I just showed what is currently being taught on math teaching websites, as to how to divide by a monomial. See Lumen Learning.com, Cue Math.com, Greene Math.com, BYJUS.com teaching website, etc., instructing students to "Rewrite as a fraction," when they are presented with a linearly written division expression using an obelus as the division symbol. That is because, remembering back to 5th grade math, students are taught that Fraction=Division (and therefore, Division=Fraction). On those teaching websites, there are a number of examples given to current Basic Algebra students, with the solutions, which show this clearly to be the case. Here are a few more examples of this, on math teaching websites to help current Basic Algebra students :
from Teachoo .com:
https://www.teachoo.com/9708/2961/Dividing-monomial-by-monomial/category/Dividing-two-monomials/
"Dividing Monomial by Monomial"
"Let's do some more examples
6x^3 ÷ 3x^2
... = 2x "
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from Cool Math .com:
https://www.coolmath.com/algebra/05-division-of-polynomials/01-dividing-by-monomials-01
"Dividing by Monomials"
"Let's do one
(18x^4 -10x^2 + 6x^7) ÷ 2x^2
Let's rewrite it like this:
18x^4 -10x^2 + 6x^7
--------- [over] -------- =
2x^2
...
9x^2 - 5 + 3x^5
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from Mometrix Test Preparation:
https://www.mometrix.com/academy/dividing-monomials/
See example #3 on the video:
8x^5y^3 ÷ x^2y
Note that no parentheses are used in that horizontal division expression.
The eventual answer is shown to be 8x^3y^2...which only works if 8x^5y^3 is the entire numerator & x^2y is the entire denominator of the top-and-bottom fraction.
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If you still need to see more of this from other math teaching websites, just say the word & I will provide additional examples of students being instructed to rewrite monomial division expressions as a top-and-bottom fraction, when it was, originally written horizontally with an obelus without parentheses around the divisor (denominator) monomial.
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In teaching your students how to 'process' a division expression such as a/b/c, yes, additional parentheses are definitely necessary, to indicate the order of the multiple divisions in the expression. When there is only one division symbol in an expression, however, it is clear that the dividend/numerator is everything to the left of the division symbol (slash or obelus) & the divisor/denominator is everything to the right of the division symbol. See above examples from teaching websites.
In no Basic Algebra textbook are students taught that a numerical coefficient of a term can be separated from its other factor or factors -- with or without parentheses surrounding the term. Quite the contrary -- students are taught that a monomial term such as "2a" holds a SINGLE VALUE, which is the PRODUCT of "2" & "a." When a=(2+2), the monomial term 2a equals 8.
As demonstrated on a myriad of math teaching websites showing students how to divide by a monomial, the value of a monomial does not change when a monomial such as "2a" is preceded by a division symbol (slash or obelus). The two in "2a" is not a separate, stand-alone quantity any more than the two in "2 dozen" is a stand-alone quantity. Two dozen equals 24, even when there's a division symbol immediately to the left of that term. Once again, see all those Basic Algebra teaching websites for confirmation of how to divide by a monomial.
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As for students using calculators, if they are taught the proper way to execute monomial division in the first place, then if they do not get the same result on a calculator, they know it is due to faulty programming. Some manual & online calculators do get it correctly, however. If they get what they understand is an erroneous answer from a calculator program, then they can go back & add more (unnecessary) parentheses.
With the proper knowledge & understanding of how to divide monomials, there is nothing confusing or ambiguous about an expression such as 6 ÷ 2(1+2). 8 ÷ 2(2+2), or 48 ÷ 2(9+3).