6÷2(1+2)
6÷2(1+2)
I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It's about a 30min read so thank you in advance if you really take the time to read it, but I think it's worth it if you joined such discussions in the past, but I'm probably biased because I wrote it :)
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Honestly, I do disagree that the question is ambiguous. The lack of parenthetical separation is itself a choice that informs order of operations. If the answer was meant to be 9, then the 6/2 would be isolated in parenthesis.
It's covered in the blog, but this is likely due to a bias towards Strong Juxtaposition rules for parentheses rather than Weak. It's common for those who learned math into advanced algebra/ beginning Calc and beyond, since that's the usual method for higher math education. But it isn't "correct", it's one of two standard ways of doing it. The ambiguity in the question is intentional and pervasive.
My argument is specifically that using no separation shows intent for which way to interpret and should not default to weak juxtaposition.
Choosing not to use (6/2)(1+2) implies to me to use the only other interpretation.
There's also the difference between 6/2(1+2) and 6/2*(1+2). I think the post has a point for the latter, but not the former.
I don't know what you want, man. The blog's goal is to describe the problem and why it comes about and your response is "Following my logic, there is no confusion!" when there clearly is confusion in the wider world here. The blog does a good job of narrowing down why there's confusion, you're response doesn't add anything or refute anything. It's just... you bragging? I'm not certain what your point is.
your response is “Following my logic, there is no confusion!”
That's because the actual rules of Maths have all been followed, including The Distributive Law and Terms.
there clearly is confusion in the wider world here
Amongst people who don't remember The Distributive Law and Terms.
The blog does a good job of narrowing down why there’s confusion
The blog ignores The Distributive Law and Terms. Notice the complete lack of Maths textbook references in it?
None of this has a point. We're talking over a shitpost rant about common use of math symbols. Even the conclusion boils down to it being a context dependent matter of preference. I'm just disagreeing that the original question as posed should be interpreted with weak juxtaposition.
I originally had the same reasoning but came to the opposite conclusion. Multiplication and division have the same precedence, so I read the operations from left to right unless noted otherwise with parentheses. Thus:
6/2=3
3(1+2)=9
For me to read the whole of 2(1+2) as the denominator in a fraction I would expect it to be isolated in parentheses: 6/(2(1+2)).
Reading the blog post, I understand the ambiguity now, but i’m still fascinated that we had the same criticism (no parentheses implies intent) but had opposite conclusions.
6/2=3
3(1+2)=9
You just did division before brackets, which goes against order of operations rules.
For me to read the whole of 2(1+2) as the denominator in a fraction
You just need to know The Distributive Law and Terms.
Read the linked article
The linked article is wrong. Read this - has, you know, actual Maths textbook references in it, unlike the article.
But it isn’t “correct”
It is correct - it's The Distributive Law.
it’s one of two standard ways of doing it.
There's only 1 way - the "other way" was made up by people who don't remember The Distributive Law and/or Terms (more likely both), and very much goes against the standards.
The ambiguity in the question is
...zero.
Did you read the blog post?
Hooray! Correct! Anyone who downvoted or disagrees with this needs to read this instead. Includes actual Maths textbooks references.