Casting Out Nines is a very fast way to sanity check your work. It is a great way to quickly catch most errors. Casting Out Nines can be used when dividing numbers of any size.
It is important to note that Casting Out Nines can tell you if an answer is definitely incorrect. Failing the Casting Out Nines test means that an answer is incorrect. However, passing the Casting Out Nines test still leaves a small potential that an answer can still be incorrect. Therefore, Casting Out Nines can tell you if an answer is wrong but it cannot confirm that it is right.
Casting Out Nines will not catch an error in digit reversal. For example, finding the answer as 43 instead of 34 in the division problem. Use Casting Out Elevens in order to catch digit reversal errors.
Step 1
Find the digit sum for each number being divided AND for the answer.
748 digit sum is 1
22 digit sum is 4
34 digit sum is 7
Step 2
Multiply the digit sum of the division problems answer by the digit sum of number you are dividing by.
7 x 4 = 28
Step 3
Find the digit sum of the answer in Step 2.
28 digit sum is 1
Step 4
The division problems answer is probably correct if the digit sum found in Step 3 and the digit sum of the number being divided are the same.
748 digit sum is 1
28 digit sum is 1
1 = 1 so 34 is probably correct.
Remainders
For division problems with remainders simply subtract the remainder from the number being divided before proceeding with the rest Casting Out Nines for division check.
752 / 22 = 34 Remainder 4
752 - 4 = 748
So, the problem becomes 748 / 22 = 34 for the Casting Out Nines check.