Take 2 circles. One of size 1, and One of size 2. Cut one of the biggest circle and roll it flat. Now take the smaller circle and roll it along the flat circle.
How many times that circle rolls is going to be your gear ratio. If you turn(roll) the smaller gear one revolution, youll find that it has only gone halfway around the smaller gear.
as for gears and RPMs is the same concept but in terms of speed. One circle with a radius of 1 meter and one circle with a radius of 2 meters. No matter how large the circle is, if you spin it once, its going to get spun once. But in order for the larger one to make that spin in same amount of time, it has to spin proportionally faster. So the smaller gear spins at 3.14 meters per second and the larger one at 6.28 meters per second.
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