Posted by Anjali Kaur on Dec 06, 2021
Numbers, quantification, and numerical applications

Numbers, quantification, and numerical applications

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

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Numbers, quantification, and numerical applications

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

  1. If a + b = c

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




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:

  1. Logical Reasoning – Basics
  2. What are functions?
  3. What is probability?
  4. Relations and functions
  5. Sets and Venn diagram
  6. What are the different types of sets?
  7. Set theory

Happy Learning!

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