The mass of Earth's moon is `7.36 xx 10^22` kg. The Moon's Radius is `1.74 xx 10^6` m.
The mass of the Earth is `5.98 xx 10^24` kg, and its radius is `6.37 xx 10^6` m.
According to Newton's law of gravitation the Force F of gravity between two objects of masses `m_1` and `m_2` that are r meters apart is `F=G(m_1m_2)/(r^2)` where G is the Gravitational constant `6.67 xx 10^-11` `N*m^2/(kg)^2` or `m^3(kg*s^2)`
The average mass of a human man is about 75 kg. The Shell theorem states that "A uniform spherical shell of matter attracts a particle that is outside the shell as if all the shell's mass were concentrated at its center." Although the Earth and moon are not uniform spheres, they are close enough approximations that the shell theory will be effective for our calculations.
The force of Gravity between an average man on Earth, and the earth is `6.67xx10^-11 (75*5.98xx10^24)/(6.37xx10^6)^2~~737N`
By contrast, the force of Gravity between that same man and the Moon on the Moon would be `6.67xx10^-11 (75*7.36xx10^22)/(1.74xx10^6)^2~~121N` `121:737~~1:7` So the astronauts experienced about 1/7 Earth Gravity. i.e. their weight on the moon was 1/7 that of their weight on Earth.