VEDIC MATHS-32

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 32 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Base method of multiplication"

The base method of multiplication is having large contribution in Vedic Mathematics. The name Base method is given by Vedic Mathematics in western countries. 

Actual Sanskrit sutra as given by Swamiji to define this system is:

‘Nikhilam Navatascaramam Dasatah.’ It means ‘all from 9 and the last from 10.’

For all practical purposes, we shall be calling the system elaborated in this chapter as the 'Nikhilam method' or simply the ‘Base Method'.

This method is used to multiply numbers. It is helpful in many  cases where traditional multiplication takes a long time to calculate the answer. Let us take the case of multiplying the number 9999999 by 9999991. 

If you go by the traditional method it will take a long time to multiply the numbers and calculate the product. However with the technique described in the Base Method one can find the answer in less than 5 seconds. The study of the Base Method is important to understand the other formulae of Vedic Mathematics.

There is a corollary of the Base Method which is called the Yavadunam Rule. This sutra is used in squaring numbers that we will discussed in the next post of our blogs.

Reference:

We had already learn about "Concept relating to Base" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-31".

4 primary steps that we have to use while solving problem by base method of multiplication:
  1. Find the base and Difference
  2. Number of digit on the RHS = Number of zeroes in the base
  3. Multiply the difference on The RHS
  4. Put the Cross Answer on the LHS
Examples:
  
1.       9 7
       * 9 9
    ------------

STEP1: Find the Base and the Difference

Here in this example, both the number are closer to 100 and we know that as a base we can take only power of 10's thus we will take 100 as a base.
In this example, the difference between 100 and 97 is 3 and the difference between 100 and 99 is 1.
After completing step 1, the question look as given below:

                 100
             9 7  -  3
          *  9 9  -  1
         ------------------


STEP 2: Number of digit on the RHS = Number of zeroes in the base

In the example, base 100 has two zeros. Hence, the RHS will be filled in by two-digit number.

                 100
             9 7  -  3
          *  9 9  -  1
         ------------------
                     | _ _


STEP 3: Multiply the difference on The RHS

In this example, we multiply the difference , viz.. -3 by -1 and get the answer as 3. However, the RHS has to be filled by two-digit number. hence we convert the answer 3 into 03 and put it on RHS.

                 100
             9 7  -  3
          *  9 9  -  1
         -----------------
                    | 03

STEP 4:  Put the cross answer in the LHS

In given example, the cross answer can be obtained by doing (97 - 1) or (99 - 3). in either case the answer will be 96. This 96 we will put on the LHS. But we already had 03 on the RHS.

Thus out multiplication process is complete.

                 100
             9 7  -  3
          *  9 9  -  1
         ------------------
              9 6 | 03

Hence complete answer is 9603.


2.       9 9 8 9
       *  9 9 9 5
    -------------------

STEP1: Find the Base and the Difference

Here in this example, both the number are closer to 10000 and we know that as a base we can take only power of 10's thus we will take 10000 as a base.
In this example, the difference between 10000 and 9989 is 11 and the difference between 10000 and 9995 is 5.
After completing step 1, the question look as given below:

                     10000
             9 9 8 9  -  1 1
         *  9 9 9 5  -     5
         --------------------------


STEP 2: Number of digit on the RHS = Number of zeroes in the base

In the example, base 10000 has four zeros. Hence, the RHS will be filled in by two-digit number.

                     10000
             9 9 8 9  -  1 1
         *  9 9 9 5  -     5
         ---------------------------
                          | _ _ _ _
 
STEP 3: Multiply the difference on The RHS

In this example, we multiply the difference , viz.. --11 by -5 and get the answer as 55. However, the RHS has to be filled by four-digit number. hence we convert the answer 55 into 0055 and put it on RHS.

                     10000
             9 9 8 9  -  1 1
          *  9 9 9 5  -    5
         -----------------------------
                          | 0 0 5 5

STEP 4:  Put the cross answer in the LHS

In given example, the cross answer can be obtained by doing (9989 - 5) or (9997 - 11). in either case the answer will be 9984. This 96 we will put on the LHS. But we already had 0055 on the RHS.

Thus out multiplication process is complete.

                     10000
             9 9 8 9  -  1 1
          *  9 9 9 5  -    5
         ------------------------------
              9 9 8 4 | 0 0 5 5

Hence complete answer is 99840055.

At first glance, this system might appear too cumbersome and lengthy. In fact, we have taken more than single page to solve one simple examples. However, because I was explaining the technique for the first time, I elaborated every single step and provided explanation for it. Thus, it appears lengthy. In reality it is not so and will be evident by the examples that we solve next.
Hence, undoubtedly the Base Method has a lot of utility in terms of getting instant answers.

3.Multiply 9750 by 9998

Since both the numbers are closer to 10000, we take it as the base.

The difference between 10000 and 9750 is 250 and the difference between 10000 and 9998 is 2. 

Next, the base 10000 has four zeros and hence the RHS will be filled by a four-digit answer.

Next, we multiply -250 by -2 and write the answer as 0500 (converting it into a four-digit number) and putting it on the RHS. Finally, we subtract 2 from 9750 and put it on the LHS. 

                     10000
             9 7 5 0  -  2 5 0
          * 9 9 9 8  -         2
         ------------------------------
              9 7 4 8 | 0 5 0 0

The final answer is 97480500.

Examples:

Find multiplication of following:

  1. 667*997=664999
  2. 808*999=807192
  3. 9988*9996=99840048
  4. 9500*9991=94914500
  5. 123456*100001=12345723456
The simplicity of this method can be vouched from examples given above.


You may try following example:

Find Multiplication of followings

1. 977 * 980

2. 1230 * 1003

3. 10020 * 10020

You may answer this in comment box. You may ask your any query or doubt in comment box. I will try to resolve as early as possible.

In next blog we will discuss about "Example of Base method of multiplication when the number of digits in RHS exceeds number of zeros in the Base".     


Are you excited for this?...
Then, please wait for it.
I will post my new blog in next week.

We will meet very soon through our next  blog. Till that stay connected, stay healthy and stay safe.

Thanks

for giving your valuable time.

Good day😊.

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