Binary Operations Involving Modular Arithmetic | SHS 2 CORE MATH

In this video, we are going to look at the topic Modular Arithmetic.
We are going to calculate the value of numbers for a given modulo using binary operations.
Binary operations
Binary means two. Hence binary operations is a rule that combines any two elements in a set S to produce a third element which or may not be in that set.

Properties of Binary Operations
Closure
Commutative
Associative
Distributive.

Modular Arithmetic sometimes referred to as Modular Arithmetic / clock arithmetic is a system a arithmetic for integers, where numbers "wrap around" after they reach a certain value - the modulos.
The best way to introduce modular arithmetic is to consider the face of a 12-hour clock.
It is realized that the numbers go from 1,2,3,4,5,6,7,8,9,10,11,12.
Now lets assume that it is 8 o'clock now, what will be the time in 5 hours? = 1 o'clock
Again assume that it is 10 o'clock now, what will be the time in 4 hours? = 2 o'clock.

Binary operations involving Modulos:
In solving binary operations involving modulos, you first need to solve the binary operation and later you convert the result to modulos.

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What about n raised to power p=n(mod p)