Calvin cleans 3/5 of his bathroom with 1/3 of a bottle of cleaning solution how much solution would he use if he cleaned the whole bathroom

The answer is:  "5/9 of a bottle" .

Explanation:

(1/3) / (3/5) = x / (5/5) ;  solve for "x" ;  in which "x" is the number of bottles used to clean the whole bottle;

Rewrite as:

(1/3) / (3/5) = x / (1) ;

Rewrite as:  (1/3) / (3/5) = x ;

 {since "x / 1 = x" ;  since any value, divided by "1", results in that same value}.

 (1/3) / (3/5) = x

 (1/3) / (3/5) = (1/3) * (5/3) = (5*1) / (3*3) = x = 5/9 .

The answer is:  "5/9 of a bottle" .