Here is a distributive law lesson for grade 4

That's the Distributive Property actually. The dead giveaway is the multiply sign, as in "The Distributive Property of Multiplication over Addition". There's no Multiply sign in The Distributive Law, a(b+c)=(ab+ac)

Here’s another, and another.

Also The Distributive Property. "The distributive law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately" - no, the Distributive Property says that.

These were the first results

Welcome to the problem with using the internet and not looking at Maths textbooks

It being used in an algebra course doesn’t mean it’s in the domain of algebra

It being taught in Algebra most certainly does mean it's in the domain of Algebra

Algebra is also used in calculus, but algebra isn’t the domain of calculus, correct?

It's all Algebra. You can't do Calculus if you haven't learnt Algebra yet, just like you can' do a(b+c) if you haven't learnt Algebra yet.

It’s algebra when it’s using variables

and the rules of Algebra, like a(b+c)=(ab+ac). Arithmetic doesn't have any rules that aren't in Algebra, but Algebra does have rules which aren't in Arithmetic.

and you’re solving for an equation

I can solve 1+1= without using Algebra

2(3+4) is arithmetic

Nope, it's Algebra

2(x+4)=0 is algebra

Yep, now substitute x=3 in 2(x+4) and tell me what you get 😂

the application of the operations of addition, subtraction, multiplication, and division to them

Yep. Notice how Distribution was not mentioned?? 😂

and formal manipulations

Yep, such as a(b+c)=(ab+ac)

rather than specific numbers

Soooo, a+b is Algebra, but 2a+3b+4 isn't Algebra, because it has specific numbers in it?? 😂

Note: Algebra includes the use of arithmetic

Yep, it sure does.

t being used in algebra does not mean it is part of algebra

NOT being used in Arithmetic means it's not part of Arithmetic. 🙄 You know we've only had Brackets in Maths for 300 years, and that Arithmetic is much older than that, right?

https://en.wikipedia.org/wiki/Order_of_operations

isn't a Maths textbook

In mathematics and computer programming, the order of operations is a collection of conventions

and rules 🙄 Haven't even got past the first sentence you quoted and it's already wrong

These conventions

Rules

but some programming languages and calculators

May disobey the rules and give wrong answers, like Texas Instruments calculators

With math, you can invent your own notation if you like

Yep, but you cannot invent your own rules 🙄

This is done often.

No it isn't.

And if it makes sense, you can also change the order of operation

No you can't, or you get wrong answers, like Texas Instruments calculators

The notation you learn in school is just a common one, but other notations are equally valid and can be useful

But the rules are universal. You seem to be confusing notation with the rules

Therefore this kind of question is not a pure math question

Yes it is

what kind of conventions or notations people want to use

We can see for ourselves quite clearly what notation they have used. There's no mystery or debate about it

The context is what allows the math question to have a single answer

The rules of Maths is what gives it a single answer - that's what they're for! 😂

The rules of math itself are much more fundamental and they don’t care about how people decided to write formulas down.

Yep, one of which is The Distributive Law, a(b+c)=(ab+ac).

Please read this section of Wikipedia which talks about these topics better than I could

Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there's plenty in here

It shows that there is ambiguity in the order of operations

and is wrong about that, as proven by Maths textbooks

especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication

That's because Multiplication and Division can be done in any order

It addresses everything you’ve mentioned

wrongly, as per Maths textbooks

Multiplication denoted by juxtaposition (also known as implied multiplication)

Nope. Terms/Products is what they are called. "implied multiplication" is a "rule" made up by people who have forgotten the actual rules.

s often given higher precedence than most other operations

Always is, because brackets first. ab=(axb) by definition

1 / 2n is interpreted to mean 1 / (2 · n)

As per the definition that ab=(axb), 1/2n=1/(2xn).

