I'd use it to solve it, as per my previous comment on the difference between solving and simplifying.
“simplify” literally means to make the equation easier to understand
Nope. It means to present it in the simplest way possible. e.g. 5/10=1/2.
You are arguing that “expand and simplify” is the exact same thing as “simplify”
No I'm not. I'm saying "expand and simplify" is a thing in all high school Maths textbooks, "factor and simplify" isn't a thing in any of them.
"Sometimes factoring is prudent" - if you're trying to solve an equation, yes, but solving and simplifying aren't the same thing. If I arrive at an answer of 5/10 then I have solved but not simplified. Sometimes it's not even possible to simplify, because the answer is already in the simplest form possible, such as an answer of 1/2. I teach students when to recognise when something can be simplified and when it can't. Your original contention that the Term was already simplified, and it wasn't.
"And thanks for the downvotes." - I downvote anything that is incorrect, just like a student would lose marks for same.
No, it isn't. Division before subtraction.
Just make sure you don't use an e-calculator, nor a Texas Instruments calculator.
Got quick feedback from Gerald on Mastodon. This is a change that went live with 8.0.3 in November (then we had all those fun and games with 8.0.3 not updating!), hence why the GA users are only just now running into it. If we need the folder - i.e. in order to have something to link to - then just manually add the net8.0 back into the csproj, do a dotnet restore, and then it will build.
Sorry. I forgot about we were ending daylight savings this past weekend, so the times are actually GMT+10 now.
Sorry. I forgot about we were ending daylight savings this past weekend, so the times are actually GMT+10 now.
Semantically, yes they are
No, they're not. Terms are separated by operators (division) and joined by grouping operators (fraction bar).
If you’d ever taken any advanced math, you’d see that the answer is 1 all day
Don't need to do advanced Maths - every rule you need to know for this problem is taught in Year 7.
without providing evidence for your own position
You know full well it's all in my thread. Where's yours?
I’m saying I shouldn’t have to go looking
You didn't have to go looking - you could've just accepted it at face-value like other people do.
You’ve provided a single textbook,
No, multiple textbooks. If you haven't seen the others yet then keep reading. On the other hand you haven't provided any textbooks.
the argument is that both sides are valid and accepted
But they're not. The other side is contradicting the rules of Maths. In a Maths test it would be marked as wrong. You can't go into a Maths test and write "this is ambiguous" as an answer to a question.
here’s an article from someone who writes textbooks
Not high school textbooks! Talk about appeal to authority.
Yep, seen it before. Note that he starts out with "It is not clear what the textbook had intended with the 3y". How on Earth can he not know what that means? If he just picked up any old high school Maths textbook, or read Cajori, or read Lennes' letter, or even just asked a high school teacher(!), he would find that every single Maths textbook means exactly the same thing - ab=(axb). Instead he decided to write a long blog saying "I don't know what this means - it must be ambiguous".
Not only that, but he also didn't know how to handle x/x/x, which shows he doesn't remember left associativity either. BTW it's equal to x/x² (which is equal to 1/x).
the ambiguity exists
...amongst people who have forgotten the rules of Maths. The Maths itself is never ambiguous (which is the claim many of them are making - that the Maths expression itself is ambiguous. In fact the article under discussion here makes that exact claim - that it's written in an ambiguous way. No it isn't! It's written in the standard mathematical way, as per what is taught from textbooks). It's like saying "I've forgotten the combination to my safe, and I've been unable to work it out, therefore the combination must be ambiguous".
You are correct, I suppose a mathematics professor from Harvard (see my previous link for the relevant discussion of the ambiguity) isn’t at the high school level.
Thank you. I just commented to someone else last night, who had noticed the same thing, I am so tired of people quoting University people - this topic is NOT TAUGHT at university! It's taught by high school teachers (I've taught this topic many times - I'm tutoring a student in it right now). Paradoxically, the first Youtube I saw to get it correct (in fact still the only one I've seen get it correct) was by a gamer! 😂 He took the algebra approach. i.e. rewrite this as 6/2a where a=1+2 (which I've also used before too. In fact I did an algebraic proof of it).
the ambiguity exists and one side is not immediately justified/‘correct’
The side which obeys the rules of Maths is correct and the side which disobeys the rules of Maths is incorrect. That's why the rules of Maths exist in the first place - only 1 answer can be correct ("ambiguity" people also keep claiming "both answers are correct". Nope, one is correct and one is wrong).
That’s a leading question and is completely unhelpful to the discussion.
Twice I said things about it and you said you didn't believe my interpretation is correct, so I asked you what you think he's saying. I'm not going to go round in circles with you just disagreeing with everything I say about it - just say what YOU think he says.
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?
post containing link to recording of this talk