# Vedic Mathematics Shortcuts for Multiplication - Lesson 1

Friends, we have already discussed some Special Cases of Vedic math Multiplication in our last post. Today we shall discuss a simple method to perform multiplications. This method is called "Nikhilam Method". In this method the process of multiplication is carried out with the aid of basic Vedic formulae such as "Nikhilam navatascaramam Dasatah".

In this Nikhilam method selecting the base pays a vital role. Generally, we consider 10, 100, 1000..... so on, as bases depending on the given problem. The symbol of Nikhilam depends on the number. Suppose, 8 is the given number and we consider the nearest 10 as the base then 2 as Nikhilam. The symbol of the Nikhilam is (-) because we are getting the Nikhilam by subtracting the number from teh base. In the same way if 13 is the given number and we consider the nearest 10 as the base then 3 is the Nikhilam and the symbol of Nikhilam is (+) because we are getting the number by adding the Nikhilam to the base. In other words we can say Nikhilam is (+) if the number is greater than the base and Nikhilam is (-) if the number is less than the base. Also, these symbols play a vital role in all the calculations which is explained in detail through the following examples.

Example : 1 Let us consider a small example 8 X 7

Solution :

Method 1 : (Direct Method)
Let us consider the base as 10
• Step 1 : Arrange the numbers in the specific order. Find Nikhilam of each of them and note down on the right side to them.
• Step 2 : Write down the symbol of Nikhilam.
• Step 4 : Now, multiply the numbers in right hand side. Here, we get 2X3=6. Keep the product in the right side of the answer row. Remove the separating mark, we get the required answer.
Method 2 : (Cross subtraction Method) {This method is applicable when the two given numbers are less than the base}
Here, in this method again consider the base as 10.  Arrange the numbers in the specific order. Find Nikhilam of each of them (2 and 3) and write to the right of them. Write down the symbol of Nikhilam. Here, we get (-), because both 8 and 7 are less than the base 10. Now we should apply the operation cross subtraction. That means, we have to subtract either the number right bottom from left top or right top from left bottom. Here, in the present example (8-3) or (7-2) in both the cases we get the same as 5 which is to be taken as the left part of the answer and the remaining right part of the answer is same as in the Method 1, the product of Nikhilam, is 6 and the answer is 56.
Example : II) Find the product 13 X 14.
Solution :
Method 1 : (Direct Method)
Let us consider the base as 10.
Step 1 : Arrange the numbers in the specific order. Find Nikhilam of each of them and write down to the right of the given digits.
Step 2 : Write down the symbol of Nikhilam
Step 3 : Add the given numbers (here 13 and 14). We get 27. Now, subtract the base 10 from 27 we get 17. Keep 17 in the left side of the answer row and keep a separating mark between teh left side and the right side of the answer row as shown in the example.
Step 4 : Now, multiply the number in right hand side. Here, we get 3X4=12. Keep the product in the right side of the answer row. Remove the separating mark, we get the required answer after adding the subscript (1) to 17. That is 182.
That's all for now friends. In our next post we shall discuss some more multiplication shortcuts with examples.

Answers to the Last Post's (Special Cases of Multiplication) Exercises :
1. 4225
2. 7225
3. 9025
4. 5625
5. 3025
6. 15625
7. 18225
8. 21025
9. 27225
10. 11025
11. 30625
12. 24025
13. 65021
14. 126024
15. 207009
16. 429016
17. 731021
18. 912009 Rupali Shete (M.Sc., M.Phil., Ph.D) is a gold medalist from Osmania University (Hyderabad), one of the working members of Rananujan Mathematics Academy and Institute of Scientific Research on Vedas (ISERVE), Currently working in University of Pune.

1. Thank you for sharing valuable method. Really Interesting. Kindly Provide the Method for Division also. I'm eagerly waiting.

2. 1. we r eagerly waiting for review of todays exam

3. thank you

4. Hi mam/sir
We Use The "Antyayordasakepi" For Numbrs Like 56*54, 65*65, 78*72.
Wt is The Shortcut For Numbrs Whose Sum Of Units Digits Is Not 10.
For Exampl 54*53, 79*73, 67*64,..........etc