When the Chessmaster analyzes a game, it shows a depth fraction (ex.Depth 7/15 or Depth 15/15). What does this fraction mean?

I doubt you have seen 15/15 (OK, perhaps in endgame on an almost empty board).


7/15 means that the engine has gone through all 7 plies (half-moves) combinations, and all relevant combinations (the ones that the engine thinks are potentially good) to a depth of at least 15 plies.