A Casting Out Elevens digit sum is a single digit number used for checking your work. A digit sum can be created for any number. Checking your work by Casting Out Elevens becomes easy when you master creating a digit sum.
There are two different techniques that you can use for creating a Casting Out Elevens digit sum. Choose the one that is easiest for you.
Technique 1
To create a Casting Out Elevens digit sum alternately subtract and add each digit starting from the right.
Example
234526 digit sum is 6
Step 1
Alternately subtract and add each digit starting from the right.
6 - 2 + 5 - 4 + 3 - 2 = 6
If a digit sum yields a number with more than two digits continue calculating the Casting Out Elevens digit sum of the answer until a single digit is reached.
Example
170516 digit sum is 5
6 - 1 + 5 - 0 + 7 - 1 = 16
6 - 1 = 5
If the final Casting Out Elevens digit sum is less than zero then add 11 to it. Remember that in Casting out Elevens adding eleven is essentially the same as adding zero when it comes to the final answer.
Example
158193 digit sum is 2
3 - 9 + 1 - 8 + 5 - 1 = -9
-9 + 11 = 2
Technique 2
To create a Casting Out Elevens digit sum subtract the left most digit from the next digit, then the result from the next digit, and so on until a single digit is reached.
Example
234526 digit sum is 6
Step 1
Subtract the left most digit from the next digit, then the result from the next digit, and so on until a single digit is reached.
2 from 3 = 1
1 from 4 = 3
3 from 5 = 2
2 from 2 = 0
0 from 6 = 6
If a subtraction will lead to a negative answer then first add 11 to the digit to the right. Remember that in Casting out Elevens adding eleven is essentially the same as adding zero when it comes to the final answer.
Example
170516 digit sum is 5
1 from 7 = 6
6 from 0 = -6
-6 is negative so add 11 to zero before doing the subtraction
6 from 11 (0 + 11) = 5
5 from 5 = 0
0 from 1 = 1
1 from 6 = 5
Example
158193 digit sum is 2
1 from 5 = 4
4 from 8 = 4
4 from 12 (1 + 11) = 8
8 from 9 = 1
1 from 3 = 2