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 :)
You lost me on the section when you started going into different calculators, but I read the rest of the post. Well written even if I ultimately disagree!
The reason imo there is ambiguity with these math problems is bad/outdated teaching. The way I was taught pemdas, you always do the left-most operations first, while otherwise still following the ordering.
Doing this for 6÷2(1+2), there is no ambiguity that the answer is 9. You do your parentheses first as always, 6÷2(3), and then since division and multiplication are equal in ordering weight, you do the division first because it's the left most operation, leaving us 3(3), which is of course 9.
If someone wrote this equation with the intention that the answer is 1, they wrote the equation wrong, simple as that.
The calculator section is actually pretty important, because it shows how there is no consensus. Sharp is especially interesting with respect to your comment because all scientific Sharp calculators say it's 1. For all the other brands for hardware calculators there are roughly 50:50 with saying 1 and 9.
So I'm not sure if you are suggesting that thousands of experts and hundreds of engineers at Casio, Texas Instruments, HP and Sharp got it wrong and you got it right?
There really is no agreed upon standard even amongst experts.
No, those companies aren't wrong, but they're not entirely right either. The answer to "6 ÷ 2(1+2)" is 1 on those calculators because that is a badly written equation and you(not literally you, to be clear) should feel bad for writing it, and the calculators can't handle it with their rigid hardcoded logic. The ones that do give the correct answer of 9 on that equation will get other equations wrong that it shouldn't be, again because the logic is hardcoded.
That doesn't change the fact that that equation worked out on paper is absolutely 9 based on modern rules of math. Calculate the parentheses first, you then have 6 ÷ 2(3). We could solve from here, but to make the point extra clear I'm going to actually expand this out to explicit multiplication. "2(3)" is the same as "2 x 3", so we can rewrite the equation as "6 ÷ 2 x 3". All operators now inarguably have equal precedence, which means the only factor left in which order to do the operations is left to right, and thus division first. The answer can only be 9.
If you'd ever taken any advanced math, you'd see that the answer is 1 all day. The implicit multiplication is done before the division because anyone taking advanced math would see 2(1+2) as a term that must be resolved first. The answer still lies in the ambiguity of the way the problem is written though. If the author used fractions instead of that stupid division symbol, there would be no ambiguity. It's either 6/2 x 3 = 9 or [6/(2x3)] = 1. Comment formatting aside, if someone put 6 in the numerator, and then did or did NOT put all the rest in the denominator underneath a horizontal bar, it would be obvious.
TL;DR It's still a formatting issue, but 9 is definitely not the clear and only answer.
Don't need to do advanced Maths - every rule you need to know for this problem is taught in Year 7.
"Always remember to solve using PEMDAS once you've used the distributive property!" Link%20and%20subtraction%20(S).)
(emphasis mine)
And...? Not sure what your point is, but the link is VERY badly worded...
That you're still wrong? As I said, the true answer is that the problem is written poorly due to the obelus and thus is open to interpretation. You're entitled to your own interpretation since it's written poorly, I just find it pretty obviously less logical than multiplying using the distributive property first to resolve the term with the parentheses fully as you would in any advanced math.
Also, distributive law and distributive property are the same thing per Khan academy "The distributive property is sometimes called the distributive law of multiplication and division."
Wait till you hear that "i before e except after c" wasn't true either. It's wild that you think 7th grade math overrules grad school math though lol.
About? You haven't pointed out anything that's wrong.
Oh, you're one of those people. Good, maybe we can finally get an answer then (this was also talked about in the blog). What other interpretation of an obelus is possible other than division? People keep saying it's ambiguous, but no-one has ever said why (other than some stuff that makes no sense in the context, as explained in the blog)
Yes, and sometimes people call Koalas "Koala bears", but that doesn't mean they're bears. Now bearing that in mind, read again what Khan said - the page which is called "Distributive property explained", not "Distributive Law explained".
Wait till you hear that's not a rule of Maths.
Umm, never said anything of the kind...
But it's not ambiguous, as per the reason you already gave.
If you use fractions then the whole thing is a single term, if you use division it's 2 terms.
1 is definitely the only answer.
https://www.theleafchronicle.com/story/news/2019/08/08/viral-math-problem-answer-obelus-austin-peay-apsu/1933750001/
This is the only symbols I've ever seen used (but feel free to provide a reference if you know of any where it isn't - the article hasn't provided any references)...
Ratio is only ever colon.
Division is obelus (textbooks/computers) or slash (computers, though if it's text you can use a Unicode obelus).
Fraction is fraction bar (textbooks) or obelus/slash inside brackets (computers). i.e. (a/b).
It's not badly written, and the reason Texas Instruments gets it wrong is right there in their manual (disobeys The Distributive Law).
The order of operations rules haven't changed in at least 100 years, and more likely at least 400 years. Don't listen to Youtubers who can't cite a single Maths textbook.
No, it's the same as (2x3), as per The Distributive Law and Terms.