The Earth and the Moon roughly have the same mass.

The story behind the answer

False. Earth is vastly more massive than the Moon—about 81 times. The Moon’s mass is only ~1.2% of Earth’s (7.35×10^22 kg vs 5.97×10^24 kg), which is why lunar surface gravity is just about one-sixth of Earth’s. This big mass difference also keeps the Earth–Moon system’s center of mass (barycenter) inside Earth.

Context: The Moon likely formed after a giant impact early in Earth’s history, leaving it with less iron and a lower average density than Earth. Memory tip: the “6–81 rule”—the Moon has roughly 1/6 the surface gravity and 1/81 the mass of Earth.