An proper fraction represents a part of a whole, that is, the numeral one.
A whole could be a cake, a pie or a bar of chocolate. Anything that can be cut or divided into equal pieces.
If we cut a cake into two equal pieces, we have divided it in half. Writing this as a proper fraction, we write one as the fraction’s numerator and two as its (“downstairs”) denominator.
Should we give one half of the cake to a friend. Our friend has been given one part out of two.
Therefore, the numerator informs us that our friend has one part of the cake and the denominator shows into how many equal parts the cake has been divided.
Three-quarters (written as three over four) shows possession of three equal parts out of a possible four. Seven-eighths (seven over eight), seven out of a total of eight equal parts.