Multiplication By Urdhva Tiryak

Sutra : Urdhva Tiryagbhyaam

Meaning : Vertically and crosswise.

This is the most powerful sutra when it comes to   Vedic Multiplication. 

Consider the following example :

            37 * 33

Step 1 : Write it as follows

                    37

                    33

Step 2 : Multiply the left most column vertically and  write it below.

             Multiply 3 * 3 to get 9

                    37

                    33

                    9

Step 3 : Next multiply diagonally and add

            i.e. (3*3) + (3*7) = 9 + 21 = 30

Since 30 is a 2 digit number put the last digit (here '0' ) next to 9 and the other digits (here '3' ) below 9

                    37

                    33

                    90

                    3

Step 4 :  Now multiply the RHS column and put it below and total to get the Answer.

                    37

                    33

                    901

                    32 

                   1221

  Hence 1221 is the Answer

The Above Steps can be easily remembered by the following line diagrams

1)  2)  3)

This method can be extended for any number of digits.

For 3 digit numbers, the line diagram can be represented as follows

1)  2)   3)

4)  5)

Example

Let us consider 532 * 472

Step 1 :

                    532

                    472

                  20

Step 2 :

                    532

                    472 

                  207

                    4

Step 3 :

                    532

                    472

                  2079

                    43

Step 4 :

                    532

                    472 

                  20790

                    432

Step 5 :

                    532

                    472   

                  207904

                    432   

                  251104     (By Addition)

Hence the Answer is 251104

The Line Diagram for four digits is given below

1)  2)  3)

4)  5)  6)

7)

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