He will have 8 fields in the total area of his land.
Explanation
Both length and width of each square field are [tex]\frac{1}{4}[/tex] mile
So, the area of each square field [tex]= (\frac{1}{4}*\frac{1}{4})=\frac{1}{16} [/tex] square mile.
Total area of the land bought by the farmer is [tex]\frac{1}{2}[/tex] square mile.
For finding the number of fields, we need to divide the total area of land by the area of each field.
So, the number of fields = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{16}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{16}{1}[/tex] = [tex]\frac{16}{2}[/tex] = 8
