Multiplication of two numbers 1< base and another > base


Multiplication of two numbers one is greater than base and another is lesser than base

In Vedic Maths, Multiplication of two numbers can be done by Nikhilam Sutra (Base Method)

For Example:- 104 x 96
Step 1 –

Number Base Difference
104 (X1) 100 (Y) +4 (Z1)
96 (X2) 100 (Y) -4 (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000. Thus nearest power of 10 to the numbers 104 and 96 is 100.
= X – Y, Z = X 2 – Y

Step 2 –

Part A Part B
104 – 4 (+4) x (-4)
100  - 16

Part A = (X1 + Z 2)
Part B = Z1 x Z2 

Step 3 -

Part A Part B
100-1 100- 16
99 84

Ans :- 9984

Rule 2 :- Part B should never be negative so we will borrow 1 from Part A.
Rule 1:- No. of zeros in base is equal to no. of digits in part B. 
Here no. of zeros in base is equal to no. of digits in part B 
Now Club Part A with Part B for Final Answer.

 

Take Another Example:- 112 x 95
Step 1 –

Number Base Difference
112 (X1) 100 (Y) +12 (Z1)
95 (X2) 100 (Y) -5 (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000. Thus nearest power of 10 to the numbers 112 and 95 is 100.
Z 1 = X 1 – Y, Z 2 = X 2 – Y

Step 2 –

Part A Part B
112 – 5 (+12) x (-5)
107 - 60

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 -

Part A Part B
107 - 1 100 - 60
106 40

 Ans :- 10640 

Rule 2 :- Part B should never be negative so we will borrow 1 from Part A.
Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Here no. of zeros in base is equal to no. of digits in part B
Now Club Part A with Part B for Final Answer

Take Another Example:- 1005 x 986
Step 1 –

Number Base Difference
1005 (X1) 1000 (Y) +5 (Z1)
986 (X2) 1000 (Y) -14 (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000. Thus nearest power of 10 to the number           
1005 and 986 is 1000.
Z 1 = X 1 – Y, Z 2 = X 2 – Y

Step 2 –

Part A Part B
1005 – 14 (+5) x (-14)
991 - 70

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 -

Part A Part B
991 - 1 1000 - 70
990 930

Ans :- 990930 

Rule 2 :- Part B should never be negative so we will borrow 1 from Part A. 
Rule 1:- No. of zeros in base is equal to no. of digits in part B. 
Here no. of zeros in base is equal to no. of digits in part B
Now Club Part A with Part B for Final Answer

 

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