# Numbers, quantification, and numerical applications

Numbers, quantification and numerical applications, applied mathematics, class XII.

Feel free, first join my YouTube channel, Facebook group for applied maths students, subscribe to this website, and get a monthly collated mailer.

## Modulo Arithmetic

Consider the remainder when an integer is divided by another integer.

For example, if a/b, and a = bq+r

where q-quotient

r -remainder

a mod b = r

like 14 mod 5 = 4

## Modulo Addition

- If a + b = c

then, a (mod n) + b (mod n) = c (mod n)

2.

3.

4.

## Modular Subtraction

(A – B) mod C = (A mod C – B mod C) mod C

## Congruence Modulo

Let a,b be two integers and m be a positive integer other than 1. Then ‘a’ is said to be congruent to ‘b’ modulo m, if m divides (a-b).

a = b (mod m)

For example, 123 = 21 (mod 6) why?

(123-21)/6 = 102/6 = 17.

So, yes

a = b (mod m), because m divides (a-b) completely.

Thank You!

You can check the following posts related to applied mathematics:

*Logical Reasoning – Basics*- What are functions?
- What is probability?
- Relations and functions
- Sets and Venn diagram
- What are the different types of sets?
- Set theory

Happy Learning!

*Disclosure: Some of the links on the website are ads, meaning at no additional cost to you, I will earn a commission if you click through or make a purchase. Please support me so that I can continue writing great content for you.*