Natural numbers #NN#: 1,2,3,4,5,6 and so one.... serve to count things: you can have three apples, seven lemons or 100 potatoes. If you take 3/5 of an apple you will have only a piece of an apple, not an integer apple. Humans like to complicate things and add zero and the negative numbers thus giving the group of integer numbers #ZZ#:... -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.... Notice the difference between consecutive integer numbers is always 1. There's no place here for parts of apples.

For a mathematical point of view, a fraction only represents an integer if the numerator (above) is multiple of the numerator (below). eg. 10/5=2.