Hi Fmath,
On the "modify" toolbar, there is an icon directly below (or to the right depending on orientation) the FILLET icon that is the SPLIT command. Now for whatever reason, there are two split commands, you want the first one. The description when hovering over the icon reads "BREAKS A SELECTED ENTITY AT A SINGLE POINT: SPLIT". You will then be prompted to select an entity and point. If you ESNAP on, you can locate the midpoint and after you click, the line/curve will be split in two. I hope this helps.
Best,
Medeski