Well, the link doesn’t load for me

Yeah, they’re doing an upgrade right now. Yes, it’s the Maths explanation - -25 is the correct answer.

-5**2 is apparently -25 because of the order of operations)

Which is correct

As a Maths teacher, almost daily 😂

you’re just a tutor and not actually a teacher?

Both - see the problem with the logic you use?

Let me know when you decide to consult a textbook about this.

a single sentence of a wikipedia article without me handfeeding it to you

And I told you why it was wrong, which is why I read Maths textbooks and not wikipedia.

I’m sorry for your students

My students are doing good thanks

The notation is not intrinsically clear

It is to me, I actually teach how to write it.

Exactly! It’s in math textbooks, in both ways!

And both ways are explained, so not ambiguous which is which.

Ummm, I was agreeing with you??

Anyways, I’m a Maths teacher who has taught this topic many times - what would I know?

You can define your notation that way if you like

Nothing to do with me - it’s in Maths textbooks.

without knowing the conventions the author uses, it’s ambiguous

Well they should all be following the rules of Maths, without needing to have that stated.

which clearly states that the distributive property is a generalization of the distributive law

Let me say again, people calling a Koala a Koala bear doesn’t mean it actually is a bear. Stop reading wikipedia and pick up a Maths textbook.

You seem to be under the impression that the distributive law and distributive property are completely different statements

It’s not an impression, it’s in Year 7 Maths textbooks.

this certainly is not 7th year material

And yet it appears in every Year 7 textbook I’ve ever seen.

Looks like we’re done here.

If you read the wikipedia article

…which isn’t a Maths textbook!

also stating the distributive law, literally in the first sentence

Except what it states is the Distributive property, not The Distributive Law. If I call a Koala a Koala Bear, that doesn’t mean it’s a bear - it just means I used the wrong name. And again, not a Maths textbook - whoever wrote that demonstrably doesn’t know the difference between the property and the law.

This is something you learn in elementary school

No it isn’t. This is a year 7 topic. In Primary School they are only given bracketed terms without a coefficient (thus don’t need to know The Distributive Law).

be assured that I am sufficiently qualified

No, I’m not assured of that when you’re quoting wikipedia instead of Maths textbooks, and don’t know the difference between The Distributive Property and The Distributive Law, nor know which grade this is taught to.

Wikipedia is not intrinsically less accurate than maths textbooks

BWAHAHAHAHA! You know how many wrong things I’ve seen in there? And I’m not even talking about Maths! Ever heard of edit wars? Whatever ends up on the page is whatever the admin believes. Wikipedia is “like an encyclopedia” in the same way that Madonna is like a virgin.

but you are misunderstanding them

And yet you have failed to point out how/why/where. In all of your comments here, you haven’t even addressed The Distributive Law at all.

Whether you write it as a(b+c) = ab + ac or as a*(b+c) = ab + ac is insubstantial

And neither of those examples is about The Distributive Law - they are both to do with The Distributive Property (and you wrote the first one wrong anyway - it’s a(b+c)=(ab+ac). Premature removal of brackets is how many people end up with the wrong answer).

If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous

The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).

P.S. feel free to read through and use my thread on order of operations.

inside radicals

I had to look up what that meant (should’ve done that the first time - sorry) - have never heard that before, must be a local terminology.

So, square roots (or other roots) can be expressed as an exponent - e.g. the square root of 2 is the same as 2 to the power ½ - so that’s covered by “E”, exponents! (or I for Index, or O for to the Order of, depending on your area)

I appreciate your mention of the importance of teaching the difference between operators and terms

Thank you.

My pedagogical background is in the sciences and I’m much better at doing math than teaching it

Oh god, welcome to why I have so many people argue with me, a Maths teacher, about it. There’s a whole bunch of Youtubes and blogs out there by Physics majors. I’m like “OMG, why are you trusting someone with a Physics major over someone with a Maths major - god help me”.

I would like if math classes (in my area) did more explicitly teach the difference between terms and operators

So what area are you in? A country will do. You said PEMDAS so I’m guessing the U.S.? I’ve heard via Youtubes/blogs that indeed there is more confusion with what is taught there, but I ended up Googling for U.S. textbooks, and found the same thing being taught in the textbook, so I’m not sure where this “that’s not what they teach in the U.S.” is coming from (why I was Googling for U.S. textbooks in the first place). Is the standard of teachers there actually worse than elsewhere? Or is it perhaps (possibly more likely) that there’s just more U.S. people posting, therefore more people who’ve forgotten the actual rules, and are just (as I’ve seen many times) they’re just blaming it on what they were taught (which I’ve usually found isn’t true at all).

Do you not understand that syntax is its own set of rules?

Yes, the rules of Maths, as I was already saying. I’m a Maths teacher. I take it you didn’t read the link then.

Please learn some math

I’m a Maths teacher - how about you?

Quoting yourself as a source

I wasn’t. I quoted Maths textbooks, and if you read further you’ll find I also quoted historical Maths documents, as well as showed some proofs.

I didn’t say the distributive property, I said The Distributive Law. The Distributive Law isn’t ax(b+c)=ab+ac (2 terms), it’s a(b+c)=(ab+ac) (1 term), but inaccuracies are to be expected, given that’s a wikipedia article and not a Maths textbook.

I did read the answers, try doing that yourself

I see people explaining how it’s not ambiguous. Other people continuing to insist it is ambiguous doesn’t mean it is.

That just states that a*(b + c) = ab + ac

No, The Distributive Law states that a(b+c)=(ab+ac), and that you must expand before you simplify.

For some simple exanples,

Examples by people who simply don’t remember all the rules of Maths. Did you read the answers?

If they weren’t ambiguous, then you wouldn’t see them getting popular

#MathsIsNeverAmbiguous They get popular because people who don’t remember all the rules of Maths want to argue with the people who do remember all the rules of Maths. #DontForgetDistribution

different systems of infix notation

There’s not different rules of Maths though, and the people “debating” the answer are those who don’t remember all the rules.

Those math questions that rely on purposeful ambiguity in order to drive engagement

#MathsIsNeverAmbiguous The engagement is driven by people not remembering the rules of Maths. #DontForgetDistribution