20 million views!

@idontclickbait8453

2 жыл бұрын

Really a good video!

@lavion8090

2 жыл бұрын

lesgo

@gandolph999

2 жыл бұрын

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.

@mlas1308

2 жыл бұрын

@@idontclickbait8453 It is a good video

@alfredoooooooooooooooooooooooo

2 жыл бұрын

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

@javin9743

4 жыл бұрын

daniel rushing this is probably 5th or 6th

@danielrushing55

4 жыл бұрын

Ya true but either way

@adomnibest5099

4 жыл бұрын

Nope, it's 2nd (in my country)

@alexreede2555

4 жыл бұрын

adomnibest lol I learned it at 5, #homeschooliscool

@indevious9659

4 жыл бұрын

5th grade too

This is not a math problem... this is a rule problem....

@RS-fg5mf

4 жыл бұрын

The rules support the correct answer 9

@blubber0_0

4 жыл бұрын

Yeah, technically this rule doesn’t have to be a thing. Just for convenience.

@jude3426

4 жыл бұрын

Blubber Beast um it definitely DOES have to be a thing. It’s there for a reason

@RS-fg5mf

4 жыл бұрын

@@jude3426 it doesn't give priority to multiplication over division... It is for convenience and less clutter....

@LunaEllis

4 жыл бұрын

@@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

@afsdfsadhasfh

8 ай бұрын

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.

@IILiamHD

8 ай бұрын

@@afsdfsadhasfh absolutely spot on. couldnt put it better myself

@IILiamHD

8 ай бұрын

@@afsdfsadhasfh the question is deliberately misleading

@thepsychologist8159

8 ай бұрын

@@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.

@WobblePizza

7 ай бұрын

Jesus. This is dangerous. Hopefully you stay in school and don't go actually build something one day.

IMO the real answer is "don't write expressions this way." You write expressions so that they can't be easily misinterpreted. If there's any possible confusion, add parentheses to resolve the confusion. This is particularly so when dealing with non-commutative operations such as subtraction and division. This probably comes from a background in computer programming; you don't want to make assumptions about order of operations, because while the people who implement the languages usually have standards to work from, they sometimes screw up. (To make things even more complicated, in computer programs sometimes operations have side effects - like "x++ + x" in C - "x++" evaluates x then increments it, so the value depends on whether the left or right side of the addition is interpreted first. The solution is "don't write it that way.". Eliminates confusion and therefore bugs.)

@GanonTEK

11 ай бұрын

100%

@northwestclasspnw7974

10 ай бұрын

Amen

@benvergus1573

10 ай бұрын

Its just the correct way of writing it, there isn't much to be confused about

@benvergus1573

10 ай бұрын

Basically you just read from left to right and solve brackets first, whats so confusing?

@ronnycook3569

10 ай бұрын

@@benvergus1573 The fact that it's debated at all indicates that it's found confusing. This whole kerfuffle would not EXIST if people didn't find it confusing. The implicit multiplication when concatenating terms - as is done in this particular problem - complicates matters further. What is 4x/2x ? Left to right you get 4x, divided by 2, multiplied by x, so 2x^2. But I read it habitually as 4x divided by 2x and get 2, and I'm betting that 90% of people trained with strict left to right in evaluating PEMDAS/BODMAS do the same. Writing with clarity in mind, and avoiding any possible confusion, is never a bad thing. Particularly when dealing with a field where precision matters, such as mathematics or engineering.

The correct answer is 9 but the way I was taught math makes me keep saying 1

@tclauk79

4 жыл бұрын

MOLO 27 yes 🤔

@dbzayan

4 жыл бұрын

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.

@berdyie

4 жыл бұрын

@@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.

@raynatumbeva780

4 жыл бұрын

@@berdyie there is no such a rule in Maths.

@berdyie

4 жыл бұрын

@@raynatumbeva780 For my incorrect way of thinking or for the correct method in the video?

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.

@awesomemccoolname7111

2 жыл бұрын

Explain that to a teacher. Go ahead.

@walkingman8943

2 жыл бұрын

They only thing common about school now is that every child is getting left behind.

@rileyjeffries1282

2 жыл бұрын

That’s why no mathematically inclined individual worth their salt uses the division symbol.

@justingray8161

2 жыл бұрын

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.

@jgt2598

2 жыл бұрын

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.

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.

@spamspamspamspam3459

7 ай бұрын

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

@adrianmcbride1666

4 ай бұрын

​@@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).

@spamspamspamspam3459

4 ай бұрын

@@adrianmcbride1666 That is absolutely not true, () in bidmas only applies to whats inside the parenthesis.

@adrianmcbride1666

4 ай бұрын

​@@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.

@adrianmcbride1666

4 ай бұрын

@@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.

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

@RS-fg5mf

9 ай бұрын

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

8 ай бұрын

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

@RS-fg5mf

8 ай бұрын

@@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.

@WobblePizza

7 ай бұрын

No they aren't. There is nothing wrong or ambiguous with the equation as written. Not everyone is using a whiteboard.

@davidbrattain1446

6 ай бұрын

How on earth do you operate a calculator without those two symbols available?

the correct answer is this is a poorly written problem.

@revdarian

8 жыл бұрын

You are 100% correct, this is the proper answer.

@jamesgcrawford

8 жыл бұрын

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!

@matlohn9381

8 жыл бұрын

+James Crawford yeah realistically equations would never be written this way but I think the majority of math rules indicate the answer is nine

@Theaksten

8 жыл бұрын

In mathematics, there is no such thing as bad problems. Only bad rules and the misuse of good ones.

@Theaksten

8 жыл бұрын

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.

@MrGamecatCanaveral

2 жыл бұрын

No the problem is teachers changing they way they teach things.

@babyyoda7749

2 жыл бұрын

@@MrGamecatCanaveral Not teacher the education system.

@MrGamecatCanaveral

2 жыл бұрын

@@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.

@aeroljameslita4975

2 жыл бұрын

@@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.

@aquaneko14

2 жыл бұрын

@@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.?

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.

@wadabid6165

6 ай бұрын

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

@snekarmy4559

5 ай бұрын

The parentheses are just around 3 though, not 2*3

@markprange4386

4 ай бұрын

@@wadabid6165: 2y is grouped. Just like 2π, 2π, or 24.

@whoff59

3 ай бұрын

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.

@markprange4386

2 ай бұрын

@@whoff59: PEMDAS is not an official rule anywhere. It's not even a rule.

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

@qwenettadixon6911

10 ай бұрын

Same here. Aleays remembered pemdas, but didnt hear bodmas til recently

@3Deez3

10 ай бұрын

I never heard bobmas b4 lol I said brackets to be inclusive I guess lol.

@mikehuston2132

10 ай бұрын

I was taught to expand the products in parenthesis first. So 2(1+2) would be 2+4 which is 6. 6/6=1

@solidmercury8026

10 ай бұрын

exactly mate@@mikehuston2132

@mirandahotspring4019

10 ай бұрын

@@qwenettadixon6911 We learned it as BEDMAS (E = exponent)

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.

@burnerjack01

2 жыл бұрын

And that's why I used to hate computers so much.

@brianfedelin7015

2 жыл бұрын

It would be 13 cartons because of the and boolean logic instead of or.

@keesdenheijer7283

2 жыл бұрын

I'm truly thankful for the opportunity to give thumbs-up #42.

@4_youtube_is_dead

2 жыл бұрын

tf

@Dan.Bielecki

2 жыл бұрын

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.

