Who am I?

a) I am an improper fraction less than 2 and my denominator is 20.

b) I am a proper fraction. Both my numerator and denominator are one digit prime numbers but none of them is a factorof 10.

An improper fraction is one in which the numerator is greater than denominator.

Since the denominator is 20 and the fraction is less than 2,

so, the numerator can be any number between 20 and 40.

A proper fraction is one in which the numerator is smaller than denominator.

One digit prime numbers which is not a factor of 10 are 3, 7.

Thus, the proper fraction is