Principle: ABC
= 100A+ 10B+ 1C
=(99+ 1)A+(9+ 1)B+ 1C
=99A+9B+(A+B+C)
=9M+(A+B+C)
Therefore, we can know that:
ABC≡A+B+C (mod9)
So in the operation of ABC+DEF=GHI,
ABC+DEF≦(A+B+C)+(D+E+F)≡G+H+I(mod9)
The sum of A+B+C can still be decomposed, and so on.
Extended data:
Checking calculation method
Take1978 6901× 8098678443 =16024774852475143 as an example:
1978690 1 ? 1+9+7+8+6+9+0+ 1=4 1 ? 4+ 1 = 5
8098678443 ? 8+0+9+8+6+7+8+4+4+3 = 57 ? 5+7 = 12 ? 1+2 = 3
160247748582475 143 ? 78 ? 15 ? 1+5 =6
5 × 3 = 15 ? 1+5 =6
Therefore, it is proved that this formula may be correct. If the left and right sides of the equation are the same after removing 9, it means that the equation may be correct. If the results on both sides of the equation are different after removing 9, then the formula must be incorrect.
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