Proving the finger trick for multiplying by 9

Here's the proof:

Thus, we need to prove \(9n = 10(n - 1) + (10 - n).\)

$$\begin{align} 9n &= 10(n - 1) + (10 - n) \\ &= 10n - 10 + 10 - n \\ &= 9n \end{align}$$