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We consider a one-dimensional stochastic differential equation driven by aWiener process, where the diffusion coefficient depends on an ergodic fastprocess. The averaging principle is satisfied: it is well-known that the slowcomponent converges in distribution to the solution of an averaged equation,with generator determined by averaging the square of the diffusion coefficient.  We propose a version of the averaging principle, where the solution isinterpreted as the sum of two terms: one depending on the average of thediffusion coefficient, the other giving fluctuations around that average. Boththe average and fluctuation terms contribute to the limit, which illustrateswhy it is required to average the square of the diffusion coefficient to findthe limit behavior.

The averaging principle for stochastic differential equations driven by a Wiener process revisited