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**Nikhilam**.

**Nikhilam**means

**Complement**(please read the process of finding complements from here if you are new to this). This sutra can be used for multiplications in some special cases. If the numbers to be multiplied are nearer to 10, or 100 or 1000 etc., the result can be obtained very easily.

**Important Note :**Having a quick glance of this post wont help you much. Take a pen and paper and practice the following procedure so that you can understand the procedure well.

### Multiplication of numbers which are nearer to 10 (Base 10)

**Example 1 : 9x8 = ?**

####
**Step 1**

i) Complement of 9 = 1

ii) Complement of 8 = 2

iii) Put the above 1 and 2 along with the minus symbol as shown below

####
**Step 2**

i) Put one blank each for both the parts of the results as shown above.

ii) Multiply the complements along with the sign indicator.

iii) (-1) x (-2) = 2

Put this 2 in the RHS blank of the result as shown below

iv) Add the complements to the given numbers cross wise.

9+(-2) = 7 or

8+(-1)=7

v) Put this value in the LHS blank of the result

so, 9 x 8 = 72

**Example 2 :**8 x 7 = ?

So, 8 x 7 = 56

**Note**: in the above examples, the product obtained after multiplication of the complements is less than the base, that is, 10. Hence all the blanks are filled.

###
**When the product of the complements is more than the base**

**Example 3 :**

7 x 6 = ?

In the above example the product of the complements 3 and 4 is 12. But the base of the numbers, that is 10, allows only 1 digit number. As the product is higher than the base, you keep the 2 and write the 1 by side. To avoid confusion, we are writing the product 12 as

_{ 1}**2**.**Present status :**

####
**Step 2 :**

i) Add the complements to the given numbers cross wise.

7+(-4) =3, or, 6+(-3)=3

ii)

**Present Status :**
iii) Add the digit 1 (that was written slightly below and on LHS of 2) to the digit 3. 3+1 = 4

Present Status :

So, 7 x 6 = 42

### Multiplication of the numbers which are nearer to 100 (Base 100)

**Example 4 : 96 x 96 = ?**

#### Step 1:

i) The given numbers are having 100 as the base. Hence the result will have two blanks for each of the two parts.

ii) Complement for the first number 96 = 04

iii) Complement for the second number 96 = 04

iv) Find the product of the complements

(04) x (04) = 16

v) Put this product 16 in the RHS blanks of the result.

vi)

**Present Status :**#### Step 2 :

i) Add the complements to the given numbers cross wise.

ii) 96 + (-04) = 92

iii) Put this value 92 in the LHS blanks of the result.

**Present Status :**

so, 96 x 96 = 9216

**Example 5 : 89 x 89 = ?**

So far, all the numbers that were selected for multiplications are less than the base value. In our next post we shall discuss a technique for multiplication of the numbers

**which are higher than the base**. Happy Reading :)

**About The Author***is a gold medalist from Osmania University (Hyderabad), one of the working members of*

**Rupali Shete (M.Sc., M.Phil., Ph.D)****Rananujan Mathematics Academy**and

**Institute of Scientific Research on Vedas (ISERVE)**, Currently working in

**University of Pune.**

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