In the previous section we read that 0 and 9 in Digit Sums are effectively the same, because adding 9 to any number does not change its Digit Sum.

When finding the Digit Sum of a number, 9’s can be “cast out”.

“Cast Out” means it can be removed or get rid of without impacting the calculation.

For example:

The Digit Sum of 94993 is 9+4+9+9+3 = 34 = 3+4 = 7.
If we “cast out” the 9’s, then Digit Sum of 94993 is 4+3 = 7.
So, you can easily remove the 9s while finding the Digit Sum.

There is another case.

When finding the Digit Sum of a number, group of numbers whose sum is 9 can be “cast out”.

The Digit Sum of 549673 is 7.
Just “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!