Hello there, coyote1964.
It sounds like you are unable to update your Mac OS X to El Capitan because you are getting a "not enough free space" message from your MacBook Air. The following Knowledge Base article offers up some pointers on resolving space issues with your Mac:
OS X: What is "other" space in About This Mac?
To view Storage information for your connected volumes, select About This Mac from the Apple menu, then click the More Info button in the window that appears. Next, click the Storage tab to display storage information

Sometimes the "Other" category in the About This Mac window may seem large. About This Mac uses this category to count any files that aren't recognized as one of the other listed file types (audio, movie, photos, apps, backups). Examples of files that may be calculated as "other" include:
- Items in the OS X folders such as the System folder and caches
- Personal information such as documents, contacts, calendar data
- App Plugins or extensions
- Media files that cannot be classified by Spotlight as a media file because they are located inside of a package
- File types not recognized by Spotlight
Freeing up disk space
If you need to increase the amount of available disk space on your startup drive, examine the items in your home folder. Look in the Documents, Downloads or Desktop folders to see if there are any files you don't need anymore. Use these suggestions to reclaim disk space from these folders:
- Delete items you don't need, or have copies of elsewhere, by dragging them to the Trash.
Once you're sure you don't need the items in the Trash, empty the trash to reclaim disk space. From the Finder, choose Finder > Empty Trash. - Move items to another drive, such as an external hard disk or flash drive.
- Compress items you don't use frequently. Delete the originals of these files and keep the compressed copy instead.
Be sure to only delete items you no longer need, or have copies of elsewhere. It's a good idea to create backups of important files in case you accidentally delete an important item later.
See this article for additional suggestions on how to increase disk space.
Safe Mode and disk space
When your computer is started in Safe Mode, the About This Mac window doesn't try to categorize your disk space. It simply displays all used space as "other". This is expected behavior. Not all features are available in OS X when started in Safe Mode.

If you're still feeling inclined to reinstall OS X as new, the following article provides those steps:
How to reinstall OS X on your Mac
Erase your drive and install OS X
Generally you don't need to erase your startup disk to reinstall OS X. The OS X Installer is designed to allow you to perform an install in place over the same version or earlier versions of OS X. If you're transferring your Mac to a new owner, you might want to erase your built-in startup disk before reinstalling OS X.
Important: Before you erase and reinstall, back up your important files. If you’re using a MacBook, MacBook Air, or MacBook Pro, make sure the power adapter is connected and plugged in while performing these steps.
You can use these steps to erase the files on your startup disk and install a new copy of OS X:
- Before you begin, make sure your Mac is connected to the Internet.
- Restart your Mac. Immediately hold down the Command (⌘) and R keys after you hear the startup sound to start up in OS X Recovery.
- When the Recovery window appears, select Disk Utility then click Continue.
- Select the indented volume name of your startup disk from the left side of the Disk Utility window, then click the Erase tab.
- If you want to securely erase the drive, click Security Options. Select an erase method, then click OK.
- From the Format pop-up menu, select Mac OS Extended (Journaled). Type a name for your disk, then click Erase.
- After the drive is erased, close the Disk Utility window.
- If you’re not connected to the Internet, choose a network from the Wi-Fi menu.
- Select the option to Reinstall OS X.
- Click Continue and follow the onscreen instructions to reinstall OS X.
Additional options
If you want to reinstall the version of OS X that came with your Mac, or if you need to reformat your entire startup disk, hold down Command-Option-R at startup instead. This starts your Mac from Internet Recovery.
If you have more than one partition (like Boot Camp) and you want to erase the entire startup disk, you can use Disk Utility to remove partitions or repartition your drive. Start your Mac from Internet Recovery, then use Disk Utility to repartition your startup disk before you erase it. Make sure you back up any important data from all partitions before repartitioning a drive.
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Kind Regards.