Nikhilam mulltiplication is a quick and easy method for multiplying two numbers which are both close to a power of 10, 100, 1000 etc. In this method, the calculations are made easier using a complement or deficiency. You can refer my earlier blog on complements.
To understand this method, let us start with simple multiplication using base 10.
Base 10
multiplying below base 10
We know, 6 x 8 = 48
Lets do this by Nikhilam multiplication.
Here, 10 is the base as both 6 & 8 are nearest to 10.
Step 1
Find the complement of 6 & 8.
Complement of 6 = 4
Complement of 8 = 2
Step 2
Write these complements on RHS with connecting minus sign.
10
6 - 4
X 8 - 2
________
/
Note:-
Minus sign shows that the complements ate both less than 10.
/ is used to distinguish two parts of the answer.
Step 3
On the RHS, vertically multiply the two compliment digits and write it down
4 x 2 = 8
10
6 - 4
X 8 - 2
________
/ 8
Step 4
For LHS, cross subtract
Either 6 - 2 or 8 - 4,
The result will be same i. e. 4
Write down on the left.
10
6 - 4
X8 - 2
__________
4 / 8
So, the final answer is 48
Try one more example
7 x 9
10
7 - 3
9 - 1
________
6 / 3
Multiplying above base 10
When numbers are above base 10 then instead of deficiencies, above the base has surpluses. So the subtraction part changes to addition.
i. e. Cross add instead of cross subtract.
Let's do 12 x 11
Step1
First set down the surpluses 02 and 01.
12 is 2 more than base 10
11 is 1 more than base 10
12 + 02
X 11 + 01
__________
Step 2
Multiply 2 x 1 and write the answer on RHS.
12 + 02
X11 + 01
__________
/ 2
Step 3
Cross add 12 + 1 or 11 + 2 , answer is 13
Write on LHS
12 + 02
X11 + 01
_________
13 / 2
Answer is 132.
Ofcourse, calculations are quicker if we know tables but this method becomes highly useful in higher numbers having the base close to 100, 1000 and so on.
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