On the last period our teacher had 1/2 of an eraser left she gave that to her 2 students equally how much of the eraser did every student take home

To find how much each student got, just divide 1/2 by 2. To do this, multiply 1/2 by the reciprocal of 2, which is 1/2.

   1/2 x 1/2 = 1/4.  (multiply the numerators and the denominators)

So each student will take 1/4  of the eraser home.