Calvin cleans $\frac{3}5$ of his bathroom with $\frac{1}3$ of a bottle.
At this rate, what fraction of the bottle of will Calvin use to clean his entire bathroom?
Khan Academy solve this via $\frac {\frac{1}3}{\frac{3}5} = \frac{5}9$
I don't understand how dividing $\frac{1}3$ into $\frac{3}5$ will result in the remaining $\frac{2}5$ or total sum of $\frac{5}5$ giving it's corrosponding bottle usage. Help me understand the logic?
Dividing the bottle solution 1/3 into the surface area 3/5, yields the rest of the bottle solution to remaining surface area? That's the area of my confusion
Think of the part of the room and part of the bottle as a ratio.
Think of the whole room and some part of the bottle as a second ratio.
Assuming Calvin's rate of use does not change, these two ratios should be equal.
So we get 1/3 bottle per 3/5 room is equal to x bottle per 1 room.
This simplifies to just x = 1/3 divided by 3/5