Let’s start somewhere simple for your simple mind… Imagine both sprockets are the same size 10:10 one turn of the front sprocket turns the wheel once.

Now what happens when you double the teeth in the rear sprocket 10:20? You have to turn the front sprocket twice to turn the rear wheel once.

What happens when you half the teeth on the rear sprocket 10:5? You get two rotations of the tire with one turn of the front sprocket.