem initially looks too simple to have a video (and it is an excellent video). I wondered if I missed something and chose to watch. So, the order of operations rules were revised and both 9 and 1 are correct answers. I thought it was 1 (the algebraic grouping of terms as you noted). Great to know the rules changed. Thanks for making the video.
Great video, still slightly confused because I am taught that x(y) is one term and should be treated as 1 number but glad to learn that there are 2 different systems
MaxMisterC Both of them state that multiplication and division have the same importance, and are some left to right. Put it in a calculator if you disagree.
@@MaxMisterC Heck it wasn't even that for me. I always just ASSUMED (don't remember if it was actually in the education I got) that anything next to a bracket was in itself inside "invisible" brackets. So if you had 2(1+2), it would simply be read as (2(1+2)) = 6 regardless of what was put in front of it. I guess I never really bothered searching up if this was wrong, OR that my teacher might have been in the same group that still insists on this sort of thinking. Either way the new method (answer of 9) is correct and there just isn't much you can do about it. That's the rule and that's how maths works I guess.
as an engineer who has done advanced university level maths for about 7 years now, I would get 1. its the convention usually followed in physics/engineering textbooks to solve as terms and let implicit multiplication (brackets esp) go first
I'm in a similar position and I 100% agree. It's disingenuous by the video to imply there's one correct order, when so many physics and engineering books do operations in the 2nd way. The video is also wrong in stating that calculators all calculate in the same way. Mine doesn't. I guarantee that if any engineers I know saw something like "6÷2x" they'd calculate the 2x first. It has nothingo to do with the division symbol. Implied multiplication (for example, 2x rather than 2*x) in all the engineering I've learned always takes priority over normal multiplication. If you write it as 2(1+2) instead of as 2*(1+2) there has to be a reason for it, and common sense (mine at least) dictates it's because you mean the order of operations to be different. Real world math isn't a puzzle designed by someone to fool you, it's an objective way to state things and should be written accordingly. The problem here is the question, not the answer. Just write it as (6÷2)(1+2) or as a fraction and the problem is solved.
@@afsdfsadhasfh Conclusively, the experts say this. The equation is ambiguous and indeed, it can yield two different answers. Like the use of language, to convey something such that it can't be misinterpreted, it must be delivered with clarity, the intention should be made clear. The same with maths equations. To yield only one result, the equation should not be written with ambiguity and the intention of the writer must be clear. If it does or can, the equation should be re-written.
What is the correct answer? I don't know man, math isn't typically fully divorced from reality, let's look at the reasons why you're crunching these numbers and we can re-write it so it makes sense!
No, the first premise in PEMDAS, is to solve for the answer within parentheses. You never distribute into parentheses first because you would then misapply the order of operations. PEMDAS: Parenthesis, Exponents, Multiplication And Division, Addition And Subtraction (IF the same precedence, then left to right). Any order with And in between has the same precedence! Since the problem is 6/2*3 or 6/2(3), we must follow the premise regarding left to right because the problem involves only multiplication and division, orders of the same precedence. Parenthesis is only a symbol of multiplication when a number or expression is adjacent to it. If the problem were 6/(2*3), then the logical answer is 1, because we solve for the answer within parentheses first, as according to the first order of the order of operations. The answer to 6/2(2+1) is not 1.
@@babyyoda7749 no teachers are the ones. Teachers are teaching about gender and sexuality for example. The education system is not telling them to teach that.
@@MrGamecatCanaveral Teachers change the way they teach things because we discover new things over time. Before, it was thought that the earth is the center of the solar system. Copernicus discovered that it is actually the sun. Now, do we need to change the way we teach about the solar system? Yes. It's crazy that what we believe in the present will never be entirely 'true' as it could be proven false in the future.
@@aeroljameslita4975 from a subjective point of view, isn't the point of perception the center of your reality? So the Earth is the center of the universe for everyone on it.?
The programmer's wife sends him to the store. She says "Get one carton of milk, and if they have eggs, get a dozen". The programmer came home with 12 cartons of milk, because they did have eggs.
Agreement with Brian Fedelin. 13 cartons of milk. One carton, and if there are eggs, get a dozen. So 1 + 12 = 13. And the issue with computers is not the logic of them, it is how a human evaluates a human expression and then programs the computer. In this case, the issue was with the wife, since the expression was not clearly defined from the start by defining a dozen of WHAT was desired, the milk or the eggs. See, it is actually a trap by wife against the husband. No matter what he were to bring home, it would be incorrect since she could then change WHAT was the dozen to be of.
If you substitute all numbers with variables: a÷b(c+d) = You would get a/b(c+d) = a/(bc+bd) Not a/b × (c+d) That's how algebraic functions are ordered.
That's using implicit multiplication vs bodmas. You're coming with the assumption that b(c+d) multiplication holds higher priority than a/b part. That's all it is
@@spamspamspamspam3459it does because you first need to resolve the parenthesis. They are not resolved until you distribute them out (by multiplying the coefficient into the brackets).
@@spamspamspamspam3459my father studied to masters in mathematics, he has stated that in different areas both methods are correct. Within South Africa, and from what I have gathered much of the rest of the world) that is exactly how it is done. Simple reason, it should not matter in which order one does the multiplication or division whether right to left or left to right as long as it does not combine any addition or subtraction.
@@spamspamspamspam3459 again, differs from location. However in my country, that is the correct method to resolve the parenthesis. Notably from the logic my father gave me, this method means that it does not matter in which order you do the multiplication and division once the brackets are solved. The method you use requires that one solves the equation in a specific order lest the answer be different (I. E. If one first does multiplication before division). As was said, the purpose of the bodmas is so that regardless of the order one solves the equation (within each relative Order) in that it will arrive at the same answer. The method we use, the order in which division and multiplication is done matters not.
We shouldn't change things like the order of operations, it's incredibly dangerous in things like engineering to have two different people unknowingly using two different standards.
order of operations never changed, it's always been the same. He just explained that that specific symbol for division meant something very specific other than just division over 100 years ago but the actual order of operations has never changed.
That's why for any serious communication of mathematics you have to be more explicit than this ambiguous problem. Hence why peer-reviewed papers use fractional notation and make copious use of parenthesis to remove ambiguity.
Some people were taught that multiplication by juxtaposition takes precedence over explicit operations… hence why 3/2n is 3/(2n) and not (3/2)n The same juxtaposition glue applies to parenthetical coefficients… and in this case, 2 is that parenthetical coefficient. So using PEMDAS, but assigning multiplication by juxtaposition a higher priority than explicit division, the answer is 1. Additionally, if you use the distributive property from the get-go to resolve the parentheses, you get 1.
@Jure Lukezic That only works for very large values for 0. I was representing numbers in base-2; however, if we're talking string concatenation then yaaaaaaaaassssss!!!
@Jure Lukezic So how does it feel that your joke went over our heads? Don't you feel bad for us smug little pedantic bastards? We could have strung that out, like "I was writing in binary" ... "no you weren't" ... "yes I was" ... "no" ...
Atomicninja - It is really 1 the ( ) go first. So it's 1+2 first which equals 3 obviously. Then the equation is 6/2 x 3 (the / is a division symbol). Then you multiply 2 into 3 then it's 6/6 and then your final answer is one. Simple to learn in school easy math.
first off 6/2=3 is already wrong because there is no multiplication 6/2(3) is not the same as 6/2*3 or 6/2*(1+2) if you want to elimate (1+2) the equation should be (6/3) / (2(1+3)/3) then you get 2 / 2 =1 or simply just 6/6=1 The correct answer is 1 because 2(3) is somewhat like y(x) which means the value of y is multiplied by x time.. going that approach 2(3) is interpreted as 2+2+2 = 6 6 / 6 = 1 the algebraic expression is z / y(x)=
I graduated in 2003. I was and am pretty good in math subjects. I was taught to solve this with the answer of 1. The brackets are to be dealt with b4 other division of multiplication occurs
Seems we all historical and the new version only rules in special areas, clearly the areas where I’m not. I live in South Africa and here the answer is still 1🤣 should you want the answer to be 9 it would be written as a fraction not a division sign(which can’t even be found on my keyboard, so let’s just all retire the devision symbol and I’d be happy to concede that the answer is 9😂
Basically the answer isn't "wrong" if you use the historical version... they're just asking different things... in modern math, it you wanted to ask the exact same question as the historical you would have to write is 6÷[2(1+2]
@@willwalker24601 It comes down to "just use brackets to make clear what you mean". Mathematics is supposed to be a universal language, but there are still a lot of dialects, aka different notations. I see that a lot lately as I am german but using english youtube videos to review some things since I am studying for a new profession. They are doing a lot of things differently than I learned them at school 20 years ago. Maybe they do them that way in schools now too, I don't know. But since such differences exist, one should strive to write expressions as clearly and unambiguously as possible. Most of those "puzzles" thrive on their ambiguouty.
✔️✔️✔️👍👍 Correct answer is surely 1 To those who are telling it 9 Dont know how? For this xy ÷ xy = 1 But Its not y²(according to those who are telling answer to be 9) Similarly, 6÷2(3)=6/(2*3)=1 As simple as that...
I can ensure you that in most Stem environments the symbols ÷ and / are pretty much forbidden, every division must be written as a fraction, so all formulas and expressions are just sequences of products of franctions, and the length of an horizontal line is clearer than any pemdas rule
6 ------(1+2) = 6÷2(1+2)= 9 2 6 ---------- = 6÷(2(1+2))=1 2(1+2) WHY?? Because the vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum groups operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator... ________ 2(1+2) = (2(1+2)) two grouping symbols each Objective facts...
@@realGBx64 Most people confuse and conflate an Algebraic Convention given to coefficients and variables that are directly prefixed and form a composite quantity by this convention to Parenthetical Implicit Multiplication. They are not the same thing... 1/2x = 1/(2*x) by Algebraic Convention 1/2x^3= 1/(2*x^3) by Algebraic Convention 1/2(x)= (1/2)(x) by the Distributive Property 1/2(x^3)= (1/2)(x^3) by the Distributive Property... 1/2x and 1/2(x) are not the same thing.
The comments section is amazing. One of the top comments concludes that you are doing a disservice to kids trying to learn mathematical protocols. I bet you didn't see that coming.
Your math teacher has issues but as long as he is grading you I suppose you need to do what is expected... There is nothing wrong with the way the expression is written just the ignorance people have about parenthetical implicit multiplication...
@@RS-fg5mf Isn't that the whole point - it is perfectly valid but makes it unclear and you have to think about it - are you mad because you got it wrong? I would be a bit concerned about your math's teacher.
@@justcheck6645 I am a math teacher and I didn't get it wrong. LMAO When you actually understand and apply the Order of Operations and the various properties and axioms of math correctly you get the correct answer 9.... Did you get it wrong??
Edit: I was wrong, operator precedence makes the answer clearly 9. A way to avoid this confusion from people like me who got lost in the order of operations would be to set up the equation as (6/2)(1+2) or (6/2) * (1+2). Note: Contrary to popular belief in this thread, I did graduate with my bachelors and also complete Basic Calculus with high marks. I am capable of error and my original comment was one of those errors. Thank you for the correction. Original comment: I graduated with my Bachelors in 2019, the answer according to the way I was taught throughout my education is 1. Because I was instructed by my professors to visualize this problem as 6/(2(1+2)) or 6/6 which equals 1. The person who wrote this did so in a way that is designed, purposefully or ignorantly so, to cause confusion. Dr. Trefor Bazett has an insightful video on this topic
Are you saying that you took university level math within the past 10 years and your professors taught you that in the case of 6➗2(1+2) you’d make 6 the numerator with the 2(1+2) being the denominator? Ima have to throw the bs flag on that one. It doesn’t even make sense that your professors would have even been instructing you on this when this is just basic math that young kids learn. It’d be like saying “When I was pursuing my master’s degree and my professor was teaching me my times tables…” If you took this stuff recently, you’d have been taught to solve left to right 6/2x3 =3x3 =9
Dr. Trevor Bassett is wrong and so are you... 6 ------(1+2)= 6÷2(1+2)= 9 2 6 ---------- = 6÷(2(1+2))= 1 2(1+2) The vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum groups operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator. ________ 2(1+2) = (2(1+2)) Two grouping symbols each ________ 2(1+2) has two grouping symbols (2(1+2)) has two grouping symbols
@@trickortrump3292the bigger question would be why a University would be using the grade school obelus to teach higher level math... We have reviewed the video and the penalty flag stands... Good call Ref....LOL
@@RS-fg5mf Yeah I deserved that. When I first looked at it, I solved it your way and then the video told me I was wrong. I bought into the reasoning for why I was wrong. This question is just a mess! I went down the rabbit hole yesterday after my comment. It’s insane to me that so many experts seem to say that the right answer is “there is no right answer” because it can be correctly solved two different ways, yielding two different answers. I can’t accept that. If both answers are correct, that makes both answers wrong too. I’ve removed the bs flag I originally threw. 👍😉
@@trickortrump3292 don't remove it. LOL The red flag stands on the play because you are absolutely correct... The only correct answer when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended is 9 I was agreeing with you. Don't let these mathematical numpties change your mind. Those who understand and apply the basic rules and principles of math correctly as intended will get the correct answer 9 Those who fail to understand and apply the basic rules and principles of math correctly as intended will get the wrong answer 1 Those who can't prove 1 and can't accept 9 will argue ambiguity... Failure to understand and apply the basic rules and principles of math correctly as intended doesn't make the expression ambiguous and isn't a valid argument against the expression...
I am 45 years old and have honours degrees in Engineering and Science. We were always taught that the answer should be 1, because of the order of operations rule that we were taught to use. If you change the rule, you change the answer. I was not aware that the rules had changed!
