Imagine you are playing with a lot of marbles that you want to move from one container to another container. The number of marbles you move per second is called the flux (or flow rate). Mass-flux is like the weight of the marbles, which means some marbles are heavy while some are light, and you need to consider their weight while moving them.
Now, let's say you want to move only red marbles from one container to another container. The mass-flux fraction of red marbles is the weight of the red marbles that you move per second divided by the weight of all the marbles you are moving per second. So, if you are moving 1000 marbles per second with a total weight of 50 kg, and 200 of those marbles are red with a total weight of 10 kg, then the mass-flux fraction of red marbles is 10 kg/50 kg or 0.2.
In simpler terms, the mass-flux fraction tells you how much of the total weight being moved is made up of a particular type of object. It helps you understand the composition of the moving material and their weight distribution.