Trisha bought a 1/4 of a pound of clay for the students in her pottery class. she then divided the clay into 2 equal pieces for her students to use for making vase and pots. how much did each piece weight?

1/4lb / 2 = 1/8lb.

The answer is 1/8 of a pound.

She began with 1/4 pound of clay, 
divided into 2, means (1/4)/2 for making vase and (1/4)/2 for making pots

now, first you must realise, that when we divide by 2, we are really dividing by 2/1, because every number, including 2, divided by 1 is itself. so 2/1 = 2
however, if we invert this (turn it upside down) , then 2/1 becomes 1/2 or a half. 

so if we have (1/4)/(2/1) and we turn 2/1 upside down (1/2) and multiply this by (1/4) we get : (1/4) x (1/2)  = 1/8

[To get 1/8 simply multiply the number on the top of the first fraction by the other number on the top of the second fraction, and then multiply the number on the bottom of the first fraction, by the number on the bottom of the second fraction].

Now, we have to do this twice, because, remember at the start the question said: (1/4)/2 for vase and (1/4)/2 for pots:

So each piece weighs 1/8 pounds.of clay