Works for subtraction also.

468,745 - 327, 395 = 141,350.

Add the digits of the first number, 468,745, and you get 34. Cast out the nines. In this case, there are three 9s, which equals 27. 34 minus 27 equals 7.

Add the digits of the second number, 327,395, and you get 29. Cast out nines leaving 2.

7-2 equals 5.

Add the digits of the answer, 141,350, to get 14. Cast out the only nine and the answer is 5.

Since 5 equals 5, the answer of 141,350 is correct.

Works equally well for addition and division.