Just graduated and I was legitimately taught that "historical way" all through school

@mansuryayas

2 жыл бұрын

Same here

@kayking2536

2 жыл бұрын

I graduated high school 15-16 yrs ago and got my associate degree in '08, that's how I was taught, the old way.

@fiveoctaves

2 жыл бұрын

That's terrible.

@sikksotoo

2 жыл бұрын

Ditto, and I aced math in school

@pentowerchannel5306

2 жыл бұрын

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

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

@adrianmcbride1666

4 ай бұрын

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.

@4IdiotsProductions

Ай бұрын

Exactly

I understand both methods. It will be interesting what my books say when I get to this type of problem. I am studying from pre-1900 Maths books right now.

think of it like a fraction. there's a reason why in higher math '÷' isn't used.

@erickbangle3781

8 жыл бұрын

dont forget that 2(3) is one term

@FusedAtoms

8 жыл бұрын

I know right... I'm suprised the education system is failing this hard to teach math.

@thomasgronek6469

8 жыл бұрын

but it's not a fraction. there is the discrepancy in the solution

@DrenRawr

8 жыл бұрын

all division is a fraction lol

@supervegetto1087

8 жыл бұрын

Exactly Erick!! we use the division sign just to teach kids but it is wrong in advanced math.

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!

@bigbadlara5304

2 жыл бұрын

I just graduated high school and my answer to this problem was 9. I guess it's taught correctly now atleast :)

@GanonTEK

2 жыл бұрын

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.

@nixboox

2 жыл бұрын

@@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

2 жыл бұрын

That is correct. This video made a mistake when it ignored the distributive property. The entire problem is wrongly represented here.

@GanonTEK

2 жыл бұрын

@@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.

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.

I'm pretty sure you missed a different confusion. I get that some would interpret the division sign as you did, but there is also the belief that implied multiplication has priority over other division and multiplication, because it was implied, it has to be resolved. You can't just change 2(3) into 2x3, because they are bound. 2x(1+2) does not just equal 2(1+2), because 2(1+2) = (2(1+2)). I realize it doesn't make a difference until (÷) gets put in front of them. Say we wanted to divide energy by 12. Would we write 12 ÷ mc^2 or would we write 12 ÷ (mc^2). We all recognize mc^2 as energy, m and c^2 are bound by implied multiplication. a completely different thing that 12 ÷ m x c^2. Or divide 12 by the area of a circle: 12 ÷ πr^2. π x r^2 is implied and therefore bound. this is the real argument implied multiplication has priority of not.

Its gonna go viral again because its in my recommended

@miguelgm808

4 жыл бұрын

6 / (2*1 + 2*2) = 1

@frozenx1337

4 жыл бұрын

@@miguelgm808 did u even watch the video?

@devannatesan5053

4 жыл бұрын

Ya

@danielje97

4 жыл бұрын

Nobody care

@Araqius

4 жыл бұрын

@@miguelgm808 (4/2+2/2)(3) = 9

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 😂😂😂

@RS-fg5mf

3 жыл бұрын

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...

@justcheck6645

3 жыл бұрын

@@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.

@RS-fg5mf

3 жыл бұрын

@@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??

@RS-fg5mf

3 жыл бұрын

@Christopher Butler if you don't care, why bother replying?? LOL Enjoy your show. 😁😁

@violinplayer3518

3 жыл бұрын

I graduated math in 80s, cannot believe people are discussing primary school math

I do not recall the "same precedence" rule. So, I have always taken PEMDAS to be performed, literally, left-to-right. But, knowing the rule now, I think a better mnemonic would be (P)(E)(MD)(AS). It will be mine from now on! Thanks for the lesson.

@clowncircus-dm3fd

11 ай бұрын

BODMAS

@InsanityoftheSanities

10 ай бұрын

@@clowncircus-dm3fd WHO CARES AMERICA SAYS PEMDAS.

@hat_cbw6972

10 ай бұрын

@@InsanityoftheSanitiesjokes on you, some American schools use BODMAS

@InsanityoftheSanities

10 ай бұрын

@@hat_cbw6972 Jokes on you, who cares and who asked?

@hat_cbw6972

10 ай бұрын

@@InsanityoftheSanities Jokes on you, we can assume that who asked is an imaginary number. An imaginary number that we know of is sqrt(-1) which is i. Conclusion: I asked.

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

@trickortrump3292

10 ай бұрын

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

@RS-fg5mf

10 ай бұрын

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

@RS-fg5mf

10 ай бұрын

​@@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

@trickortrump3292

10 ай бұрын

@@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. 👍😉

@RS-fg5mf

10 ай бұрын

@@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...

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.

@MarioLandscape

3 жыл бұрын

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

3 жыл бұрын

@@MarioLandscape nope

@MarioLandscape

3 жыл бұрын

​@@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.

@MarkQub

3 жыл бұрын

@@MarioLandscape you see how you lost. You got mad/serious over someone who just simply said “nope”

@MarioLandscape

3 жыл бұрын

@@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?

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.

@RS-fg5mf

3 жыл бұрын

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...

@Superdada

3 жыл бұрын

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.

@alxlej

3 жыл бұрын

@@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?

@borismuller1086

3 жыл бұрын

@@alxlej They mean using fractions instead of a symbol and having everything next to eachother.

@alxlej

3 жыл бұрын

@@borismuller1086 but the meaning and therefore the resulting operation are still the same, aren't they? what am i missing?

what if it was a+b in the parenthesis, how to solve the parenthesis then?

Can a mathematician explain to me why implied brackets (something thats not really there) would take precedence over reading the expression left to right as is (following thr rules that are there)?

@RS-fg5mf

8 ай бұрын

It's implicit multiplication not implicit grouping.... No they can't explain why, because it's wrong... The problem stems from an Algebraic Convention given to coefficients and variables that are directly prefixed and form a composite quantity by Algebraic Convention.... 6/2y = 6/(2y) because the 2y is a directly prefixed coefficient and variable that forms a composite quantity by Algebraic Convention... They confuse and conflate this convention to Parenthetical Implicit Multiplication. They are not the same thing... The Distributive Property allows you to multiply the TERM outside the parentheses across each TERM within the parenthetical. Terms are separated by addition and subtraction not multiplication or division. 6÷2 is a single TERM sub-expression juxtaposed outside the parentheses as a whole not just the numeral 2. The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... 6÷2(1+2)= 6÷2×1+6÷2×2= 9 Distributive Property

@GanonTEK

8 ай бұрын

Sure. Academically, multiplication by juxtaposition implies both multiplication and grouping. It is a shorthand notation used to save space, look better, and originally to apparently reduce cost too. You have to interpret all implicit notation in a question before you can use any rules or properties. So, academically, 6÷2(1+2) implies 6÷(2×(1+2)) and now you can use properties and rules to get 1. Literally/programming-wise, multiplication by juxtaposition implies only multiplication. So 6÷2(1+2) implies 6÷2×(1+2) instead. Now you can use the very same rules and properties to get 9. L to R is an arbitrary convention also, it's not a rule. For equal priority operations the order doesn't matter (hence the name equal priority). You have to take the whole expression into account to know how to approach it properly. So, to answer your question, Interpreting the notation (the language of maths) comes before using any rules or properties, so notation conventions take prescidence over any rules or properties.

