Can't create partition on free space with Disk Utility
Your volume Macintosh HD is a Core Storage Logical Volume and part of a Core Storage volume group and thus can't be modified by iPartition or Disk Utility.

You have to boot from an external disk, a thumb drive or in the Internet Recovery Mode to be able to modify the volume with some Terminal commands.

The following diskutil cs resizeStack command is vastly undocumented and as such potentially destructive.

Please backup your Mac OS X before proceeding.

A 2nd computer or an iPhone with the stackexchange credentials to enter the site or the chat is usefull.

Please start Terminal from /Applications/Utilities and enter  diskutil cs list to get an impression.

Example output of diskutil cs list  

$ diskutil cs list
CoreStorage logical volume groups (1 found)
|
+-- Logical Volume Group 08436957-C5CD-4DC6-B9FA-05B51A3EEFC8
    =========================================================
    Name:         Macintosh HD
    Status:       Online
    Size:         86908663234 B (80.94 GB)
    Free Space:   35364864 B (35.4 MB)
    |
    +-&lt; Physical Volume FFC67A8D-65A8-415E-A594-D7A6BED71844
    |   ----------------------------------------------------
    |   Index:    0
    |   Disk:     disk0s2
    |   Status:   Online
    |   Size:     86908663234 B (80.94 GB)
    |
    +-&gt; Logical Volume Family 56C0E988-502B-43D5-90DD-EFBE58143896
        ----------------------------------------------------------
        Encryption Status:       Unlocked
        Encryption Type:         None
        Conversion Status:       NoConversion
        Conversion Direction:    -none-
        Has Encrypted Extents:   No
        Fully Secure:            No
        Passphrase Required:     No
        |
        +-&gt; Logical Volume 4F26F5C3-8D94-419F-AFF1-B652E9DCDEF4
            ---------------------------------------------------
            Disk:                  disk1
            Status:                Online
            Size (Total):          86479166504 B (80.54 GB)
            Conversion Progress:   -none-
            Revertible:            No
            LV Name:               Macintosh HD
            Volume Name:           Macintosh HD
            Content Hint:          Apple_HFS


Your Mac OS X partition (Macintosh HD) visible on the desktop is equivalent to the Logical Volume F26F5C3-8D94-419F-AFF1-B652E9DCDEF4. 

Reclaim the free space:



After resizing some dozens of disks with diskutil cs resizeStack LVUUID I never had a problem with the Recovery HD. So step 1-6 may be considered dispensable and you may directly start with step 7.




First you have to backup your Recovery HD: Start Terminal.app and enter
defaults write com.apple.DiskUtility DUDebugMenuEnabled 1 press enter and quit Terminal.app
Start Disk Utility and enable 'Show every Partition' in the Debug menu
After a few seconds all partitions should be visible
Choose Recovery HD on the left side and mount the partition Recovery HD


Verify the disk


Create a disk image of Recovery HD and save it read-only externally


Check the disk image for restore


Detach all external drives
Restart into Internet Recovery Mode by pressing altcmdR
or a bootable Mavericks or Yosemite Thumb Drive (full system or install).
start Terminal from the menubar/utilities
enter following command at the Terminal prompt: 


  diskutil cs list

Copy the Logical Volume (LV) alphanumeric UUID of your CoreStorage volume. The LVUUID should be the fourth listed. In the above example the alphanumeric is:
F26F5C3-8D94-419F-AFF1-B652E9DCDEF4.
Run the following command:  

diskutil cs resizeStack LVUUID partsize  


According to the number found above it would be:  

diskutil cs resizeStack F26F5C3-8D94-419F-AFF1-B652E9DCDEF4 100%


If you get an error ("A percentage value (100%) cannot be specified for this operation.") use this instead:

diskutil cs resizeStack F26F5C3-8D94-419F-AFF1-B652E9DCDEF4 0g


This will hopefully expand your CoreStorage volume to allmost full 120 GB. Depending on your disk this will take several seconds (SSD) or minutes (HDD). After a successful resize check with diskutil list if the  Recovery HD still exists.
Quit Terminal.app and start Disk Utility and verify the expanded volume.
Reboot to Recovery HD and your main drive. Delete the disk image created in step 5 if everything works as expected