ideals in ring of fractions

Question

Let $S$ be a multiplicative set in a commutative ring $R$ and let $I$ and $J$ be ideals in $R$. If $S^{-1}I =\{a/s|a\in I, s\in S\}$ is the ring of fractions of $I$, how do you show that $S^{-1}(I\cap J)=S^{-1}I\cap S^{-1} J$? (This is Theorem 4.7(ii) in Hungerford.)