Casting Out Elevens is a slightly slower but more accurate way to sanity check your work. It is a great way to catch most errors including digit reversals (transposing two digits).
Casting Out Elevens can be used when adding numbers of any size.
Example
{% scaleimage l502_example.png %}
Step 1
Find the digit sum for each number being added.
52853 digit sum is 9
94829 digit sum is 9
Step 2
Add together each digit sum.
9 + 9 = 18
Step 3
Find the digit sum of the answer in Step 2
18 digit sum is 7
Step 4
Find the digit sum for the addition problems answer.
147682 digit sum is 7
Step 5
The addition problems answer is probably correct if the digit sums found in Step 3 and Step 4 are the same.
7 = 7 so 147682 is probably correct
Bonus
Casting Out Elevens can also be used for checking your work when adding multiple numbers together.
Example
{% scaleimage l502_bonus_example.png %}
89675 digit sum is 3
45914 digit sum is 0
95830 digit sum is 9
64801 digit sum is 0
3 + 0 + 9 + 0 = 12
12 digit sum is 1
296220 digit sum is 1
1 = 1 so 296220 is probably correct