you’re in for a surprise

I'm not actually. A lot of people don't want to confront evidence that they're wrong.

She didn’t reference any math textbooks because she made the video for commoners, aka not math majors.

Did you notice she's a Physics major? In other words, she doesn't have any Maths textbooks to reference.

Her explanations make sense

So, even when she couldn't explain why one calculator "sometimes obeys juxtaposition, sometimes doesn't", that still made sense to you?

technically wrong

Bingo!

I don’t think many people are going to see your reply

These comments are going to show up in search results for the rest of eternity, so I'm quite happy to debunk the disinformation in it.

you seem to have copy/pasted the reply on several comments

3 different people referred to the same video, so yeah I did something I don't normally do and copy/pasted for those 3 people. Read my other replies and you'll find they're all specific to the person I'm replying to.

It’s like you searched for the YouTube link

No, I've had multiple people tell me about it previously, as "proof" that Maths is ambiguous, hence why I wrote a thread debunking the claims she (and others) made.

It just seems suspect

It's all legit, so feel free to go back and read what I've written given that context.

Right idea, but wrong terminology.

There's no such thing as implicit multiplication

xy is a Term - Terms are separated by operators (none in this case) and joined by grouping symbols.

x(y) is a Bracketed Term, and is therefore subject to The Distributive Law, which is the first step in solving Brackets.

And yes, a multiplication symbol is an operator - which therefore separates Terms (which is why ab and axb aren't the same thing - it's 1 term vs. 2 terms), and the "M" in the mnemonics refers literally to multiplication signs, and nothing else.

Division is usually written in fractions

Division and fractions aren't the same thing.

fractions which has an implied set of parenthesis

Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1÷2 is 2 terms, but ½ is 1 term.

8/2(2+2) could be rewritten as 8×1/2×(2+2)

No, it can't. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.

2+2 first because P. That’s 4.

P is 2(2+2)=(2x2+2x2)=(4+4)=8

Then 8/2 because it’s left of 4(4).

If you do 8/2 when you still have brackets, then you just did division before brackets and disobeyed order of operations rules. You also broke the rule of Terms, since 2(4) is a single term.

Don’t take my word for it.

I see you didn't read my thread then. I have a section on calculators, which points out that WolframAlpha does it wrong. i.e. they also break the rule of Terms.

If frac and div are different functions, then multiplication would have two different inverses. How could that be?

The opposite of div is to multiply. The opposite of frac is to invert the fraction.

No, I’m saying your “maths” textbook is wrong

No, you're saying every Maths textbook is wrong. You think I only have one? 😂

Well, they demonstrably are all wrong, as per the rules of Maths.

Google it if you don’t believe me

BWAHAHAHA! 😂 Google gets it wrong too. Try looking in a Maths textbook instead (I have plenty of them since I'm a Maths teacher).

2 (4) is the same thing as 2 * 4.

No, as I already pointed out, it's the same as (2x4). You can't remove brackets unless there is only 1 term left inside. 2x4 is 2 terms, so can't remove brackets yet.

Division and multiplication are equal in the order of operations

I didn't say they weren't. I said...

Doing division before brackets goes against the order of operations rules

You did 8/2x4, which is the same as (8/2)(2+2), which isn't the same as 8/2(2+2)=8/2(4)=8/(2x4).

Check a high school Maths textbook - even easier!

Yes, unfortunately there are some bad teachers around. I vividly remember the one I had in Year 10, who literally didn't care if we did well or not. I got sick for an extended period that year, and got a tutor - my Maths improved when I had the tutor (someone who actually helped me to learn the material)!