Why $\vec{AB} - s\vec{AB} = (1-s)\vec{AB}$?

Question

I'm having issues wrapping this in my head:

For some $s \in \mathbb{R}$:

$$\vec{AB} - s\vec{AB} = (1-s)\vec{AB}$$

I can see it happening, like $s = 1$ then of course $\vec{AB}-\vec{AB} = 0\cdot\vec{AB} = 0$, but still, I don't see the underlying logic here.

Answer 1

$\vec{AB}=1\vec{AB}=(1-s+s)\vec{AB}=(1-s)\vec{AB}+s\vec{AB}$. Now subtract $s\vec{AB}$ from each side.

Answer 2

Maybe replace $\vec{AB}$ by any quantity you may use in your life : if your earn one dollar and buy something for s dollar(s) the result is (1-s) dollar(s)