I am trying to split a clip and then add back on part of the original clip. In my previous versions I just grabed the end of the clip and move it to add back on the part I need back but when I do it in this version it changes the speed of the clip.
If you are referring to MEP 2016 please use the full version name to avoid confusion with the earlier version 16.
Check the Mouse Mode you have selected - I suspect it is in Stretch mode, indicated in red below, when you should be in Single object mode indicated in blue below
You probably got into this mode using the keyboard shortcut key 0