I can't thank you enough, I'm no expert in maths but getting answers different from the public's general "opinion" really put me off because I thought all I had learned over the years had gone to waste now since I cannot even solve a simple problem. It crippled my confidence in maths. I'm really glad the equation was wrong 😌.
This has nothing to do with the division sign, it is only a matter of convention for the order of operations. If you want to compute "2+3x4" you need a convention, either it is ambiguous. Just fix the convention and everything is good. The most common convention, used typically in programming language, is () first, then / and x, then + and -, and reading left to right. Using this, your equation is equal to 16.
2:46 I now see the argument people have for the option on the right. I’ve always assumed that type of division problem should technically be done after the multiplication, and that’s because you can write the problem without causing an issue, by just writing it as (2+2)*8/2 if that’s what you meant. It’s always ambiguous on purpose, but it’s nonetheless super interesting to see peoples vehement reactions…
I dont know if I'm dumb but i learned that you do parentheses first, then you do division or multiplication and then subtraction or addition. But if there is something like "8÷2*4" you just go from left to right. So first 8÷2 which is 4 and then 4*4 which is 16. So either my teacher was wrong or this problem isnt really a problem. I dont know honestly😅
I think this is special to me because I don’t know math at all and I am in g.e.d class and we need to know everything from k-12 and I forgot a lot but your website is helping me god bless you Taren Kelly hogan Los Angeles bye
its not at all ambiguous... its just most people do not speak this language daily and so they speak it wrong. and the problem isnt the division. what trips up "normies" is the missing multiplication symbol. if you add the multiplication symbol, then this pemdas thing (i never heard of it in school, nothing similar even) would work
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 (academic or programming). 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.
The order of operations states that you do brackets first. This is done by distributing the outside number by each term in brackets. The answer is one. It's not even debatable look up the distributive law and it is clear.
No beaucause then, when you do the distribution first, you assume that the multiplication comes before the division by convention, which is generally false. When we say that we calculate the brackets first, it means we compute what's inside the bracket first (here simply 2+2).
Thanks for over 1 million views!
Anyways anyone notice how all these videos are in 4K? I don't know why either.
I can't thank you enough, I'm no expert in maths but getting answers different from the public's general "opinion" really put me off because I thought all I had learned over the years had gone to waste now since I cannot even solve a simple problem. It crippled my confidence in maths. I'm really glad the equation was wrong 😌.
I am so glad i subscribed.I hv been confused about this type of equations..now i know most of them were wrong.Thank you😁.
Yes! I'm 100% with you.
These types of questions online are bogus questions.
There's no correct answer until you add the parentheses 😁
This has nothing to do with the division sign, it is only a matter of convention for the order of operations. If you want to compute "2+3x4" you need a convention, either it is ambiguous. Just fix the convention and everything is good. The most common convention, used typically in programming language, is () first, then / and x, then + and -, and reading left to right. Using this, your equation is equal to 16.
2:46 I now see the argument people have for the option on the right. I’ve always assumed that type of division problem should technically be done after the multiplication, and that’s because you can write the problem without causing an issue, by just writing it as (2+2)*8/2 if that’s what you meant. It’s always ambiguous on purpose, but it’s nonetheless super interesting to see peoples vehement reactions…
I dont know if I'm dumb but i learned that you do parentheses first, then you do division or multiplication and then subtraction or addition. But if there is something like "8÷2*4" you just go from left to right. So first 8÷2 which is 4 and then 4*4 which is 16. So either my teacher was wrong or this problem isnt really a problem. I dont know honestly😅
Yes I think this is the commonly accepted convention
Good video. Thank you
I love these videos!
This is why we need to use polish notation.
Why?
@@burnercolt6647 avoiding ambiguity and need of clarity I believe?
I think this is special to me because I don’t know math at all and I am in g.e.d class and we need to know everything from k-12 and I forgot a lot but your website is helping me god bless you Taren Kelly hogan Los Angeles bye
I wouldn't be surprised if Equations like these were put in the Common Core Math exams.
日本人ですよね？？
楽しい動画だ🙂🙂
8/2(2+2)=?
It would make sense for me to say 1
(8/2)(2+2) ? Fractional representation remains unclear
@@vibhav6551 , fractions with multiplication are same importance, but since division is first, it goes first.
@@Quixidion division is just confusing and a basic way to use fractions for little kids
its not at all ambiguous... its just most people do not speak this language daily and so they speak it wrong.
and the problem isnt the division. what trips up "normies" is the missing multiplication symbol. if you add the multiplication symbol, then this pemdas thing (i never heard of it in school, nothing similar even) would work
Why? Division and multiplication have equal precedence.
That does not sound right
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 (academic or programming).
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.
Let’s goooooo
It depends: are you an uneducated kindergarten teacher using an American teacher's guide...... or did you graduate middle school lol.
The order of operations states that you do brackets first. This is done by distributing the outside number by each term in brackets. The answer is one. It's not even debatable look up the distributive law and it is clear.
No beaucause then, when you do the distribution first, you assume that the multiplication comes before the division by convention, which is generally false. When we say that we calculate the brackets first, it means we compute what's inside the bracket first (here simply 2+2).
@TKZprod that's why the order of operations must be followed and it states very clearly, for those that can read, brackets are done first.