Calculate g at the midpoint of the earth moon system.
I assume you mean half-way to the moon, about 120,000 miles from Earth.
The moon's contribution will be quite small there. The gravity acceleration due to the Earth will be reduced by the ratio [Re/((D/2)]^2 . Re is the Earth radius (about 4000 miles) and D is the earth-moon distance (about 240,000 miles). That makes the factor about 1/900