If you want to divide things willy-nilly by random deflators, you might want to read this (free) manual First of all.
For a more compact exposition, see this blog post 2008with link to Diewert JEP piece.
I must confess that when I first learned about the “Fisher Ideal Price Indices” as a student, I was baffled. But I appreciated this knowledge when I became a research assistant.
