Question

N/F = n/f
If i have N and n is proportional to C and c, can i say
C/F = c/f ?

Answer 1

if \[ \frac{N}{F} = \frac{n}{f} \text{ then } \\ \frac{N}{n}= \frac{F}{f} \]
you show this by cross multiplying to get
N f = F n and then divide both sides by f n to get N/n = F/f

if you also have
\[ \frac{N}{C} = \frac{n}{c} \]
then you have
\[ \frac{N}{n} = \frac{C}{c} \]
Because
\[ \frac{N}{n}= \frac{F}{f}\text { and } \frac{N}{n} = \frac{C}{c} \]
you can say
\[ \frac{F}{f}= \frac{C}{c} \]
which can be re-arranged. cross multiply
\[ F c = C f \]
divide both sides by F f to get
\[ \frac{F c}{F f} = \frac{C f}{F f} \\ \frac{c}{f}= \frac{C}{F}\]