Jump-roping

Aren't you getting the same benefits of jump-roping by just jumping? You aren't improving your hand-eye-coordination, but you are still doing the main exercise correct?
 
Fundamentally, yes.

But you'd look like a tool just jumping up without a rope. Also, the way you hold the rope creates a certain balance that makes the jumping what it is. Furthermore, your arms are recruited for the activity much more than without the rope.
 
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