Casting out nines is a sanity check to ensure that hand computations of sums, differences, products, and quotients of integer

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

s are correct. By looking at the digital root

Digital root

The digital root of a number is the value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum...

s of the inputs and outputs, the casting-out-nines method can help one check arithmetic calculations. The method is so simple that most schoolchildren can apply it without understanding its mathematical underpinnings.
The method involves converting each number into its "casting-out-nines" equivalent, and then redoing the arithmetic.