It seems that multiplication by juxtaposition, ab or a(b) etc., may impliy grouping, or it may not, so the notation is ambiguous making both answers valid. It depends on context (e.g. academic or programming). It's just bad writing. Modern international standards, ISO-80000-1, mention that brackets are required to remove ambiguity if you use division on one line with multiplication or division directly after it. The American Mathematical Society's official spokesperson literally says "the way it's written, it's ambiguous" even though they use the explicit interpretation. Wolfram Alpha's Solidus article mentions this ambiguity also. Microsoft Math gives both answers. Many calculators, even from the same manufacturer, don't agree on how to interpret multiplication by juxtaposition. No consensus. Other references are: Entry 242 in Florian Cajori's book "A History of Mathematical Notation (1928)" (page 274) "The American Mathematical Monthly, Vol 24, No. 2 pp 93-95" mentions there was multiplication by juxtaposition ambiguity even in 1917 (and not the ÷ issue) "Common Core Math For Parents For Dummies" p109-110 addresses this problem, states it is ambiguous. "Twenty Years Before the Blackboard" (1998) p115 footnote says "note that implied multiplication is done before division". "Research on technology and teaching and learning of Mathematics: Volume 2: Cases and Perspectives" (2008) p335 mentions about implicit and explicit multiplication and the different interpretations they cause. Other credible sources are: - The PEMDAS Paradox (a paper by a PhD student on this ambiguity) - The Failure of PEMDAS (the writer has a PhD in maths) - Harvard Math Ambiguity (Cajori's book above is talked about here) - Berkeley Arithmetic Operations Ambiguity - PopularMechanics Viral Ambiguity (AMS's statement is here) - Slate Maths Ambiguity - Education Week Maths Ambiguity - The Math Doctors - Implicit Multiplication - YSU Viral Question (Highly decorated maths professor says it's ambiguous) - hmmdaily viral maths (Another maths professor says it's ambiguous) The volume of evidence highly suggests it's ambiguous.
@@bigbadlara5304 The answer is one because this video makes a mistake by ignoring that these equations require the distributive property. If you "just graduated" I'm not at all surprised that no one taught this...
@@nixboox Distribution can give both answers as it is a notational ambiguity. There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. I.e. does 2(1+2) = (2×(1+2)) or 2×(1+2)? Implicit: 6÷(2×(1+2)) = 6÷(2+4) = 1 which is used by academic writing. Explicit: 6÷2×(1+2) = (6÷2×1 + 6÷2×2) = (3 + 6) = 9 which is used by modern programming and also by the American Mathematical Society according to their statement on the matter. That's why it's ambiguous. The rules can't help when the problem is the notation which has to be interpreted first. It's just written poorly and not in line with modern international standards. It should be (6/2)(1+2) for 9 or 6/(2(1+2)) for 1. Those are unambiguous and follow the guidelines.
Seems like so, since there is an implied multiplication that _normally_ implies grouping with parentheses, so it's *6 ÷ 2(1+2) = 6 ÷ (2 × (1+2)),* not simply *6 ÷ 2 × (1+2).* Though I guess some people in the comments might not agree with this position (just like the author of this video).
@@godelnahaleth No, you were not taught to follow PEMDAS as 6 exact steps... SMDH Own your mistakes and stop blaming your teachers for your failure to pay attention in class and learn correctly...
@@RS-fg5mf Nope. 2(3) is not the same as 2*3. Anyway it's been 4 years since I came across ÷ sign. I only use fractions and never had to come accross controversial problems like this one.
Check Wiki on the order of operation, it is indication that there is an ambiguity/confusion with expression like 1/2x for some it is (1/2)*x = x/2 and for other it is 1/(2*x) Here we have the same type of problem : a/bc, so same problem : is it (a/b)*c or a/(b*c) If for you it is not confusing, then you do not know math enough, because to remove the confusion in that sort of expression, there is a rule that apply to in-line math expression : "Always add parentheses to delineate compound denominator" So here the first thing to say is that "that expression do not follow the rule for in-line math, so It can't be solved using the order of operation; It has to be corrected first" And the problem is that it seems that a lot of people do not know that rule, so they give the result corresponding to one interpretation or the other ... making it viral Should all of those people go back to school ? Or should only the one that wrote that ambiguous expression go back to school ?
It's simply ambiguous notation. A trick. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity. Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too. Multiple professors and mathematicians have said so also like: Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc. Even scientific calculators don't agree on one interpretation or the other. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why. A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4
I prefer using ÷ over /. I only use / with fractions, but use ÷ when dividing numbers. Using improper fractions instead of using the division symbol is something that I rarely ever do. I never find it confusing when using ÷, and it never confuses me.
@@MarkQub. What do you mean 'nope'? I just stated that I prefer using this: *÷* of this: */,* when dividing. The person said that nobody uses ÷, because it's confusing, so I said that I do use ÷, and that it doesn't confuse me.
Me too! And I was born long after 1917. My scientific calculator may be old, but it too was built long after 1917 and according to that calculator the answer is 1.
@@InsanityoftheSanitiesthere is no rule in math that says you have to open, clear, remove, take off, eliminate, get rid of or dissolve parentheses. The RULE is to evaluate operations WITHIN the symbol of INCLUSION as a priority and nothing more... (1+2) is a parenthetical priority. 2(3) is not a parenthetical priority and is mathematically the same as 2×3 There is no mathematical difference between 6÷2(1+2) and 6÷2×(1+2) despite the false and misleading information and willful ignorance people have about parenthetical implicit multiplication...
Eventually, yes. This is a fifth-grade expression used to teach and reinforce the order of operations. This is pretty much ground zero. From there, we stop using the obelus in favor of the solidus and vinculum and go into fractions, as well as teaching reciprocals and the multiplicative inverse. People just forget how to evaluate expressions using the order of operations due to lack of practice. Sometimes, all they remember is an acronym and then convince themselves that there are six steps instead of four and that multiplication always comes first when it doesn't.
@@pirilon78 Who says I did? I never even hinted that we don't use the order of operations beyond junior high. It should be common knowledge that we do.
I'm 40 y/o and was taught the historical way in school. I don't feel historical though. I feel f*cked over because somewhere along the line people decided to change the rules of the game (and didn't inform me!!)
I hate order of operation squabbles. That is not math, it is convention. If there is a governing body for math they should get together and design a convention that is definite, obvious, and universally agreed upon and taught. I was taught the historical method, but knew the current method, so I knew there were two possible answers depending on which system you used. (Not counting the latest anti-racist belief that every answer is correct because saying there is a definite answer would be racist.)
@@PuzzleAdda we cant. All of these numbers are in the form 2+4k where k is any number from { 0, 1, 2, ... , 14 }. The equation would be (2+4k)+(2+4l)+(2+4m)=60. After we simplify this we obtain k+l+m=27/2 but all of k, l and m are whole numbers. Therefore it is impossible to obtain 27/2 by suming k+l+m and the equation does not hold.
@tepig360 pikachu720 Assume A = 1+2 then 6/2A = 6/2(1+2). And that means 6/2(1+2) = 6/2A. 6/2A has no parenthesis. How the hell will you "do the parentheses" when there is no parenthesis?
Not sure where you're getting your "modern interpretation" from but certainyl in the UK 6 ÷ 2(1+2) wouldn't be treated as (6 ÷ 2)(1+2) because the implicit multiplication where no dot or multiplication symbol is used takes the same priority as the bracket. So, 6 ÷ 2(1+2) would be read as 6 ÷ 2y where y=1+2 If the original were written as 6 ÷ 2 x (1 + 2) then 9 is the correct answer but when written as 6 ÷ 2(1+2) 1 is still the correct answer.
You are wrong. It's the same thing whether it's written as 6 ÷2(1+2) or 6 ÷ 2 × (1 + 2). The multiplication symbol is implicit. The only way it could be written to equal 1 is 6 ÷ (2(1+2)).
Yep very sleepy there when I wrote that. I meant that in order of operations 2y is treated there as a single unit, 6 ÷ 2y = 6/(2y) rather than (6/2)y ie 3/y vs 3y
How can we get 60 by adding only three numbers out of these: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, & 58? Answer - ruclips.net/video/LZN4m-cPJkg/видео.html #PuzzleAdda
As you climb higher in math, virtually 100% of physicists, engineers and mathematicians will interpret the answer as 1. There is no debate over this at all. The implicit multiplication of 2 on the bracket is a SINGLE quantity that takes precedence prior to division. Most physicists/engineers/mathematicians would never even write such a potentially ambiguous expression. They would instead write 6/2(1+2) where the / is a horizontal line. Alternatively, they would write 6/(2(1+2)) leaving NO ROOM FOR AMBIGUITY. PEMDAS is NOT universally accepted. The implicit multiplication on the bracket does indeed take precedent. You are doing a disservice to kids trying to learn mathematical protocols. PEMDAS isn't the total protocol.
It is really funny indeed, because it gives a hint from "where people are coming". I studied physics for some time and it was completely obvious to me, that a juxtaposition has a higher order than "read left to right". It's "obviously" 1. As mentioned; 6/2y with y=1+2 is 3/y, not 3y.
Tom Yes. You give a great example. According to PEMDAS, x/yz = xz/y which is OBVIOUSLY unconventional. The implied multiplication of yz binds the two components of 'y' and 'z' together.
What does attending school in Appalachia have to do with it? Yes, I did and I was taught the 1917 way I guess from 1996-2013. WCU was still using in it in 2013, and so was all the other kids from other parts of the US.
honestly i dont know how long ago people didnt use the order of operations but im sure that in the 80s all mathematicians used it. id go as far as to say it probably existed at least a thousand years ago
realistic dan Appearantly my wife was retaught the correct way when she went to UMiss. Guess that why my kids always come home with the wrong answers when I help them do their school work
@@sensei5668 sure it is the same thing. but with fractions the error couldn't happen as the order is directly visible. I personally haven't seen that operator once in university. If you are forced to write in one line (e.g. in programming) people use "/"
First of all: 6/2(1+2) is the same like 6/2*(1+2). Even if it is not written, the * is between the 2 and the brackets. 6/2*(1+2) Solve the brackets first = 6/2*3 Solve the division = 3*3 Solve the multiplication = 9
It is not the same. A scientific calculator makes a difference between 6÷2(1+2) and 6÷2*(1+2). Mine gets 1 for 6÷2(1+2) and 9 for 6÷2(1+2). It's simply not the same.
after you add the numbers in the brackets, its not a bracket anymore, it simply becomea 6 ÷ 2 × 3- then because in BODMAS division comes before multiplication, you do 6÷2 which is 3, and then multiply that by 3.
It’s 9.. how is this even viral, it’s 5th grade math.. Also, I’m referring to PEMDAS which is taught in 5th grade. Watch the video if the answer you got wasn’t 9..
Please read this comment, thank you. Solve for the 2 in parentheses, it is not a bracket [ ] 6/2(1+x)=9 3(1+x)=9 3+3x=9 3x=6 X=2 The problem is that people who think that it is 1 believe that after simplifying 2(1+2) is that they think it is the denominator of the fraction. For that to be true, there must be a parentheses in front of the 2.... (2(1+2)). You will do that first if that was in the problem, but it isn’t. 6/2(1+x)=1 6/2+2x=1 Now you see that there is a fraction, but what can it be. If it is 2+2x, you get 2 as your final answer, which is correct. If it is just 2, you get -1, which is incorrect. However, you do division before addition, so you do 6/2 to get 3, eventually getting -1 as the solution. 3+2x=1 2x=-2 X=-1 This is incorrect, because we are trying to solve for 2 in the parentheses... 6/2(1+x)=1 X should equal 2. People think that after distributing the 2 into (1+x), the whole thing stays in the parentheses. It disappears after you distribute. Thank you for your time.
In France i've been taught it in a way, that this equation equals 1. Basically 6/2(1+2) has brackets. We were taught that brackets were always a priority with the number infront of it. So what we would do is first 2*1 + 2*2 = 6, and once we got the brackets completely gone, we can finish the equation which would be 6/6 = 1. Also even if i added the numbers, it was always important to clear the brackets. Here 6/2(3) still has a bracket and doesnt just dissapear. So i would multiply 2 and 3 to get rid of the bracket. Thus we still receive 6/6 = 1 I was always taught this way and was surprised seeing that the correct answer was 9. This blew my mind
I'm pretty sure that in germany we were taught the second answer as well (equasion equaling 1) for the exact same reason you describe here (getting rid of the brackets first) and then finally dividing anything on the left side by what is left on the right side. From my point of view the answer 9 is "wrong". And even if it's just a "rule" thing, we'd better universalise that rule. To me, somehow, the answer "1" also makes more sense in a mathematical- asthethical way.
People in Europe, born before 1970, learned, that multiplication goes before division. Just a fact. I mentioned 1917, because in that year, in the USA it became official that multiplication and division are equal and You start from left to right. In 1980 is was commpn practice all around the globe. ( In the Netherlands it took till 1992 to use the 1917-method). Mathematics is about agreements and those changed over the years to an (new) international standard...
@@j.r.arnolli9734 Thank you for this insight. Anyhow I was born in 1980 and I'm pretty sure that if I showed this "problem" to my old schoolmates/ peers here in germany 99% would come up with the anwer "1". Yet again maybe I'm wrong. If this really is new international standard it still doesn't make a whole lot of sense to me in terms of logical usage of mathematical language.
Yes you are correct the answer is 1. You solve the brackets first to get a number on its own then you finish off by 6 ÷ the answer in the brackets. If your answer is 9 then you are inventing your own mathematics !
Just ask them if they've taken advanced functions or calculus, and then tell them if they ever used the ÷ symbol instead of /. I think thats some pretty solid evidence I should say
As a trained engineer in his forties, I immediatey turned the expression into a fraction. I also have to say I don’t think I’ve ever seen that division sign used anywhere after fourth or fifth grade.
And in 4th or 5th grade arithmetic the correct answer is 9 .... The symbol is found on almost any calculator. Best to understand it than to be confused by it...
Funny, I just left a similar comment. I’m an engineer (39 yrs old) and did same as you. That’s the reason engineers and physicists don’t use that silly division symbol.
@@Superdada i don't understand the debate about the division symbol. what difference does it make whether you use : or / ? they do mean the same, don't they?
