Cut a rope into three sections and tie the ends together.
Make a magic swipe with your right hand over the rope and, tada! The knots are gone and the rope is whole.
Show a single rope.
Double it and then triple it in your hand so that you have three sections in your palm.
Tie a cat-shank knot in each end. (Run the tail of the rope through the large loop and then around itself and down through the small loop you just formed. Essentially, this is a simple overhand knot with the large loop stuck inside.)
Tighten the knots so they'll stay in place.
Show the audience that you have divided the rope into three sections and announce that you will now cut the rope.
Don't cut the loops; cut the short section of rope with the knot at the end.
Grasp the rope by the ends you just made and pull the rope tight between your hands. The knots will stay in place if you tied them tight enough and it will look like you have three cut pieces tied together.
Wrap the rope around your left hand with your right. As you get to the knots, conceal them while sliding them down to the end and off the rope.
Drop the knots inconspicuously in a pocket or on the floor if you are behind something.