Wheel and Axle mechanics

I have a question about the simple machine: the wheel and axle. I know already that mechanical advantage through a wheel and axle system is achieved by force being applied through the wheel to turn the axle. This mechanical advantage would be in the form of you applying less force, but over a greater distance. But, if you do the opposite and apply the force through the axle to turn the wheel, then you would have to apply much more force, but over a shorter distance right?