Double-Checking Addition Problems

Besides using a calculator, is there any way children can check long columns of numbers they have added? -- Checking Addition
Answer: Actually, there is a fairly easy way to do this. It goes by the names of "digital roots" and "casting out nines" and is easy and fun for children to do. Here is how it works:
1. Add the digits of each number that is being added as many times as needed until you have a single digit. For example, for the number 5,793, add 5 + 7 + 9 + 3 = 24. Then add 2 + 4 = 6 to get a single digit.
2. Now, add the single digits of all the numbers being added. Do this until you get a single digit once more. So if the sum of all the single digits were 37, you would add 3 + 7 = 10, and then add 1 + 0 = 1.
3. Look now at the answer to be checked for correctness. Add all the digits until you have a single digit.
4. If both the sum of the digits in the answer and the sum of the digits in step 2 are equal, the answer that you got for the addition problem is correct.
While most students check subtraction problems by using addition, there is another way similar to the one above.
1. Add the digits of each number in the problem until you get a single digit just like you did for addition.
2. Then subtract the numbers you arrived at and compare this number to the single digit representing the answer.
3. There is one extra twist. If the difference in the single digit sums is a negative number or 0, add 9 to it.
There are several benefits beyond checking answers to having your children use this method. It exposes them to the joy and mystery of math. It makes math fun and magical. And best of all, it gives them a better understanding of the underlying principles of math.
We received these helpful hints from Professor Arthur Benjamin of Harvey Mudd College, who has amused and amazed students all over the world with his rapid-fire calculations. If your children are interested in learning the secrets of mental math, look for them in his latest book, "Secrets of Mental Math."