Clock Arithmetic or Modular Arithmetic

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6 + 9 = 3, Is this possible ?? Sometimes, we say this is a fallacy. But in Mathematics has an area that is called Clock Arithmetic or Modular Arithmetic.
A familiar use of the clock arithmetic is in the 12-hour clock. Let’s explain the example. Here 6 means 6 o’clock and 9 means 9 hours later it will be 3:00.
While I was studying in Mathematics at that time I was thinking this is totally bullshit, I could not apply anywhere. Seriously believe me. But I am proud of myself because I have completed my graduation in mathematics.
Modular arithmetic mainly using in the cryptography area. Sample