Is mechanical advantage given by : (length of effort arm)/(length of resistance arm) or (length of resistance arm)/(length or effort arm)?
Simple machines that include the lever, pulley, screw, etc. are used to increase the force or torque that is applied. The ratio of the output force or torque and the input force or torque is greater than 1 and is defined as the mechanical advantage of the simple machine.
There are many types of levers; the variation is in the location of the fulcrum, where the load is applied and where the load is placed. In all kinds of levers the mechanical advantage is equal to the distance over which the effort is applied to the distance over which the load is moved. By using a lever it becomes possible to apply a small force over a large distance and the result is a very large force acting for a small distance on the load.
Mechanical advantage is given by (length of effort arm)/(length of resistance arm). If you were using a lever over a fulcrum to lift a weight, the effort arm is the side of the lever you push on, and the resistance arm is the side of the lever that lifts the weight. So, if the side of the lever you push on is 4 feet long and the side of the lever that lifts the weight is 1 foot long, the mechanical advantage of this lever would be (4 feet)/(1 foot) = 4. This means that the force the lever puts on the weight is 4 times what you apply; your push is multiplied by 4, which is why it is called an "advangate".