the short answer is: when their fractions add up to full integers.
For examples, two halves make up a whole, or
\(\frac{1}{2} + \frac{1}{2}=1\)
so the mixed numbers with those will add up to full integers:
\(-12\frac{1}{2} + (-3\frac{1}{2})=(-(12+3+1)=-16\)
but if they don't add up to an interger, the whole sum won't be an integer:
\(-12\frac{3}{4} + (-3\frac{3}{4})=(-(12+3+1\frac{1}{2})=-16\frac{1}{2}\)