@RS-fg5mf

8 ай бұрын

@@GanonTEK It does not Academically mean 6÷(2(1+2)) ... Total Bullsh1te

oh sorry i’m late, KZread just recommended me this video 3 YEARS LATER

@TristanSGS

5 жыл бұрын

chris yeah me too

@sanpiaupiau6093

5 жыл бұрын

same

@onurakar3694

5 жыл бұрын

isnt it 2 years

@chris-jn2wu

5 жыл бұрын

Onur Akar technically, yes

@everythingever9037

5 жыл бұрын

Me2

I did this in 10 seconds... how can it be viral?

@ghislainmaury2065

5 жыл бұрын

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 ?

@j.a_

5 жыл бұрын

@@ghislainmaury2065 English translation please?

@davidesguevillas

5 жыл бұрын

This is so easy, I solved it in 5 seconds

@abvolts-animation6008

5 жыл бұрын

Defaulty Boi lol.

@abvolts-animation6008

5 жыл бұрын

Letucces Satan yeah... I’ll pass thanks I’d gladly take yours though

If one knows that equations are to be solved left to right, could anyone explain what the purpose is to write equations, out of order? What is a logical reason for having extra formulas like pemdas, when by just using brackets, and going left to right, how to solving equations would be clarified, is it just to confuse or make things more complicated?

What about all the applications that had used the old way?

I used the historical version all my life. I must be rather ancient.

@michellevanzyl

3 жыл бұрын

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😂

@willwalker24601

3 жыл бұрын

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]

@ute.fritzkowski

3 жыл бұрын

@@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.

@CorgiCorner

3 жыл бұрын

I think the difference is people forget about the brackets so they just disappear

@abhisheksilverrrrr

3 жыл бұрын

✔️✔️✔️👍👍 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...

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.

@Araqius

7 жыл бұрын

Totally wrong and nonsense. What is the inverse of "implicit multiplication"?

@NeelDhar

7 жыл бұрын

I agree with ZoeCat

@TomJacobW

7 жыл бұрын

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.

@ZoeTheCat

7 жыл бұрын

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.

@cameronparkes6629

7 жыл бұрын

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.

After learning calculus, this answer is 1. Visualize the division line, 6 is the numerator, the 2(1+2) is the denominator. From there solve the denominator however you want, you’ll end up with 6. 6/6 = 1

@paulblart7378

9 ай бұрын

Incorrect, and this has nothing to do with calculus, it's fundamental algebra. Division is division, not an implied fraction. If anything, it's the other way around: a fraction is implied division

@admiralvirhz

9 ай бұрын

If you write it as algebraic equation you can clearly see how it’s supposed to be done. X/Y(A+B) = X/(YA+YB), since you need to distribute property of Y among entire parenthesis first, and fully evaluate that before going back to division of X. Using numbers it’s: 6/2(1+2) = 6 / (2*1 + 2*2) = 6/6 = 1 This is how math works. People outside of America aren’t thought any of PEDMAS, BODMAS or whatever bdsm acronym is used. People are thought how order of operations works in practice, often explained by definitions, and orders, and with a help of algebraic equations, since when you remove numbers it’s clearer to see how things are evaluated.

@paulblart7378

9 ай бұрын

@@admiralvirhz Incorrect. The distributing property is multiplication, which has no precedence over division. It would be wrong to distribute 2(1+2) before doing 6/2. The first operation would leave you with 3(1+2) and then you can distribute to get 3+6=9

@admiralvirhz

9 ай бұрын

@@paulblart7378you’re making logical error here. Multiplication doesn’t have priority over division, you’re right about this and it’s set in stone, but to fully value what’s inside parenthesis you need to distribute 2 over it. There’s no sign of multiplication, so you need to understand that it is 6 divided by double parenthesis. You see your logical mistake here? It’s not 2 multiply parenthesis since there’s no multiplication sign. It’s double parenthesis. It’s really bad written problem to deal with, I no wonder why so many people get this wrong.

@paulblart7378

9 ай бұрын

@@admiralvirhz It's an implicit multiplication. It can be rewritten as 6/2*(1+2), the fact that there isn't an explicit sign doesn't change the problem. I don't know what you mean by "6 divided by double parenthesis", but there is no rule that implicit multiplication groups the operands together. You would do 6/2 first, then multiply that by (1+2)

I was under the impression that multiplication came before division in the order of ops. Glad to see my math wasn't completely off since I ended up with 1 in the end. Still, need to brush up on that stuff.

@Arcessitor

6 ай бұрын

It does, depending on the system. Video maker is wrong.

Oh, I had the 1917 math class, then

@TheHerothief

3 жыл бұрын

Me too 😂 honstly, not surprised, though

@MistyHelloKittyWorld2

3 жыл бұрын

Me too.

@mathfullyexplained

3 жыл бұрын

Try my channel mathfullyexplained

@cluix6260

3 жыл бұрын

I guess I didn’t.. I got 9

@daystar862003able

3 жыл бұрын

Me too ✋

Maybe that’s why no one past fifth grade uses that division symbol

@nielsheirbaut4120

4 жыл бұрын

Finally someone with logics

@supertron6039

4 жыл бұрын

Yup, you're right.

@alonso3184

4 жыл бұрын

Yes thank you

@sageight818

4 жыл бұрын

Looks like someone didn’t pass grade 3 English. passed*

@fatkidinc.3058

4 жыл бұрын

@@sageight818 if you're gonna roast someone on spelling, please atleast be right next time. Thanks

I.. thought it was 1. Does not multiplication come before division thereby rendering the order right to left post resolving the parenthesis... I've not done math as such since college and was philosophy and applied linguistics double major 20 years ago... sigh.

@RS-fg5mf

9 ай бұрын

Division is Multiplication by the reciprocal and Thetford they share equal priority and can be evaluated equally from left to right as they appear.... The correct answer is 9

Your reference to the history of typography where a division sign was preferred over multiple parentheses is interesting. But today such problems do no service to math literacy or math education. They only create confusion, chaos, and distraction and alienate students sitting on the fence. Math is beauty. There is no scope for ambiguity in it. Only sadistic teachers who derive pleasure in putting others down so as to guard their positions design such problems. I think one easy way to write an unambiguous arithmetic expression is to enter it into an Excel (or Google) spreadsheet which is now easily accessible around the globe. Excel will not accept the division sign, or the parentheses without a multiplication sign preceding it. Thus, you will have to write 6/2*(1+2) if you want 9 as answer, or 6/(2*(1+2)) if you want 1 as answer.

@Mariam-kg7fr

7 ай бұрын

I wish you could have been my math professor in college:)

@SuperChuckRaney

6 ай бұрын

Math teachers are invariably one step below orangutans in critical thinking. Math teachers drool, Physics rule. A "math teacher" can easily prove that 2+2=5. And be correctly following "math rules". Here with 6:2(1+2)..... These "math teachers" incorrectly apply pedmas by only doing HALF of the 'p'. Do you see a Multiplicative Operator hanging around between 2 and ( ...? no? Then it's "Implied" hence it's the Coefficient of the (1+2). The 2 is the coefficient of the (1+2) variable. It achieved the place in the expression as a reduction of (2+4). Since (2+4) simplified is 2(1+2). 2x+2y is 2(x+y), right? Soo, to insert the Google example here ... some/most of the math calculsators are incorrect for the reason you mention..... and further THE PARENTHETCAL EXPRESSION includes it's Coefficient Modifier. It's the literal definition of Parentheses. YOU ARE ONLY DOING HALF THE PARENTHETICAL EXPRESSION by only solving inside the (). Common solution isn't following pedmas, and just cause a drunk guy in 1920 provided a solution in a bar on a napkin, doesn't make it true. 2+2 still don't equal 5. Sounds like he had good marketing tho.

