This method is also called the nines-remainder method. The concept of digit-sum consists of this:
1. We get the digit-sum of a number by " adding across the number. For instance, the digit-sum of 13022 is 1 plus 3 plus 0 plus 2 plus 2 is 8.
II. We always reduce the digit-sum to a single figure if it is not already a single figure. For instance, the digit-sum of 5264 is 5 plus 2 plus 6 plus 4 is 8 (17, or 1 plus 7 is 8).
III. In" adding across " a number, we may drop out 9's. Thus, if we happen to notice two digits that add up to 9, such as 2 and 7, we ignore both of them; so the digit-sum of 990919 is 1 at a glance. (If we add up 9's we get the same result.)
IV. Because" nines don't count " in this process, as we saw in III, a digit-sum of 9 is the same as a digit-sum of zero. The digit-sum of 441, for example, is zero.
# Quick Addition of Digit-sum: When we are" adding across" a number, as soon as our running total reaches two digits we add these two together, and go ahead with
a single digit as our new running total.
For example: To get the digit-sum of 886542932851 we do like: 8 plus 8 is 16, a two-figure number. We reduce this 16 to a single figure: 1 plus 6 is 7. We go ahead with this 7; 7 plus 6 is 4 (13, or 1 + 3 = 4), 4 plus 5 is 9, forget it. 4 plus 2 is 6. Forget 9 .... Proceeding this way we get the digit-sum equal to 7.
For decimals we work exactly the same way. But we don't pay any attention to the decimal point. The digit-
sum of 6.256, for example, is 1.
Note: It is not necessary in a practical sense to understand why the method works, but you will see how
interesting this is. The basic fact is that the reduced digit-sum is the same as the remainder when the number is divided by 9.
For example: Digit-sum of 523 is 1. And also when 523 is divided by 9, we get the remainder 1.
