Brake and Make Easy Sum Methods

Digit Sums of Perfect Squares

žAll Perfect Squares

  end in 1, 4, 5, 6, 9 or 0

                            and

  digit sums are 1, 4, 7 or 9

Example :4539

  ends in 9

  digit sum is 3

  Therefore, 4539 is not a perfect square

Example 5776

         ends in 6

  digit sum is 7

  Therefore, 5776 may be a perfect square  

9 Point Circle & Digital Sum

Methods of finding Digit Sum

Casting Out 9’s

žWhen finding the Digit Sum of a number,

  9’s can be “cast out”

žThe Digit Sum of 94993 is 4+3 = 7

  “cast out” the 9’s.

ž

When finding the Digit Sum of a number,

  Group of numbers that sum to 9 can be “cast out”.

ž

The Digit Sum of 549673 is 7

  “cast out” the 5+4, 9 and 6+3, leaving just 7

žBy Casting Out 9’s,

  Finding a Digit Sum can be done more quickly and mentally!

FEW FACTS OF DIGIT SUM

žA number is divisible by 3 if its digital Sum is divisible by 3 (that is, it is 0, 3, 6, or 9).

○1236 is divisible by 3 because 3 is divisible by 3.

○Note (1+2+3+6 = 12) and (1+2 = 3).

○Recall: 1x(999+1) + 2x(99+1) + 3x(9+1) + 6

ž   If the sum of the digits is greater than 9, then sum the digits of the result again until the result is less than 10

žA number is divisible by 9 if its digital Sum is divisible by 9 (that is, it is 0 or 9).

The digital Sum of a number is the remainder obtained by dividing it by 9.

žDigital Sums can be calculated quickly by casting out 9s.
More Facts OF DIGIT SUM

Digital Sum of a square is 1, 4, 7, 9 or 0

žDigital Sum of a perfect cube is 1, 8 or 9

žDigital Sum of a prime number (except 3) is 1, 2, 4, 5, 7, or 8

žDigital Sum of a power of 2 is 1, 2, 4, 5, 7, or 8

žDigital Sum of multiple of 9 is always 9.

žDigital Sum does not affect adding 9 to a number.

ž

Digit Sum /Digital Sum/Digital Root
      When the Samuccaya is the Same it is Zero

•Digit : The word digit stands for single figure number; the number.

•Single figure numbers : 1,2,3,4,5,6,7,8,9 & 0.

•Sum :Means addition

žDigit Sum: A Digit Sum is the sum of all of the digits of a number and is found by adding all of the digits of a number’

1. •Adding again if required till the time it becomes single digit number.
2. žKeep finding the Digit Sum of the result until it’s less than 10

ž0 and 9 are equivalent!

žDigital Sum of a number is the single digit number obtained by repeatedly summing all the digits of a number.

žThe digital root of  a number is also the reminder we find when that number is divided by 9.

žExample: 

○Digital   Sum  of  2547 = 9

  because (2 + 5 + 4 + 7 = 18) and (1 + 8 = 9)

○Digital   Sum  of  98194 = 4

  because (9 + 8 + 1 + 9 + 4 = 31) and (3 + 1 = 4)