Congruence relation

Okay kiddo, let me try to explain congruence relation to you in a simple way.

Do you know what congruent means? It means when two things have the same shape and size. For example, if you have two identical cookies, we can say they are congruent cookies.

Now, in math, we use the term congruence relation to compare numbers. Let's say we have two numbers, 4 and 9. They are not equal to each other, but we can say that they are related to each other under the congruence relation.

How do we know if two numbers are related under a congruence relation? Well, we use something called a modulus. A modulus is like a rulebook that tells us how to compare numbers. For example, if we use modulus 5, we say that 4 is congruent to 9 (mod 5) because when we divide both of them by 5, they leave the same remainder (4 and 9 both leave a remainder of 4 when divided by 5).

So, when we say that 4 is congruent to 9 (mod 5), we mean that 4 and 9 are related under the modulus 5 rule. We use the symbol “≡” to represent the concept of a congruence relation between numbers. So, we can write 4 ≡ 9 (mod 5) to show that they are related under the modulus 5 rule.

I hope that helps you understand congruence relation, kiddo!