Write and solve a real world problem in which the part of a whole results in a number greater than the whole itself.

I can think of one case like this: when the whole is negative.

for example, if your family has a debt of 200 dollars, this means that the family has -200 dollars.

Now, the family has four members. How much money does each of the member have?

and the way to solve is is this:

-200/4=-50.

so each person "has" -50 dollars, which is more than -200!