I tried creating a square, turning it into a path (Path > Object to Path) and then placing four rectangles over it that are also paths and doing path > division.
But the square does not divide into four rectangles. Thoughts?
This can be done, but note that Division can only be used with one path at a time. But that's easy to fix. Also there's no need to convert the shapes to paths beforehand.
draw a square (rectangle)
draw the four rectangles over it (or copy and paste one, three times)
select the four rectangles and do Path > Combine
select all of the rectangles, now Path > Division will work, since a combined path is considered to be a single path
I was able to accomplish the task, but my methodology isn't likely to be the most efficient. Using the "snap to midpoint" feature, I drew a line across the midpoint of each edge, then selected the square and line. Using path, division worked and created two equal squares. Repeating this created two more on the other segment remaining.
You ask for four rectangles, but the result is four squares, which are rectangles.