(A + B) mod C = (A mod C + B mod C) mod C We can also perform calculations on modulo operations. Let's sum up what we've learned about different representations of modulo operations – all those statements below are equivalents: Modular arithmetic is, generally speaking, an arithmetic system for integers, where numbers 'wrap around' a certain number. If the modulo definition doesn't appeal to you, and you're still unsure how to calculate modulo, have a look at the next paragraph, and everything should become crystal clear. Otherwise, the number r is the remainder of the division, where x is the dividend, and y is the divisor. Is true if such an integer q (called quotient) exists, then: y * q + r = x. In mathematics, there are many types of more elaborate modulo operations that require more thought. Modulo operations in the case of the clock are so intuitive we don't even notice them. You just calculated you will wake up at 7 am 🕖. To find the correct answer, you need to perform a modulo operation (mod 12) – you add these two numbers, and keep subtracting 12 until you get a number lower than 12. You can't just add 8 to 11, as there is no such time as 19 am. You wonder what the time will be when you wake up after 8 hours of sleep.
Let's say it is late at night – 11 pm 🕚.
