Introducing "forgiving" division - one of the latest fads from the wonderful world of the educrats, where constructivist philosophy decrees that constantly reinventing the wheel is somehow nobler and more memorable than instruction in the proper use of tools in the first place. Sure it works, but that in and of itself is no reason to advocate the abandonment of traditional long division.
You could pound nails with a rock. That "works," but you'll never catch a joiner or master craftsman tossing out his hammer and filling his toolbox with various chunks of gneiss.
If you have the stomach, witness the silliness: