1 can be interpreted as a "whole" thing, and smaller than 1 is a part of a thing.
imagine: if you have some cakes and you count the number of cake pieces, those will be more than the number of cakes: as each cake will have more than one piece! (otherwise it wouldn't be called a piece!)
so the result of a division by a fraction is bigger than the original number, there are more parts than wholes in the results, as each whole has multiple parts!
for example: divide 3 cakes into pieces which are 1/4th of a cake. how many such pieces would there be? 12! more than the 3 original cakes;
