Use the format option :
or Format -> Number -> More Formats -> Custom number format...
Solution 1 :
Use 0.0"/20" as a custom format on the cell containing 19.5.
WARNING : It has still the value 19.5 but is display as 19.5/20.
Use the ??/20 custom format on a cell with =19.5/20
Long story short : it has the value 19.5/20 = 0.975 ...
Put the numerator and denominator in different cells. Use an extra column to calculate the decimal representation of the fraction (eg d2 = b2/cd) to use in calculations, and convert the original cells to text for display use.