Construct isomorphism $M\cong M/N+N$?

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I think that $M\cong M/N+N$ holds, where $M,N$ are $R$ modules for a certain ring $R$.

This equality makes sense to me, for example if I take $M=\mathbb{Z}$ and $N=2\mathbb{Z}$ it makes sense. However I cannot construct an isomorphism to show that this actually holds. Can you help me?