I am selling a home. The buyer is paying me cash. Can I pay my mortgage holder 1/2 of my balance and keep making payments on the rest?

The buyer of your home will not have clear title or ownership of the property you are selling. Your mortgage company will not release their interest in the property (their right to foreclose) until you pay them off.

Also look at your mortgage document. Most mortgages will have a "Due on Sale" clause which requires you to pay the mortgage in full if you sell the property.

More than likely, the title company handling the transaction will also require that certified funds be brought to the closing to satisfy the existing mortgage in order to properly transfer a clear title to the buyer.