We study inhomogeneous Diophantine approximation with rational numbers of reduced form. The central object is the set W ( f , θ ) = { x ∈ [ 0 , 1 ] :∣∣∣x -m + θ ( n )n∣∣∣<f ( n )n for infinitely many coprime pairs m , n } , where { f ( n )}n ∈ N and { θ ( n )}n ∈ N are sequences of real numbers in [ 0 , 1 / 2 ]. We will completely determine the Hausdorff dimension ofW ( f , θ ) in terms of f and θ. As a by-product, we also obtain a new sufficient condition forW ( f , θ )to have full Lebesgue measure; this result is closely related to the Duffin – Schaeffer conjecture with extra conditions.