The method of eliminating nine is a method of checking addition, subtraction, multiplication and division. The application of nine division can be traced back to Sassanian dynasty. At that time, Islamic cultural trade flourished, and the nine division was produced to check the calculation in the transaction.

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.

Baidu encyclopedia-nine ways to get rid of it