What’s the safest way to resize partitions in a Windows–Ubuntu dual boot?

Shrink the Windows partition from inside Windows using Disk Management. Windows can account for files that Linux tools may not safely move, such as the pagefile, restore points, sparse files, and update data. After that, boot a live Ubuntu environment and use GParted to move or expand the Linux partition into the unallocated space. Back up important data first, and make sure Windows Fast Startup and hibernation are disabled before making changes.

The alternative is to back up your files, erase the Windows partitions, resize the Ubuntu partition, and reinstall Windows. That works, but it requires installation media and a complete Windows reinstall, so it is much more disruptive—especially when both systems are on one drive.

Windows Disk Management is generally the safest choice for reducing the Windows volume because it knows which parts of the filesystem cannot be relocated. It may not let you reclaim every apparently free gigabyte, depending on where those files are located. Once the Windows partition has been reduced, GParted can be used from live media to extend the Linux partition.