Question

What is the product a-3/7 ÷ 3-a/21​

Answer 1

the sum shown is (20/21)a -(1/7)

Explanation:

As written, the sum is ...

`a-((3)/(7))/(3)-(a)/(21)=\boxed{(20)/(21)a-(1)/(7)}`

__

We wonder if you mean the quotient ...

((a-3)/7)/((3-a)/21)

`(\left((a-3)/(7)\right))/(\left((3-a)/(21)\right))=(a-3)/(7)\cdot(21)/(3-a)=(-21(3-a))/(7(3-a))=\boxed{-3}`

_____

Comment on the problem presentation

Parentheses are required when plain text is used to represent fractions. The symbols ÷, /, and "over" all mean the same thing: "divided by." The denominator is the next item in the expression. If arithmetic of any kind is involved in the denominator, parentheses are needed. This is the interpretation required by the Order of Operations.

When the expression is typeset, fraction bars and text formatting (superscript) serve to group items that require parentheses in plain text.

__

Please note that some authors make a distinction between the various forms of division symbol. Some use ÷ to mean ...

(everything to the left)/(everything to the right)

and they reserve / solely for use in fractions. Using this interpretation, your expression would be ...

(a -(3/7))/(3 -(a/21)) = (21a -9)/(63 -a)

That distinction is not supported by the Order of Operations.