Given a monetary amount, calculate the equivalent change
Without loops or similar "advanced" structures, there isn't much you can do to simplify this. 

You could save the duplication in extra variables. It might look like this:

int hundred = valueIntegral / 100;

int remainderHundred = valueIntegral % 100;
int fifty = remainderHundred / 50;

int remainderFifty = remainderHundred % 50;
int twenty = remainderFifty / 20;

int remainderTwenty = remainderFifty % 50;
int ten = remainderTwenty / 10;

[...]


You have to decide if it's more readable. It's certainly less complex (and mistakes/typos are easier to catch), but it might take away some clarity.

Misc


you have a bit too much vertical space. Not every line needs its own paragraph. 
your comments don't add all that much value. The variable names already tell me all the comments do.