@BlueDragon-gv3ky

5 ай бұрын

I was taught that when there isn’t a * between a number and a parentheses, you had to do them first! Just as if it were 2x

@SuperChuckRaney

5 ай бұрын

@@BlueDragon-gv3ky I've repeated that to be shouted down by the chorus. Distributive Property of multiplication, it is. They rip the coefficent off the parentectical. You would NOT do it with an Exponent.

@harrymatabal8448

5 ай бұрын

Mr canasta forget parenthesis. If you multiply first then we have 6×3÷2=9.

Next viral problem.. 1+1 = 2 or 11.. 🤔🤔🤔

@jdpace4371

3 жыл бұрын

1+1 = 10 ;) 1+1+1 = 11, 1+1+1+1 = 100.

@parzival8786

3 жыл бұрын

@Jure Lukezic binary smh

@jdpace4371

3 жыл бұрын

@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!!!

@jdpace4371

3 жыл бұрын

@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" ...

@whod

3 жыл бұрын

10

I solved this in 5 seconds this shouldn't be a problem for anyone who attended school.

@lailaaa24

4 жыл бұрын

Same

@jessetarpley4

4 жыл бұрын

Exactly, I always loved doing really long order of operations math problems.

@_mahiii

4 жыл бұрын

Same, idk why they are making fuss over this? I mean this is taught in school....

@suboryoulldiein24hours48

4 жыл бұрын

@@_mahiii lol he got 14 million views it served its purpose

@thejaramogi1

4 жыл бұрын

Unless your History teacher doubled as your Maths teacher!

I grew up in the 1960's and back then 1 would have been the answer. I think one of the main reasons that kids struggle with math is because of problems just like this. 90 + percent of all people will never encounter this type of problem in their lifetimes outside of school. I think kids today to be taught a more practical math Kids today can't make change. If you want to know where we are headed as a society, rent the movie Idiocracy. We are closer to it than you think.

if you were using quarters: 0.25(3+5) = 1/4(3+5) =1/4(8) would you have $2 or $0.03?

@nikolasperrakis5775

10 ай бұрын

2

After all this debate and discussion, I think we can all agree that this is why we use fractions instead.

@jamesfiddler1976

2 жыл бұрын

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.

@godlikefish1193

2 жыл бұрын

All my homies hate ÷

@pirilon78

2 жыл бұрын

@@jamesfiddler1976 how the hell do you not use order of operations im highschool? You need to use them for literally any equation

@jashickey

2 жыл бұрын

@@godlikefish1193 - Me too my friend. All forms.

@jamesfiddler1976

2 жыл бұрын

@@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.

Please excuse my dear Aunt Sally. I thought everyone was taught that.

@RS-fg5mf

4 жыл бұрын

PEMDAS = 9 and some people were taught other acronyms that mean exactly the same thing, like BODMAS

@godelnahaleth

4 жыл бұрын

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.

@RS-fg5mf

4 жыл бұрын

@@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...

@achyuththouta6957

4 жыл бұрын

@@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.

@hannahdewert

4 жыл бұрын

Exactly its easy

I never got so tired of something as Algebra. Along with this and too many other horrors made me stage an escape! Still don’t regret it to this day.

To make this easy look at the division symbol, it’s a dot over a line over a dot. This tells you that what is on the left of the symbol goes on top and what’s on the right goes on the bottom.

Me: Answer is obviously 1 "Answer is 9" Me: Well fuck me.

@kaicluster6783

7 жыл бұрын

It's actually 1 :) The person explaining made a crucial mistake thinking that () is the same as x. As many explained, it's not

@thegreatchinesedragon4610

7 жыл бұрын

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.

@belalmangrio383

7 жыл бұрын

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

@marving.5436

7 жыл бұрын

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)=

@sam9s

7 жыл бұрын

Divide should precede Multiply so 6/2x3 should be 3x3=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

@lastannahme

Жыл бұрын

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.

@j.r.arnolli9734

Жыл бұрын

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...

@lastannahme

Жыл бұрын

@@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.

@antsfur

Жыл бұрын

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 !

@barbarashirland9078

Жыл бұрын

I was taught that way also. In the US, but three generations ago. I’m old.

What is the rule to open the bracket ?

I can see where he is coming from you were going to the order of operations, but, since the symbol does not appear you would not do that until after you have done every single that has appeared

in short don’t use the outdated division symbol, just use the typical numerator and denominator removes all uncertainty

@charliedallachie3539

2 жыл бұрын

It still becomes 6/2*3. So if it’s multiplication before division that’s 6/6 =1

@o_sch

2 жыл бұрын

@@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

@charliedallachie3539

2 жыл бұрын

@@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

2 жыл бұрын

@@charliedallachie3539 but it isn't multiplication before division. they are equal, so it is left to right.

@Wexexx

2 жыл бұрын

@@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.

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!!)

@Marc_NL666

3 жыл бұрын

Good ol' "Meneer Van Dalen Wacht Op Antwoord" for the Dutch viewers...

@Marc_NL666

2 жыл бұрын

@@manofculture9051 Your mom sends her regards! And dinner's at six, be on time please.

@kennethmiller2333

2 жыл бұрын

The problem isn't that the rules were changed; the problem is that they are being misapplied.

@HQBergeron

2 жыл бұрын

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.)

@michaelangellotti4773

2 жыл бұрын

@@HQBergeron Agreed. It's mathematical semantics. #planetpluto

The sequence of operations seems to be random! It was random previously when division came last and it is random now when the left to right sequence is preferred. In algebra, where division is symbolized by /, we still do divisions last. Why?

@RS-fg5mf

10 ай бұрын

We don't do division last...Division is nothing more than multiplication by the reciprocal and that is why we can evaluate EQUALLY from left to right... 6÷2(1+2)= 6×0.5(1+2)

Honestly I wasn't sure what to do with no visible sign. That is why i checked this out. I have always wondered why there were so many different answers in the past . If this second way to figure it out was from so long ago ... well I wonder why there is still such a divide.

@GanonTEK

10 ай бұрын

The reason there is such a divide still is because of a key point the video neglects to mention. That being, multiplication by juxtaposition. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. This is completely separate to the old meaning of ÷ which isn't used. All the scientific calculators that give 1 do not use that old meaning of ÷, for example. 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 (1). 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 (1). 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 So, still a very common usage of multiplication by juxtaposition. The video is unfortunately biased and incomplete.

Congrats, this just became topical again. Expect another influx of views my man.

@darlinn7195

3 жыл бұрын

i just came to check if im braindead turns out nah

@kolowar6600

3 жыл бұрын

I dont know why people think this is hard

@Nash-

3 жыл бұрын

@@kolowar6600 because they failed second grade

@qc7511

3 жыл бұрын

Anf another influx of ignorants disliking this video again.

@sadbird6644

3 жыл бұрын

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

Just came to check if my brain was working and it is, I’m tired of fighting over the right answers through Twitter 🏃‍♀️

@blazecraze3652

3 жыл бұрын

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

@katie-hy6ii

3 жыл бұрын

NOT ALL OF US COMING FROM THAT TWEET BYEAKSJSKSJ 😭

@Araqius

3 жыл бұрын

@@blazecraze3652 ÷ and / are both division sign.

