  Crackling noise is a common feature in many systems that are pushed slowly,
the most familiar instance of which is the sound made by a sheet of paper when
crumpled. In percolation and regular aggregation clusters of any size merge
until a giant component dominates the entire system. Here we establish
`fractional percolation' where the coalescence of clusters that substantially
differ in size are systematically suppressed. We identify and study percolation
models that exhibit multiple jumps in the order parameter where the position
and magnitude of the jumps are randomly distributed - characteristic of
crackling noise. This enables us to express crackling noise as a result of the
simple concept of fractional percolation. In particular, the framework allows
us to link percolation with phenomena exhibiting non-self-averaging and power
law fluctuations such as Barkhausen noise in ferromagnets.
