Methods of finding Digit Sum
Casting Out 9’s
When finding the
Digit Sum of a number,
9’s can be “cast out”
The Digit Sum of
94993 is 4+3 = 7
“cast out” the 9’s.
When finding the
Digit Sum of a number,
Group of numbers that sum to 9 can be “cast
out”.
The Digit Sum of
549673 is 7
“cast out” the 5+4, 9 and 6+3, leaving just 7
By Casting Out 9’s,
Finding a Digit Sum can be done more quickly
and mentally!
FEW FACTS OF DIGIT SUM
FEW FACTS OF DIGIT SUM
A 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
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
A 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.
Digital Sums can be
calculated quickly by casting out 9s.
More Facts OF DIGIT SUM
More Facts OF DIGIT SUM
Digital Sum of a square is 1,
4, 7, 9 or 0
Digital Sum of a perfect cube is 1,
8 or 9
Digital Sum of a prime number
(except 3) is 1, 2, 4, 5, 7, or 8
Digital Sum of a power of 2 is 1,
2, 4, 5, 7, or 8
Digital Sum of multiple of 9 is
always 9.
Digital Sum does not
affect adding 9 to a number.
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