When you add friends on Facebook, Facebook notifies your friends that you are friends with this person. If you want to stop this here is how to do, Follow Steps carefully
3. Click on small icon as shown in picture, You will get settings, “Highlights and Other Stories”, “New Friend Reports” and “Recent Activity” under “Friend activity can show up in”.
Leave “New Friend Reports“ unmarked ( remove tick), and click OK.
Now other won’tknow if you become friends with someone.