There are lots of great ideas here. I have one more. If you are cutting a lot of identical pieces -- once you have found the right place on the line -- mark it with a piece of tape. Put the tape along the appropriate line on the rules and use it as your cutting line. I use a short piece of painter's tape cause it comes off easily, can be reused and leaves no residue.
By marking your line with tape, you won't have to figure out where you want to position the ruler each time you move it. I read this idea years ago and have been very successful with it.