sensory and mental faculties is a significant method for understanding it.
     The first instance of scale we will examine is an astronomical related one, where the relative sizes of the Earth and Sun will conceivably be revealed in a more vivid fashion.

Example 3
Suppose the Sun were reduced to the size of a regulation basketball.  Using the same scale, how large would the Earth be?  Identify a common object whose actual size corresponds to the answer.

     Some physical facts* are needed in order to proceed; the radius of the Earth (3960 miles), the radius of the Sun (432,500 miles) and the radius of a standard basketball (4.75 inches).  Armed with these details, we wish to use a basketball to represent the Sun, so that it makes sense to write the scale for our exercise as the rate: Just why this particular arrangement from a number of possible combinations?  'Tis a good question whose truly consummate answer is a bit long-winded.  To make a long story short, it was a rather judicious choice made out of all the possibilities, and one based on experience with a strategy employed to incorporate the (unknown)

quantity that we are seeking into the numerator (on the opposite side of the proportion).  This is a crafty feature which will make solving the resulting equation easier than some of the other scenarios.  Anyway, onward now to the ultimate construction of the proportion.  Next, observe that the scaled measure is in the numerator while the true measure is located in the denominator. Hence the right-hand side should shape up with the Earth's scaled measurement (our sought-after unknown) to be found in the top and its actual measurement winds up in the bottom of the fraction (ratio).  With this in mind, and denoting the unknown scaled radius of the Earth, E-sc.rad, we can now write: Time to multiply both sides by what quantity?  Are you thinking to use 3960 miles?  If so, then your problem is virtually solved already.  The idea being that we need to remove the clutter which surrounds the sought-after unknown (E-sc.rad) which we are doing our darnedest to discover.  At long last, our situation now looks like the following: