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


(a) Multiplication of two 2 digit numbers.

Ex.1: Find the product 14 X 12

i) The right hand most digit of the multiplicand, the first number (14) i.e.,4 is
multiplied by the right hand most digit of the multiplier, the second number
(12) i.e., 2. The product 4 X 2 = 8 forms the right hand most part of the answer.

ii) Now, diagonally multiply the first digit of the multiplicand (14) i.e., 4 and
second digit of the multiplier (12)i.e., 1 (answer 4 X 1=4); then multiply the
second digit of the multiplicand i.e.,1 and first digit of the multiplier i.e., 2
(answer 1 X 2 = 2); add these two i.e.,4 + 2 = 6. It gives the next, i.e., second
digit of the answer. Hence second digit of the answer is 6.

iii) Now, multiply the second digit of the multiplicand i.e., 1 and second digit of
the multiplieri.e., 1 vertically, i.e., 1 X 1 = 1. It gives the left hand most part of
the answer.

Thus the answer is 16 8.