How to Check Division Problems

If you’re new here, you may want to subscribe to my RSS feed. Thanks for visiting!

They way we are usually taught to check division problems in school is unnecessarily complex. There is a better way. I always wondered why, after thousands of years of mathematics, schools generally haven’t figured that out. But I’d rather try solving the Riemann zeta-hypothesis than figure out why schools teach the way they do.

An astute reader in Iceland (yes, we get readers from the coolest places!) asked the following question:

I have a minor problem regarding crunching division problem. How would you crunch a problem like 275 divided by 11 = 25?

By crunching, he is referring to the method of checking your answer that is taught in “The See-Say-Write Method of Speed Addition“. If you haven’t gotten that booklet, the following post may not mean anything to you.
That is one of the reasons why I continually recommend that booklet. It’s not just about adding. The checking method is at least as valuable as the addition technique.

By the way, another benefit of the S-S-W method is that it is the key to performing large multiplications. Yes, you read that right. When you get into speed-addition, you will find that the hardest part about it is the mental addition involved with it. S-S-W is the perfect solution for that.

Here is something interesting about checking division by crunching - You might think that, just as with multiplication, you just plug in the crunched numbers in the operation, and compare them to the original problem.

Warning: this method does not tell you if your place value is correct, just if the digits are correct.

That works fine if there is no remainder.

In the case of 275 div 11 = 25:

So the crunch for the problem is 7.

So the crunch for the answer is also 7.

That means that as far as the digits are concerned, the answer is probably correct.

Warning: This method does not tell you if your place value is correct, just if the digits is correct.

Another example to check would be:

100 divided 4 = 25

When you crunch 100 you get 1

So the crunch for the problem is 7.

And the crunch for the answer is 7.

Looks good to me.

Let’s try one that gives us a remainder, though. It’s a little trickier.

354/9 = 39 remainder 3

So the answer is 3, remainder 3.
The check doesn’t work, but the answer is right.

So we have to go about it another way. You know that you normally check division by multiplying the quotient (answer) by thedivisor (the number you are dividing by).

So normally, to check 100/4=25, you’d multiply 25×4=100 and see if that’s right.

We can do the same thing with crunching. Take the above problem:

354/9 = 39 remainder 3

So the crunch to the problem is 0, remainder 3

So the crunch to the answer is 0, remainder 3

The crunch to the problem matches the crunch to the answer, so the answer is very probably right.

Let’s take one more problem to “lock it in.”

8432/64 = 131 r. 48

So the crunch to the problem is 5, remainder 48

So the crunch to the answer is 5, remainder 48

The crunch to the problem matches the crunch to the answer, so the answer is very probably right.

In a nutshell:
The way to check division is to use multiplication, but with crunching.

I’d like to mention, that even if you do understand what we are talking about by crunching, “The See-Say-Write Method of Speed Addition” teaches many subtleties and shortcuts to it.

Next posts will be about a shortcut for doing divisions, to make your work much easier. It helps with doing it on paper, as well as doing it mentally.

Tags: