You have a very small drive but fast 16 gig. I would think you would
only want 1 operating system on this drive. How much RAM do you have installed?
You have a LVM partition with 11 gig Fedora and on sda3 looks to be a /boot partition of 528 meg for fedora. And 3 gig or so for Ubuntu on sda1. With the extended partition holding a 1 gig swap in sda5.
We can delete all partitions except sda1 and then resize sda1 to take all but 1 gig at end and make new 1 gig for swap at end of drive being sda2. (gparted will make all sda#'s for you)
Put in your live Cd and or USB and open a app called gparted and give us a screenshot (live cd is install Cd using Try Ubuntu)
if you can.
If not right click on all partitions to the right of sda1 in gparted and delete them.
right click on sda1 resize sda1 to take up all but 1 gig. Now right click on 1 gig left over and make new partition and make it swap. You must hit green apply arrow after each instance to make it happen.
While in the Live CD (the same place you ran the boot script from.)
Now open a terminal and copy and paste this.
sudo mount /dev/sda1 /mnt
Grub for Ubuntu is now reinstalled in mbr (master boot record) or your drive and will
sudo grub-install --root-directory=/mnt /dev/sda
boot off of the files in sda1 your Ubuntu install.
Below is graphic for running gparted
to get rid of all and resize sda1 to take all of drive but 1 gig. ( you will now have a Ubuntu partition sda1 of 15 gig and a 1 gig swap to take up all of your 16 gig drive.
HowToPartition - Community Ubuntu Documentation