His bed is 2/5 of his room, which is 1/8th of the house. In order to know how much of the entire houre the bed takes we have to multiply this: (2/5)*(1/8). When we multiply fractions, we can multiply "independently" the numerator and denominator, like this:
(2*1)/(5*8)
That's 2/40, or 1/20. So his bed takes up 1/20 of his house.