Nikhilam Sutra Division – All from 9 and last from 10
Division using Vedic Mathematics when Divisor is CLOSER and SLIGHTLY SMALLER than power of 10.
Stuff you need to know before starting:
In this post I will guide you through the vedic maths division by nikhilam method. But before starting with shortcut to divide numbers using Nikhilam Sutra, you need to go through the concepts of Vinculum, How to play with Quotients and Remainders and Nikhilam Sutra.
- Vinculum & Concept of playing with Quotients and Remainders
- Nikhilam Method of Multiplication (This will help you to understand meaning of Nikhilam)
# 12/9.(See Below)
- 9 is 1(deficiency) less than 10(nearest power of 10). (that 1 is written in white color below divisor in below example)
- Split Dividend in 2 parts (Quotient & Remainder) in such a way Remainder to
have same number of digits as that of Divisor. In this case its 1 digit.
- Take 1st digit – 1 down as it is.
- Multiply the above deficiency (1) with the 1 and put
below 2 and add them column wise.
- Thus Quotient=1 & Remainder=3.
# 3483/99.(See Below)
- 99 is 01(deficiency) less than 100(nearest power of 10). (Concept of Nikhilam – All from 9 and last from 10)
- Split Dividend in 2 parts (Quotient & Remainder) in such a way Remainder to have same number of digits as that of Divisor. In this case its 2 digits.
- Take 1st digit – 3 down as it is .
- Multiply the above deficiency (01) with the 3 and put them below 4 and 8(as shown), add 1st column (4+0=4).
- Multiply the above deficiency (01) with the 4 now and put in next columns (as shown), add 1st column (8+3+0=11).
- In General, Repeat this process till a number comes in last column. In this example a number (4) has appeared in last column so stop here and add columnwise.
- Q = 34 and R = 117. But we know concept that Remainder can NEVER be >= Divisor. As R(117) > D(99) Apply ‘Method of How to play with Quotients and Remainders‘ i.e. Divide 117 by 99 gives Sub-Quotient = 1 and Sub-Remainder = 18. Add Sub-Quotient(1) with original Quotient (34) = 35 and now sub-Remainder becomes our Final Remainder.
- Thus Quotient=35 & Remainder=18.
Also Read => More Division Sutras in Vedic Mathematics
Similarly apply same process for rest of the examples.
Again…Vinculum can be applied whenever we have bigger digits in either Quotient or Remainder.
In above example we had 172…We can convert it to Vinculum for more simplication.
Lets see similar problem in which we can convert to Vinculum and then apply Nikhilam.
Eg: 167388/87 = ? … (As Quotient is having bigger digits convert it to Vinculum Number).
Nikhilam Division Tips:
- Do not fail to consider 0/0’s after subtraction in initial case of Divisor. (1000-996 = 004)
- We can convert the deficiency to Vinculum Number for simplicity. For above example divisor 828 is 172 less than 1000, so we had to multiply by 7’s. You can convert 172 to vinculum number i.e. 2(bar3)2 and then apply Nikhilam to avoid multiplication with 7’s.
In above examples we obtained answers in terms of Quotient and Remainders. But if we need answers in form of Decimal still we can apply same Sutra.
# 3483/99 (same above example but in terms of Decimal Point)
- Split Dividend in 2 parts in such a way later part to have same digits as that of Divisor. In this case its 2 digits.
- Append Zeroes’s at end of dividend as shown below.
- Now apply same discussed process .Only stop when you feel stopping or till required number of digits after decimal point.
- In previous examples, if Remainder obtained >= Divisor then we divide and carry forward thus obtained quotient and add with the quotient obtained earlier and New remainder becomes actual remainder. But since in this process we have answer in terms of decimal, we just carry forward if any carry forward present. Hence we carry forwarded 1 as it is to add with 34.
- Decimal point will come at same place from where Remainder would have started.
- Final Answer: 35.1818(till 4 digits)
Similarly find answer for above examples in decimal form (HomeWork :))
What You Think ????
How the following examples can be solved using Nikhilam Sutra !!!
|1) 2345 / 97
2) 873457 / 972
3) 3523 / 922
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