@carterangliss9288

3 жыл бұрын

Same lol

@paisleigh1989

3 жыл бұрын

@@blazecraze3652 UK don't take calculus or advanced functions as a separate subject so that wouldn't work

This is a nesting problem. (order operation) should we assume this is a precedence of bracket over binary operators? Let me skip it. Thanks.

@RS-fg5mf

Ай бұрын

The binary operation is implicit, implied though not plainly expressed... There is no mathematical difference between 6÷2(1+2) and 6÷2×(1+2) despite the false and misleading information, subjective opinions and willful ignorance people have about parenthetical implicit multiplication...

If the things on the right are to be divided by the left then you need to put parenthesis around everything on the right.

Let me guess...next viral thing is 1+1

@onezaproductions

5 жыл бұрын

Answer is obviously 0

@GatsDomineaux

5 жыл бұрын

Lmao

@romanblecha1102

5 жыл бұрын

1+1=11 no? :D :D

@andreflores4486

5 жыл бұрын

There are no possible solutions to that equation.

@zeuxlaught2797

5 жыл бұрын

wrong

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..

@rohmanatasi1771

4 жыл бұрын

It's 1

@angie___nn7352

4 жыл бұрын

It’s 7

@PankajKumar-ts9hq

4 жыл бұрын

Noob, its one

@dominatinggamerguy5795

4 жыл бұрын

Not even 5th grade math. It’s like 2nd grade math

@realhi144

4 жыл бұрын

It depends on pemdas or bodmas

so how much is 8:4:2(using the historical usage)?

@RS-fg5mf

10 ай бұрын

You're using a ratio symbol not a division symbol. The historical method is BS. It was a mistake by some text book printing companies who pushed the use of the obelus in a manner similar to the vinculum because the vinculum took up too much vertical page space, was difficult to type set and more costly to print with the printing methods at that time... 8÷4÷2= 1

Its 9, look it up. You go left to right on the multiplication and division stage of PEMDAS.

@GanonTEK

2 ай бұрын

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.

@RS-fg5mf

2 ай бұрын

Yes, the correct answer is 9

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

@maximilianomolina5975

2 жыл бұрын

Yep i remeber i got so used to fraction that when i saw the division simbol at first i thought it was percentage xD

@GanonTEK

2 жыл бұрын

100%

@anonymes2884

2 жыл бұрын

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.

@GanonTEK

2 жыл бұрын

@@anonymes2884 100% and ISO-80000-2 says that ÷ should no longer be used also.

@wallytruman9433

2 жыл бұрын

I don't know algebra

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.

@Nga_Babaye

8 жыл бұрын

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.

@realisticdan3302

8 жыл бұрын

same here...thank god for comments almost gave up on my math.

@Henry-mq2fv

8 жыл бұрын

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

@sanfrand22

8 жыл бұрын

Don't be jackass Steve

@Nga_Babaye

8 жыл бұрын

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

Is this math not being taught in schools any more? Order of operations was 6th grade math for me , where did math go wrong?

By the reading order of the multiplicatives, so it's 6 ÷ 2 x 3. That's what I was taught. Just get rid of the weak factors or something or should you say it's the other way around.

Imagine using division symbol instead of fraction.

@mrpickle8959

3 жыл бұрын

Yeah that's how that goes...?

@hochigaming14yearsago90

3 жыл бұрын

It's 5th grade man

@sensei5668

3 жыл бұрын

@@mrpickle8959 fractions is also division 1/2 is the same as 1÷2, and this works for anything.

@Langweiler11

3 жыл бұрын

@@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 "/"

@sensei5668

3 жыл бұрын

@@Langweiler11 that's my point

Watching 5th grade math at 2AM even though I'm 15🤦‍♂️

@jctorres6112

4 жыл бұрын

well theres only one truth. math is attractive 😂😂

@anelaknezevic5680

4 жыл бұрын

Sameee 😂

@melodymartinez7003

4 жыл бұрын

Same

@asher7124

3 жыл бұрын

Im 11

@blinkcatmeowmeow8484

3 жыл бұрын

Im 15 too

I would have thought the presenter of the equation asked us to "Divide six by twice whatever value is within the brackets". The equation can be written as A divided by B where B=2(1+2). So if [A divided by B] = 1 and A =6, then B=6, This implies 2(1+2)=6 which is correct. If [A divided by B] = 9, and A=6, then B= 6/9or 2/3. This implies 2(1+2)=2/3 which is incorrect. The rule 'brackets first' is short for "Solve the brackets first" This implies the removal of the brackets from the equation first. In adding 1+2, you do not get rid of the brackets! You are still left with 2(3), and one cannot remove brackets from the equation without solving them. In this case you must multiply 3 by 2 to the brackets. You cannot just add in or take out brackets ad lib! In applying values, 2(3) is a single Value and is expressly implied in the equation. 2 x (1+2) is two values and is not implied in the equation. It appears to me the problem lies in the computerisation of the equation. To me the equation is simple and unambiguous and means the same now as it did 50 years ago!

The American mathematical society says in its style guide that multiplication with juxtaposition is done before division. That is generally how people do it. Most calculators do it so with the exception of TI. Even at the TI they admit it should be so but US math teachers insist that multiplication is always done at the same time as division.

@RS-fg5mf

10 ай бұрын

Ummm the AMS gives priority to ALL multiplication over division and suggests that you use multiplication by the reciprocal instead of Division... The ANS is specifically stateing a change to the STANDARD Order of Operations in their STYLE GUIDE... The AMS is also not dealing with basic 4th grade arithmetic expressions. While I don't like the idea of the AMS going against the standard rules and principles of math they have inducated it was for formatting and printing purposes and it only applies to their publication... 6÷2(1+2) = 6*2⁻¹(1+2) is how the AMS prefer you write it. The majority of scientific calculators and online math engines give you the correct answer 9. CASIO has admitted to programming different models for different markets based on popularity and opinion not the rule of math. When you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended you get the only correct answer 9

Fifth grade math: im gonnna end America's whole career

@glitzyx4x852

4 жыл бұрын

Răzvan Ruse literally

@Name-ru1kt

4 жыл бұрын

Anthony Lo hey guess what he deleated his comment now yours makes no sense

@glitzyx4x852

4 жыл бұрын

Fallout Mods who deleted what

@razvanruse68

4 жыл бұрын

Um what?

@jacobschoenbaum7689

4 жыл бұрын

Just the people that aren’t in school anymore

1:59 “And this gets us to the correct answer of dine”

@chickenfeet6123

4 жыл бұрын

Nicolas T-R 😂😂

@spookbarkee9345

4 жыл бұрын

You brainwashed me and now that’s all I here instead I of nine

@kingblue8868

4 жыл бұрын

lol

@ZJC_9

4 жыл бұрын

Speechless of laughter 🤭😂😆

@someguy5354

4 жыл бұрын

lol

The answer is 1. Especially since the distributive property applies to the expression in parenthesis. 2(1+2) = (1x2+2x2) = (2+4) = 6

@RS-fg5mf

10 ай бұрын

The Distributive Property supports 9 not 1 The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Order of Operations work because of the Properties and Axioms of math not in spite of them... The Distributive Property when fully applied is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in... If you can't draw a factor in and get the same result as drawing the TERMS inside the parentheses out then you haven't applied the Distributive Property correctly... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... The axiom a(b+c)= ab+ac however the variable "a" represents the TERM or TERM value i.e Monomial factor of the TERM outside the parentheses not just a numeral next to the parentheses. In this case a = 6÷2 OR 3. People just automatically assume that "a" is a single numeral... 6÷2(1+2)= 6÷2×1+6÷2×2 Distributive Property Parentheses removed... 6÷(2(1+2))= 6÷(2×1+2×2) Distributive Property. Inner parentheses REMOVED This can be further demonstrated using the vinculum.... 6 ------(1+2)= 6÷2(1+2)= 9 2 6 ------------ = 6÷(2(1+2))= 1 2(1+2) A 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 That over bar (vinculum) is a grouping symbol _______ _________ 2(1+2) = 2×1+2×2 one grouping symbol each Note that when applying the Distributive Property one grouping symbol was REMOVED from each notation...

