  Studies both of entire galaxies and of local Galactic star formation indicate
a dependency of a molecular cloud's star formation rate (SFR) on its dense gas
mass. In external galaxies, such measurements are derived from HCN(1-0)
observations, usually encompassing many Giant Molecular Clouds (GMCs) at once.
The Andromeda galaxy (M31) is a unique laboratory to study the relation of the
SFR and HCN emission down to GMC scales at solar-like metallicities. In this
work, we correlate our composite SFR determinations with archival HCN, HCO$^+$,
and CO observations, resulting in a sample of nine reasonably representative
GMCs. We find that, at the scale of individual clouds, it is important to take
into account both obscured and unobscured star formation to determine the SFR.
When correlated against the dense-gas mass from HCN, we find that the SFR is
low, in spite of these refinements. We nevertheless retrieve an SFR - dense-gas
mass correlation, confirming that these SFR tracers are still meaningful on GMC
scales. The correlation improves markedly when we consider the HCN/CO ratio
instead of HCN by itself. This nominally indicates a dependency of the SFR on
the dense-gas fraction, in contradiction to local studies. However, we
hypothesize that this partly reflects the limited dynamic range in dense-gas
mass, and partly that the ratio of single-pointing HCN and CO measurements may
be less prone to systematics like sidelobes. In this case, the HCN/CO ratio
would importantly be a better empirical measure of the dense-gas content
itself.
