Urdhva Tiryagbhyam

Feeling lengthy to use the multiplication technique taught at school....??

Now  we will discuss a method which is very powerful technique that can be use to multiply any n-digit number with any other n-digit number..

First let us understand this technique with the below figure.

From the above figure we can understand how the multiplication is performed using Urdhva Technique.

Step 1:    Initially the number in the unit’s digit is multiplied i.e. vertical multiplication.

Step 2:   The number in the unit’s digit of one number is multiplied with the tens digit of other  number in the criss crosses way.

Step 3:   The number in the unit’s digit is multiplied with the number in the hundreds digit in a  criss crosses way and the number in the tens digits are multiplied in a vertical way.

Step 4:   The number in the tens digit of a number is multiplied with hundreds digit of other    number in a criss cross way.

Step 5:   The number in the hundreds digit are multiplied i.e. vertical multiplication is carried      out.

Now let us take two three digit decimal numbers and understand the Urdhva technique in a better way. Let the first number be 123 and the second number be 456.

           Explaining of Urdhava Thiryagbhyam sutra with an example showing of  3-bit  numbers

Step 1:   Initially the unit’s digit numbers are multiplied and the unit’s digit of the                     

              product i.e. 8 is kept as the unit’s digit of the result, the carry 1 is kept aside.

Step 2:  The unit’s digit of the first number is multiplied with the tens digit of the second number and vice versa and both the products i.e. 12, 15 are added with the carry i.e. 1 which we attained in the step1. Now the units digit of the total sum i.e.8 is kept as the tens digit of the result and the carry i.e. 2 is kept aside.

Step 3:  The number in the unit’s digit of first number is multiplied with the number in the hundreds digit of second number and vice versa, the number in the tens digit are also multiplied. Now the sums of all the products i.e. 6, 12, 10 are added with the carry i.e. 2 which we attained in the step2. Now the units digit of the total sum i.e. 0 is kept as the hundreds digit of the result and the carry i.e. 3 is kept aside.

Step 4:  The number in the tens digit of first number is multiplied with the number in the hundreds digit of second number and vice versa and the products i.e. 5, 8 are added with the carry i.e. 3 which we attained in the step3. Now the unit’s digit of the total sum i.e. 6 is kept as the thousands digit and the carry i.e. 1 is kept aside.

Step 5:   The number in the hundreds digit of both the numbers are multiplied and the product i.e. 4 is added with the carry i.e. 1 attained in the step4. Now the result of the sum i.e. 5 is kept in the ten thousands digit.

Thus the product of the two numbers 123 and 456 is 56088.

This technique can be generalized even for N*N multiplication.