Multiplication of 3 digit number lesser than base
Multiplication of three-digit numbers
In Vedic Maths, Multiplication of three numbers can be done by Nikhilam Sutra (Base Method)
Case 2:- When both Numbers are lesser than Base (1000)
For Example :- 992 x 997
Step 1 –
| Number | Base | Difference |
|---|---|---|
| 992 (X1) | 1000 (Y) | - 8 (Z1) |
| 997 (X2) | 1000 (Y) | - 3 (Z2) |
Y= nearest power of 10 i.e. 10, 100, 1000, 10000.
Thus nearest power of 10 to the number 992 and 997 is 1000.
Z 1 = X 1 – Y, Z 2 = X 2 – Y (here Y is greater than X Therefore Z will be negative)
Step 2 -
| Part A | Part B |
|---|---|
| 992-3 | (-8) x (-3) |
| 989 | 24 |
Part A = (X1 + Z 2)
Part B = Z1 x Z2
Step 3 -
| Part A | Part B |
|---|---|
| 989 | 24 |
| 989 | 024 |
Ans :- 989024
Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Here no. of zeros in base is greater than no. of digits in part B so we added one zero before number in part B
Now Club Part A with Part B for Final Answer
Another Example of Three Digit Numbers lesser than Base
995 x 993
Step 1 –
| Number | Base | Difference |
|---|---|---|
| 995 (X1) | 1000 (Y) | - 5 (Z1) |
| 993 (X2) | 1000 (Y) | - 7 (Z2) |
Y= nearest power of 10 i.e 10, 100, 1000, 10000.
Thus nearest power of 10 to the number 995 and 993 is 100.
Z 1 = X 1 – Y, Z 2 = X 2 – Y (here Y is greater than X therefore Z will be negative)
Step 2 -
| Part A | Part B |
|---|---|
| 995- 7 | (-5) x (-7) |
| 988 | 35 |
Part A = (X1 + Z 2)
Part B = Z1 x Z2
Step 3 -
| Part A | Part B |
|---|---|
| 988 | 35 |
| 988 | 035 |
Ans :- 988035
Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Here no. of zeros in base is greater than no. of digits in part B so we added one zero before number in Part B
Now Club Part A with Part B for Final Answer.