The fraction 
(written alternatively as 
), where 
is a non negative integer and 
is a positive integer, was historically obtained by dividing a unit length into equal parts and taking of these parts.
For example, 
refers to 3 of 5 equal parts of the whole, taken together.
In the fraction the number is the numerator and the number is the denominator.
It is a proper fraction if 
and an improper fraction otherwise.