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.
Z 1 = X 1 – Y, Z 2 = 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