Number magic: not actually magic

A thing I've seen around the internet is "if you add your age to the last two digits of your birth year, it is 111! magic!" - I've tried explaining why this isn't magic, but haven't made it as simple and clear as nbisby on the opera blog. To paraphrase:

• Consider your age is (2011 - yearborn)
• The last two digits of your birth year is (yearborn - 1900)
• Added together is (2011 - yearborn) + (yearborn - 1900)
• The year you were born cancels out:
• 2011 - 1900 = 111

The magic where you have a ring of numbers, and no matter where you start the instructions always have you finish in the same place, use similar cancelling-itself-out tricks :3