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.
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.
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.
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.
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.
Bingo!
It’s the same thing, where y=3+1.
Yes, it’s 1/(7y) as per the definition of Terms.
It’s the standard in literally every Maths textbook.
Why the hell are you commenting on my 4 month old comments trying to argue. Fuck off.
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.
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.
It’s clearly defined in any Maths textbook you pick up.