SmartmanApps

The P in PEMDAS means to solve everything within parentheses first

and without a(b+c)=(ab+ac), now solve (ab+ac)

there is no “distribution” step or rule

It's a LAW of Maths actually, The Distributive Law.

that says multiplying without a visible operator

It's not "Multiplying", it's Distributing, a(b+c)=(ab+ac)

So yes, 36 is valid here

No it isn't. To get 36 you have disobeyed The Distributive Law, thus it is a wrong answer

It’s mostly because

people like you try to gaslight others that there's no such thing as The Distributive Law

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

Treat a + b/c + d as a + b/(c + d)

No don't. That rule was changed more than 130 years ago. a+b/c+d=a+(b/c)+d, Division before Addition

Because people never use that after they learn fractions,

Yes they do, because not every division is a fraction

PE(MD)(AS) Now just remember to account for those parentheses first

Those Brackets don't matter. I don't know why people insist it does

order of appearance is ‘the rule’ when commutative properties apply

That's because students often make mistakes with signs when they do it in a different order, so we tell them to stick to left to right

I did not flip any signs

Yes you did! 😂

merely reversed the order in which the operations are written out

No, merely reversing the order gives -3-2+1 - you changed the signs on the 1 and 3.

If you read the right side from right to left, it

Starts with -3, which you changed to +3

it has the same meaning as the left side from left to right

when you don't change any of the signs it does 😂

Hell, the convention that the sign is on the left is also just a convention

Nope, it's a rule of Maths, Left Associativity.

Right, because 1-2-3=3-2-1

No, 1-2-3=-3-2+1. You changed the signs on the 1 and the 3.

addition and subtraction, left to right is correct

You can do addition and subtraction in any order and it's still correct

Social conventions are real, well defined things

So are the laws of nature, that Maths arises from

Some mathematicians like to pretend they aren’t, while using a truckload of them; that’s a hypocritical opinion

No, you making false accusations against Mathematicians is a strawman

That’s not to say you can’t change them

You can change the conventions, you cannot change the rules

But all of basic arithmetic is a social convention

Nope, law of nature. Even several animals know how to count.

you can redefine the numbers and operations any time you want too

And you end up back where you started, since you can't change the laws of nature

I mean, arithmetic order is just convention

Nope, rules arising from the definition of the operators in the first place.

not a mathematical truth

It most certainly is a mathematical truth!

But that convention works in the way we know, yes, because that’s what’s… well… convention

The mnemonics are conventions, the rules are rules

this is just a writing standard that is globally agreed on

No, it's a universal rule of Maths

The writing rules are defined by humans not by natural force

Maths is for describing natural forces, and is subject to those laws

That one thing and another thing are two things, is a rule from nature

Yep, there are even some animals who understand that, and all of Maths is based upon it.

Some people insist there’s no “correct” order for the basic arithmetic operations.

And those people are wrong

And worse, some people insist the correct order is parenthesis first, then left to right

As per Maths textbooks

Both of those sets of people are wrong

All Maths textbooks are wrong?? 😂

And in some languages a number can be used as a name of a variable or a function

Not in Maths it can't

so it can be anything really

No, it can only be a Factorised Term, ab+ac=a(b+c). You also can't call a function by any letter that you've used as a pronumeral

Wouldn’t we just assume function expressions are always “in parenthesis”?

No, because factorised Terms also are, ab+ac=a(b+c).

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

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

the original question was arithmetic

No, it's actually Algebra. There is no a(b+c) in Arithmetic

You are one of them bc you do not know what an equation is.

You are one of the people who doesn't know what a(b+c) is

There is no algebra here

Yes there is, 5(8-5).

This is arithmetic

There's no a(b+c) in Arithmetic

Implications or assignment?

Umm, neither?? 😂

They didn’t specify notation

a(b+c)=(ab+ac) is taught in Algebra, The Distributive Law, it can't mean anything else - it's the reverse operation to Factorising ab+ac=a(b+c).

Technically not algebra, right?

No, it actually is Algebra. The Distributive Law isn't taught to students until they start on Algebra.

This is just arithmetic

There's no a(b+c) in Arithmetic.