  In this study, we estimate the fraction of binaries with high mass ratios for
202 open clusters in the extended solar neighbourhood (closer than 1.5 kpc from
the Sun). This is one of the largest homogeneous catalogues of multiplicity
fractions in open clusters to date, including the unresolved and total
(close-binary) multiplicity fractions of main-sequence systems with mass ratio
larger than $0.6_{-0.15}^{+0.05}$. The unresolved multiplicity fractions are
estimated applying a flexible mixture model to the observed Gaia
colour-magnitude diagrams of the open clusters. Then we use custom Gaia
simulations to account for the resolved systems and derive the total
multiplicity fractions. The studied open clusters have ages between 6.6 Myr and
3.0 Gyr and total high-mass-ratio multiplicity fractions between 6% and 80%,
with a median of 18%. The multiplicity fractions increase with the mass of the
primary star, as expected. The average multiplicity fraction per cluster
displays an overall decreasing trend with the open cluster age up to ages about
100 Myr, above which the trend increases. Our simulations show that most of
this trend is caused by complex selection effects (introduced by the mass
dependence of the multiplicity fraction and the magnitude limit of our sample).
Furthermore, the multiplicity fraction is not significantly correlated with the
clusters' position in the Galaxy. The spread in multiplicity fraction decreases
significantly with the number of cluster members (used as a proxy for cluster
mass). We also find that the multiplicity fraction decreases with metallicity,
in line with recent studies using field stars.
