# Conservation of Momentum - Rocket

I was wondering why the mass of the fuel is regarded as -dm and the mass of the rocket as m+dm? I understand that the total mass has to be unchanged (ie m). Why can't I say that the rocket's mass is m-dm and the mass of the fuel being ejected is dm? When I do that and continue with the suggested answer, I get v but in the opposite direction. Would appreciate any explanation

Here, $$\mathscr{d}m$$ is inherently negative because rockets mass decreases with time.
$$\mathscr{d}m = -|dm|$$
$$m + \mathscr{d}m = m - |\mathscr{d}m|$$