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In this article we construct an extended relativistic f(R) theory of gravitywith matter-curvature couplings F(R,L_matt) for which its weak field limit ofapproximation recovers the simplest version of MOND. We do this by (a)performing an order of magnitude approach and (b) by perturbing the resultingfield equations of the theory to the weakest field limit of approximation. Wealso compute the geodesic equation of the resulting theory and show that it hasan extra force, a fact that commonly appears in general matter-curvaturecouplings. This arxiv version includes a section at the end with an Erratum.

MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling