There are much simpler methods to divide a width using a sector or a ruler. I won't go into how to use a sector or where to get one, I had to make mine, but you can goggle it. The ruler method is related to the sector and easier to explain.
If you want to divide the width of a board into seven equal increments, just take a ruler and lay it across the width of the board with one end at the edge of the board and the seven mark on the other edge. The ruler should be at an angle across the board. Now make a tic mark at each one inch increment and you have just divided the board into seven even increments! No trial and error, no math. Try it, it's easy!
Now using this knowledge, think about how to make a marking guage that will scratch a center line down the width of a board with parallel edges. Bob
Life's too short to use old sandpaper.