The gear ratio tells us how fast one gear is rotating when compared to another.

If our input gear (10 teeth) is rotating at 5 rpms, and it is connected to our output gear (50 teeth), our output gear will rotate at 1 rpms.

Why?

Our gear ratio is 50:10… or 5:1

If our small gear rotates 1x, our large gear only rotates 1/5. It takes 5 rotations of our small gear to = 1 rotation of our large gear. Thus our large gear is rotating at 1/5 the speed = 1rpm.

What if our gear ratio where 1:3 ?

In this case our input gear is 3x larger as large as our output gear.

If our input gear were rotating at 20 rpms…. each rotation, would result in 3 rotations of our output gear. Our output would be 60 rpms.