If friend have ever multiplied large numbers together, then you know that that is simple to gain lost and also make mistakes.

And periodically it doesn’t assist solving the again come check, specifically if you acquire a various answer the 2nd time. Friend never know which one is correct!

In this pre-Algebra tip, us look in ~ an easy way of checking your answers to multiplication problems.

You are watching: How to check a multiplication problem

We will look at how we have the right to use digit sums to check our multiplication answers.

Digit Sums

The digit sum of a number is found by including all the digits in the number. If the sum is more than one digit, we include all the digits again till we gain a single digit answer.

For example:

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

So the digit sum is 8.

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

The sum is 12 i beg your pardon has much more than one digit, so we repeat the process by adding 1 + 2.

So the digit amount of 57 is 3.

Checking Multiplication by number Sums

When we multiply two numbers, the digit sum of the product of your digit sums will certainly be equal to the digit amount of the product the the initial numbers.

That’s fairly a mouthful!

Let’s take an example so we obtain how an easy it really is:

363 x 11 = 3,993

The digit sum of 363 is 3.

The digit amount 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 same then her multiplication price is most probably correct*.

If the digit sums room not equal, then her answer is certainly incorrect!

< *If your answer has actually the same set of digits as the correct answer favor 3,939, it will offer the exact same digit sum also if it is no correct. >

Multiple an option Questions

If you are given a multiple choice question, girlfriend can likewise use number sums come eliminate options that are definitely wrong.

For example:

What is 352 x 867?

302,514305,184305,284315,284

The digit amount of 352 is 1.

The digit amount of 867 is 3.

So, the digit amount of the answer need to be same to 1 x 3, which provides us 3.

We can remove all the selections that don’t have 3 as the number sum.

This pipeline us with 305,184 as the exactly answer.

See more: How Far Is Chicago From Fort Wayne, In To Chicago, Il, Distance From Fort Wayne, In To Chicago, Il

Did you understand that number sums can likewise be used to examine other arithmetic computations? Read much more about it in thing 2 of the “Algebra Made basic as Arithmetic” book.