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 :)
FACT CHECK 1/5
No, you are. You've ignored multiple rules of Maths, as we'll see...
Except it's not ambiguous at all
...and an entire subset of those people are high school Maths teachers!
A change to the rules of Maths that's not in any textbooks yet, and somehow no teachers have been told about it yet either
I can do something for you though - fact-check your blog
There's no "belief" when it comes to rules of Maths - they are facts (some by definition, some by proof)
#MathsIsNeverAmbiguous
There's no such thing as "implicit multiplication". You won't find that term used anywhere in any Maths textbook. People who use that term are usually referring to Terms, The Distributive Law, or most commonly both! #DontForgetDistribution
Nope. It's a valid notation for a factorised Term. e.g. 2a+2b=2(a+b). And the reverse process to factorising is The Distributive Law. i.e. 2(a+b)=(2a+2b).
The only type of multiplication there is is explicit. Neither Terms nor The Distributive Law is classed as "multiplication"
There is a single, standard, order of operations rules
Also, see my thread about people who say there is no evidence/proof/convention - it almost always ends up there actually is, but they didn't look (or didn't want you to look)
...they have forgotten about Terms and/or The Distributive Law, and are trying to treat a Term as though it's a "multiplication", and it's not. More soon
Let me paraphrase - people disagree about made-up rule
There's no such thing - there's either juxtaposition or not, and if there is it's either Terms or The Distributive Law
...factorised term after that
There's no ambiguity...
multiplication sign - multiplication
brackets with no multiplication sign (i.e. a coefficient) - The Distributive Law
no multiplication sign and no brackets - Terms (also called products by some. e.g. Lennes)
Why didn't you ask a teacher before writing your blog? Maths tests are only ever ambiguous if there's been a typo. If there's no typo's then there's a right answer and wrong answers. If you think the question is ambiguous then you've not studied enough
This question already is clear. It's division, NOT a fraction. They are NOT the same thing! Terms are separated by operators and joined by grouping symbols. 1÷2 is 2 terms, ½ is 1 term
BTW here is what happened when someone asked a German Maths teacher
You should literally NEVER use "weak juxtaposition" - it contravenes the rules of Maths (Terms and The Distributive Law)
...and high school, where it's first taught
If that was what was meant then that's what would've been written - the 6 and 2 have been joined together to make a single term, and elevated to the precedence of Brackets rather than Division
You should know, without being told, to follow the rules of Maths when solving it. Voila! No ambiguity
It stirs up drama because many adults have forgotten the rules of Maths (you'll find students get this right, because they still remember)
No, you just put the cart before the horse - the problem existing in the first place (programmers not brushing up on their Maths first) is why some calculators do it wrong
Yes, we use / to mean divide with computers (since there is no ÷ on the keyboard), which you therefore need to put into brackets if it's a fraction (since there's no fraction bar on the keyboard either)
Nope. See previous comment.
Because programmers didn't check their Maths first, some calculators give wrong answers
According to this video mostly not these days (based on her comments, there's only Texas Instruments which isn't obeying both Terms and The Distributive Law, which she refers to as "PEJMDAS" - she didn't have a manual for the HP calcs). i.e. some manufacturers who were doing it wrong have switched back to doing it correctly
P.S. she makes the same mistake as you, and suggests showing her video to teachers instead of just asking a teacher in the first place herself (she's suggesting to add something to teaching which we already do teach. i.e. ab=(axb)).
ANY calculator which doesn't obey all the rules of Maths is wrong!
So a calculator, which has a specific purpose of solving Maths expressions, giving a wrong answer to a Maths expression isn't "unintended behaviour"? Do go on