I have the following Fraction:
$ \frac{89*87*86}{49*47*46} $
and it is given that
Upper
-
$ \frac{89*87*86}{49*47*46} > \frac{90*90*90}{50*50*50} $
Lower
-
$ \frac{89*87*86}{49*47*46} <= \frac{85*85*85}{45*45*45} $
Could someone provide an Intuition on how to directly see that these inequalties hold (without using a calculator)?
For 1) it is easy to see that $ \frac{89*87*86}{49*47*46} > \frac{89*87*86}{50*50*50} $ but for the increase in the numerator I imagine one would have to make a general statement about the growth/decay of the two products given their elements. For example: The relative difference of $(89*87*86)$ --> $(90*90*90)$ is smaller than $(49*47*46)$ --> $(50*50*50) $ so the fraction is decreasing.