SmartmanApps

and another which says “first multiply two by three, then add it to two”

No we don't. We have another notation which says to do paired operations (equivalent to being in brackets) first.

why on earth do the “rules” have anything further to say about order of operations?

Because if you don't obey them you get wrong answers 🙄

How are you gonna write 2 + 2 ÷ 2 with repeated addition?

You don't, because the second 2 is associated with a Division that has to be done before the addition. Maybe go back to school and learn how to do Maths 🙄

That doesn’t mean it has to be expanded first.

Yes it does. Everything has to be expanded before you do the addition and subtraction, or you get wrong answers 🙄

2+3x4=2+3+3+3+3=2+12=14 correct

2+3x4=5x4=5+5+5+5=20 wrong

You could expand 2 + 2 × 3 as (2+2)+(2+2)+(2+2)

Says someone who can't tell the difference between (2+2)x3=12 and 2+2x3=8 🙄

you are unable to tell me what mathematical law prohibits it

The order of operations rules 😂

reverse polish notation wouldn’t work as it does

It works because it treats every operation as bracketed without writing the brackets. Also that's only a Maths notation, not the Maths itself.

In RPL, 2 2 + 3 × is 12

Because the way it calculates that is (2+2)x3, not complicated. Same order of operations rules as other Maths notations - just a different way of writing the same thing

If you had to expand multiplication first, how would it work?

It works because Brackets - 2 2 + = (2+2) - are before Multiplication

The same can be done with prefix notation

Another Maths notation, same rules of Maths

Different programming languages have different orders of operations

Maths doesn't

those languages work just fine

They don't actually. Welcome to most e-calcs give wrong answers because the programmers failed to deal with it correctly.

Your argument amounts to saying that it makes the most sense to do multiplication before addition

No, my argument is it's a universal rule of Maths, as found in Maths textbooks 🙄

that only gives you a convention, not a rule

Left to right is a convention (as is not writing the brackets in RPN). Brackets before Multiplication before Addition are rules.

knowledge on this subject without qualification

I'm a Maths teacher with a Masters - thanks for asking - how about you?

while ignoring my larger point

You mean your invalid point, that I debunked?

what are conventions if not agreed upon rules?

Conventions are optional, rules aren't.

here is a history of how we actually came to agree upon the aforementioned rules which you may find interesting

He's well-known to be wrong about his "history", and if you read through the comments you'll find plenty of people telling him that, including references. Cajori wrote the definitive books about the history of Maths (notation). They're available for free on the Internet Archive - no need to believe some random crank and his blog.

The rules are about how you interpret the notation

No, the notation definitions are about how to interpret the notation. The rules are about how to do the Maths.

That’s not true

Yes it is

PEDMAS: 8÷2x4 = 4x4 = 16

Yep.

PEMDAS: 8÷2x4 = 8÷8 = 1

Nope. PEMDAS: 8x4÷2 = 32÷2 = 16. What you actually did is 8÷(2x4), in which you changed the sign in front of the 4 - 8÷(2x4)= 8÷2÷4 - hence your wrong answer

PE M|D A|S: 8÷2x4 = 4x4 = 16

Yep, same answer regardless of the order 🙄

And thats not even getting into juxtaposition operations,

Which I have no doubt you don't understand how to do those either, given you don't know how to even do Multiplication first in this example.

where fields like physics use conventions that differ from most other field

Nope! The obey all the rules of Maths. They would get wrong answers if they didn't

you’re missing the point

No, you are...

It could be SAMDEP and math would still work

No it can't because no it wouldn't 😂

you’d just rearrange the equation.

Says someone who didn't rearrange "PEMDAS: 8÷2x4 = 8÷8 = 1" and got the wrong answer 😂

The rules don’t change

Hence why "PEMDAS: 8÷2x4 = 8÷8 = 1" was wrong. You violated the rule of Left Associativity

All I can assume from you is that you never did multiple choice questions in University

That would be a wrong assumption.

There’s a reason essay questions are considered easier.

They're not! 😂

Ok than I guess according to you PEMDSA doesn’t work

Oh course it does, and I have no idea why you think I would think otherwise! 😂

Or what about PEDMAS or PEDMSA maybe?

Yep, they all work

Oh wait we made up that order cuz it’s easier to say?

No, you made it up because your country has a chip on it's shoulder about doing it the same way as the rest of the world. 🙄

no one would ever write a problem like this

And yet Maths textbooks do! 😂

when was the last time I saw an X to mean multiplication

In a Maths textbook

1+1÷2 doesn’t even register in my brain properly

You don't know that the obelus means divide??

having an agreed-upon convention absolutely matters for arriving at expected computational outcomes,

Proven rules actually

we call it a convention

No we don't - the order of operations rules

it’s not a “correct” vs “incorrect” principle of mathematics

The rules most definitely are

It’s just a rule we agreed upon to allow consistent results

proven rules which are true whether you agree to it or not! 😂

any good math educator will be clear on this

Yep

If you know the PEMDAS convention already, that’s good, since it’s by far the most common today

No it isn't.

But if you don’t yet, don’t worry

As long as you know the rules then that's all that matters

You’ve completely not understood that order of operations is an arbitrary convention

No, you've completely not understood that they are universal rules of Maths

How did you decide to expand the definition of multiplication before evaluating the addition? Convention

The definition of Multiplication as being repeated addition

You can’t write 2 + 2 ÷ 2 like this

Yes you can

so how are you gonna decide whether to decide to divide or add first?

The rules of Maths, which says Division must be before Addition

PEMDAS isn’t obvious to “common people”?

Everyone is taught the rules of Maths

If “×” means “groups of,”

It means repeated addition actually

“2+2×4” means “two plus two groups of four”

No, it means 2+2+2+2+2

Sure the order of operations could be arbitrarily different

No they can't

I feel like we settled on that order because it simply makes more sense intuitively

It's because Multiplication is defined as repeated addition, so if you don't do it before addition you get wrong answers

Your obviously is only a convention

Nope. Rules of Maths

it would have to have different order or parentheses or both.

Neither. Multiplication is always before Addition, hence "obviously"

Of course everything in math is convention

Nope. The vast majority of it is proven rules

2+(2*4) is more obvious to common people

Weird then how many people were able to get this right without brackets for centuries before we started using brackets in Maths (which we've only had for 300 years)