Question

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

Answer 1

The answer is:  "5/9 of a bottle" .
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Explanation:
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(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}.
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 (1/3) / (3/5) = x

 (1/3) / (3/5) = (1/3) * (5/3) = (5*1) / (3*3) = x = 5/9 .
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The answer is:  "5/9 of a bottle" .
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Answer 2

The whole bathroom means 1.
Next, what we have to do is compare the statements. That will be;
3/5 of bathroom=1/3 solution
1=Y
I represented the unknown with Y
Next, you need to cross and multiply. That means 1 will multiply 1/3 to give 1/3 and Y will multiply 3/5 to give 3Y/5. So you will have;
3Y/5=1/3
Cross and multiply again. 5 will multiply 1 to give 5 and 3Y will multiply 3 to give 9Y. That will be;
9Y=5
Divide both sides by 9. That will be;
Y=5/9
The answer is 5/9 of the bottle.
Hope that helped. Have a nice day