What's the difference between 126 1/4 78 2/3

Difference means subtract, so we use subtraction:

*first we need to make the fractions have the same denominator

1/4 = 3/12
2/3 = 8/12

126(3/12) - 78(8/12)
*since the fraction in the first term is smaller than the second, make it improper

125(15/12) - 78(8/12)

now simply subtract:

125 - 78 
= 47

15 - 8 
= 7
* this is now (7/12)

now put them back together:

47(7/12) 

That's the final answer!

The method to find the female dormitory is 2-d=800