A division symbol should never be used after fractions are introduced.
But a fraction is a single term, 2 numbers separated by a division is 2 terms. Terms are separated by operators and joined by grouping symbols.
SmartmanApps
joined 1 year ago
Don't need any extra letters - just need people to remember the rules around expanding brackets in the first place.
No matter how many times I explain that this is a notation for multiplication
It ISN'T a notation for multiplication - it's a notation for a factorised term, and if you ignore The Distributive Law going back the other way then you just broke the factorised term dotnet.social/@SmartmanApps/110886637077371439
any competent person that has to write out one of these equations will do so in a way that leaves no ambiguity.
This one already does have no ambiguity.
there’s absolutely no difference in n(n-1) and n*(n-1)
There is - the first is 1 term and the 2nd is 2 terms. Makes a difference if it's preceded by a division.
it’s just matter of convenience you can leave it off.
It's a matter of how many terms as to whether it's there or not.
So you are saying exactly what I said; people can misinterpret things that other people have written
No, I'm not. They're "misinterpreting" something that isn't even a rule of Maths. There's no way to misinterpret the actual rules, there's no way to misinterpret the equation. There's no alternative interpretations of the notation. Someone who didn't remember the rules literally made up "implicit multiplication", and then other people argued with them about what that meant. 😂
I only just found the thread yesterday. There's only 1 "interpretation", and the only back and forth I've seen about interpretations is about implicit multiplication, which isn't a thing, at all - it's people conflating The Distributive Law and Terms dotnet.social/@SmartmanApps/110925761375035558
I Looked up doing factorials and n! = n(n – 1) is used interchangeably with n! = n*(n – 1)
Yeah, there's a problem with some lazy textbook authors, which I talked about here. A term is defined as ab=(axb), and yet many textbooks lazily write it as ab=axb, which is fine if that's the whole expression, but NOT fine if the expression is a/bc (a/(bxc) and a/bxc AREN'T the same thing!), and so we end up with people removing brackets prematurely and getting wrong answers. In other words, in your case, only n!=n(n – 1) and n!=(nx(n – 1)) can be used interchangeably.
The ÷ sign isn’t used by “Americans”, it’s used by small children
I don't know where you're from, but it's used universally in Australia - textbooks, calculators, all ages - and from what I've seen the U.K. too.
written like this (÷) means it’s a fraction?
No, that means it's a division. i.e. a÷b. To indicate it's a fraction it would need to be written as (a÷b). i.e. make it a single term. Terms are separated by operators and joined by grouping symbols (such as brackets or fraction bars).
put the whole 2(1+2) down there, there’s no reason for that.
There is - it's a single bracketed term, subject to The Distributive Law. i.e. the B in BEDMAS.
Just write it better.
6/(2(1+2))
If you really wanted extra brackets it'd be 6/(2)(1+2). Of course, since there's only 1 term in the first brackets they're redundant, hence 6/2(1+2) is the fully simplified form, and is the way it's written in Maths textbooks.
Except it breaks the rules which already are taught.
But they're not rules - it's a mnemonic to help you remember the actual order of operations rules.
Juxtaposition - in either case - isn't a rule to begin with (the 2 appropriate rules here are The Distributive Law and Terms), yet it refuses to die because of incorrect posts like this one (which fails to quote any Maths textbooks at all, which is because it's not in any textbooks, which is because it's wrong).