I haven't read any comments yet, but you could also be wrong in your interpretation of the order of operations. once you add 1 and 2 you're left with a 3 inside parentheses, and a convincing case may be made that since it's inside a parentheses, your're supposed to resolve that operation before the division, since parentheses trump multiplication/division... so again 1
Yeah, that's the logic my father taught me. It should not matter what order you do multiplication and division so long as one does not cross addition and subtraction (once parenthesis have been solved). The method being shown means that it is neccesary to solve the division and multiplication in a specific order because you will either end up with a 6/6 or a 3*3 depending on which order you do multiplication and division.
This means you were taught incorrectly or that you remembered it wrong. There is no ambiguity for modern usage of mathematics, and the RUclipsr you just watched said it himself. DO NOT distribute before dividing because you are essentially multiplying that number to the other numbers inside the parenthesis, which breaks the rule of precedence
@@FloraLemonYT You always distribute 1st as this is part of solving the parenthesis. The value of the parenthesis is 6 not 3. (2*1+2*2)=(2+4)=(6)=6 Remove Factor 2(1+2)=(2+4)=(6)=6 combine terms 2(3)=(2*3)=(6)=6 Although the common factor has been "removed" and written before the parenthesis. It remains a part of the parenthesis. It must figure in the evaluation of the parenthesis to get the correct value of 6. This is why they say that the 2 is stuck to... or a prisoner of...- the parenthesis, it can not be used anywhere else or the parenthesis will not evaluate properly. So 6/2(1+2) = ? 6 / 2(1+2) = ? 6 / 2(3) = ? 6 / 6 = 1
@@mikestuart7674 the coefficient of a set of parentheses is NOT part of the parentheses because it is essentially a means of multiplication. Thus, you are multiplying first while there is a division operation behind it, making it a non legal method.
@@charliedallachie3539 thats not using the numerator and denominator, when you use an actual numerator or denominator you would have a certain part be under it. Either 6/(2*3) or (6/2)*3
@@o_sch yea I understand the two answers but in other problems which is which? I’ve always wondered PEMDAS in general I’m sure there’s a complex mathematical proof of it out there somewhere Edit* there is no proof it’s a convention.
@@JakobSchade Sure, but that's if you use PEMDAS or whatever else. There's still plenty of books where they don't use PEMDAS and have a difference between implicit and explicit multiplication. 2*3 is explicit (a * sign) and 2(3) is implicit. In that case, implicit is many times higher of importance than explicit. So 6/2(1+2) would simply be 6/6=1.
It depends on which interpretation of multiplication by juxtaposition you use. Modern international standards like ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
+Jacob Riley stop acting the smarts. It's not about not being able to solve sums, it's about the different ways of solving it leading to different answers, and the debate around it.
+aaron melrose That doesn't excuse the people who blatantly ignore the rules explained to them in 5th grade math class. But it is fun to see the discussion over whether people think the distributive property should take hold first, or if the current use of PEMDAS has priority, or even if they prefer the historical reference of (whatever)÷(whatever).
+Jacob Riley You realise the answer is actually 1? Turn the sum into a fraction you 1. Plug the sum as appeared into the video into you calculator you get 1. Use bodmas until you get to 6 divided by 2(3). This can be represented as X divided by 2(Y). This is not the same as (X divided by 2)(Y). So it can't even be 9 because X is one term and 2Y is a separate term.
1 isn't wrong though. It is just as valid as 9 as It's simply ambiguous notation. A trick. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. So it's the juxtaposition of 2(3) allowing 6 with the academic interpretation, not because of the parentheses. 2×(3) instead still has parentheses but no juxtaposition so 6÷2×(3) would be 9 using both interpretations. Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity. Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too. Multiple professors and mathematicians have said so also like: Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc. Even scientific calculators don't agree on one interpretation or the other. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why. A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4
@@DadgeCity The expression 6/2(1+2) will not evaluate to that. You are violating the Distributive Property. In order to fully understand this I will impose a set of parenthesis that does not change the expression. (6/2)(1+2) which will evaluate to (3)(3) = 9 or (3 + 6) = 9. In order for you to have the 6 solely in the numerator and the expression 2(1+2) in the denominator you would have to impose this set of parenthesis which will change the expression 6/(2(1+2)). Then this will evaluate to 1. Therefore (6/2)(1+2) != 6/(2(1+2)) and if you don't believe me put both expressions into a TI Graphing Calculator!
If you dont carefully listen to what your teacher says then you will get it wrong. I remember my teacher saying that if multiplication and division are the only ones left, you'll solve them from left to right. Same goes to addition and subtraction (If they're the only ones left)
As a person with a masters in math, I totally agree with you and if I needed to communicate some math operations, and I would never rely on PEMDAS; use parentheses!!!
The graphic of the equation is textbook normal. 6 ÷ 2(1+2) Note the position of the 2( No space. It's presented no differently than any n(x) So it's a coefficient of the single quantity, in which x(a+b) = (xa + xb) By distribution. The graphic is presented with 2 as a coefficient. Answer: 1, not ambiguous. That's how the graphic depicts it.
Sir, I am in MAT 85 at a community college and recently learned about the distributive law,,,,2(1+2)=2(1)+2(2)=6 and was going to show it on this problem, but when I used the distributive law to get rid of the brackets I ended up with 7 and know the correct answer to be 9. Why does the distributive law not work here and how do you know when you can use it to get rid of brackets?
+Kenney Simple. y ÷ x(a+b) as given. That returns y ÷ (xa + xb) 6 ÷ 2(1+2) as given. That returns 6 ÷ (2 + 4) That's 6 ÷ (6) = 1 Had there been different spacing, or some graphic difference, there might be a lawyer's argument. But 2(1+2) is s monomial; single quantity.
dont worry, this issue will never show up in important engineering situations because the division symbol would never be used. instead using a fraction would make everything a lot more clear
The real-life solution, as per the ISO recommendation, is just to use brackets to disambiguate. (6/2)(1+2) is totally clear regardless of division symbol used and works for handwriting, calculators, typed documents etc.
The term 2(1+2) = x(a+b) = (xa+xb) = (2x1+2x2) = (6) Thus: 6÷2(1+2) = 6÷(2x1+2x2) = 6÷(2+4) = 6÷(6) = 1 There are 4 terms in this equation, not 5: 1) the 6 2) the 2(a+b) containing: 3) the 1 4) the 2 If it were written as 6÷2*(1+2) THEN there would be 5 terms and answer would be 9. 1) the 6 2) the 2 3) the (a+b) containing: 4) the 1 5) the 2 The 2(1+2) is a SINGLE term which must be resolved first before being divided by 6. The issue is that 2(1+2) --> (2x1+2x2) --> (6) RETAINS THE PARENTHESES thus resulting in 6÷(6) = 1
You distributed. Distribution is a property of multiplication and division. So essentially you multiplied first. But you can't do that! Parentheses go first, as stated in PEMDAS. So first you must reduce (1+2) to (3).
lohphat 2(3) is not a single unresolved term, it is two different resolved terms multiplied together. You can't just divide 6 by it, you must remove the brackets first and turn it into 2*3. Then you divide, so 6/2*3 = 3*3, which is 9. Remember, just because there is no multiplication sign (it's called implicit multiplication), it does not make it a single term - after you solved 2(1+2) into 2(3), you can (and HAVE to) remove the brackets, so 2(3) = 2*3.
lohphat You're not changing anything. Who taught you that 2(3) is not 2*3? It's called implicit multiplication. It is used when the multiplication sign can be substituted by a pair of brackets. It does not change the value of the equation at all. 2(3) = 2*3 in all cases. Just because the multiplication is implicit, it does not hold any priority over the normal (explicit) multiplication, unless you want to invent a new rule or something.
Olaoluwa Johnson According to his “procedure”, you work left to right when you have multiplication and division across the problem. If you do it that way, then 6➗2/3 = 1. If you punch that into a calculator, you get what I get, 9. In addition, what’s the point of solving inside the parentheses first, when you later show that it doesn’t matter. Just say (6 ➗2)(2 +1) = ?
Anthony Melvin following what I was taught, I’d be: 2(1+2)=2(3) It started in parentheses, so it stays in it. And because it’s in a parenthese, it goes before division (*P*EMDAS): 2(3)=6 6/6=1
I might decide that I want the word "its" to mean the same as "sit" but it wouldn't make much sense. Here is a link to order of operation rules: www.mathsisfun.com/operation-order-pemdas.html
And presh don't deviate by using z and y just concentrate on 6×1/2×3 = 9. Don't use your own rules. From where you get 2×3=6. It is ÷2×3=3/2. Go do your homework before you open your mouth
you need to change schools, or actually, and more accurately, go to school in the first place. i say you're full of shit, and that you have no exam next week.
+Henry Lembeck no, it is not. Multiplication before devision .... New math "rules" don't apply because nobody can change them without consent from all humans. That never happened so ...
Clearing the parens is not simply performing the operation within but also performing the operation dictated by the parens. Therefore the operation requires multiplying 2x3 to get 6 prior to the next operation. If the equation was: 6 divided by 2y there would be no ambiguity that it would be 6/(2y)not (6/2) x3.
Nope, if you got 6÷2y you do 6/2 times y. Its just the current rules, i agree its weird and maybe confusing because we never use "÷", we always use fractions, but the rules are the rules and they say that if theres no parenthesis, you only divide by the first number, the closer to the "÷" symbol. Which is 2, therefore 6/2 × 3 = 9
You are using PEJMDAS like in some calculators (not all of them). J meaning Juxtaposition. But this is not PEMDAS which is the official math rule for instance in USA.
@@siyamchowdhury9492 And you're the bad grammar guy, duh ding ding ding ding ding ding ding ding (I don't like Billie Eilish for those who r gonna go mad at me and I did copy paste the name)
srsly. That's just an example for bad notation. Of course the answer is 9. It's still bad notation. This division symbol just shouldn't be used anymore.
EXACTLY! It's a matter of confusing notation, but in *that* notation, the answer is 9. If you rearrange it using the "/" sign, the answer will be different! That's because (1+2) is actually a coefficient of 6/2!
***** I am aware of that. But I guess even at my university there are some people who would get this wrong. This is terrible notation that is not useds in real life.
I also got 1. But that is because I do not see 3(2+1) and 3x2+1 as being the same. It seems logical to me that if the lack of space between the "3" and the bracket means that this 3 is multiplied by whatever is in the brackets then they should be viewed as inseparable and therefore that operation comes first. Then, and only then is the product a usable number in the overall equation which is the division of 6 by whatever is on the right side of what was obviously meant to be the last operation, the division itself.
Oh, wait... I used the wrong original equation. I meant that the "2" is up against the bracket. so from 6 -:- 2(2+1) I get 6 -:- 2(3), then 6 -:- 6 = 1
Glad I'm not alone. ;-) I remember when math made logical sense.. Now they change a detail somewhere in the text and everything is off, again! How are we supposed to use this "universal language" that is Math to communicate with aliens if we can't even agree on the rules?! There's only so much you can do with tinfoil. LOL
It’s 9 because let me show you so pemdas is parentheses first exponents next multiplication and division in the same step and then it is addition and subtraction in the same step so 6/2(2+1) so 2+1=3 then it is 6/2•3 ,6/2=3 and 3+3=9 SO THE ANSWER IS 9
It's simply ambiguous notation. A trick. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. That's the issue. You can't prove either answer since it comes from notation conventions, not any rules of maths. Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity. Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too. Multiple professors and mathematicians have said so also like: Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc. Even scientific calculators don't agree on one interpretation or the other. Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why. A recent example from another commenter: Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example 8 ÷ 4(2) = 8 ÷ 8 = 1 but 8 ÷ 4 • 2 = 2 • 2 = 4
My gut instinct was 1. I assume most people who go through higher math or science courses will naturally gravitate toward 1. To get 9 as the answer you'd be limiting yourself to notational rules and not applying the formula in any way with applied meaning.
Now that I think about it a bit more, it might be illuminating to check the math by rewriting the problem as an algebraic formula: 6÷2(1+x)=1, solve for x. First you'd distribute the parenthetical expression and get 6÷(2+2x)=1. Then you'd multiply both sides of the equation to get 6=2+2x. Then subtract 2 from both sides to get 4=2x and thus through division you see that x=2.
Yeah I think they are not getting that 2(x+1) whilst it looks the same as 2*(x+1), it is NOT as the brackets are still in play. You would be required to drop the operator precedence to change 2(x+1) to 2*(x+1) The former is a single calculation and the later is two calculations.
Lame problem. Don't use the division symbol inside more complicated expressions is the only lesson here. But, does anyone read x÷2y as anything other than x/(2y) in practice? Regardless, sloppy use of notation does not an interesting math problem make.
The answer is most definitely one. Put it into a fraction and you divide top and bottom by 2 leaving 3/3. Even you use bodmas,my out get 6 divided by 2(3). This can be represented as (X divided by 2(Y)). Which is not the same as (X divided by 2)(Y). The answer is 1
Yea i'm 19 and I've never seen where you would do 6 divided by 2 first. I was also taught the division sign and the fraction notation are interchangeable.
Yes, Harlequin, I believe you're right. In algebra, for solving equations to find unknowns, x divided by 2y had better be understood as x/(2y) and not (x/2)y if one wants to get the correct answer. I also think that it is better to have the same rules across algebra and arithmetic so as not to confuse ourselves. Thus, even though the presenter says that x/(2y) is an older convention, I feel it is the more useful convention and not the supposedly current one. This is seen from the following steps: 6 divided by 2(1+2) = 6 divided by [2X1 + 2X2] = 6 divided by [2+4] = 6 divided by 6 = 1 (sorry, I don't know how to reproduce the 'divided by' sign)
Pretty nice way of saying it. It's like "A union B intersection C" in sets and expecting a certain answer. You can't write that either because it's ambiguous.
