Check numbers are a method of checking addition. Sometimes, this is called Casting out Nines. Check numbers also works with subtraction, multiplication, and division. I like to think of check numbers as a cool tool for my math toolbox. Some people use check numbers frequently, others, not so much. However, if we don’t let people know about these cool things, we’ll never know who might use them!

Let’s look at how to find check numbers, then how to apply them. We also have a presentation on check numbers for you to review. Check numbers are first taught in RightStart™ Mathematics Level D, starting in lesson 47, and Level E, lesson 4, and Math Card Games, game #A63.

**Finding Simple Check Numbers**

Check numbers are one digit numbers from 0 to 8. We will designate the check numbers by using parenthesis.

Let’s start with a simple two-digit number: 17

Add the digits together: 1 + 7 = 8

Check number of 17 is (8).

Now let’s try another: 49

Add the digits together: 4 + 9 = 13

Remember check numbers are only one digit, so we’ll need to take the 13 found above, and continue to add the digits together: 1 + 3 = 4

Check number of 49 is (4).

Another: 99

Add the digits together: 9 + 9 = 18

And again: 1 + 8 = 9

However, remember we said that check numbers are from 0 to 8? There are no 9s. Now what? Well, all 9s are 0s. So, on this example, we have 1 + 8 = 9, and 9 = 0.

Check number of 99 is (0).

Because all 9s = 0s, we have a quick shortcut to help find check number.

Let’s back up to our second example: 49

If 9 = 0, then it looks like this: 4 + 0 = (4),

which is what we had the “long” way. Neat, right?

Let’s reapply to our third example: 99

Well, that’d be: 0 + 0 = (0)

Remember the other name for Check Numbers is Casting Out Nines. If we “cast” the 9s out, which is the same as 0, our work is simplified!

**Finding More Check Numbers**

Let’s find check numbers with a four-digit number: 4639

Add the digits together: 4 + 6 + 3 + 9 = 22

And again: 2 + 2 = 4

Check number of 4639 is (4).

Let’s try this again using some of our newly discovered shortcuts.

Remember, 9 = 0. 4639

We can “cast out” the 9, so now we have: 4 + 6 + 3 + 0

But 6 + 3 = 9, so let’s “cast” that out too! 4 + 0 + 0 + 0 = 4

Well! That was easy! Check number of 4639 is quickly found as (4).

Another one: 7326

See anything to “cast”? How about 7 & 2 and 3 & 6? Check number is (0).

**Applying Check Numbers**

So now that we can find check numbers, let’s use them!

Consider the following equation:

. 4639

+ 7326

. 11965

If you’re like me, you wonder if you added it correctly and often will double check either by recalculating and/or checking on a calculator. We can check accuracy by using check numbers!

So, figure the check numbers:

. 4639 (4)

+ 7326 (0)

. 11965 (4)

Look at the check numbers! (4)+(0)=(4)!

Let’s do another:

. 364

+ 4426

Calculate the answer then calculate the check numbers. Did you do it right?

Should look like this:

. 364 (4)

+ 4426 (7)

. 4790 (2)

and the check numbers are correct too.

Now, let’s assume you came up with a wrong sum (which happens) and it looked like this:

. 364 (4)

+ 4426 (7)

. 4780 (1) ERROR

Notice now how the check numbers don’t add up. (4) + (7) does not equal (1). This becomes our check! We now know something is wrong and needs to be corrected.

**More Applying Check Numbers**

As we can see, check numbers are a method of checking and verifying addition calculations. If the check numbers are not adding up, the answer is probably wrong.

Remember that check numbers work with subtraction, multiplication, and division? We’re going to save that for another post. Meanwhile, play around and see what you discover! Stay tuned……

Jen says

Thank you for this little tutorial. For some reason I could not grasp this idea in the text. The one “ooooh” for me was “casting out nines”. Thank you, thank you! Now I can come back to my daughter tomorrow with a clearer understanding.

Thanks-very well explainedl

Can you please give an example of using check numbers to verify an answer in division?

thank you!

Hi, Kelly. Here is a link to our pre-recorded webinars. https://rightstartmath.com/resources/pre-recorded-webinars/ Here you can view a webinar on check numbers. If you move to the 13.38 time marker on the webinar, you will see an example of using check numbers for division. Hopefully, that will help!

Have a great day!

I am currently working on check numbers with my son but I notice in the curriculum that Right Start mentions that check numbers do not always work out. So, my question is, can you explain when and why they wouldn’t work out, and what is the purpose of check numbers if they aren’t always helpful? I think this is an amazing technique and I want to be able to fully understand it so I can explain it and allow my son to utilize it properly when it will benefit him. Thank you!

Mandy – good question! Check numbers always work, but they might not identify a problem in your calculations.

For example, let’s look at 34 + 87 = 121.

Check numbers are now in parentheses:

34 (7)

+ 87 (6)

= 121 (4)

Other than I didn’t draw the underline, it looks good, right? No problem with the check numbers adding up.

Now let’s say we made an error and came up with 34 + 87 = 112. I added 7 and 4 wrong, then forgot to add the ten. Let’s check our work with check numbers….

34 (7)

+ 87 (6)

= 112 (4)

What? The check numbers are good: 7 + 6 = 13, which is 4. So check numbers didn’t catch my error! Happily, it will catch most errors. Here we made two errors which ended up with the check numbers looking good, even though my calculations on the problem was wrong. Most of the time, we’re off one number and generally don’t make multiple mistakes in calculations.

So, are they fool-proof? No. Do the catch a LOT of errors? YES! Are they useful? ABSOLUTELY!!

Thank you! I finally understood it after reading this. It wasn’t explained well in the text. This is neat! Thank you

Did you ever post how to use these with multiplication and division??? I’m having trouble finding it.

Hi, Carolyn.

Thank you for your post. Here is a link to our pre-recorded webinars: https://rightstartmath.com/resources/pre-recorded-webinars/. If you scroll down, you will see Check Numbers. This video will show you how to use check numbers for addition, subtraction, multiplication and division.

Let us know if you have any additional questions.

Rachel Anderson

Struggling to explain check numbers to my children using subtraction, for example:

7452 (0) — 5603 (5) = 1849 (4)

I do not understand how to demonstrate that the check numbers work in this type of problem. Thanks for your help!

Hi,

So, subtraction is a little different from addition. Let’s look at the problem you list:

7452 – 5603 = 1849

That could also be written as:

1849 + 5603 = 7452, right?

That is how we are going to do the check numbers. In subtraction, we are going to add the difference (or remainder) + the subtrahend = the minuend. Let’s look at your problem again:

7452 (0) – 5603 (5) = 1849 (4); 4 + 5 = 9, which cancels to 0.

Does that help?

If you have any additional questions, please do not hesitate to repost here, or you can email us at [email protected].

Have a great day!

Rachel