"From 9 to Infinity: The Art of Multiplying by Numbers Like 9, 99, 999 and so on........"

    Hi friends, in this blog we will learn how to multiply numbers having the series of 9, 99, 999, 9999 and so on. In this vlog we will use "Ekanyunena Purvena" technique of Vedic mathematics. This will simplify the process of complex traditional method of multiplication and you will be able to perform the complex multiplication by just looking at the numbers.

   "Ekanyunena Purvena" is an important Sanskrit term in Vedic mathematics, meaning "By one less than the previous one." This is often used in problems where numbers like 9, 99, 999, etc., are involved, and it refers to a method for simplifying multiplication by working with the number just less than the given number (e.g., 8 for 9, 98 for 99, 998 for 999).

     We can simply do the problem such as a X 9, ab X 99, abc X 999, abcd X 9999, a X 99, abcde X 99, abc X 99999 and beyond, quickly without any delay. 

Lets start with some simple examples such as 777 X 999, 77 X 99 and 7 X 9,

777 X 999 = ??????

We will do it in two steps, In (i) step we will substract one from the 777,

777 - 001 = 7 7 6

This number 776 will be the first, three digit of our answer. So,

777 X 999 = 776???

In step (ii), we will substract the 776 from 999 as follows,

999 - 776 = 2 2 3

The above mentioned number will be the remaining digits of our answer, by writing both the number together, we will get the answer of 777 X 999 such as,

777 X 999 = 776223

    That's it, isn't it wonderful.

Similarly you can solve 77 X 99 as follows,

77 X 99 = ????

We will do it in two steps, In (i) step we will substract one from the 77,

77 - 01 = 7 6

This number 76 will be the first, two digit of our answer. So,

77 X 99 = 76??

In step (ii), we will substract the 76 from 99 as follows,

99 - 76 = 2 3

The above mentioned number will be the remaining digits of our answer, by writing both the number together,, we will get the answer of 77 X 99 such as,

77 X 99 = 7623

Now you can solve easily 777777 X 999999, 77777777 X 99999999 in very easy way.

  Lets take some more examples such as 662 X 999, 4843 X 9999, 54326 X 99999,

For demonstration, I will choose 54326 X 99999 = ??????????

54326 X 99999 = ????

We will do it in two steps, In (i) step we will substract one from the 54326,

54326 - 00001 = 5 4 3 2 5

This number 54325 will be the first, five digit of our answer. So,

54326 X 99999 = 54325?????

In step (ii), we will substract the 54325 from 99999 as follows,

99999 - 54325 = 4 5 6 7 4

The above mentioned number will be the remaining digits of our answer, by writing both the number together, we will get the answer of 54326 X 99999 such as,

54326 X 99999 = 5432545674

Now you can do it mentally just by looking at the numbers, the answer of 662 X 999 will be 661338 and the answer of 4843 X 9999 will be 48425157.

Do the following problems by yourself and become a master of mental calculations,

1) 483 X 99999

2) 2460 X 99

3) 3465 X 99

4) 894 X 99999

5) 62 X 999