A typical example is to consider the relationship between light and distance give by the equation:

This reads as `brightness is proportional to the inverse of the distance squared'. Which we rewrite using the variable 'b' for brightness and 'D' for distance, such that:

Now when we compare two numbers, say the brightness of object 1 and the brightness
of object 2 (which have distances, D_{1} and
D_{2}), then a proportionality means that we can divide
the two equations by each other to give:

This equation can be manipulated in the following manner:

Where multiplying by D_{1} over D_{1} and D_{2} over D_{2} is the same as multiplying by 1. This results in

Notice that the D_{1} term is now demonminator and the
D_{2} term in is the numminator. With this form of the
inverse distance law, one can plug in a value for the distance of the Sun to Jupiter
in terms of the Earth's distance (i.e. D_{Jupiter} is 5
times D_{Earth}) so that the formula becomes