@@GanonTEK PEMDAS is not ambiguous. 6/2(1+2) Parentheses first 6/2(3) Multiplication and division left to right 3(3) 9 There is no ambiguity. The ambiguity is people not recognizing 6/2(3) = 6/2*(3) = 6/2*3 = 9. Implied multiplication is treated the same as regular multiplication. The it’s the same as “I didn’t read the question correctly, therefore I am not wrong”
@@Owen_loves_Butters There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not. I.e. does 2(1+2) = (2×(1+2)) or 2×(1+2)? Both are widely used. 6÷(2×(1+2)) = 1 (using PEMDAS) 6÷2×(1+2) = 9 (also using PEMDAS) PEMDAS isn't the problem. The notation used is. That's the cause of the ambiguity. That's why there is such a large disagreement and even calculators from the same manufacturer don't agree. You shouldn't write a/bc or a/b(c) anymore. It's not acceptable notation. ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove any ambiguity. A PhD student wrote a paper on the ambiguity called The PEMDAS Paradox if you want to look it up.
"implied multiplication" - there's no such thing - you won't find it in any Maths textbook. "it is simply a poorly written expression" - no it isn't. a(b+c) is the standard form of a Factorised Term, to be expanded according to The Distributive Law, a(b+c)=(ab+ac), as part of the Brackets step.
@@cyberagua Do you mean what is it's correct name? A Factorised Term - I already said that. ab+ac=a(b+c), Factorisation. a(b+c)=(ab+ac), Distribution. A Factorised Term, being a Bracketed Term, is solved at the Brackets step. It's not "multiplication" because there's no multiplication sign, which is what "Multiplication" quite literally refers to. ax(b+c), multiplication. a(b+c), distribution. In a(b+c)=(ab+ac), the "multiplication" - if you even write it at all - is INSIDE THE BRACKETS, (axb+axc). If you treat Distribution as "Multiplication" then you end up with wrong answers, as we've seen!
@@smartmanapps5588But why do you use x's instead of the regular multiplication signs "×" or "•"? Are you typing from a Mac or PC that doesn't have these symbols on the keyboard? It slightly interferes with reading and understanding your messages, since *axb* reads as *a·x·b.*
@@smartmanapps5588> you won't find it in any Maths textbook Do instructions to the calculators count? Calculators are _math_ devices. From Wiki: "In algebra, multiplication involving variables is often written as a juxtaposition, also called implied multiplication." Source: "Now, _implied multiplication_ is recognized by the AOS and the square root, logarithmic, and trigonometric functions can be followed by their arguments as when working with pencil and paper."
The issue is, I agree that with the same precedence you go left to right so if it said 6 ÷ 2 × 3 I would correctly answer that as 9. However by wording it as 6 ÷ 2(1 + 2), my mind goes to expand the bracket first which gives 6 ÷ 6 = 1.
This. I was taught (in the US) completing the parentheses/brackets meant you did all involved with the parentheses/brackets. Here, the parenthesis is what symbolizes the 2x3 so you still do that before the division.
The rule is called BODMAS or BIDMAS It is the order of what you do first Brackets Indices (or other) Division & Multiplication Addition & Subtraction So here first we do the brackets 6 ÷ 2 (1+2) 6÷ 2 (3) 6 ÷ 2*3 Next we do division 6÷2*3 3*3 Next we do multiplication 3*3 9
![NOSFERATU - Official Trailer [HD] - Only In Theaters December 25](http://i.ytimg.com/vi/nulvWqYUM8k/mqdefault.jpg)
20 million views!
Really a good video!
lesgo
It has millions of views because the problem initially looks too simple to have a video (and it is an excellent video).
I wondered if I missed something and chose to watch.
So, the order of operations rules were revised and both 9 and 1 are correct answers.
I thought it was 1 (the algebraic grouping of terms as you noted).
Great to know the rules changed.
Thanks for making the video.
@@idontclickbait8453 It is a good video
Great video, still slightly confused because I am taught that x(y) is one term and should be treated as 1 number but glad to learn that there are 2 different systems
1960 we will have flying cars in the future
2020: world debate over 5th grade math
daniel rushing this is probably 5th or 6th
Ya true but either way
Nope, it's 2nd (in my country)
adomnibest lol I learned it at 5, #homeschooliscool
5th grade too
The correct answer is 9 but the way I was taught math makes me keep saying 1
MOLO 27 yes 🤔
MaxMisterC Both of them state that multiplication and division have the same importance, and are some left to right. Put it in a calculator if you disagree.
@@MaxMisterC Heck it wasn't even that for me. I always just ASSUMED (don't remember if it was actually in the education I got) that anything next to a bracket was in itself inside "invisible" brackets. So if you had 2(1+2), it would simply be read as (2(1+2)) = 6 regardless of what was put in front of it. I guess I never really bothered searching up if this was wrong, OR that my teacher might have been in the same group that still insists on this sort of thinking. Either way the new method (answer of 9) is correct and there just isn't much you can do about it. That's the rule and that's how maths works I guess.
@@berdyie there is no such a rule in Maths.
@@raynatumbeva780 For my incorrect way of thinking or for the correct method in the video?
This is not a math problem... this is a rule problem....
The rules support the correct answer 9
Yeah, technically this rule doesn’t have to be a thing. Just for convenience.
Blubber Beast um it definitely DOES have to be a thing. It’s there for a reason
@@jude3426 it doesn't give priority to multiplication over division...
It is for convenience and less clutter....
@@RS-fg5mf Can we just agree to use the fraction sign when diving? It makes the intended outcome a whole lot clearer
as an engineer who has done advanced university level maths for about 7 years now, I would get 1. its the convention usually followed in physics/engineering textbooks to solve as terms and let implicit multiplication (brackets esp) go first
I'm in a similar position and I 100% agree. It's disingenuous by the video to imply there's one correct order, when so many physics and engineering books do operations in the 2nd way. The video is also wrong in stating that calculators all calculate in the same way. Mine doesn't.
I guarantee that if any engineers I know saw something like "6÷2x" they'd calculate the 2x first. It has nothingo to do with the division symbol. Implied multiplication (for example, 2x rather than 2*x) in all the engineering I've learned always takes priority over normal multiplication. If you write it as 2(1+2) instead of as 2*(1+2) there has to be a reason for it, and common sense (mine at least) dictates it's because you mean the order of operations to be different.
Real world math isn't a puzzle designed by someone to fool you, it's an objective way to state things and should be written accordingly. The problem here is the question, not the answer. Just write it as (6÷2)(1+2) or as a fraction and the problem is solved.
@@afsdfsadhasfh absolutely spot on. couldnt put it better myself
@@afsdfsadhasfh the question is deliberately misleading
@@afsdfsadhasfh Conclusively, the experts say this. The equation is ambiguous and indeed, it can yield two different answers. Like the use of language, to convey something such that it can't be misinterpreted, it must be delivered with clarity, the intention should be made clear. The same with maths equations. To yield only one result, the equation should not be written with ambiguity and the intention of the writer must be clear. If it does or can, the equation should be re-written.
Jesus. This is dangerous. Hopefully you stay in school and don't go actually build something one day.
the correct answer is this is a poorly written problem.
You are 100% correct, this is the proper answer.
What is the correct answer? I don't know man, math isn't typically fully divorced from reality, let's look at the reasons why you're crunching these numbers and we can re-write it so it makes sense!
+James Crawford yeah realistically equations would never be written this way but I think the majority of math rules indicate the answer is nine
In mathematics, there is no such thing as bad problems. Only bad rules and the misuse of good ones.
No, the first premise in PEMDAS, is to solve for the answer within parentheses. You never distribute into parentheses first because you would then misapply the order of operations.
PEMDAS: Parenthesis, Exponents, Multiplication And Division, Addition And Subtraction (IF the same precedence, then left to right).
Any order with And in between has the same precedence!
Since the problem is 6/2*3 or 6/2(3), we must follow the premise regarding left to right because the problem involves only multiplication and division, orders of the same precedence. Parenthesis is only a symbol of multiplication when a number or expression is adjacent to it.
If the problem were 6/(2*3), then the logical answer is 1, because we solve for the answer within parentheses first, as according to the first order of the order of operations.
The answer to 6/2(2+1) is not 1.
The problem isint the equation itself, it's whoever wrote it.
No the problem is teachers changing they way they teach things.
@@MrGamecatCanaveral
Not teacher the education system.
@@babyyoda7749 no teachers are the ones. Teachers are teaching about gender and sexuality for example. The education system is not telling them to teach that.
@@MrGamecatCanaveral Teachers change the way they teach things because we discover new things over time. Before, it was thought that the earth is the center of the solar system. Copernicus discovered that it is actually the sun. Now, do we need to change the way we teach about the solar system? Yes. It's crazy that what we believe in the present will never be entirely 'true' as it could be proven false in the future.
@@aeroljameslita4975 from a subjective point of view, isn't the point of perception the center of your reality? So the Earth is the center of the universe for everyone on it.?
The programmer's wife sends him to the store. She says "Get one carton of milk, and if they have eggs, get a dozen". The programmer came home with 12 cartons of milk, because they did have eggs.
And that's why I used to hate computers so much.
It would be 13 cartons because of the and boolean logic instead of or.
I'm truly thankful for the opportunity to give thumbs-up #42.
tf
Agreement with Brian Fedelin. 13 cartons of milk. One carton, and if there are eggs, get a dozen. So 1 + 12 = 13. And the issue with computers is not the logic of them, it is how a human evaluates a human expression and then programs the computer. In this case, the issue was with the wife, since the expression was not clearly defined from the start by defining a dozen of WHAT was desired, the milk or the eggs. See, it is actually a trap by wife against the husband. No matter what he were to bring home, it would be incorrect since she could then change WHAT was the dozen to be of.
If you substitute all numbers with variables:
a÷b(c+d) =
You would get a/b(c+d) =
a/(bc+bd)
Not a/b × (c+d)
That's how algebraic functions are ordered.
That's using implicit multiplication vs bodmas. You're coming with the assumption that b(c+d) multiplication holds higher priority than a/b part. That's all it is
@@spamspamspamspam3459it does because you first need to resolve the parenthesis. They are not resolved until you distribute them out (by multiplying the coefficient into the brackets).
@@adrianmcbride1666 That is absolutely not true, () in bidmas only applies to whats inside the parenthesis.
@@spamspamspamspam3459my father studied to masters in mathematics, he has stated that in different areas both methods are correct. Within South Africa, and from what I have gathered much of the rest of the world) that is exactly how it is done. Simple reason, it should not matter in which order one does the multiplication or division whether right to left or left to right as long as it does not combine any addition or subtraction.
@@spamspamspamspam3459 again, differs from location. However in my country, that is the correct method to resolve the parenthesis. Notably from the logic my father gave me, this method means that it does not matter in which order you do the multiplication and division once the brackets are solved. The method you use requires that one solves the equation in a specific order lest the answer be different (I. E. If one first does multiplication before division). As was said, the purpose of the bodmas is so that regardless of the order one solves the equation (within each relative Order) in that it will arrive at the same answer. The method we use, the order in which division and multiplication is done matters not.
Its gonna go viral again because its in my recommended
6 / (2*1 + 2*2) = 1
@@miguelgm808 did u even watch the video?
Ya
Nobody care
@@miguelgm808
(4/2+2/2)(3) = 9
Just graduated and I was legitimately taught that "historical way" all through school
Same here
I graduated high school 15-16 yrs ago and got my associate degree in '08, that's how I was taught, the old way.
That's terrible.
Ditto, and I aced math in school
Old technique is correct because
a=6/2(1+2)is not equal to.
b=6/2*(1+2)
In this video he is using second technique
No doubt 1 answer
We shouldn't change things like the order of operations, it's incredibly dangerous in things like engineering to have two different people unknowingly using two different standards.
Explain that to a teacher. Go ahead.
They only thing common about school now is that every child is getting left behind.
That’s why no mathematically inclined individual worth their salt uses the division symbol.
order of operations never changed, it's always been the same. He just explained that that specific symbol for division meant something very specific other than just division over 100 years ago but the actual order of operations has never changed.
That's why for any serious communication of mathematics you have to be more explicit than this ambiguous problem. Hence why peer-reviewed papers use fractional notation and make copious use of parenthesis to remove ambiguity.
Some people were taught that multiplication by juxtaposition takes precedence over explicit operations… hence why 3/2n is 3/(2n) and not (3/2)n
The same juxtaposition glue applies to parenthetical coefficients… and in this case, 2 is that parenthetical coefficient. So using PEMDAS, but assigning multiplication by juxtaposition a higher priority than explicit division, the answer is 1. Additionally, if you use the distributive property from the get-go to resolve the parentheses, you get 1.
Oh, I had the 1917 math class, then
Me too 😂 honstly, not surprised, though
Me too.
Try my channel mathfullyexplained
I guess I didn’t.. I got 9
Me too ✋
Next viral problem..
1+1 = 2 or 11.. 🤔🤔🤔
1+1 = 10 ;) 1+1+1 = 11, 1+1+1+1 = 100.
@Jure Lukezic binary smh
@Jure Lukezic That only works for very large values for 0. I was representing numbers in base-2; however, if we're talking string concatenation then yaaaaaaaaassssss!!!
@Jure Lukezic So how does it feel that your joke went over our heads? Don't you feel bad for us smug little pedantic bastards? We could have strung that out, like "I was writing in binary" ... "no you weren't" ... "yes I was" ... "no" ...
10
Me: Answer is obviously 1
"Answer is 9"
Me: Well fuck me.
It's actually 1 :) The person explaining made a crucial mistake thinking that () is the same as x.
As many explained, it's not
Atomicninja - It is really 1 the ( ) go first. So it's 1+2 first which equals 3 obviously. Then the equation is 6/2 x 3 (the / is a division symbol). Then you multiply 2 into 3 then it's 6/6 and then your final answer is one. Simple to learn in school easy math.
