Idon't understand how 251/4 divided by (-3/8)= -502/3

I must assume you meant 251 / 4 (not 25 1/4).

251

  4

   -3

     8

can be evaluated by inverting the second fraction and multiplying the result:

251       -8
 *
   8        3

The 8s cancel, leaving us with -251/3.  Note that -248/3 = -83, so that the magnitue of -251/3 must be a little larger than -83.  

251 divided by 3 is 83 with a remainder of 2:  251/3 = 83 2/3

So -251/3 = -83 2/3 (answer)