Mathemagic by R.Gopalakrishnan,  CPSU Officer (Retd.)

Mathemagic

The concept of ‘Digit Sum’ is of practical utility in that it helps in checking additions and multiplications in Mathematics without actually going the process all again. The Digit Sum method when applied to additions and multiplications makes the method of checking such calculations a mathematical pleasure. Let us, for instance take the following addition:-

Numbers                 Digit sum

34935                       6

45381                        3

57891                        3

138207                     12      =>   3

In order to check up the addition one has to simply find the digit sum of each of the numbers and add them together till a single digit is obtained. Number nine and numbers that add up to nine and multiples of nines found in the actual numbers may be ignored as these will not make any change in the final digit sum. The answer arrived at by the routine method of addition is to be reduced to a single digit by the same way. In the above sum of the digits in the answer is 3 as 1+3+8+2+0+7=3 which tallies with the digit obtained by the check-method. So there is no error in the calculation.

In the same way multiplications can also be checked easily.

e.g.          32×64 =2048,  5×1   =5

Presence of zeroes in the actual numbers is to be noted carefully, in order to eliminate any error in the placement value.