### Digit-Sum Method

This method is not used for quick calculations in vedic maths but it helps in verifying the answers.This technique has a wonderful application for the students giving competitive exams as they are already provided four alternative to every answer.

The digit-sum method can be used to check answers involving multiplication, division, addition, adtaction, squares, square roots, cube roots etc. The procedure is very simple.. We have to convert any given number into a single digit by repetitive adding of all the digits of that number.

The digit sum of 2467539

Ans: The number is 2468539

We add all the digits of that number

2+4+6+8+5+3+9 = 37

and 1+0=1

Example

Find the digit - Sum of 67769539

Ans: 6+7+7+6+9+5+3+9=51

5+1=6

Now we shall solve a variety of examples involving different arithmetical operations.

Example.

Verify 467532 multiplied by 107777 equals 50389196364

Ans. First calculate the digit sum of multiplicand and then calculate the digit-sum of multiplier.

The digit sum of 467532 is 9

The digit sum of 107777 is 2

When we multiply 9 X 2 we get answer 18

Again the digit sum of 18 is 9

Now we will get the digit sum of the product 50389196364, it comes out 9.

Hence we assume that the answer is correct.

Example 2

Varify whether 2308682040 divided by 36524 equals 63210.

We will use the same formula that we learnt in school.

Dividend=Divisor X Quotient + Remainder

2308682040 = 36524 X 63210 + remainder (0)

we have written the reminder 0 because we assume it as 0.

But, here we will use the digit-sum

6= 2X3 +0

6=6 We assume the answer is correct.

ONE MORE SHORT CUT WHILE CALCULATING DIGIT SUM OF A NUMBER, YOU CAN ELIMINATE ALL THE NINES AND THE NUMBERS THAT ADD-UP T0 NINE. SUPPOSE YOU HATWO 9'S IN A NUMBER AND 3 AND 6 THEN 2 AND 7 YOU CAN ELIMINATE ALL THESE WHILE TOTALLING.

This elimination will have no effect on the final result.

Example

Find the digit-sum of 6372819923.

6+3+7+2+8+1+9+9+2+3 = 50 and 5+0=5

Short cut: Eliminate 9's and numbers add up to nine.

eliminate 6,3 7,2 8,1 9 9

What is left 2+3=5

NOTE: IF THE DIGIT SUM OF A NUMBER IS 9, ELIMINATE 9 AND THE DIGIT SUM BECOMES "0"

Example :MULTIPLICATION

Q: Varify whether 999816 multiplied by 727235 is 727101188750

Ans: The digit sum of 999816 can be instantly found by eliminating 9's and 8 and 1.The remaining is 6

The digit sum of 727235 is 8

The digit sum of 727101188750 is 2

The digit sum doesn't match, so the answer is wrong.