Kai Cluster I don't agree I think the answer is 9 because you add the parentheses P, then you go from left to right so 6/2=3 and 3x3=9
first off 6/2=3 is already wrong because there is no multiplication
6/2(3) is not the same as 6/2*3 or 6/2*(1+2)
if you want to elimate (1+2) the equation should be (6/3) / (2(1+3)/3) then you get 2 / 2 =1
or simply just 6/6=1
The correct answer is 1 because 2(3) is somewhat like y(x) which means the value of y is multiplied by x time.. going that approach 2(3) is interpreted as 2+2+2 = 6
6 / 6 = 1
the algebraic expression is z / y(x)=
Divide should precede Multiply so 6/2x3 should be 3x3=9
I graduated in 2003. I was and am pretty good in math subjects. I was taught to solve this with the answer of 1. The brackets are to be dealt with b4 other division of multiplication occurs
Same here. Aleays remembered pemdas, but didnt hear bodmas til recently
I never heard bobmas b4 lol I said brackets to be inclusive I guess lol.
I was taught to expand the products in parenthesis first. So 2(1+2) would be 2+4 which is 6. 6/6=1
exactly mate@@mikehuston2132
@@qwenettadixon6911 We learned it as BEDMAS (E = exponent)
oh sorry i’m late, RUclips just recommended me this video 3 YEARS LATER
chris yeah me too
same
isnt it 2 years
Onur Akar technically, yes
Me2
think of it like a fraction. there's a reason why in higher math '÷' isn't used.
dont forget that 2(3) is one term
I know right... I'm suprised the education system is failing this hard to teach math.
but it's not a fraction. there is the discrepancy in the solution
all division is a fraction lol
Exactly Erick!! we use the division sign just to teach kids but it is wrong in advanced math.
I used the historical version all my life. I must be rather ancient.
Seems we all historical and the new version only rules in special areas, clearly the areas where I’m not. I live in South Africa and here the answer is still 1🤣 should you want the answer to be 9 it would be written as a fraction not a division sign(which can’t even be found on my keyboard, so let’s just all retire the devision symbol and I’d be happy to concede that the answer is 9😂
Basically the answer isn't "wrong" if you use the historical version... they're just asking different things... in modern math, it you wanted to ask the exact same question as the historical you would have to write is 6÷[2(1+2]
@@willwalker24601 It comes down to "just use brackets to make clear what you mean". Mathematics is supposed to be a universal language, but there are still a lot of dialects, aka different notations. I see that a lot lately as I am german but using english youtube videos to review some things since I am studying for a new profession. They are doing a lot of things differently than I learned them at school 20 years ago. Maybe they do them that way in schools now too, I don't know. But since such differences exist, one should strive to write expressions as clearly and unambiguously as possible. Most of those "puzzles" thrive on their ambiguouty.
I think the difference is people forget about the brackets so they just disappear
✔️✔️✔️👍👍
Correct answer is surely 1
To those who are telling it 9
Dont know how?
For this xy ÷ xy = 1
But Its not y²(according to those who are telling answer to be 9)
Similarly, 6÷2(3)=6/(2*3)=1
As simple as that...
I can ensure you that in most Stem environments the symbols ÷ and / are pretty much forbidden, every division must be written as a fraction, so all formulas and expressions are just sequences of products of franctions, and the length of an horizontal line is clearer than any pemdas rule
6
------(1+2) = 6÷2(1+2)= 9
2
6
---------- = 6÷(2(1+2))=1
2(1+2)
WHY?? Because the vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum groups operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator...
________
2(1+2) = (2(1+2))
two grouping symbols each
Objective facts...
What about implicit multiplication? I know many people would interpret 1/2x as 1/(2*x) while 2x^3 is never understood as (2x)^3
@@realGBx64 Most people confuse and conflate an Algebraic Convention given to coefficients and variables that are directly prefixed and form a composite quantity by this convention to Parenthetical Implicit Multiplication. They are not the same thing...
1/2x = 1/(2*x) by Algebraic Convention
1/2x^3= 1/(2*x^3) by Algebraic Convention
1/2(x)= (1/2)(x) by the Distributive Property
1/2(x^3)= (1/2)(x^3) by the Distributive Property...
1/2x and 1/2(x) are not the same thing.
No they aren't. There is nothing wrong or ambiguous with the equation as written. Not everyone is using a whiteboard.
How on earth do you operate a calculator without those two symbols available?
10 million views!
Gratz
I can't believe people don't know this. Congrats on the views.
The comments section is amazing. One of the top comments concludes that you are doing a disservice to kids trying to learn mathematical protocols. I bet you didn't see that coming.
MindYourDecisions wow nice
So 6÷2a = 9 if a=3?
As a math student, I’m mad at the way this is written. My teacher said he would fail anyone who wrote math problems like this 😂😂😂
Your math teacher has issues but as long as he is grading you I suppose you need to do what is expected...
There is nothing wrong with the way the expression is written just the ignorance people have about parenthetical implicit multiplication...
@@RS-fg5mf Isn't that the whole point - it is perfectly valid but makes it unclear and you have to think about it - are you mad because you got it wrong? I would be a bit concerned about your math's teacher.
@@justcheck6645 I am a math teacher and I didn't get it wrong. LMAO
When you actually understand and apply the Order of Operations and the various properties and axioms of math correctly you get the correct answer 9....
Did you get it wrong??
@Christopher Butler if you don't care, why bother replying?? LOL
Enjoy your show. 😁😁
I graduated math in 80s, cannot believe people are discussing primary school math
I solved this in 5 seconds this shouldn't be a problem for anyone who attended school.
Same
Exactly, I always loved doing really long order of operations math problems.
Same, idk why they are making fuss over this? I mean this is taught in school....
@@_mahiii lol he got 14 million views it served its purpose
Unless your History teacher doubled as your Maths teacher!
Edit: I was wrong, operator precedence makes the answer clearly 9. A way to avoid this confusion from people like me who got lost in the order of operations would be to set up the equation as (6/2)(1+2) or (6/2) * (1+2).
Note: Contrary to popular belief in this thread, I did graduate with my bachelors and also complete Basic Calculus with high marks. I am capable of error and my original comment was one of those errors. Thank you for the correction.
Original comment:
I graduated with my Bachelors in 2019, the answer according to the way I was taught throughout my education is 1. Because I was instructed by my professors to visualize this problem as 6/(2(1+2)) or 6/6 which equals 1. The person who wrote this did so in a way that is designed, purposefully or ignorantly so, to cause confusion. Dr. Trefor Bazett has an insightful video on this topic
Are you saying that you took university level math within the past 10 years and your professors taught you that in the case of 6➗2(1+2) you’d make 6 the numerator with the 2(1+2) being the denominator? Ima have to throw the bs flag on that one. It doesn’t even make sense that your professors would have even been instructing you on this when this is just basic math that young kids learn. It’d be like saying “When I was pursuing my master’s degree and my professor was teaching me my times tables…”
If you took this stuff recently, you’d have been taught to solve left to right 6/2x3
=3x3
=9
Dr. Trevor Bassett is wrong and so are you...
6
------(1+2)= 6÷2(1+2)= 9
2
6
---------- = 6÷(2(1+2))= 1
2(1+2)
The vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum groups operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator.
________
2(1+2) = (2(1+2))
Two grouping symbols each
________
2(1+2) has two grouping symbols
(2(1+2)) has two grouping symbols
@@trickortrump3292the bigger question would be why a University would be using the grade school obelus to teach higher level math...
We have reviewed the video and the penalty flag stands... Good call Ref....LOL
@@RS-fg5mf Yeah I deserved that. When I first looked at it, I solved it your way and then the video told me I was wrong. I bought into the reasoning for why I was wrong. This question is just a mess! I went down the rabbit hole yesterday after my comment. It’s insane to me that so many experts seem to say that the right answer is “there is no right answer” because it can be correctly solved two different ways, yielding two different answers. I can’t accept that. If both answers are correct, that makes both answers wrong too.
I’ve removed the bs flag I originally threw. 👍😉
@@trickortrump3292 don't remove it. LOL The red flag stands on the play because you are absolutely correct...
The only correct answer when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended is 9
I was agreeing with you. Don't let these mathematical numpties change your mind.
Those who understand and apply the basic rules and principles of math correctly as intended will get the correct answer 9
Those who fail to understand and apply the basic rules and principles of math correctly as intended will get the wrong answer 1
Those who can't prove 1 and can't accept 9 will argue ambiguity...
Failure to understand and apply the basic rules and principles of math correctly as intended doesn't make the expression ambiguous and isn't a valid argument against the expression...
Let me guess...next viral thing is 1+1
Answer is obviously 0
Lmao
1+1=11 no? :D :D
There are no possible solutions to that equation.
wrong
Congrats, this just became topical again. Expect another influx of views my man.
i just came to check if im braindead turns out nah
I dont know why people think this is hard
@@kolowar6600 because they failed second grade
Anf another influx of ignorants disliking this video again.
I’m here to see if I’m brain dead this is basic I’m not through the video yet so I’m pretty sure it’s 1
I am 45 years old and have honours degrees in Engineering and Science.
We were always taught that the answer should be 1, because of the order of operations rule that we were taught to use.
If you change the rule, you change the answer.
I was not aware that the rules had changed!
I just graduated high school and my answer to this problem was 9. I guess it's taught correctly now atleast :)
It seems that multiplication by juxtaposition, ab or a(b) etc., may impliy grouping, or it may not, so the notation is ambiguous making both answers valid. It depends on context (e.g. academic or programming).
It's just bad writing.
Modern international standards, ISO-80000-1, mention that brackets are required to remove ambiguity if you use division on one line with multiplication or division directly after it.
The American Mathematical Society's official spokesperson literally says "the way it's written, it's ambiguous" even though they use the explicit interpretation.
Wolfram Alpha's Solidus article mentions this ambiguity also.
Microsoft Math gives both answers.
Many calculators, even from the same manufacturer, don't agree on how to interpret multiplication by juxtaposition. No consensus.
Other references are:
Entry 242 in Florian Cajori's book "A History of Mathematical Notation (1928)" (page 274)
"The American Mathematical Monthly, Vol 24, No. 2 pp 93-95" mentions there was multiplication by juxtaposition ambiguity even in 1917 (and not the ÷ issue)
"Common Core Math For Parents For Dummies" p109-110 addresses this problem, states it is ambiguous.
"Twenty Years Before the Blackboard" (1998) p115 footnote says "note that implied multiplication is done before division".
"Research on technology and teaching and learning of Mathematics: Volume 2: Cases and Perspectives" (2008) p335 mentions about implicit and explicit multiplication and the different interpretations they cause.
Other credible sources are:
- The PEMDAS Paradox (a paper by a PhD student on this ambiguity)
- The Failure of PEMDAS (the writer has a PhD in maths)
- Harvard Math Ambiguity (Cajori's book above is talked about here)
- Berkeley Arithmetic Operations Ambiguity
- PopularMechanics Viral Ambiguity (AMS's statement is here)
- Slate Maths Ambiguity
- Education Week Maths Ambiguity
- The Math Doctors - Implicit Multiplication
- YSU Viral Question (Highly decorated maths professor says it's ambiguous)
- hmmdaily viral maths (Another maths professor says it's ambiguous)
The volume of evidence highly suggests it's ambiguous.
@@bigbadlara5304 The answer is one because this video makes a mistake by ignoring that these equations require the distributive property. If you "just graduated" I'm not at all surprised that no one taught this...
That is correct. This video made a mistake when it ignored the distributive property. The entire problem is wrongly represented here.
@@nixboox Distribution can give both answers as it is a notational ambiguity.
There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not.
I.e. does 2(1+2) = (2×(1+2)) or 2×(1+2)?
Implicit: 6÷(2×(1+2)) = 6÷(2+4) = 1 which is used by academic writing.
Explicit: 6÷2×(1+2) = (6÷2×1 + 6÷2×2) = (3 + 6) = 9 which is used by modern programming and also by the American Mathematical Society according to their statement on the matter.
That's why it's ambiguous. The rules can't help when the problem is the notation which has to be interpreted first. It's just written poorly and not in line with modern international standards.
It should be
(6/2)(1+2) for 9 or
6/(2(1+2)) for 1.
Those are unambiguous and follow the guidelines.
It 1 because 2+1 is 3 x 2 is 6 divided by 6
Seems like so, since there is an implied multiplication that _normally_ implies grouping with parentheses, so it's *6 ÷ 2(1+2) = 6 ÷ (2 × (1+2)),* not simply *6 ÷ 2 × (1+2).* Though I guess some people in the comments might not agree with this position (just like the author of this video).
Maybe that’s why no one past fifth grade uses that division symbol
Finally someone with logics
Yup, you're right.
Yes thank you
Looks like someone didn’t pass grade 3 English. passed*
@@sageight818 if you're gonna roast someone on spelling, please atleast be right next time. Thanks
Please excuse my dear Aunt Sally. I thought everyone was taught that.
PEMDAS = 9
and some people were taught other acronyms that mean exactly the same thing, like BODMAS
That's how I learned it in high school, class of 1998, and then in college in the early 00's... to do it in the exact order of the sentence.
@@godelnahaleth No, you were not taught to follow PEMDAS as 6 exact steps... SMDH
Own your mistakes and stop blaming your teachers for your failure to pay attention in class and learn correctly...
@@RS-fg5mf Nope. 2(3) is not the same as 2*3. Anyway it's been 4 years since I came across ÷ sign. I only use fractions and never had to come accross controversial problems like this one.
Exactly its easy
I did this in 10 seconds... how can it be viral?
Check Wiki on the order of operation, it is indication that there is an ambiguity/confusion with expression like 1/2x
for some it is (1/2)*x = x/2 and for other it is 1/(2*x)
Here we have the same type of problem : a/bc, so same problem : is it (a/b)*c or a/(b*c)
If for you it is not confusing, then you do not know math enough, because to remove the confusion in that sort of expression, there is a rule that apply to in-line math expression :
"Always add parentheses to delineate compound denominator"
So here the first thing to say is that "that expression do not follow the rule for in-line math, so It can't be solved using the order of operation; It has to be corrected first"
And the problem is that it seems that a lot of people do not know that rule, so they give the result corresponding to one interpretation or the other ... making it viral
Should all of those people go back to school ?
Or should only the one that wrote that ambiguous expression go back to school ?
@@ghislainmaury2065 English translation please?
This is so easy, I solved it in 5 seconds
Defaulty Boi lol.