It's just simple BODMAS rule application. Parenthesis is removed after the expression inside it is solved, thus the expression becomes 6/2*3, which by BODMAS rule is 3*3 = 9.

funny how i got both answers and then blamed my math teacher for making me so indecisive

@stephensteinhauer3346

2 жыл бұрын

Same. I got both answers and then watched the video to see what obscure rule they would pull out of their hat.

For things like this we don't use the ÷ symbol anymore, it's just easier to use a fraction so you can differentiate (6/2)×3 from 6/(2×3)

@vostokk

4 жыл бұрын

That's exactly what I was thinking.

@Lucian24

4 жыл бұрын

It's not its 1

@Lucian24

4 жыл бұрын

You work left to right

@_MrMoney

4 жыл бұрын

@@Lucian24 What I meant is that we now use fractions so we don't need to specify which goes first. You operate all on the top and divide it by all on the bottom. So you can differenciate: (6/2)×3 = 3×3 = 9 From 6/(2×3) = 6/6 = 1

@Lucian24

4 жыл бұрын

That makes sense

I try to see 6 / 2(3) as 6 / 2 * 3 = 6 x 1/2 x 3. That way, no risk of confusion. With the historical way, a parenthesis gets introduced when it originally wasn't there. In the sample, it should be x/2y, which is ambiguous (can be read as x * 1/2 * y or x/(2y)). It would have needed to be written as "x divided by (2y)" to make it clear

@RS-fg5mf

10 ай бұрын

2y is a composite quantity by Algebraic Convention... The biggest mistake that people make is incorrectly comparing 6÷2(1+2) as 6÷2y. This is an inaccurate comparison... 6÷2(1+2) does not Algebraically equate to 6÷2y it correctly equates to y(1+2) where y is equal to the Monomial Factor of the TERM outside the parentheses. 6÷2 is juxstaposed to the parentheses as a whole not just the numeral 2 All variables have a coefficient. Constants can be coefficients but constants do not have coefficients. There are no coefficients in this expression... 6÷2y the coefficient of y is 2 BUT 6÷2(a+b) the coefficient of a and b is 3 not 2 Many people confuse and conflate an Algebraic Convention (special relationship) between a variable and its coefficient that are directly prefixed (juxstaposed) and forms a composite quantity by this convention to Parenthetical Implicit Multiplication... They are not the same thing... Convention doesn't trump LAW and the Distributive Property is a LAW. 6/2y = 6/(2y) = 3/y by Algebraic Convention BUT 6/2(y)= 3y by the Distributive Property... ABC/ABD = C/D by Algebraic Convention ABC/AB(D) = CD by the Distributive Property 6/2(a+b)= 3a+3b not 6/(2a+2b) The Distributive Property is a PROPERTY of Multiplication, NOT Parentheses and not Parenthetical Implicit Multiplication. As such has the same priority as Multiplication and Multiplication does not have priority over Division... The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication.... The Distributive Property, when FULLY applied, is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in. The Distributive Property, when FULLY applied, REQUIRES you to multiply all the TERMS inside the parentheses with the TERM or TERM value i.e Monomial factor of the TERM outside the parentheses not just the numeral next to it... TERMS are separated by addition and subtraction not multiplication or division... 6÷2 is a single TERM juxstaposed to the parentheses as a whole not just the numeral 2 FURTHERMORE people misunderstand Parenthetical Priority... The rule is to evaluate OPERATIONS INSIDE the symbol as a priority before joining the rest of the expression outside the symbol. It does NOT literally mean that the parentheses have to be evaluated BEFORE anything else in the expression can be done... A(B+C)= AB+AC where A is equal to the TERM VALUE i.e. monomial factor outside the parentheses not just the factor next to it... A=6÷2 = 3 Monomial factor B= 1 C= 2 6÷2(1+2)= 6÷2×1+6÷2×2 no parentheses required 3×1+3×2= 3+6= 9 You can't factor a denominator without maintaining all operations of that factorization WITHIN a grouping symbol. You can factor out LIKE TERMS from an expanded expression. 6÷2×1+6÷2×2= 6÷2(1+2) as the LIKE TERM 6÷2 was factored out of the expanded expression..... When a constant, variable or TERM is placed next to parentheses without an explicit operator the OPERATOR is an implicit multiplication symbol meaning you multiply the constant, variable or TERM with the value of the parentheses. TERMS are separated by addition and subtraction not multiplication or division. 6÷2 is a single TERM juxstaposed to the parentheses as a whole not just the numeral 2 6÷2(1+2)= 3(1+2) no rules have been broken 2×2×4(a+b) partial Distribution 2×2(4a+4b) However the TERM outside the parentheses when simplified equals 16 and 16(a+b) 2×2(4a+4b)= 2(8a+8b)= 16a+16b which is the same as 16(a+b) 2×2×4(a+b) when fully Distributed is 2×2×4×a+2×2×4×b and the LIKE TERMS can be factored out of the expanded expression. The LIKE TERMS being 2×2×4 So... 2×2×4(a+b) 6÷2×1+6÷2×2+6÷2×3-6÷2×4= 6÷2(1+2+3-4) as the LIKE TERM 6÷2 was factored out of the expanded expression... Let y = 0.5 6y(1+2)=? 6y*1+6y*2= ? 6/y⁻¹*1+6/y⁻¹*2= ? If you answered 9 to all three algebraic expressions then it would be ILLOGICAL and INCONSISTENT as well as hypocritical to say that 6/y⁻¹(1+2) doesn't also equal 9 The rules of math have to remain logical and consistent across the board...

@MrGreensweightHist

9 ай бұрын

@@RS-fg5mf "2y is a composite quantity by Algebraic Convention...' Yes, but 2(y) is not. And that is what we have in this problem

@RS-fg5mf

9 ай бұрын

@@MrGreensweightHist I'm aware of that... LOL

6÷2(1+2) =6÷(2x1 + 2x2) = 6÷ 6=1??? can't i apply distributive property?

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.

@SPACKlick

7 жыл бұрын

I have and did.

@UnderMan

7 жыл бұрын

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)).

@SPACKlick

7 жыл бұрын

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.

@Araqius

7 жыл бұрын

SPACKlick 6 ÷ 2y = 3y

@SPACKlick

7 жыл бұрын

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

for me as a programmer, this was very clearly a 9.

@sebastianteixeira2290

3 жыл бұрын

I'm not even a programmer, I just use basic bodmas knowledge

@ftn4513

3 жыл бұрын

Yea

@velziqmapping3884

3 жыл бұрын

pog

@PuzzleAdda

3 жыл бұрын

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?

@zoltanfridrich1934

3 жыл бұрын

@@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.

