There are two seperate things you are trying to do:
Get rid of the version of UBUNTU you no-longer want and
make better use of the space it used to take up.
Your suggested course of action:
Not quite, there is one more step which is to re-size your existing partition in order to make use of the space you just freed up. How to do this depends on weather or not you are using LVM (logical volume management).
The easiest way to tell what kind of volumes you are using is to look at /etc/fstab