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# Base Multiplication Method: Multiplication Short Trick for Aptitude

Base Multiplication method is a easiest method of multiplication of a number which are close to the working bases of powers of 10. In Vedic mathematics it is known as Nikhilam Navatascaramam Dastah (Nikhilam Sutra).

General Formula:

Let the multiplicand and multiplier be x and y respectively, then

### xy = X ( X ± a ± b ) ± ab

where X is working base and a and b are complement of x and y respectively.

This method can be used to solve 4 types of cases.

### Case 1: When both the Numbers are Less Than the Nearest working Base

Let us understand how it works by multiplying 91 X 93

Here, x = 91 & y = 93

Step 1: Select a working base of 10 nearest to the multiplicand and multiplier and define it in X.

Here, X = 100

Step 2: Find the complement of multiplicand and multiplier by finding out it difference from the working base.

Here, complement of 91 on 100 = - 9

complement of 93 on 80 = - 7

- negative sign before complement denotes that number is lesser than the working base.

a = - 9 & b = - 7

Step 3: Put the values in the general formula:

xy = X ( X ± a ± b ) ± ab

79 X 76 = 100 ( 100 - 9 - 7 ) + { ( -9 ) X ( -7 ) }

= 100 X 84 + 63

= 8400 + 63

= 8463

### Case 2: When both the Numbers are Greater Than the Nearest working Base

Let us understand how it works by multiplying 114 X 112

Here, x = 114 & y = 112

Step 1: Select a working base of 10 nearest to the multiplicand and multiplier and define it in X.

Here, X = 100

Step 2: Find the complement of multiplicand and multiplier by finding out it difference from the working base.

Here, complement of 114 on 100 = + 14

complement of 112 on 100 = + 12

+ positive sign before complement denotes that number is greater than the working base.

a = + 14 & b = + 12

Step 3: Put the values in the general formula:

xy = X ( X ± a ± b ) ± ab

114 X 112 = 100 ( 100 + 14 + 12 ) + { ( +14 ) X ( +12 ) }

= 100 X 126 + 168

= 12600 + 8

= 12768

### Case 3: When one number is Less Than working Base and the other is Greater Than working Base

Let us understand how it works by multiplying 1013 X 986

Here, x = 1013 & y = 986

Step 1: Select a working base, a multiple of 10 nearest to the multiplicand and multiplier and define it in X.

Here, X = 1000

Step 2: Find the complement of multiplicand and multiplier by finding out it difference from the working base.

Here, complement of 1013 on 1000 = + 13

complement of 986 on 1000 = - 14

a = + 13 & b = - 14

Step 3: Put the values in the general formula:

xy = X ( X ± a ± b ) ± ab

1013 X 986 = 1000 ( 1000 + 13 - 14 ) + { ( +13 ) X ( -14 ) }

= 1000 X 999 - 182

= 999000 - 182

= 998818

### Case 4: When Numbers are not Nearer to working Base

Let us understand how it works by multiplying 65 X 57

Here, x = 65 & y = 57

Step 1: Select a working base, a multiple of 10 nearest to the multiplicand and multiplier, such that it forms cross sum (left side of the resultant) when multiplied by the number (which is obtained by dividing assumed base by last working base) and it is defined in X.

Here, X = 60

Step 2: Find the complement of multiplicand and multiplier by finding out it difference from the working base.

Here, complement of 65 on 60 = + 5

complement of 57 on 60 = - 3

a = + 5 & b = - 3

Step 3: Put the values in the general formula:

xy = X ( X ± a ± b ) ± ab

65 X 57 = 60 ( 60 + 5 - 3 ) + { ( +5 ) X ( -3 ) }

= 60 X 62 - 15

= 3720 - 15

= 3705

By this method, we can find any product using the nearest multiple of 10 but this method is useful only to the numbers which are nearer to base of powers of 10.

For any other multiplication, go for the cross-multiplication method.
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