Letucces Satan yeah... I’ll pass thanks
I’d gladly take yours though
For the people wondering it got solved in several videos and the correct answer is indeed 1️⃣ press the button if this helped!!
👇
WRONG. The correct answer is 9
It's simply ambiguous notation. A trick.
Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not.
Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too.
Multiple professors and mathematicians have said so also like:
Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc.
Even scientific calculators don't agree on one interpretation or the other.
Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why.
A recent example from another commenter:
Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example
8 ÷ 4(2) = 8 ÷ 8 = 1
but 8 ÷ 4 • 2 = 2 • 2 = 4
@@RS-fg5mf You're still living in fairyland, Richard.
That's why nobody uses the division symbol. It's confusing and it leads to errors. Both in math and physics, fractions are the way to go.
I prefer using ÷ over /.
I only use / with fractions, but use ÷ when dividing numbers.
Using improper fractions instead of using the division symbol is something that I rarely ever do.
I never find it confusing when using ÷, and it never confuses me.
@@MarioLandscape nope
@@MarkQub.
What do you mean 'nope'?
I just stated that I prefer using this: *÷* of this: */,* when dividing.
The person said that nobody uses ÷, because it's confusing, so I said that I do use ÷, and that it doesn't confuse me.
@@MarioLandscape you see how you lost. You got mad/serious over someone who just simply said “nope”
@@MarkQub.
What on Earth?
Lost what?
What did I lose? Please explain.
All I did was ask you what you meant by nope.
How was that getting mad?
i was taught the 1917 version
Me too! And I was born long after 1917. My scientific calculator may be old, but it too was built long after 1917 and according to that calculator the answer is 1.
MissEB47 ikr
I checked it on my calculator, the value it gave is 1. And my calculator is an fx-96SG PLUS, a relatively new model.
So So mine gave 9
@@relentlesssume3047 Maybe it's because I'm Australian? Different countries have different rules for solving that equation.
It's just freaking easy the answer is 9.
hah its 1 i know
It's 1
Mira Acharya no.... It's 9
Private_Onion Gaming ..I thought it was 5
Its 2
There is no controversy. Following the order of operation, the answer is 9.
Yeah, folding the order of operations the answer is 1. You forgot to dissolve the parentheses.
@@InsanityoftheSanities I'm going by the F.O.I.L order of operation.
@@AFK-47x Are you able to reproduce to me your work? I'm interested in what the F.O.I.L order of operations is.
@@AFK-47xthere is no FOIL in this expression but the answer is 9
@@InsanityoftheSanitiesthere is no rule in math that says you have to open, clear, remove, take off, eliminate, get rid of or dissolve parentheses.
The RULE is to evaluate operations WITHIN the symbol of INCLUSION as a priority and nothing more... (1+2) is a parenthetical priority. 2(3) is not a parenthetical priority and is mathematically the same as 2×3
There is no mathematical difference between 6÷2(1+2) and 6÷2×(1+2) despite the false and misleading information and willful ignorance people have about parenthetical implicit multiplication...
Watching 5th grade math at 2AM even though I'm 15🤦♂️
well theres only one truth.
math is attractive 😂😂
Sameee 😂
Same
Im 11
Im 15 too
After all this debate and discussion, I think we can all agree that this is why we use fractions instead.
Eventually, yes. This is a fifth-grade expression used to teach and reinforce the order of operations. This is pretty much ground zero. From there, we stop using the obelus in favor of the solidus and vinculum and go into fractions, as well as teaching reciprocals and the multiplicative inverse. People just forget how to evaluate expressions using the order of operations due to lack of practice. Sometimes, all they remember is an acronym and then convince themselves that there are six steps instead of four and that multiplication always comes first when it doesn't.
All my homies hate ÷
@@jamesfiddler1976 how the hell do you not use order of operations im highschool? You need to use them for literally any equation
@@godlikefish1193 - Me too my friend. All forms.
@@pirilon78 Who says I did? I never even hinted that we don't use the order of operations beyond junior high. It should be common knowledge that we do.
I'm 40 y/o and was taught the historical way in school. I don't feel historical though. I feel f*cked over because somewhere along the line people decided to change the rules of the game (and didn't inform me!!)
Good ol' "Meneer Van Dalen Wacht Op Antwoord" for the Dutch viewers...
@@manofculture9051 Your mom sends her regards! And dinner's at six, be on time please.
The problem isn't that the rules were changed; the problem is that they are being misapplied.
I hate order of operation squabbles. That is not math, it is convention. If there is a governing body for math they should get together and design a convention that is definite, obvious, and universally agreed upon and taught. I was taught the historical method, but knew the current method, so I knew there were two possible answers depending on which system you used. (Not counting the latest anti-racist belief that every answer is correct because saying there is a definite answer would be racist.)
@@HQBergeron Agreed. It's mathematical semantics.
#planetpluto
9 order of operations.
Fifth grade math: im gonnna end America's whole career
Răzvan Ruse literally
Anthony Lo hey guess what he deleated his comment now yours makes no sense
Fallout Mods who deleted what
Um what?
Just the people that aren’t in school anymore
for me as a programmer, this was very clearly a 9.
I'm not even a programmer, I just use basic bodmas knowledge
Yea
pog
How can we get 60 by adding only three numbers out of these:
2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, & 58?
@@PuzzleAdda we cant. All of these numbers are in the form 2+4k where k is any number from { 0, 1, 2, ... , 14 }. The equation would be (2+4k)+(2+4l)+(2+4m)=60. After we simplify this we obtain k+l+m=27/2 but all of k, l and m are whole numbers. Therefore it is impossible to obtain 27/2 by suming k+l+m and the equation does not hold.
Anyone got 1.
No one..
Just me...
Ok :/
NatDa One LoLOlOloLoL
@tepig360 pikachu720
Assume A = 1+2 then 6/2A = 6/2(1+2).
And that means 6/2(1+2) = 6/2A.
6/2A has no parenthesis.
How the hell will you "do the parentheses" when there is no parenthesis?
It's one
@@Leileilovesyou
It's nine.
Me.
I dont undeerstand why change things.
Y ÷ 2x has always been y/(2x) not (yx)/2
9 mate. Get over it
People: nine.
Me, an intellectual: *nein*
Ivan09 Ja Ja! Ich spreche auch Deutsch
Translation: Yes yes! I also speak German!
@@rydh6zgjhbfvrwhb259 Grüße aus NRW XD
@@Brontok Heyyyyyyyyy! Ich grüße dich zurück! Natürlich auch aus NRW!
@survival pete ??
Ivan: posts a meme containing a fraction of german
The comments: iCh bIn dEmEnT
Not sure where you're getting your "modern interpretation" from but certainyl in the UK
6 ÷ 2(1+2) wouldn't be treated as (6 ÷ 2)(1+2) because the implicit multiplication where no dot or multiplication symbol is used takes the same priority as the bracket. So, 6 ÷ 2(1+2) would be read as 6 ÷ 2y where y=1+2
If the original were written as 6 ÷ 2 x (1 + 2) then 9 is the correct answer but when written as 6 ÷ 2(1+2) 1 is still the correct answer.
I have and did.
You are wrong. It's the same thing whether it's written as 6 ÷2(1+2) or 6 ÷ 2 × (1 + 2). The multiplication symbol is implicit. The only way it could be written to equal 1 is 6 ÷ (2(1+2)).
UnderMan UnderMan So are you saying, you would read 6 ÷ 2y as 3y? Because if so, I've no idea where you're doing mathematics.
SPACKlick
6 ÷ 2y = 3y
Yep very sleepy there when I wrote that. I meant that in order of operations 2y is treated there as a single unit, 6 ÷ 2y = 6/(2y) rather than (6/2)y ie 3/y vs 3y
why am i watching this...
covid has me down bad lmao
You ain't alone brother.
down bad w u
to improve your knowledge
Same, no clue why I clicked on this lol
How can we get 60 by adding only three numbers out of these:
2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, & 58?
Answer - ruclips.net/video/LZN4m-cPJkg/видео.html
#PuzzleAdda
9
As you climb higher in math, virtually 100% of physicists, engineers and mathematicians will interpret the answer as 1. There is no debate over this at all. The implicit multiplication of 2 on the bracket is a SINGLE quantity that takes precedence prior to division. Most physicists/engineers/mathematicians would never even write such a potentially ambiguous expression. They would instead write 6/2(1+2) where the / is a horizontal line. Alternatively, they would write 6/(2(1+2)) leaving NO ROOM FOR AMBIGUITY. PEMDAS is NOT universally accepted. The implicit multiplication on the bracket does indeed take precedent.
You are doing a disservice to kids trying to learn mathematical protocols. PEMDAS isn't the total protocol.
Totally wrong and nonsense.
What is the inverse of "implicit multiplication"?
I agree with ZoeCat
It is really funny indeed, because it gives a hint from "where people are coming". I studied physics for some time and it was completely obvious to me, that a juxtaposition has a higher order than "read left to right". It's "obviously" 1.
As mentioned; 6/2y with y=1+2 is 3/y, not 3y.
Tom Yes. You give a great example.
According to PEMDAS, x/yz = xz/y which is OBVIOUSLY unconventional. The implied multiplication of yz binds the two components of 'y' and 'z' together.
Zoe TheCat Agree with you 100%. I'm an engineer and my first response was to say the answer is 1. Everything on the right is just a factored 6.
The "1917" example is exactly how I was taught both in high school algebra and in college algebra. That was in the 80's, not 100 years ago, lol.
What does attending school in Appalachia have to do with it? Yes, I did and I was taught the 1917 way I guess from 1996-2013. WCU was still using in it in 2013, and so was all the other kids from other parts of the US.
same here...thank god for comments almost gave up on my math.
honestly i dont know how long ago people didnt use the order of operations but im sure that in the 80s all mathematicians used it. id go as far as to say it probably existed at least a thousand years ago
Don't be jackass Steve
realistic dan
Appearantly my wife was retaught the correct way when she went to UMiss. Guess that why my kids always come home with the wrong answers when I help them do their school work
Imagine using division symbol instead of fraction.
Yeah that's how that goes...?
It's 5th grade man
@@mrpickle8959 fractions is also division 1/2 is the same as 1÷2, and this works for anything.
@@sensei5668 sure it is the same thing. but with fractions the error couldn't happen as the order is directly visible. I personally haven't seen that operator once in university. If you are forced to write in one line (e.g. in programming) people use "/"
@@Langweiler11 that's my point
1 is correct answer
6 / 2(1+2) Solve the brackets first
= 6 / 2(3) Solve the brackets first
= 6 / 6 Solve the division
= 1 Basic
First of all: 6/2(1+2) is the same like 6/2*(1+2). Even if it is not written, the * is between the 2 and the brackets.
6/2*(1+2) Solve the brackets first
= 6/2*3 Solve the division
= 3*3 Solve the multiplication
= 9
It is not the same. A scientific calculator makes a difference between 6÷2(1+2) and 6÷2*(1+2). Mine gets 1 for 6÷2(1+2) and 9 for 6÷2(1+2). It's simply not the same.
Alneon I had a scientific calculator once. It did _not_ give the same answer as yours. Is yours a TI calculator?
after you add the numbers in the brackets, its not a bracket anymore, it simply becomea 6 ÷ 2 × 3- then because in BODMAS division comes before multiplication, you do 6÷2 which is 3, and then multiply that by 3.
you can solve as 2(1+2)=(2x1+2x2)=(2+4)
It’s 9.. how is this even viral, it’s 5th grade math..
Also, I’m referring to PEMDAS which is taught in 5th grade. Watch the video if the answer you got wasn’t 9..
It's 1
It’s 7
Noob, its one
Not even 5th grade math. It’s like 2nd grade math
It depends on pemdas or bodmas
History biggest question: How did a 5th grade math question create a riot on the media
It's not even 5th grade, it was 3rd or 4th grade
I learned this in 5th grade and solved this in approximately 5 seconds.
Please read this comment, thank you.
Solve for the 2 in parentheses, it is not a bracket [ ]
6/2(1+x)=9
3(1+x)=9
3+3x=9
3x=6
X=2
The problem is that people who think that it is 1 believe that after simplifying 2(1+2) is that they think it is the denominator of the fraction. For that to be true, there must be a parentheses in front of the 2.... (2(1+2)). You will do that first if that was in the problem, but it isn’t.
6/2(1+x)=1
6/2+2x=1
Now you see that there is a fraction, but what can it be. If it is 2+2x, you get 2 as your final answer, which is correct. If it is just 2, you get -1, which is incorrect.
However, you do division before addition, so you do 6/2 to get 3, eventually getting -1 as the solution.
3+2x=1
2x=-2
X=-1
This is incorrect, because we are trying to solve for 2 in the parentheses... 6/2(1+x)=1
X should equal 2. People think that after distributing the 2 into (1+x), the whole thing stays in the parentheses. It disappears after you distribute.
Thank you for your time.
Lol
norman hughmin because people are morons
Answer is 9
In France i've been taught it in a way, that this equation equals 1.
Basically 6/2(1+2) has brackets. We were taught that brackets were always a priority with the number infront of it. So what we would do is first 2*1 + 2*2 = 6, and once we got the brackets completely gone, we can finish the equation which would be 6/6 = 1.
Also even if i added the numbers, it was always important to clear the brackets. Here 6/2(3) still has a bracket and doesnt just dissapear. So i would multiply 2 and 3 to get rid of the bracket. Thus we still receive 6/6 = 1
I was always taught this way and was surprised seeing that the correct answer was 9. This blew my mind
I'm pretty sure that in germany we were taught the second answer as well (equasion equaling 1) for the exact same reason you describe here (getting rid of the brackets first) and then finally dividing anything on the left side by what is left on the right side. From my point of view the answer 9 is "wrong". And even if it's just a "rule" thing, we'd better universalise that rule. To me, somehow, the answer "1" also makes more sense in a mathematical- asthethical way.
People in Europe, born before 1970, learned, that multiplication goes before division. Just a fact. I mentioned 1917, because in that year, in the USA it became official that multiplication and division are equal and You start from left to right. In 1980 is was commpn practice all around the globe. ( In the Netherlands it took till 1992 to use the 1917-method).
Mathematics is about agreements and those changed over the years to an (new) international standard...
@@j.r.arnolli9734 Thank you for this insight. Anyhow I was born in 1980 and I'm pretty sure that if I showed this "problem" to my old schoolmates/ peers here in germany 99% would come up with the anwer "1". Yet again maybe I'm wrong.
If this really is new international standard it still doesn't make a whole lot of sense to me in terms of logical usage of mathematical language.
Yes you are correct the answer is 1. You solve the brackets first to get a number on its own then you finish off by 6 ÷ the answer in the brackets.
If your answer is 9 then you are inventing your own mathematics !
I was taught that way also. In the US, but three generations ago. I’m old.
Just came to check if my brain was working and it is, I’m tired of fighting over the right answers through Twitter 🏃♀️
Just ask them if they've taken advanced functions or calculus, and then tell them if they ever used the ÷ symbol instead of /. I think thats some pretty solid evidence I should say
NOT ALL OF US COMING FROM THAT TWEET BYEAKSJSKSJ 😭
@@Whatthescallop1776
÷ and / are both division sign.
Same lol
@@Whatthescallop1776 UK don't take calculus or advanced functions as a separate subject so that wouldn't work
Bruh who else did this in there head in like 10 seconds holy guacamole i finally got more than 10 likes
everyone
But answer is 9
@ZeroFollowers me obviously, and others
This is a easy one.
I
As a trained engineer in his forties, I immediatey turned the expression into a fraction. I also have to say I don’t think I’ve ever seen that division sign used anywhere after fourth or fifth grade.
And in 4th or 5th grade arithmetic the correct answer is 9 .... The symbol is found on almost any calculator. Best to understand it than to be confused by it...
Funny, I just left a similar comment. I’m an engineer (39 yrs old) and did same as you. That’s the reason engineers and physicists don’t use that silly division symbol.
@@Superdada i don't understand the debate about the division symbol. what difference does it make whether you use : or / ?
they do mean the same, don't they?
@@alxlej They mean using fractions instead of a symbol and having everything next to eachother.
@@borismuller1086 but the meaning and therefore the resulting operation are still the same, aren't they?
what am i missing?
Classmate1: i got 9
Classmate2: i got 1
Me: i got africa
Common core?
I got a rock
@@patinaz6758 i got... Abraham Lincoln?!
I got Iraq
I got 5 weeks of summer school
1:59 “And this gets us to the correct answer of dine”
Nicolas T-R 😂😂
You brainwashed me and now that’s all I here instead I of nine
lol
Speechless of laughter 🤭😂😆
lol
I haven't read any comments yet, but you could also be wrong in your interpretation of the order of operations. once you add 1 and 2 you're left with a 3 inside parentheses, and a convincing case may be made that since it's inside a parentheses, your're supposed to resolve that operation before the division, since parentheses trump multiplication/division... so again 1
Yeah, that's the logic my father taught me. It should not matter what order you do multiplication and division so long as one does not cross addition and subtraction (once parenthesis have been solved). The method being shown means that it is neccesary to solve the division and multiplication in a specific order because you will either end up with a 6/6 or a 3*3 depending on which order you do multiplication and division.
Exactly
This means you were taught incorrectly or that you remembered it wrong. There is no ambiguity for modern usage of mathematics, and the RUclipsr you just watched said it himself. DO NOT distribute before dividing because you are essentially multiplying that number to the other numbers inside the parenthesis, which breaks the rule of precedence
@@FloraLemonYT You always distribute 1st as this is part of solving the parenthesis. The value of the parenthesis is 6 not 3.
(2*1+2*2)=(2+4)=(6)=6
Remove Factor 2(1+2)=(2+4)=(6)=6
combine terms 2(3)=(2*3)=(6)=6
Although the common factor has been "removed" and written before the parenthesis. It remains a part of the parenthesis. It must figure in the evaluation of the parenthesis to get the correct value of 6. This is why they say that the 2 is stuck to... or a prisoner of...- the parenthesis, it can not be used anywhere else or the parenthesis will not evaluate properly.
So 6/2(1+2) = ?
6 / 2(1+2) = ?
6 / 2(3) = ?
6 / 6 = 1
@@mikestuart7674 the coefficient of a set of parentheses is NOT part of the parentheses because it is essentially a means of multiplication. Thus, you are multiplying first while there is a division operation behind it, making it a non legal method.
My teacher must have time-travelled from before 1917.
During the 1950s, my textbooks were from the 1930s....
😂🤣😅
So my teachers including university teachers. And my calculator as well :D
Me too. I was taught it to be 1. So does my scientific calculator
I learned the contemporary method in 1975. It's not a new idea. In fact, it's been used for over a century.
It’s 9
Edit: I knew before I watched
Ikr simple bodmas
Lol me too, We only know this bc we r in future
Me too
Jakob M same 😂
Pratyush Ṭhakur His ikr
in short don’t use the outdated division symbol, just use the typical numerator and denominator removes all uncertainty
It still becomes 6/2*3. So if it’s multiplication before division that’s 6/6 =1
@@charliedallachie3539 thats not using the numerator and denominator, when you use an actual numerator or denominator you would have a certain part be under it. Either 6/(2*3) or (6/2)*3
@@o_sch yea I understand the two answers but in other problems which is which? I’ve always wondered PEMDAS in general I’m sure there’s a complex mathematical proof of it out there somewhere
Edit* there is no proof it’s a convention.
@@charliedallachie3539 but it isn't multiplication before division. they are equal, so it is left to right.
@@JakobSchade Sure, but that's if you use PEMDAS or whatever else. There's still plenty of books where they don't use PEMDAS and have a difference between implicit and explicit multiplication. 2*3 is explicit (a * sign) and 2(3) is implicit. In that case, implicit is many times higher of importance than explicit. So 6/2(1+2) would simply be 6/6=1.
Its 9, look it up. You go left to right on the multiplication and division stage of PEMDAS.
It depends on which interpretation of multiplication by juxtaposition you use.
Modern international standards like ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
Yes, the correct answer is 9
Yes, you should look up The Distributive Law. Only 1 is correct.
What happened to the hard questions?
It's because there are people who can't math
+Jacob Riley we want geometry
+Jacob Riley stop acting the smarts. It's not about not being able to solve sums, it's about the different ways of solving it leading to different answers, and the debate around it.
+aaron melrose That doesn't excuse the people who blatantly ignore the rules explained to them in 5th grade math class. But it is fun to see the discussion over whether people think the distributive property should take hold first, or if the current use of PEMDAS has priority, or even if they prefer the historical reference of (whatever)÷(whatever).
+Jacob Riley You realise the answer is actually 1? Turn the sum into a fraction you 1. Plug the sum as appeared into the video into you calculator you get 1. Use bodmas until you get to 6 divided by 2(3). This can be represented as X divided by 2(Y). This is not the same as (X divided by 2)(Y). So it can't even be 9 because X is one term and 2Y is a separate term.
So, the problem that yielded an answer of 1 in 1917 yields 9 today. Wow - inflation is everywhere!
Trevor Keen You are correct. I was taught to do the the parenthetical expression, multiply and then divide.
The world parenthesis should be eliminated from all human language
Trevor Keen j
you were taught wrong. the end.
It's because the creator of this video is a moron
funny how i got both answers and then blamed my math teacher for making me so indecisive
Same. I got both answers and then watched the video to see what obscure rule they would pull out of their hat.
You've discovered a SECOND wrong answer !! 😧
The usual wrong answer is this:
6÷2(1+2)
6÷2(3)
6÷6
The 6 you got from the “wrong” step, I got from distributive property, which is where I find the confusion
1 isn't wrong though. It is just as valid as 9 as It's simply ambiguous notation. A trick.
Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not.
So it's the juxtaposition of 2(3) allowing 6 with the academic interpretation, not because of the parentheses. 2×(3) instead still has parentheses but no juxtaposition so 6÷2×(3) would be 9 using both interpretations.
Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too.
Multiple professors and mathematicians have said so also like:
Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc.
Even scientific calculators don't agree on one interpretation or the other.
Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why.
A recent example from another commenter:
Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example
8 ÷ 4(2) = 8 ÷ 8 = 1
but 8 ÷ 4 • 2 = 2 • 2 = 4
@@GanonTEKWrong
@@GanonTEKI’m not reading all that, nor am I smart enough to understand half of the things you just said, but you sound smart so I believe you 👍
Imagine a real mathematician ever using the divided by symbol
@Wubba Wubba mathematicians as in people who do it for a living generally don't. That's not gatekeeping - it's literally their langauge
Wubba Wubba r divided by iamsoverysmart?
If you write it properly: 6 over 2(1+2), surely the answer is 1?
@@DadgeCity yes if written with
6
----------
2(1+2)
Answer is 1
@@DadgeCity The expression 6/2(1+2) will not evaluate to that. You are violating the Distributive Property. In order to fully understand this I will impose a set of parenthesis that does not change the expression. (6/2)(1+2) which will evaluate to (3)(3) = 9 or (3 + 6) = 9. In order for you to have the 6 solely in the numerator and the expression 2(1+2) in the denominator you would have to impose this set of parenthesis which will change the expression 6/(2(1+2)). Then this will evaluate to 1. Therefore (6/2)(1+2) != 6/(2(1+2)) and if you don't believe me put both expressions into a TI Graphing Calculator!
My answer was "1" because I was taught the "historical" way. I was not aware that the rules had changed.
🤣🤣🤣🤣🤣🤣🙄
Ong
If you dont carefully listen to what your teacher says then you will get it wrong. I remember my teacher saying that if multiplication and division are the only ones left, you'll solve them from left to right. Same goes to addition and subtraction (If they're the only ones left)
The answer is 1. There is a reason the coefficient is up against the parenthesis, you multiply first.
@@Graphenor the correct answer is and always has been 9
Im so used to algebra where by the algebra rules parentheses-multiplication comes first so it would be 1
There is no such thing as "Parentheses-multiplication" in the order of operations.
i agree hehe. 1 is my final answer. video poster says 9 hehe what a troll video this is. just to stir up some views perhaps.
Haha, you are a joke. Mr Algebra man, please think about x/y(a+b) vs x/[y(a+b)].
1+1=2, x+x=2x. if we both agree to this then we're good.
so how did 2 in 2(3) magically get into the parentheses? BEDMAS = 9
23m Click's someones making some cash for putting up this argument (very clever )
In areas where the order of operations is unclear, or unintuitive, you should add some parentheses.
Well hello, again. I agree.
As a person with a masters in math, I totally agree with you and if I needed to communicate some math operations, and I would never rely on PEMDAS; use parentheses!!!
The graphic of the equation is textbook normal.
6 ÷ 2(1+2)
Note the position of the 2( No space. It's presented no differently than any n(x)
So it's a coefficient of the single quantity, in which x(a+b) = (xa + xb) By distribution.
The graphic is presented with 2 as a coefficient.
Answer: 1, not ambiguous. That's how the graphic depicts it.
Sir, I am in MAT 85 at a community college and recently learned about the distributive law,,,,2(1+2)=2(1)+2(2)=6 and was going to show it on this problem, but when I used the distributive law to get rid of the brackets I ended up with 7 and know the correct answer to be 9. Why does the distributive law not work here and how do you know when you can use it to get rid of brackets?
+Kenney
Simple.
y ÷ x(a+b) as given. That returns y ÷ (xa + xb)
6 ÷ 2(1+2) as given. That returns 6 ÷ (2 + 4)
That's 6 ÷ (6) = 1
Had there been different spacing, or some graphic difference, there might be a lawyer's argument. But 2(1+2) is s monomial; single quantity.
World debate: the answer is 9
Calculator: *_wait thats illegal_*
Its 9 on a calculator too lmao
@@redevil1748 ur calculator comes from another planet
There’s something wrong with your calculator
@@aliffruzail8624 did you put brackets
@@Bocsaphoto absolutely, just follow the question.
dont worry, this issue will never show up in important engineering situations because the division symbol would never be used. instead using a fraction would make everything a lot more clear
Yep i remeber i got so used to fraction that when i saw the division simbol at first i thought it was percentage xD
100%
The real-life solution, as per the ISO recommendation, is just to use brackets to disambiguate. (6/2)(1+2) is totally clear regardless of division symbol used and works for handwriting, calculators, typed documents etc.
@@anonymes2884 100% and ISO-80000-2 says that ÷ should no longer be used also.
I don't know algebra
9
I got laurel.
Jimmy Nobody Really? I got Yanny..
Jimmy Nobody random
Also I heard gary
Jimmy Nobody I got both.
Jimmy Nobody i saw gold and blue
The term 2(1+2) = x(a+b) = (xa+xb) = (2x1+2x2) = (6)
Thus:
6÷2(1+2) = 6÷(2x1+2x2) = 6÷(2+4) = 6÷(6) = 1
There are 4 terms in this equation, not 5:
1) the 6
2) the 2(a+b) containing:
3) the 1
4) the 2
If it were written as 6÷2*(1+2) THEN there would be 5 terms and answer would be 9.
1) the 6
2) the 2
3) the (a+b) containing:
4) the 1
5) the 2
The 2(1+2) is a SINGLE term which must be resolved first before being divided by 6.
The issue is that 2(1+2) --> (2x1+2x2) --> (6) RETAINS THE PARENTHESES thus resulting in 6÷(6) = 1
You distributed. Distribution is a property of multiplication and division. So essentially you multiplied first. But you can't do that! Parentheses go first, as stated in PEMDAS. So first you must reduce (1+2) to (3).
Is 6÷2x = (6÷2)x or 6÷(2x)?
2(3) is an unresolved term.
lohphat 2(3) is not a single unresolved term, it is two different resolved terms multiplied together. You can't just divide 6 by it, you must remove the brackets first and turn it into 2*3. Then you divide, so 6/2*3 = 3*3, which is 9. Remember, just because there is no multiplication sign (it's called implicit multiplication), it does not make it a single term - after you solved 2(1+2) into 2(3), you can (and HAVE to) remove the brackets, so 2(3) = 2*3.
