If $$u : v : w$$ = 3 : 6 : 8, then what will be the ratio of $$(\frac{u}{v}):(\frac{v}{w}):(\frac{w}{u})$$ ?

Given $$u : v : w$$ = 3 : 6 : 8

Let $$u = 3k$$, $$v = 6k$$, $$w = 8k$$

$$=$$> $$\left(\frac{\ u}{v}\right):\left(\frac{\ v}{w}\right):\left(\frac{\ w}{u}\right)=\frac{\ 3k}{6k}:\frac{\ 6k}{8k}:\frac{\ 8k}{3k}$$

$$=$$> $$\left(\frac{\ u}{v}\right):\left(\frac{\ v}{w}\right):\left(\frac{\ w}{u}\right)=\frac{ 3}{6}\times24:\frac{ 6}{8}\times24\ :\frac{ 8}{3}\times24$$

$$=$$> $$\left(\frac{\ u}{v}\right):\left(\frac{\ v}{w}\right):\left(\frac{\ w}{u}\right)=12:\ 18:\ 64$$

$$=$$> $$\left(\frac{\ u}{v}\right):\left(\frac{\ v}{w}\right):\left(\frac{\ w}{u}\right)=6:\ 9:\ 32$$