Why is n (a number) = $\frac{n}{1}$?
My reasoning is as follows:
For a fraction $\frac{a}{b}$, b (denominator) is the number of equal parts the whole (1) is divided into and a (numerator) counts how many of these parts we're interested in. So e.g. $\frac{2}{5}$, read as two-fifths, represents 1 broken up into 5 equal parts and taking 2 of them.
Quite naturally then n = $\frac{n}{1}$ as $1$ is "divided" into 1 equal "parts" which is again 1 and we take n of them (n $\times$ 1 = n).
Ergo, my brain tells me n = $\frac{n}{1}$
Is my argument sound? Is there a better (simpler/shorter/correct) proof?
Muchas gracias.