We present a straightforward derivation of the large-scale evolution of a perturbed Robertson-Walker space. The origin of the Friedmann-like behavior of the perturbed model is clarified in a comoving gauge, and thus in a corresponding gauge-invariant formalism, using the covariant equations. Thus, when the imperfect fluid contributions are negligible, the large-scale perturbations in a nearly flat background evolve like separate Friedmann models. However, there exists a preferable gauge- invariant quantity (ζ) which is conserved in the large scale even considering the background spatial curvature (for a nearly flat background model), the cosmological constant, and the anisotropic pressure. Its independence from the anisotropic pressure allows us to generalize ζ, to a class of generalized gravity theories. Our notation is that commonly used in cosmological models (even those for perturbed universes), while keeping most general expressions including the background spatial curvature and the cosmological constant. This allows simple derivations of both the integral form solution in the large scale and also Bardeen's second-order evolution equation in the general case.