Tensor product/Linear subspaces and residue class spaces/Exercise

Let $U_1\subseteq V_1,U_2\subseteq V_2,\dots ,U_n\subseteq V_n$ be linear subspaces with the residue class spaces $V_1/U_1,\dots ,V_n/U_n$. Does there exist a canonical isomorphism

$(V_1{\otimes }_{}\cdots {\otimes }_{}{V}_n)/(U_1{\otimes }_{}\cdots {\otimes }_{}{U}_n)\cong (V_1/U_1){\otimes }_{}\cdots {\otimes }_{}(V_n/U_n)?$

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