Right where to start. Think about it like your mountain bike, but having met you I'm not sure that you have one. lol
if you have a small gear at the front (pinion)(say 10 teeth) and a Large gear at the back (spur)(10 teeth) then your legs will go round lets say 1/1 so for every revolution your pedals make the rear wheel goes round once o keep it simple. This set up give vast pick up and lots of torque low down but you can't do any mid range r high speed. So lets think about the reverse, you have the biggest cog at the front(pinion)(30 teeth) and the smallest at the rear(spur)(10 teeth) now your rear wheel will do 3 revolutions to every one of your pedals giving a gear ratio of 3/1 which would give you slower acceleration but hiher top end. And there are also points where you can reach the same ratio with different size gears. if you want to keep it simple you can divide the driving gear by the driver to give the gear ratio. If you want to get more complex you will also need to know the other gears in the drive train but it is not often that these are changed and the manufacturer normally states these, so the maths isn't that hard.
Does this help or am i just waffling?
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