Algebraic Statements And Scaling. Scaling. Often one is interested in how quantities change when an object or a system is enlarged or shortened Different quantities will change by different factors!
Note that in order to compute a "factor of change" you can ask: by what factor do I have to multiply the original quantity in order to get the desired quantity? Example: Q: By what factor does the circumference of a circle change, if its diameter is halved? A: It changes by a factor 1/2 = 0.5, i.e. (new circumference) = 0.5 * (original circumference), regardless of the value of the original circumference.