Hints:

1. If improper fractions are not allowed, then it’s impossible for the two mixed numbers to be equal. However, if improper fractions are allowed, then the mixed numbers can be the same.

2. For example, using improper fractions:
   
   since ​, and both expressions equal 8.5

3. If only proper fractions are allowed, aim to make the fractional part of the first mixed number as small as possible and the fractional part of the second mixed number as close to 1 as possible.

Solution and Exploration:

If improper fractions are allowed, then it’s possible for the difference to be zero. For example:
since ​, and both expressions equal 8.5

If only proper fractions are allowed, then the goal is to make the first fractional part as small as possible and the second fractional part as large as possible. There are only a few combinations that come close:

​

Among these, the first one gives the smallest difference. Note that the whole numbers (3 and 2) can be replaced by any consecutive integers without affecting the fractional difference.