They're still wrong, in my humble opinion. I'm aware of this notion, and I've even had people share a snip from some book that states this as fact. However, this is not standardized and without the convention being widely understood and recognized as the standard in the world of mathematics (which generally doesn't use the symbol (÷) at all at post-algebra levels), there is no reason to treat it as such just because a few people assert it is should be.

It doesn't make sense at all to me that implied multiplication would be treated any differently, let alone at a higher priority, than explicit multiplication. They're both the same operation, just with different notations, the former of which we use as shorthand.

There are obviously examples that show the use of the division symbol without parentheses sometimes leads to misunderstandings like this. It's why that symbol is not used by real mathematicians at all. It is just abundantly more clear what you're saying if you use the fraction bar notation (the line with numerator on top and denominator on bottom). But the rules as actually written, when followed, only reach one conclusion for this problem and others like it. x÷y(z) is the SAME as x÷y*z. There's no mathematical or logical reason to treat it differently. If you meant for the implicit multiplication to have priority it should be in parentheses, x÷(y(z)), or written with the fraction bar notation.

[–] Tlaloc_Temporal@lemmy.ca 7 points 1 year ago (1 children)

Implicit multiplication being before regular multiplication/division is so we can write 2y/3x instead of (2y)/(3x). Without priority, 2y/3x becomes (2y÷3)•x.

Coefficients are widely used enough that mathematicians don't want to write parentheses around every single one. So implicit multiplication gets priority.

[–] kryptonianCodeMonkey@lemmy.world 3 points 1 year ago* (last edited 1 year ago) (2 children)

I think one could argue a coefficient on an unknown variable, like 2y, should take higher priority simply because it cannot be any further resolved or simplified. That is not the case with, say, 2(3+1). Although that does still leave you with potential ambiguity with division/multiplication, such has 1/7y. Is the coefficient 7, or is it 1/7? i.e. Is that 1/(7y)? Or (1/7)y? Either way, if that's not the the standard understood by everyone, then it is a non-standard, inconsistent rule. And as demonstrated, if you do use that rule, it needs to be more clearly defined. That is the source of this "ambiguity". If you don't include it, the order of operations rules, as written, are clear.

[–] SmartmanApps@programming.dev 1 points 8 months ago (1 children)

2y, should take higher priority simply because it cannot be any further resolved or simplified

Bingo!

That is not the case with, say, 2(3+1)

It's the same thing, where y=3+1.

1/7y. Is the coefficient 7, or is it 1/7? i.e. Is that 1/(7y)

Yes, it's 1/(7y) as per the definition of Terms.

Either way, if that’s not the the standard understood by everyone

It's the standard in literally every Maths textbook.

[–] kryptonianCodeMonkey@lemmy.world 1 points 8 months ago (1 children)

Why the hell are you commenting on my 4 month old comments trying to argue. Fuck off.

[–] SmartmanApps@programming.dev 1 points 8 months ago

Actually I'm educating and hoping people will stop arguing about it. You can take it on board or not. You actually nearly had it.

Also, your comments will show up in search results for all eternity unless you delete them.

[–] Tlaloc_Temporal@lemmy.ca 1 points 11 months ago (1 children)

I agree it needs to be more clearly defined, but one of the reasons it wasn't clearly defined was because mathematicians thought it was so universal it didn't need defining, like how parentheses work to begin with.

Casio tried not doing umplicit multiplication after some american teachers complained, then went back to doing it after everyone else complained. Implicit multiplication is the standard.

[–] SmartmanApps@programming.dev 1 points 8 months ago

I agree it needs to be more clearly defined

It's clearly defined in any Maths textbook you pick up.

[–] SmartmanApps@programming.dev 1 points 8 months ago

I’ve even had people share a snip from some book that states this as fact

A Maths textbook.

However, this is not standardized

It's standard in every Maths textbook.

there is no reason to treat it as such just because a few people assert it is should be

The "few people" are Maths teachers and Maths textbook authors.

It doesn’t make sense at all to me that implied multiplication would be treated any differently

There's no such thing as implicit multiplication

They’re both the same operation

No, what people are calling "implicit multiplication" is either The Distributive Law - which is the first step in solving Brackets - or Terms - and neither of these things is "multiplication". Multiplication literally refers to multiplication symbols only.

It’s why that symbol is not used by real mathematicians at all. It is just abundantly more clear what you’re saying if you use the fraction bar notation

The division symbol is used - it is not the same thing as a fraction bar.

x÷y(z) is the SAME as x÷y*z.

No, it's the same as x÷(y*z).

There’s no mathematical or logical reason to treat it differently

Terms, The Distributive Law, are why it's treated differently.