Let I and J be ideals of a ring R and let I be contained in J.

Show that J/I is an ideal of R/I and also show that (R/I)/(J/I) is isomorphic to R/J.

For the second part I am just trying to use a ring homomorphism but am having trouble defining a map.

Also if there is a better way to do the first part than to show that J/I is a sub ring and then an ideal that would be awesome.

Thanks.