Easy verification - Beejank method

Easy Verification –Beejank method

As a general practice, after completing any mathematical problem, we will do the calculations again for verification which will end up in taking almost the same time as was taken to solve the question the previous time. In vedic mathematics, we do not have to redo the entire sum to verify if we have done the calculations correctly. It just takes a few seconds to verify if our answers are correct, however big the calculations be, whatever be the operations be. Sounds interesting, right?! Let us see the power of vedic mathematics in verifying the arithmetic calculations.

The Vedic sutra – “Gunita Samuccayah” means “the whole product is same”. It means that the operations carried out with the numbers have same effect when the same operations are carried out with their Beejanks. We will use this method here.

What is Beejank

Before going into the actual verification method, we need to understand what “Beejank” means. It is the sum of the digits of any number and the beejank of any number is supposed to be a single digit. Incase the sum of all the digits turns out to be more than 1 digit number, the digits of the sum are inturn added to get the Beejank. This process is repeated till we get a single digit.

Beejank verification method

Let us now see how we can verify using Beejank method.

Step 1: Find the beejank of the numbers given in the question.

Step 2: Apply the operators as given to be applied for the numbers to the respective beejank for addition and multiplication. For subtraction and division, it is slightly different which we will see under respective headings.

Step 3: Find the beejank of the answer we got in our calculation.

Step 4: The result we got from Step 2 and Step 4 should be the same. If not, we can be sure that we have made a mistake in the calculation.

Well, the pratical application is much easier than what is being written here as its definition and rules. So let us move on to working with numbers

Addition operation

3451798 + 2356 + 198345

Let us first solve the question.

3451798 +

      2356 +

  198345

=======

3652499

=======

Now, we will apply the beejank method of verification.

Beejank of 3451798   => 3+4+5+1+7+9+8 = 37 = 3+7 = 10 = 1+0 = 1

Beejank of 2356         => 2+3+5+6 = 16 = 1+6 = 7

Beejank of 198345     => 1+9+8+3+4+5 = 30 = 3+0 = 3

===================================================

Beejank of 3652499   => 3+6+5+2+4+9+9 = 38 = 3+8 = 11 = 1+1 = 2

Since we added all the 3 numbers to get the answer, add the beejanks also,

                                   =>1+7+3 = 11 = 1+1 = 2

We get a beejank of 2 for the given numbers and the answer. Thus verified.

Subtraction operation

78945632 – 35462367

First we will solve the question

78945632-

35462367

=======

43483265

=======

Now, we will apply the beejank method to verify our calculation.

Beejank of 78945632 => 7+8+9+4+5+6+3+2 = 44 = 4+4 = 8

Beejank of 35462367 => 3+5+4+6+2+3+6+7 = 36 = 3+6 = 9

============================================

Beejank of 43483265 => 4+3+4+8+3+2+6+5 = 35 = 3+5 = 8

Since the given problem is subtraction, the immediate way to verify with beejank method is to subtract the beejanks of minuend and subtrahend. Yes, we can do that, but we may have a situation in certain cases as the one we have taken here for illustration, where the beejank of minuend is smaller than the beejank of subtrahend. So the safer way toverify a subtraction problem using beejank, is to add the beejank of difference with the beejank of subtrahend and verify if that the same as the beejank of minuend. Let us do it now.

Beejank of difference, 43483265 is 8 and beejank of subtrahand, 35462367 is 9. So adding them we get, 8 + 9 = 17 = 1+7 =8, which is the same as the beejank of minuend. Thus verified.

Multiplication operation

14506 x 23418

Let us first solve the problem. I am not using any VM method to solve this calculation as the prime focus here is to understand the verification method for the calculations we have done using beejank method. The method to solve multiplications in easy and simpler steps are defined in other topics of this blog.

14506 x 23418

===========

          116048

          14506x

        58024xx

      43518xxx

    29012xxxx

===========

     339701508

===========

Quite a big calculation!! Fine, let us now verify what we did.

Beejank of 14506         => 1+4+5+0+6 = 16 = 1+6 = 7

Beejank of 23418         => 2+3+4+1+8 = 18 = 1+8 = 9

Beejank of 339701508 => 3+3+9+7+1+5+8 = 36 = 3+6 = 9

Product of the beejanks of the given numbers = 7x9 = 63 = 6+3 = 9, which is the same as the beejank of the product we got as answer, thus verified.

Division operation

867359 ÷ 627

627) 867359 (1383

       -627

       ------------

         2403

        -1881

        -----------

         05225

         -5016

        -----------

            2099

          -1881

         ----------

              218

         ----------

The answer is quotient Q=1383 and remainder R=218

Beejank of Quotient, Q    =>  1383 = 1+3+8+3 = 15 = 1+5 = 6

Beejank of remainder, R =>  218   = 2+1+8 = 11 = 1+1 = 2

Beejank of divisor , Dr     =>  627   = 6+2+7 = 15 = 1+5 = 6

Beejank of Dividend , Dd => 867359 = 8+6+7+3+5+9 = 38 = 3+8 = 11 = 1+1 = 2

How do we verify now? It is simple, the same method we use for verifying division problems. 

Dividend = Quotient x Divisor + Remainder. But in our Beejank method, instead of doing with the actual given numbers we will work on their beejanks.

So, QxDr + R = 6 x 6 + 2 = 38 = 3+8 = 11 = 1+1 = 2

Is n’t that great?!!!