SmartmanApps

Depends on the language

No it doesn't.

if “5(” gets interpreted as “5×(”. I guess mostly no

Always no. The Distributive Law, a(b+c)=(ab+ac).

I don’t know why, but this was intuitively my first approach

Because that's what we teach students to do, though technically it should be (xy-xz)

Because there is no question

So Maths test says "2+3 ____", and you write "that's not a question" on the blank line?? 😂

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