DIGIT-SUM METHOD

All the techniques that I have discussed till now have emphasized various methods of quick calculation. In this session, I shall discuss the digit-sum method. This method is not used for quick calculation, rather it can be used to verify the answers of various calculations such as multiplication, division, addition, subtraction, squares, square roots, cube roots,etc.

METHOD

At first, we have to convert any given number into a single digit by respectively adding up all digits of that number.

Example: a)The digit sum of 2467539 is-

2+4+6+7+5+3+9=36

Now, we take the number 36 and add its digits 3+6=9

Thus, the digit sum of 2467539 is 9.

b) The digit sum of 56768439 is-

5+6+7+6+8+4+3+9=48

4+8 =12

1+2 =3

Thus, the digit sum of 56768439 is 3.

A few more examples:-

Number	Normal digit sum	Numbers left after elimination of 9’s and digits adding up to 9	Digit sum after elimination
1999999	1	1	1
63727	7	7	7
45231	6	231	6
8001579	6	573	6

From the above table we can see that the values of column 1&2 are same.

Note:if the digit sum of a number is 9, then we can eliminate the 9 straight away and the digit sum becomes 0.

examples

1)Verify whether 999816 multiplied by 727235 is 727101188760?

The digit sum of 999816 can be instantly found out by eliminating the three 9’s and the combination of 8+1. The remaining digit is 6, which is the digit sum.

The digit sum of 727235 can be found by the same way, i.e., it is 8.

When 8 is multiplied by 6, the answer is 48 and the digit sum of 48 is 3.

The digit sum of 727101188760 is 3.

Hence, the result is verified.

2) Verify whether 2308682040 divided by 36524 equals 63210?

In this case we can use the formula- Dividend=Divisor*Quotient+Remainder

The digit sum of the dividend is 6

The digit sum of divisor, quotient & remainder is 2,3&0 respectively.

Therefore, 6=2*3+0

Hence, we can assume that our answer is correct.

MATHEMATICAL OPERATION	PROCEDURE FOR CHECKING ANSWER
Multiplication	The digit sum of the multiplicand when multiplied with the digit sum of the multiplier should equal to the digit sum of the product.
Division	Use the formula dividend= divisor*quotient+remainder of the digit sums.
Addition	The digit sum of the final sum should be equal to the digit sums of all the numbers used in the addition process.
Subtraction	The digit sum of the smaller number as subtracted from the digit sum of the bigger number should equal the digit sum of the difference.
Squaring/square-rooting	The digit sum of the square root as multiplied by itself should equal the digit sum of the square. e.g., to verify whether 23 is the square root of 529 Method: The digit sum of 23 is 5 and when 5 is multiplied by itself the answer is 25. The digit sum of 25 is 7 and the digit sum of 529 is also 7.
Cubing/cube rooting	The digit sum cube root when multiplied by itself and once again itself should be equal to the digit sum of the cube. e.g., verify whether 2197 is the cube of 13 Method: The digit sum of 13 is 4. The cube of 4 is 64. The digit sum of 64 is 1 and the digit sum of 2197 is also 1.

Though the digit sum method has many utility in our day to day life, it has a drawback. Even though the digit sum of the answer matches with that of the question, you cannot be 100% sure of its accuracy.

However, if the digit sum of the answer does not match with that of the question then you can be 100% sure that the answer is wrong.