**Multiplication of numbers with a series of 9's**

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** Multiplication of numbers with a series of 9's**

In my seminars , I often have
an audience challenge round . In this round , the audience members ask me to
perform various mental calculations and give them the correct answer . They
generally ask me to multiply numbers which involve a lot of 9's in them . The
general perception is that the higher the number of 9's the tougher it will be
for me to calculate . However , the truth is exactly the opposite - the higher
the number of 9's in the question , the easier it is for me to calculate the
correct answer . I use two methods for this . The first method is given below
and the second method is explained in the chapter ' Base Method of
Multiplication ' .

Using
the method given below , we can multiply any given number with a series of
nines . In other words , we can instantly multiply any number with 99 ,
999,9999 , 99999 , etc.

The technique is divided
into three cases . In the first case , we will be multiplying a given number
with an equal number of nines . In the second case we will be multiplying a
number with a higher number of nines . In the third case , we will be
multiplying a number with a lower number of nines ,

**Case 1 **( Multiplying a number with an equal number of nines )

(
Q ) Multiply 654 by 999

**• ****654 **

**x 999**

**-------**

**=653 346 **

• We subtract 1 from 654 and write half the answer as 653 . Answer at
this stage is 653 . .

• Now we will be dealing with 653. Subtract each of the digits six ,
five and three from nine and write them in the answer one by one ,

• Nine minus six is 3. Nine minus five is 4. Nine minus three is 6
.

• The answer already obtained was 653 and now we suffix to it the digits
3 , 4 and 6. The complete answer is 653346

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( Q ) Multiply 9994 by 9999

**• 9094**

** X9099**

**----------- **

**=9993 0006**

We subtract one from 9994
and write it as 9993. This becomes our left half of the answer . Next , we . ,
447 x 900 subtract each of the digits of 9993 from 9 and write the answer as
0006. This becomes the right half of the answer . The complete answer is
99930006

(Q) Multiply 456789 by 999999

**• ** 156789

x 99999

------------------

=456789
543211

We subtract 1 from
456789 and get the answer 456788. We write this down on the left hand side .
Next , we subtract each of the digits of 456788 ( left hand side ) from 9 and
get 543211 which becomes the right hand part of our answer . The complete
answer is 456788543211

**More examples :**

** ****• **** 7777**

**X 9999 **

**----------**

**=77762223**

**• ****65432**

**X99999**

**-----------**

**=6543134568**

**• ****447**

**X999**

**----------**

**=446553**

**• ****90909**

**X99999**

**-----------**

**=9090809091**

The simplicity of this method can be vouched from the examples given above . Now we move toCase 2. In this case , we will multiply a given number with a higher number of nines .

**Case 2 **

( Multiplying a number with a higher number of nines )

** ( Q )
Multiply 45 with 999 **

45 ** →** 045X999=044955

X 999

--------

There are three nines in the multiplier . However , the
multiplicand 45 has only two digits . So we add a zero and convert 45 to 045
and make it a three digit number . After having done so , we can carry on with
the procedure explained in Case 1

. First we subtract 1 from 045 and write it down as 044. Next ,
we subtract each of the digits of 044 from 9 and write the answer as 955. The
complete answer is 044955 ,

** ( Q ) Multiply
888 with 9999**

**888 0888X9999 = 8879112**

**X9999**

We convert 888 to 0888 and
make the digits equal to the number of nines in the multiplier . Next , we
subtract 1 from 0888 and write the answer as 0887. Finally , we subtract each
digit of 0887 from 9 and write the answer as 9112. The final answer is 08879112
which is 8879112

** ( Q )
Multiply 123 by 99999 **

123 ** →** 00123 X99999 =

x 99999 00122 / 99877

The multiplicand is a three - digit number and the multiplier is a five
- digit number . Therefore we

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add two zeros in the
multiplicand so that the digits are equal in the multiplicand and the
multiplier .

We now subtract 1 from
00123 and write the left hand part of the answer as 00122. Next , we subtract
each of the digits of the left hand part of the answer from 9 and write it down
as 99877 as the right hand part of the answer . The complete answer is
12299877

**Other examples
: **

**• ****162**

** X9999**

**-----------**

**0161/9838**

**• ****5555**

**X99999**

**-----------**

**05554/94445**

**• ****363**

**X999999**

**-------------**

**000362/999637**

We can see that this technique is not only simple and easy to follow , but it also enables one to calculate the answer in the mind itself . This is the uniqueness of these systems . As you read the chapters of this book , you will realize how simple and easy it is to find the answer to virtually any problem of mathematics that one encounters in daily life and especially in the exams . And the approach is so different from the traditional methods of calculation that it makes the whole process enjoyable

**Case 3** of this technique deals with
multiplying a number with a lower number of nines . There is a separate
technique for this in Vedic Mathematics and requires the knowledge of the
Nikhilam Sutra ( explained later in this book ) . However , at this point of
time , we can solve such problems using our normal practices of instant
multiplication .

**( Q ) Multiply 654 by 99 :** In this case the number of digits are more than the number
of nines in the multiplier . Instead of multiplying the number 654 with 99 we
will multiply it with ( 100-1 ) . First we will multiply 654 with 100 and then
we will subtract from it 654 multiplied by

**1.**

**654 **

**X 99**

** **

** 65400 **

**- 654**

**--------------**

** = 64746 **

** ( Q )
Multiply 80020 by 999**

We will multiply 80020 with (
1000 - 1 ) .

80020000

- 800203

---------------

79939980

This method is so obvious that it needs no further
elaboration .