These often confused me in college, for once the parenthesis were added together, the parenthesis would often be dropped. Without the parenthesis, multiplication is no longer implied.

@RS-fg5mf

10 ай бұрын

6÷2(3) and 6÷2×3 are mathematically the same. When there are no OPERATIONS left INSIDE the parentheses to evaluate you can remove the parentheses and replace with an explicit multiplication symbol or leave them to represent implicit multiplication which is simply multiplication without the need for a physical multiplication sign...

@Man_Cave

10 ай бұрын

You jogged my memory. I used to insert a dot to the left of the parenthesis once it was solved to remind myself it was still multiplication. It's a shame that no job I had, after college, required me to know much algebra. It's not like riding a bicycle. You can and do forget.@@RS-fg5mf

@nickmcginley4570

7 ай бұрын

@@RS-fg5mf Haha, here you are after all these years, still lying, still being ignored, and still devoting your life to perpetuating your miseducation!

@shaunpatrick8345

Ай бұрын

​@@RS-fg5mfthey're not the same, because 2(3) is a single term just like 2x is. If you are allowed to make implicit multiplication explicit then 1/2x becomes x/2.

@RS-fg5mf

Ай бұрын

@@shaunpatrick8345 and once again , you're wrong... 6/2x and 6/2(3) are not the same... 6/2x= 6/(2*3) while 6/2(x)= 6/2*3 6/2x is a single TERM with a composite quantity... 6/2(x) is a single TERM with two sub-expressions...

This is really interesting because in another video someone told me the answer of 9 is incorrect because that way is learned in preschool and isn't correct because it would be only a way to make math easier for children. I personally have learned that way you get 9. But I like math and I understand the logic behind the 1 answer completely. Even the 2 answer is understandable.

@RS-fg5mf

9 ай бұрын

The only correct answer is 9 and the person who told you it was 1 is mathematically incompetent...

@GanonTEK

9 ай бұрын

Yes, it's simply ambiguous notation. A trick. Academically, multiplication by juxtaposition implies grouping but the programming/literal interpretation does not. So both answers are valid. Plenty of external evidence too. 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 The people who are wrong are those who think there is only one correct interpretation here. Like Presh in this case, unfortunately, and the other guy replying to you too.

@nickmcginley4570

7 ай бұрын

@@RS-fg5mf Ignore RS, he is a psychotic first grade teacher.

@elouanlahougue

7 ай бұрын

@@RS-fg5mf Are you in first grade? Aren't you able to understand a video? 1 is logical according to one meaning of the confusing division symbol.

@RS-fg5mf

7 ай бұрын

@@elouanlahougue 1 is NOT logical when you actually understand and apply the Order of Operations and the various properties and axioms of math... If 1 were logical based on the premise of the obelus that this video entails 6÷2×3 would equal 1 and 6÷2+4 would also equal 1 I think you need to pay more attention to what's being said in the video...

Interpretation is the key word. The problem should, in my opinion, always be written as: (6÷2)(1+2) so there is no more confusion on interpretation

@nox_cadit

2 жыл бұрын

But if this is on a test, you want to know that your students actually paid attention and learned correctly, writing the way you did removes the so called "ambiguity" (which there is none) and then there will be no way to actually know if they have learned correctly

@RS-fg5mf

2 жыл бұрын

When you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended you get the only correct answer 9 If you don't apply the basic rules and principles of math correctly then you are already confused.

@lolmom3590

2 жыл бұрын

@@RS-fg5mf the answer is 1…

@RS-fg5mf

2 жыл бұрын

@@lolmom3590 BODMAS/PEMDAS and any other acronym that is a memory tool for the Order of Operations 6÷2(1+2)= 6÷2(3)= 3(3)= 9 2(3) is not a bracketed priority and is exactly the same as 2×3 M not B or O in BODMAS. Brackets/Parentheses only GROUP and GIVE priority to operations (INSIDE) the symbol not outside .... There is no rule in math that says you have to open, clear, remove or take off parentheses. The rule is to evaluate operations (INSIDE) the parentheses and nothing more. Commutative Property 6÷2(1+2)= 6(1+2)÷2= 6(3)÷2= 18÷2= 9 Distributive Property 6÷2(1+2)= 6÷2×1+6÷2×2= 3×1+3×2= 3+6= 9 The Distributive Property is an act of removing the need for parentheses by multiplying all the TERMS inside the parentheses with the TERM outside the parentheses... TERMS are seperated by addition and subtraction. 6÷2 is one TERM attached to and multiplied with the two TERMS inside the parentheses 1 and 2 Operational inverse of division by the reciprocal 6÷2(1+2) 6(1/2)(1+2)= 6(1/2)(3)=? Multiply in any order you want you still get 9 Proper use of grouping symbols 6 -----(1+2) = 6÷2(1+2)=9 2 6 -------- = 6÷(2(1+2))=1 2(1+2) A vinculum (fraction bar) is a grouping symbol and groups operations within the denominator and when written in a linear format extra brackets are required to maintain the grouping of operations within the denominator... Another argument people tend to use incorrectly is factoring.... 6 = 2+4 No parentheses required BUT 6÷(2+4) parentheses required 2+4= 2(1+2) only one set of parentheses required. 6÷(2+4) we already have a set of parentheses and the factoring must take place within that first set of parentheses. You can NOT just dismiss the first set of parentheses out of hand in favor of the second set... The 2(1+2) must be placed within the first set of parentheses containing the (2+4) 6÷(2+4) = 6÷(2(1+2)) NOT 6÷2(1+2) Let y = (1/2) 6y(1+2)=? 6y*1+6y*2= ? 6/y⁻¹*1+6/y⁻¹*2= ? If you answered 9 to all three algebraic expressions then it would be ILLOGICAL and INCONSISTENT as well as hypocritical to say that 6/y⁻¹(1+2) doesn't also equal 9 The rules of math have to remain logical and consistent across the board... THESE ARE THE FACTS....

@RS-fg5mf

2 жыл бұрын

@@jonnel4038 x÷2y = x÷(2y) by Algebraic Convention... BUT x÷2(y)= x÷2*y by the Distributive Property... Parenthetical implicit multiplication does not have priority over division. When a constant, variable or TERM is placed next to parentheses without an explicit operator the OPERATOR is an implicit multiplication symbol meaning you multiply the constant, variable or TERM with the value of the parentheses not just the number next to it. The correct answer is 9

When programming, the correct answer is to never leave any ambiguity, so always add enough parenthesis to ensure that anyone reading it will understand your intention. So write 6 / (2 * (1 + 2)) OR write (6 / 2) * (1 + 2). Both are correct, but only one would be correct depending on what your intention is. So always make sure that you enter something that cannot be misinterpreted.

@RS-fg5mf

Жыл бұрын

So you are saying that we should be forced to write 5+(2×10) because too many people fail to understand the basic rules and principles of math and incorrectly believe that 5+2×10= 70

@StuartLynne

Жыл бұрын

@@RS-fg5mf Yes, for the same reason we add comments. Make sure that we know what is happening and that people reading it in the future know that we know what it means.

@RS-fg5mf

Жыл бұрын

@@StuartLynne then the Order of Operations and the various properties and axioms of math become redundant if you're going to add crutches for people who fail to understand and apply the basic rules and principles of math correctly

@onemorelisa3785

Жыл бұрын

@@RS-fg5mf When math is being taught completely differently between generations, it’s bound to be misinterpreted. I’d rather them be in-depth and redundant so that people in the future won’t have to just assume anything. Assuming things causes a lot of problems.

