URDHVA TIRYAGBHYAM

Urdhva – tiryagbhyam is the general formula applicable to all cases of multiplication and also in the division of a large number by another large number. It means “Vertically and cross wise.”
Multiplication of two 2 digit numbers.

Ex.1: Find the product 14 X 12
The symbols are operated from right to left .
Step i) :


Step ii) :


Step iii) :


Let us work another problem by placing the carried over digits under the first row and proceed.


Steps:

i) 4 X 6 = 24 : 2, the carried over digit is placed below the second digit.
ii) (3 X 6) + (4 x 1) = 18 + 4 = 22 ; 2, the carried over digit is placed below third digit.
iii) (2 X 6) + (3 X 1) + (4 X 3) = 12 + 3 + 12 = 27 ; 2, the carried over digit is placed below fourth digit.
iv) (2 X 1) + ( 3 X 3) = 2 + 9 = 11; 1, the carried over digit is placed below fifth digit.
v) ( 2 X 3 ) = 6.
vi) Respective digits are added.

General rule for a 3 digit by 3 digit multiplication: