The short answer is: when their fractions add up to full integers.
For examples, two halves make up a whole, or
so the mixed numbers with those will add up to full integers:
but if they don't add up to an interger, the whole sum won't be an integer:
For examples, two halves make up a whole, or
so the mixed numbers with those will add up to full integers:
but if they don't add up to an interger, the whole sum won't be an integer: