Calvin cleans \dfrac35 5 3 start fraction, 3, divided by, 5, end fraction of his bathroom with \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction of a bottle of cleaning solution. at this rate, what fraction of the bottle of cleaning solution will calvin use to clean his entire bathroom?

We are given with:
3/5 of the bathroom is cleaned by 1/3 of a bottle of cleaning solution.
This problem involves the use of ratio and proportion. If we let x as the fraction of the bottle of cleaning solution needed to clean the entire bathroom, then we have the equation:
1 / x = 3/5 / 1/3
Solving for x
x = 5/9
The bathroom needs 5/9 of the bottle of cleaning solution.