*****
By replacing the () with * you've changed the structure of the equation by changing operators. It didn't start as 6÷2*(1+2)
lohphat You're not changing anything. Who taught you that 2(3) is not 2*3? It's called implicit multiplication. It is used when the multiplication sign can be substituted by a pair of brackets. It does not change the value of the equation at all. 2(3) = 2*3 in all cases. Just because the multiplication is implicit, it does not hold any priority over the normal (explicit) multiplication, unless you want to invent a new rule or something.
Why is this difficult? I learned this in fifth grade.
What’s your answer?
People were taught differently. I was taught never to take a number out of parentheses. 2(3) never 2*3
Olaoluwa Johnson According to his “procedure”, you work left to right when you have multiplication and division across the problem. If you do it that way, then 6➗2/3 = 1. If you punch that into a calculator, you get what I get, 9. In addition, what’s the point of solving inside the parentheses first, when you later show that it doesn’t matter. Just say (6 ➗2)(2 +1) = ?
Anthony Melvin following what I was taught, I’d be:
2(1+2)=2(3)
It started in parentheses, so it stays in it. And because it’s in a parenthese, it goes before division (*P*EMDAS):
2(3)=6
6/6=1
I might decide that I want the word "its" to mean the same as "sit" but it wouldn't make much sense. Here is a link to order of operation rules: www.mathsisfun.com/operation-order-pemdas.html
And presh don't deviate by using z and y just concentrate on 6×1/2×3 = 9. Don't use your own rules. From where you get 2×3=6. It is ÷2×3=3/2. Go do your homework before you open your mouth
Answer is one. End of. Have a financial management exam next week and if I solved that as 9 I'd fuck myself out of a mark.
+Sylorinnis the answer is 9...
you need to change schools, or actually, and more accurately, go to school in the first place. i say you're full of shit, and that you have no exam next week.
+Henry Lembeck troll
+Henry Lembeck no, it is not. Multiplication before devision .... New math "rules" don't apply because nobody can change them without consent from all humans. That never happened so ...
Fox and Scully are on the way
People in 2020 : answer is covid *1* *9*
wow ur so funny
@@user-gz9wh5kx8s ikr
The answer is triangle
Covid "1" "9"
1 and 9 are the answers lol
Chasity Burrow 😂
2016 naaaa
2017 naaaaa
2018 naaaa
2019 ok
Clearing the parens is not simply performing the operation within but also performing the operation dictated by the parens. Therefore the operation requires multiplying 2x3 to get 6 prior to the next operation. If the equation was: 6 divided by 2y there would be no ambiguity that it would be 6/(2y)not (6/2) x3.
Nope, if you got 6÷2y you do 6/2 times y. Its just the current rules, i agree its weird and maybe confusing because we never use "÷", we always use fractions, but the rules are the rules and they say that if theres no parenthesis, you only divide by the first number, the closer to the "÷" symbol. Which is 2, therefore 6/2 × 3 = 9
The parentheses are just around 3 though, not 2*3
@@wadabid6165: 2y is grouped.
Just like 2π, 2π, or 24.
You are using PEJMDAS like in some calculators (not all of them).
J meaning Juxtaposition.
But this is not PEMDAS which is the official math rule for instance in USA.
@@whoff59: PEMDAS is not an official rule anywhere. It's not even a rule.
5:13 the equation looks like a face lmao
💀😭😭
Hehe yaa
@@siyamchowdhury9492 And you're the bad grammar guy, duh
ding ding ding ding ding ding ding ding
(I don't like Billie Eilish for those who r gonna go mad at me and I did copy paste the name)
thats when you know you should be in art class instead of math
@@mbadakhoury2 good guess im actually good at drawing lol
srsly. That's just an example for bad notation. Of course the answer is 9. It's still bad notation. This division symbol just shouldn't be used anymore.
EXACTLY! It's a matter of confusing notation, but in *that* notation, the answer is 9. If you rearrange it using the "/" sign, the answer will be different! That's because (1+2) is actually a coefficient of 6/2!
nice name.
*****
I am aware of that. But I guess even at my university there are some people who would get this wrong. This is terrible notation that is not useds in real life.
***** lol
I want to make this clear: This is NOT a math problem. This is a notation problem. There are many differnt mathematical notations.
I also got 1.
But that is because I do not see 3(2+1) and 3x2+1 as being the same. It seems logical to me that if the lack of space between the "3" and the bracket means that this 3 is multiplied by whatever is in the brackets then they should be viewed as inseparable and therefore that operation comes first. Then, and only then is the product a usable number in the overall equation which is the division of 6 by whatever is on the right side of what was obviously meant to be the last operation, the division itself.
Oh, wait... I used the wrong original equation. I meant that the "2" is up against the bracket. so from 6 -:- 2(2+1) I get 6 -:- 2(3), then 6 -:- 6 = 1
Robert Cartier that's how I see it
Glad I'm not alone. ;-)
I remember when math made logical sense.. Now they change a detail somewhere in the text and everything is off, again! How are we supposed to use this "universal language" that is Math to communicate with aliens if we can't even agree on the rules?!
There's only so much you can do with tinfoil. LOL
Robert Cartier me too
you are really dumb
It’s 9 because let me show you so pemdas is parentheses first exponents next multiplication and division in the same step and then it is addition and subtraction in the same step so 6/2(2+1) so 2+1=3 then it is 6/2•3 ,6/2=3 and 3+3=9 SO THE ANSWER IS 9
It's simply ambiguous notation. A trick.
Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not.
That's the issue.
You can't prove either answer since it comes from notation conventions, not any rules of maths.
Wolfram Alpha's Solidus article mentions the a/bc ambiguity and modern international standards like ISO-80000-1 mention about division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.
Even over in America where the programming interpretation is more popular, the American Mathematical Society stated it was ambiguous notation too.
Multiple professors and mathematicians have said so also like:
Prof. Steven Strogatz, Dr. Trevor Bazett, Dr. Jared Antrobus, Prof. Keith Devlin, Prof. Anita O'Mellan (an award winning mathematics professor no less), Prof. Jordan Ellenberg, David Darling, Matt Parker, David Linkletter, Eddie Woo etc.
Even scientific calculators don't agree on one interpretation or the other.
Calculator manufacturers like CASIO have said they took expertise from the educational community in choosing how to implement multiplication by juxtaposition and mostly use the academic interpretation. Just like Sharp does. TI who said implicit multiplication has higher priority to allow users to enter expressions in the same manner as they would be written (TI knowledge base 11773) so also used the academic interpretation. TI later changed to the programming interpretation but when I asked them were unable to find the reason why.
A recent example from another commenter:
Intermediate Algebra, 4th edition (Roland Larson and Robert Hostetler) c. 2005 that while giving the order of operations, includes a sidebar study tip saying the order of operations applies when multiplication is indicated by × or • When the multiplication is implied by parenthesis it has a higher priority than the Left-to-Right rule. It then gives the example
8 ÷ 4(2) = 8 ÷ 8 = 1
but 8 ÷ 4 • 2 = 2 • 2 = 4
Yes, the correct answer is 9
My gut instinct was 1. I assume most people who go through higher math or science courses will naturally gravitate toward 1. To get 9 as the answer you'd be limiting yourself to notational rules and not applying the formula in any way with applied meaning.
Now that I think about it a bit more, it might be illuminating to check the math by rewriting the problem as an algebraic formula: 6÷2(1+x)=1, solve for x. First you'd distribute the parenthetical expression and get 6÷(2+2x)=1. Then you'd multiply both sides of the equation to get 6=2+2x. Then subtract 2 from both sides to get 4=2x and thus through division you see that x=2.
Yeah I think they are not getting that
2(x+1) whilst it looks the same as 2*(x+1), it is NOT as the brackets are still in play.
You would be required to drop the operator precedence to change 2(x+1) to 2*(x+1)
The former is a single calculation and the later is two calculations.
That's exactly what I was about to say.... :/
Well said, and one of the best comments I've seen on this vid!
Lame problem. Don't use the division symbol inside more complicated expressions is the only lesson here. But, does anyone read x÷2y as anything other than x/(2y) in practice?
Regardless, sloppy use of notation does not an interesting math problem make.
The answer is most definitely one. Put it into a fraction and you divide top and bottom by 2 leaving 3/3. Even you use bodmas,my out get 6 divided by 2(3). This can be represented as (X divided by 2(Y)). Which is not the same as (X divided by 2)(Y). The answer is 1
Yea i'm 19 and I've never seen where you would do 6 divided by 2 first. I was also taught the division sign and the fraction notation are interchangeable.
Yes, Harlequin, I believe you're right. In algebra, for solving equations to find unknowns, x divided by 2y had better be understood as x/(2y) and not (x/2)y if one wants to get the correct answer. I also think that it is better to have the same rules across algebra and arithmetic so as not to confuse ourselves. Thus, even though the presenter says that x/(2y) is an older convention, I feel it is the more useful convention and not the supposedly current one. This is seen from the following steps:
6 divided by 2(1+2)
= 6 divided by [2X1 + 2X2]
= 6 divided by [2+4]
= 6 divided by 6
= 1
(sorry, I don't know how to reproduce the 'divided by' sign)
real clear
Terry Gray Thanks [if you were commenting on my comment :) ]
So it boils down to the old "I didn't give the wrong answer. You didn't ask the right question".
@MATHEMATICAL FRAUD HUNTER RESPECT TO MATHEMATICS that is not how math works bro...
Pretty nice way of saying it.
It's like "A union B intersection C" in sets and expecting a certain answer. You can't write that either because it's ambiguous.
@@GanonTEK PEMDAS is not ambiguous.
6/2(1+2)
Parentheses first
6/2(3)
Multiplication and division left to right
3(3)
9
There is no ambiguity. The ambiguity is people not recognizing 6/2(3) = 6/2*(3) = 6/2*3 = 9. Implied multiplication is treated the same as regular multiplication. The it’s the same as “I didn’t read the question correctly, therefore I am not wrong”
@@Owen_loves_Butters There is no agreed upon convention on whether multiplication by juxtaposition implies grouping or not.
I.e. does 2(1+2) = (2×(1+2)) or 2×(1+2)?
Both are widely used.
6÷(2×(1+2)) = 1 (using PEMDAS)
6÷2×(1+2) = 9 (also using PEMDAS)
PEMDAS isn't the problem. The notation used is. That's the cause of the ambiguity.
That's why there is such a large disagreement and even calculators from the same manufacturer don't agree.
You shouldn't write a/bc or a/b(c) anymore. It's not acceptable notation. ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove any ambiguity.
A PhD student wrote a paper on the ambiguity called The PEMDAS Paradox if you want to look it up.
@@GanonTEK You don’t add parentheses if there are none to begin with.
Must be 1 (due to the widely accepted higher priority of implied multiplication), but all in all it is simply a poorly written expression.
"implied multiplication" - there's no such thing - you won't find it in any Maths textbook.
"it is simply a poorly written expression" - no it isn't. a(b+c) is the standard form of a Factorised Term, to be expanded according to The Distributive Law, a(b+c)=(ab+ac), as part of the Brackets step.
@@smartmanapps5588 Hm, but what do you call multiplication by juxtaposition then? 🤔 You yourself use it in your expression *a(b+c).*
@@cyberagua Do you mean what is it's correct name? A Factorised Term - I already said that. ab+ac=a(b+c), Factorisation. a(b+c)=(ab+ac), Distribution. A Factorised Term, being a Bracketed Term, is solved at the Brackets step. It's not "multiplication" because there's no multiplication sign, which is what "Multiplication" quite literally refers to. ax(b+c), multiplication. a(b+c), distribution. In a(b+c)=(ab+ac), the "multiplication" - if you even write it at all - is INSIDE THE BRACKETS, (axb+axc). If you treat Distribution as "Multiplication" then you end up with wrong answers, as we've seen!
@@smartmanapps5588But why do you use x's instead of the regular multiplication signs "×" or "•"? Are you typing from a Mac or PC that doesn't have these symbols on the keyboard? It slightly interferes with reading and understanding your messages, since *axb* reads as *a·x·b.*
@@smartmanapps5588> you won't find it in any Maths textbook
Do instructions to the calculators count? Calculators are _math_ devices.
From Wiki: "In algebra, multiplication involving variables is often written as a juxtaposition, also called implied multiplication."
Source: "Now, _implied multiplication_ is recognized by the AOS and the square root, logarithmic, and trigonometric functions can be followed by their arguments as when working with pencil and paper."
The issue is, I agree that with the same precedence you go left to right so if it said 6 ÷ 2 × 3 I would correctly answer that as 9. However by wording it as 6 ÷ 2(1 + 2), my mind goes to expand the bracket first which gives 6 ÷ 6 = 1.
This. I was taught (in the US) completing the parentheses/brackets meant you did all involved with the parentheses/brackets. Here, the parenthesis is what symbolizes the 2x3 so you still do that before the division.
@@timelyspirit I was taught the same thing
Inside the parenthesis, outside the parentheses, then L to R.
The rule is called BODMAS or BIDMAS
It is the order of what you do first
Brackets
Indices (or other)
Division & Multiplication
Addition & Subtraction
So here first we do the brackets
6 ÷ 2 (1+2)
6÷ 2 (3)
6 ÷ 2*3
Next we do division
6÷2*3
3*3
Next we do multiplication
3*3
9
@@WokeVeganLiberal wait wasn’t it pemdas?
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Calculator: *Am I a joke to you?*
FranYato • calculators can’t do pemdas but idk if ur joking or not
Ethan Oshiki it’s a joke
.
😂 😂 😂 😂
@@illhart1690 your cell phone calculator sholde be able do this math problem
How is this viral? It's simple PEMDAS -.-
People who fell asleep during math class.
People learned an incorrect order of operations
Yeah it was pretty easy to solve for me but maybe some other people might have found it difficult.
exactly
And yet you failed to understand what he was saying -.-
as a 9th grader I got 9 :0
Good job...