VEDIC MATHS-38

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VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 38 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Application Digit-Sum Method-1".

Digit-Sum Method:

All the techniques that we have discussed in previous posts till now have emphasized various methods of quick calculation. They have helped us in reducing our time  in some cases provided the final answer without any actual calculation.

In this post, we will study the digit-sum method. This method is not used for quick calculation but only  for quick checking of answers. It will help us verify the answer that we have obtained to a particular question.

Although the digit-sum method is discussed by Jagadguru Bharati Krishna Maharaj in his study, mathematicians in other parts of the world were aware of this principle even before the thesis of Swamiji was published. Prof. Jackaw Trachtenberg and other mathematicians have dealt with this principle in their research work.

Reference:

We had already learn about "Digit-Sum Method" our previous blog. If you have missed my last blog then please visit "VEDIC MATHS-37".

Example:

(Multiplication)
1) Verify whether 467532 multiplied by 107777 equals 50389196364
  1. We will calculate the digit-sum of the multiplicand. 
  2. Then, we will calculate the digit-sum of the multiplier. 
  3. Multiply the two digit-sums thus obtained. 
  4. If the final answer equals to the digit sum of the product then our answer can be concluded to be correct
The digit sum of 467532 is 9.
The digit sum of 107777 is 2.
When we multiply 9 by 2 we get the answer 18. Again the digit sum of 18 is 9.
Thus, the digit-sum of the completed multiplication procedure is 9 which is LHS of the equation.
Now, we will check the digit-sum of the product.
The digit sum of 50389196364 is also 9 which is RHS of the equation. 
The digit sum of the LHS equals to the digit sum of the RHS.
hence we can assume that the product is correct.


2) Verify whether 999816 multiplied by 727235 is 727101188760
  1. We will calculate the digit-sum of the multiplicand. 
  2. Then, we will calculate the digit-sum of the multiplier. 
  3. Multiply the two digit-sums thus obtained. 
  4. If the final answer equals to the digit sum of the product then our answer can be concluded to be correct
The digit sum of 999816 is 6.
The digit sum of 727235 is 8.
When we multiply 6 by 8 we get the answer 48. Again the digit sum of 48 is 12, again the digit sum is 3.
Thus, the digit-sum of the completed multiplication procedure is 3 which is LHS of the equation.
Now, we will check the digit-sum of the product.
The digit sum of 727101188760 is also 2 which is RHS of the equation. 
The digit sum of the LHS not equals to the digit sum of the RHS.
hence we can assume that the product is wrong.


(Division)
1) Verify whether 2308682040 divided by 36524 equals 63210

We can use the formula,
Dividend = Divisor x Quotient + Remainder.
In this case we will be using the same formula but instead of the actual answers we will be using their digit-sums.
The digit-sum of Dividend is 6 which is LHS of equation.
The digit sum of divisor, quotient and remainder is 2, 3, and 0 respectively.
2 × 3 + 0 = 6 which is RHS of equation.
The digit sum of the LHS equals to the digit sum of the RHS.
hence we can assume that the product is correct.

(Addition)
1) Verify whether 18273645 plus 9988888 plus 6300852 plus 11111111 is 45674496.

The digit-sum of the numbers 18273645, 9988888, 6300852 & 11111111 is 0, 4, 6 and 8 respectively.
The total of these four digit sum is 18 and the digit sum of 18 is 9.
The digit sum of 45674496 is also 9.
and hence the sum is correct.


Verify whether the following answers are correct or incorrect without actual calculation.
  1. 95123 × 66666 = 6341469918 is correct
  2. 838102050 divided by 12345 = 67890 is correct.
  3. 475210 + 936111 + 315270 = 726591 is Incorrect.
The simplicity of this method can be vouched from examples given above.


You may try following example:
Verify whether the following answers are correct or incorrect without actual calculation.

1..45679 * 4579 = 209164241 

2. 6582170 - 9999999 = -3417829

3. 9999999 - 6582170 = 3417829

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 Digit-Sum Method-2".     


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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