Throwing out Nines (9’s)
After applying an arithmetic operation
to two operands and getting a result, you can use this procedure to improve
your confidence that the result is correct.
1.
Sum the digits of the first operand;
any 9’s (or sets of digits that add up to 9) can be counted as 0.
2. If the resulting sum has two or more
digits, sum those digits as in step one; repeat this step until the resulting
sum has only one digit.
3.
Repeat steps one and two with the
second operand. You now have two one-digit numbers, one condensed from the
first operand and the other condensed from the second operand. (These one-digit
numbers are also the remainders you would end up with if you divided the
original operands by 9; mathematically speaking, they're the original operands
modulo 9.)
4.
Apply the originally specified
operation to the two condensed operands, and then apply the summing-of-digits
procedure to the result of the operation.
5.
Sum the digits of the result you
originally obtained for the original calculation.
6. If the result of step 4 does not equal
the result of step 5, then the original answer is wrong. If the two results
match, then the original answer may be right, though it isn't guaranteed to be.
Say you've calculated that 6338×79 equals 500702
1.
Sum the digits of 6338: (6+3=9, so
count that as) 0 +3+8=11
2.
Iterate as needed: 1 + 1 = 2
3.
Sum the digits of 79: 7 + (9 counted as
0) = 7
4. Perform the original operation on the
condensed operands, and sum digits: 2 × 7 = 14; 1 + 4 = 5
5.
Sum the digits of 500702: 5 + 0 + 0 +
(7 + 0 + 2 = 9, which counts as 0) = 5
6. 5 = 5, so there's a good chance that we
were right that 6338 × 79 equals 500702.
You can use the same procedure with
multiple operands; just repeat steps 1 and 2 for each operand.
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