Multiplication of two digit numbers by Bhārati Kṛṣṇa Tīrtha

The general formula of multiplication which will be applicable to multiplication of any number.

Here the Sūtra

ऊर्ध्वतिर्यग्भ्याम्

Ūrdhvatiryagbhyām

(vertical and crosswise)

will be used.

Multiplication of a 2 digit number with 2 digit number

Step-1

Step 1 : Vertically multiply the two digits in the right column

Step-2

Step 2 : Cross multiply the first digit of the first column with the second digit of the second column. Second digit of the first column with the first digit of the second column and add the two products.

Step-3

Step 3: Vertically multiply the two digits in the left column

Example : 21 X 32

	Left Column	Right Column
First Digit	2	1
Second Digit	3	2

Step 1: Vertically multiply the two digits in the right column - 1 X 2 = 2

Step 2: Cross multiply the first digit of the right column with the second digit of the left column. Second digit of the right column with the first digit of the left column and add the two products. - (1 X 3) + (2 X 2) = 3 + 4 = 7

Step 3: Vertically multiply the two digits in the left column - 2 X 3 = 6

Step 4  : Put the above values got from each step in the below table.

Step 3	Step 2	Step 1
6	7	2

Answer : 21 X 32 = 672

Example : 41 X 15

	Left Column	Right Column
First Digit	4	1
Second Digit	1	5

Step 1: Vertically multiply the two digits in the right column - 1 X 5 = 5

Step 2: Cross multiply the first digit of the right column with the second digit of the left column. Second digit of the right column with the first digit of the left column and add the two products. - (1 X 1) + (5 X 4) = 1 + 20 = 21

Step 3: Vertically multiply the two digits in the left column - 4 X 1 = 4

Step 4  : Put the above values got from each step in the below table.

Step 3	Step 2	Step 1
4	21	5
4	Put 1 and carry over 2	5
4 + Carry over (2)	1	5
6	1	5

Answer : 41 X 15 = 615

Example : 72 X 56

	Left Column	Right Column
First Digit	7	2
Second Digit	5	6

Step 1: Vertically multiply the two digits in the right column - 2 X 6 = 12

Step 2: Cross multiply the first digit of the right column with the second digit of the left column. Second digit of the right column with the first digit of the left column and add the two products. - (2 X 5) + (6 X 7) = 10 + 42 = 52

Step 3: Vertically multiply the two digits in the left column - 7 X 5 = 35

Step 4  : Put the above values got from each step in the below table.

Step 3	Step 2	Step 1
35	52	12
35	52	Put 2 and carry over 1
35	52 + Carry over (1)	2
35	53	2
35	Put 3 and carry over 5	2
35 + Carry over (5)	3	2
40	3	2

Answer : 72 X 56 = 4032

See Also

दो अंकों की संख्याओं का गुणन - भारती कृष्ण तीर्थ