  We present a new estimate for the binary fraction (the fraction of stars with
a single companion) for M dwarfs using a log-normal fit to the orbital
separation distribution. We use point estimates of the binary fraction (binary
fractions over specific separation and companion mass ratio ranges) from four M
dwarf surveys sampling distinct orbital radii to fit a log-normal function to
the orbital separation distribution. This model, alongside the companion mass
ratio distribution given by Reggiani & Meyer (2013), is used to calculate the
frequency of companions over the ranges of mass ratio (q) and orbital
separation (a) over which the referenced surveys were collectively sensitive -
[0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU]. This method
was then extrapolated to calculate a binary fraction which encompasses the
broader ranges of [0.10 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a < $\infty$
AU]. Finally, the results of these calculations were compared to the binary
fractions of other spectral types. The binary fraction over the constrained
regions of [0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU] was
calculated to be $0.229 \pm 0.028$. This quantity was then extrapolated over
the broader ranges of q (0.10 - 1.00) and a (0.00 - $\infty$ AU) and found to
be $0.462^{+0.057}_{-0.052}$. We used a conversion factor to estimate the
multiplicity fraction from the binary fraction and found the multiplicity
fraction over the narrow region of [0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$
a $\leq$ 10,000 AU] to be $0.270 \pm 0.111$. Lastly, we estimate the
multiplicity fractions of FGK, and A stars using the same method (taken over
[0.60 $\leq$ q $\leq$ 1.00] and [0.00 $\leq$ a $\leq$ 10,000 AU]) and find that
the multiplicity fractions of M, FGK, and A stars, when considered over common
ranges of q and a, are more similar than generally assumed.
