Example

One of the most common forms of modular arithmetic that is also a good example is the idea of telling time on a 12 hour clock.

Let’s say you have a flight coming in at 3pm but unfortunately it is delayed with an estimate of 14 hours. What time do you expect this plane to finally land?

Well, one way to think about this is by taking \(14\) and dividing it by \(12\) which gives you a remainder of \(2\). Or in other words \(14 \equiv 2 \pmod{12}\). From this point you add the remainder of \(2\) as well as an am/pm switch to your original 3pm and you should have figured out that the plane will arrive at 5am. So just think, you’ll never be late again.