  The concept of entanglement fraction is generalized to define coherence
fraction of a quantum state. Precisely, it quantifies the proximity of a
quantum state to maximally coherent state and it can be used as a measure of
coherence. Coherence fraction has a connection with $l_1$-norm coherence and
provides the criteria of coherence distillability. Optimal coherence fraction
corresponding to a channel, defined from this new idea of coherence fraction,
obeys a complementary relation with its decohering power. The connection
between coherence fraction and $l_1$-norm coherence turns to hold for bipartite
pure states and $X$ states too. The bipartite generalization shows that the
local coherence fractions of a quantum state are not free and they are bounded
by linear function of its global coherence fraction. Dynamics of optimal
coherence fraction is also studied for single sided and both sided application
of channels. Numerical results are provided in exploring properties of optimal
coherence fraction.