@RS-fg5mf

Жыл бұрын

@@onemorelisa3785 math is only being taught differently if the prrson teaching it is incompetent.... The Order of Operations and the various properties and axioms of math were established and internationally recognized and accepted as the standard for evaluating a math expression in the early 1600's when Algebraic notation was being developed in order to eliminate ambiguity and to minimize the unnecessary and excessive use of parentheses... The basic rules and principles of math have been the same for over 400 years... Math is based on rules not popularity or personal opinion. Failure to understand and apply the basic rules and principles of math correctly as intended is not a valid argument against them...

I thought that since the three was still in the bracket it needed to be multiplied first then divide

@RS-fg5mf

10 ай бұрын

Nope... There is no mathematical difference between 6÷2(3) and 6÷2×3 Parentheses only group and give priority to operations INSIDE the symbol not outside the symbol

Instantly i got it right wrong right and only because i was curious for an answer i watched the video. Now im curious about what this math used for or what is it supposed to prepare one four.

6 / 2(1+2) Solve the brackets first = 6 / 2(3) Solve the brackets first = 6 / 6 Solve the division = 1 Basic

@Filtertuetchen

7 жыл бұрын

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

@alec95

7 жыл бұрын

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.

@SpectatorAlius

7 жыл бұрын

Alneon I had a scientific calculator once. It did _not_ give the same answer as yours. Is yours a TI calculator?

@TheRealRaghibMrz

7 жыл бұрын

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.

@AudriusN

7 жыл бұрын

you can solve as 2(1+2)=(2x1+2x2)=(2+4)

People: nine. Me, an intellectual: *nein*

@rydh6zgjhbfvrwhb259

4 жыл бұрын

Ivan09 Ja Ja! Ich spreche auch Deutsch Translation: Yes yes! I also speak German!

@Brontok

4 жыл бұрын

@@rydh6zgjhbfvrwhb259 Grüße aus NRW XD

@derechtepilz

4 жыл бұрын

@@Brontok Heyyyyyyyyy! Ich grüße dich zurück! Natürlich auch aus NRW!

@derechtepilz

4 жыл бұрын

@survival pete ??

@Cassieplays854

4 жыл бұрын

Ivan: posts a meme containing a fraction of german The comments: iCh bIn dEmEnT

What if you use the distributive property to deal with the parenthesis? Then, it’s 6 divided by 2 plus 4 = 6 divided by 2 plus 4. Then, division..6 divided by 2 = 3..plus 4 = 7

@GanonTEK

11 ай бұрын

You can only remove brackets if nothing is keeping them there. It's a mistake to say that distribution removes brackets itself, it doesn't. Distribution brings values *into* brackets. Very often, there is now nothing outside them so you are allowed to drop them. Many times you are not allowed too. E.g. 4(1+1)/2 is (4+4)/2 = (8)/2 = 4 and not 4+4/2 = 4+2 = 6 Which is the error you made with 7. Numbers multiplying or dividing brackets keep them there.

Say the equation out loud or type it: "six divided by two times, in parenthesis, one plus two." That would be 6 / 2 * (1+2) You cannot say the equation to get it to equal one UNLESS you specify that there's a bracket like this: 6 / [2(1+2)] Since there are no other extra brackets specified, order of operations say left to right and you get 9. Some school calculators get 1 because they automatically put assumed brackets because that is what is most likely meant by the user, however, what is orginally typed would equal 9, not 1. Most calculators take why you typed literally and give you 9, which is what is supposed to happen. Unfortunately people use calculators that make assumtions and then the people think that's what is supposed to happen. This is why writing code needs specifications, you cannot just let the computer make assumptions for you or else it would be wrong A LOT, you'll be wrong.

@GanonTEK

10 ай бұрын

The issue with the first line there is that it is not clear how to read it as we don't know what interpretation of multiplication by juxtaposition they used. It's like how "What is 6 divided by 2 times 3?" written like that is also not clear. It's bad writing. You need commas for clarity. So, "What is 6 divided by 2, times 3?" This would be (6/2)×3 = 9. You could also write "What is 6, divided by 2, times 3?" for the above answer. Or "What is 6, divided by, 2 times 3?" This would be 6/(2×3) = 1. Proper notation and writing makes all the difference. This is just a badly written expression. That's all.

@markprange2430

4 ай бұрын

The grouping of 2 and (1+2) is what told you that multiplication was involved. 2(1+2) and 2(3) are groups. The group remains as (2 × 3). The original expression showed 2(1+2) as a group.

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.

@timelyspirit

2 жыл бұрын

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.

@JrobAlmighty

2 жыл бұрын

@@timelyspirit I was taught the same thing

@brittanym58

2 жыл бұрын

Inside the parenthesis, outside the parentheses, then L to R.

@WokeVeganLiberal

2 жыл бұрын

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

@jorgequintero8141

2 жыл бұрын

@@WokeVeganLiberal wait wasn’t it pemdas? Parentheses Exponents Multiplication Division Addition Subtraction

So, the problem that yielded an answer of 1 in 1917 yields 9 today. Wow - inflation is everywhere!

@TeachUBusiness

6 жыл бұрын

Trevor Keen You are correct. I was taught to do the the parenthetical expression, multiply and then divide.

@tozendai840

6 жыл бұрын

The world parenthesis should be eliminated from all human language

@claudiosass

6 жыл бұрын

Trevor Keen j

@RemingtinArms

6 жыл бұрын

you were taught wrong. the end.

@DustinSilva

6 жыл бұрын

It's because the creator of this video is a moron

What if you turn the 2(1+2) into (2+4) by multiplying the 2 into the parts inside the brackets?

@nikolasperrakis5775

10 ай бұрын

2(1+2)=2+4 you don't need to put it in a parenthesis

@becausecontextmatters5260

9 ай бұрын

@@nikolasperrakis5775 By itself no, but if you do it in this equation the result changes based on which factor of the addition is first, which obviously shouldn't happen.

Basically the fraction bar and division symbol do in fact mean different things

@RS-fg5mf

7 ай бұрын

The vinculum is a grouping symbol. The obelus is not... 6 --‐-------- = 6÷(2(1+2)) not 6÷2(1+2) 2(1+2) To get 1 as the answer two grouping symbols are required...

Im so used to algebra where by the algebra rules parentheses-multiplication comes first so it would be 1

@tyalbany1064

8 жыл бұрын

There is no such thing as "Parentheses-multiplication" in the order of operations.

@moileung

8 жыл бұрын

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.

@chessten

8 жыл бұрын

Haha, you are a joke. Mr Algebra man, please think about x/y(a+b) vs x/[y(a+b)].

@moileung

8 жыл бұрын

1+1=2, x+x=2x. if we both agree to this then we're good.

@Bob-zx7io

8 жыл бұрын

so how did 2 in 2(3) magically get into the parentheses? BEDMAS = 9

History biggest question: How did a 5th grade math question create a riot on the media

@Mobilizes

4 жыл бұрын

It's not even 5th grade, it was 3rd or 4th grade

@medicine8470

4 жыл бұрын

I learned this in 5th grade and solved this in approximately 5 seconds.

@TannerK.

4 жыл бұрын

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.

@conscious5122

4 жыл бұрын

Lol

@jimmybobhead44

4 жыл бұрын

norman hughmin because people are morons

Boy this had me stumped! Thanks for the explanation!