VEDIC MATHS-56

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 56 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Application of vinculum multiplication and Division"

The technique of vinculum is very powerful and provides us with a method to convert digits in a number which are greater than 5, to digits less than 5. 
After the conversion, all arithmetic operations are carried out using the converted number, which make the operation very simple and fast.
It is not necessary to convert all the digits but a judicious conversion of certain digits (above 5) can decrease the computation effort considerably. 

VINCULUM NUMBER:
The numbers which by presentation contains both positive and negative digits are called vinculum numbers.

We will begin by seeing the method to convert any given number to its vinculum equivalent and back to its original value.

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

Reference:

We had already learn about "Concept of vinculum number & Conversion of general numbers into vinculum numbers" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-53".

We had already learn about "Concept of vinculum number & Conversion of  vinculum numbers into general numbers" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-54".

We had already learn about "Application of vinculum addition and subtraction" in our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-55".

a) Application of vinculum multiplication :

We have already observed the application of Vedic sutras in multiplication.
  • Base method of multiplication from blog number 31 to blog number 35 .
  • Multiplication based on 'Urdhva-Tiryak' Sutra from blog number 14 to 19.
Let us recall them.

The computation can be simplified further if we convert the non-vinculum digits to vinculum digits. We will see the method below.

Example :

1. 69 * 48
            _
6 9 = 7 1_
 4 8  = 5 2
Now, we will carry out a cross multiplication of these two numbers:
                    _
             7     1
   *                _
             5     2
------------------------------
              _     _
3   5  :   1     9   :  2
               _                                 
=  34  :  9  :  2              
( Carry 1 to left and  add it to 35 to get 34 )
=  33  :  1  :  2
=  3312

Answer :
69 * 48 = 3312.

2. 882 * 297

The corresponding vinculum digits are
                _
8 8 2 = 9 2 2 
(We convert the 8 in the ten’s place and do not convert the 8 in the hundred’s place) 
                   _
2 9 7 =3 0 3
Now, we will carry out a cross multiplication of these two numbers.
                      _
             9  2  2
   *                 _
             3  0  3
------------------------------
          _   _ _         _
 2 7 : 6 : 2 1 : 6 : 6
             _   _         _                 
=  2 7 : 8 : 1 : 6 : 6              
=  2 6 : 1 : 9 : 5 : 4
=  261954

Answer :
882 * 297 = 261954.

b) Application of vinculum division    

Division is carried out by the same technique ( Base method of division & substitution method) as explained before in blog number 44 to blog number 48.

The computation can be simplified further if we convert the non-vinculum digits to vinculum digits.

Solve the following example.
  1. 189 * 278 = 52542
  2. 77.7 * 5.78 = 449.106
  3. 1279 / 59 = 21.67777
  4. 49492 / 572 = 86.52447

The simplicity of this method can be vouched from examples given above.

You may try following example:
       
1. 97 * 38 
2. 69 * 88
3. 7251 / 49

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 "Application of vinculum square and cube".     

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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