Suppose the farmer buys another 1/2 square mile of land and divides all his land into square fields 1/4 mile long and 1/4 mile wide. how many fields will he have

To answer this question, you need to find the area of the divided land that the farmer want. Since it was a square with 1/4 mile length then the area would be:

1/4 mile * 1/4 mile = 1/16 miles square.

Then you can divide the total area of land the farmer buys, with the area of divided land. The calculation would be: (1/2 square miles) / (1/16 square miles) = 16/2=8 pieces of field