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Is your MBA a 2010 or 2011 model? I am not sure if this interests you or not, but I have a 2010 model and it runs Sierra terribly - El Capitan runs much better on it, although Mavericks ran far better than both, with Snow Leopard running the best. If you have a 2011, it will probably run Sierra slightly better given the 2011 has the Core i-series CPUs, where as the 2010 has the Core2Duo series CPUs.
 
. . . To macSierra, but I can't because I'm still at OS 10.6. I neglected to keep up with all the software upgrading. My Macbook Air is 6 years old. Can someone kindly put up a link as to where I can the free download for OS 10.7? I'd really appreciate it. Thank you! -Kathryne
You don't need to buy anything to get to Sierra. You'll need to upgrade to 10.11 for free first, which is done by following the process here:
https://support.apple.com/en-us/HT206886
Follow the App Store link there to get the El Capitan installer download, and follow Apple's instructions on upgrading. Then, once 10.11 El Capitan is installed, you can upgrade to Sierra from the App Store.
 
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