How to Check Multiplication Answers Using Digit Sums

If you have ever multiplied large numbers together, then you know that it is easy to get lost and make mistakes.

And sometimes it doesn’t help solving it again to check, especially if you get a different answer the second time. You never know which one is correct!

In this pre-Algebra tip, we look at an easy way of checking your answers to multiplication problems.

We will look at how we can use digit sums to check our multiplication answers.

Digit Sums

The digit sum of a number is found by adding all the digits in the number. If the sum is more than one digit, we add all the digits again until we get a single digit answer.

For example:

To find the digit sum of 35, we add 3 + 5.

So the digit sum is 8.

To find the digit sum of 57, we add 5 + 7.

The sum is 12 which has more than one digit, so we repeat the process by adding 1 + 2.

So the digit sum of 57 is 3.

Checking Multiplication by Digit Sums

When we multiply two numbers, the digit sum of the product of their digit sums will be equal to the digit sum of the product of the original numbers.

That’s quite a mouthful!

Let’s take an example so we get how simple it really is:

363 x 11 = 3,993

The digit sum of 363 is 3.

The digit sum of 11 is 2.

Multiply them together: 3 x 2 = 6

This is equal to the digit sum of 3,993, which is 6.

So, if the digit sums you get are equal then your multiplication answer is most probably correct*.

If the digit sums are not equal, then your answer is definitely incorrect!

[ *If your answer has the same set of digits as the correct answer like 3,939, it will give the same digit sum even if it is not correct. ]

Multiple Choice Questions

If you are given a multiple choice question, you can also use digit sums to eliminate choices that are definitely wrong.

For example:

What is 352 x 867?

1. 1. 302,514
   2. 305,184
   3. 305,284
   4. 315,284

The digit sum of 352 is 1.

The digit sum of 867 is 3.

So, the digit sum of the answer should be equal to 1 x 3, which gives us 3.

We can eliminate all the choices that don’t have 3 as the digit sum.

This leaves us with 305,184 as the correct answer.

Did you know that digit sums can also be used to check other arithmetic computations? Read more about it in Chapter 2 of the “Algebra Made Easy as Arithmetic” book.