Breaking a Chocolate Bar

Problem

You have a rectangular chocolate bar made up of M x N small square pieces arranged in a grid pattern (M rows and N columns). You want to break this bar into all of its individual small square pieces.

Each "break" consists of picking up a single piece of chocolate (which may be the original bar or any fragment you have already broken off) and snapping it along one of its straight grid lines, splitting it into two pieces. You may not stack pieces or break multiple fragments at once.

What is the minimum number of breaks required to separate the entire bar into all M x N individual squares? Prove that your answer is optimal.