[2][10][14][15]

Did you look at the references, and note that there are no Maths textbooks listed?

the manuscript submission instructions for the Physical Review journals

Which isn't a Maths textbook

the convention observed in physics textbooks

Also not Maths textbooks

mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik

Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer

More complicated cases are more ambiguous

None of them are ambiguous.

the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]

It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)

or [1 / (2π)] · (a + b).[18]

No, it can't mean that unless it was written (1 / 2π)(a + b), which it wasn't

Sometimes interpretation depends on context

Nope, never

more explicit expressions (a / b) / c or a / (b / c) are unambiguous

a/b/c is already unambiguous - left to right. 🙄

Image of two calculators getting different answers

With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.

6÷2(1+2) is interpreted as 6÷(2×(1+2))

6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)

(6÷2)×(1+2) by a TI-83 Plus calculator (lower)

Yep, Texas Instruments is the only one still doing it wrong

This ambiguity

doesn't exist, as per Maths textbooks

“8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:

No there isn't - you MUST obey The Distributive Law, a(b+c)=(ab+ac)

Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”

And he was wrong about that. 🙄

calls such contrived examples

Which notably can be found in Maths textbooks

I don’t think you’re right

You don't think Maths textbooks are right??

The wiki page

is full of disinformation. Note that they literally never cite any Maths textbooks

as an example of “elementary arithmetic.”

And whichever Joe Blow My Next Door Neighbour wrote that is wrong

as an example in “elementary algebra.”

Algebra isn't taught until high school

That implies that yes, this is arithmetic,

No, anything with a(b+c) is Algebra, taught in Year 7

the introduction of variables is what makes it algebra

and the rules of Algebra, which includes a(b+c)=(ab+ac). There is no such rule in Arithmetic.

It doesn’t matter what course finally teaches it to you

It does if you're going to argue over whether it's Arithmetic or Algebra.

not by definition part of that domain

The Distributive Law is 100% part of Algebra. It's one of the very first things taught (right after pronumerals and substitution).

It’s been ages since I took it

I teach it. We teach it to Year 7, at the start of Algebra

There isn’t one true order of operations that is objectively correct

Yes there is, as found in Maths textbooks the world over

that’s hardly the way most people would write that

Maths textbooks write it that way

you wouldn’t use the / symbol

Yes you would.

You’d either use ÷

Same same

It’s a good candidate for nerd sniping.

Here's one I prepared earlier to save you the trouble

I’d call that 36

And you'd be wrong

as written given the context you’re saying it in

The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).

But I’d say it’s ambiguous

And you'd be wrong about that too

you should notate in a way to avoid ambiguities

It already is notated in a way that avoids all ambiguities!

Especially if you’re in the camp of multiplication like a(b)

That's not Multiplication, it's Distribution, a(b+c)=(ab+ac), a(b)=(axb).

being different from ab

Nope, that's exactly the same, ab=(axb) by definition

and/or a × b

(axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a

The way I was taught growing up, brackets are [these]. Parenthesis are (these)

They're all brackets. Parentheses is actually the part inside the ().

Pemdas, parenthesis first, for a total of 3

Nope, a total of 15.

Then multiplication

There isn't any Multiplication, only Addition and Brackets (and Subtraction inside Brackets).

I’m sorry to tell you, friend, that your article does this too

Nope.

You don’t explain what XAML is, for instance

You know the article is about how to write a page and NOT use XAML, right?? 😂 If you don't know what it is then you don't need to (hence why I point out that it isn't pre-requisite knowledge). If you do know what it is then that's probably what brought you to my page to begin with - stop using it! 😂

Certain sentences almost read like the satire you posted:

Now read the links provided in the pre-requisite knowledge. You're the second person who thinks people learn things by reading the first paragraph only.

You also tell the reader to “edit the relevant line” which doesn’t help a total beginner

Now read the links in the pre-requisite knowledge, clone the repo, follow the instructions up to that point in the article, and guess which line you're on! 😂

I’m sure you’ll get there eventually

It's there already, if you had just bothered reading it all and following the instructions, instead of just criticising without even trying it

Just keep in mind that most people do not want to be technical writers

Probably because of people like you who criticise them without even trying to follow the directions to begin with. I'm guessing you also submit issues which say "It doesn't work. Please fix"

It's not official but it is federated, demonstrably.