*Contributor: Meghan Vestal. Lesson ID: 11809*

Working hard to solve a problem without checking your work is not a good idea. What if you were designing a rocket or serious medical device? Learn the easy, strategic way to check your long division!

categories

subject

Math

learning style

Visual

personality style

Lion, Beaver

Grade Level

Intermediate (3-5), Middle School (6-8)

Lesson Type

Skill Sharpener

How can you check to see if the following problem has been solved correctly without re-solving the problem?

There are many steps to solving a long division problem — that means there is a lot of room for error.

In the previous **Related Lesson** in our *Long Division* series, found in the right-hand sidebar, you learned how to check your work while you are solving.

- Do you remember how you can check your work as you solve a long division problem?

In addition to checking your work while you solve, there is a simple way to check your work when you are finished solving.

To find out if you have correctly solved the problem, all you need to do is use multiplication to check your work!

- But why multiplication?
- How does that help us if we are doing division?

Well, you will need to remember what you have learned about inverse operations and the relationship between multiplication and division.

(If you need to review this topic, you can visit our lesson found under **Additional Resources** in the right-hand sidebar.)

Let's quickly look at a basic math fact to prove the relationship between division and multiplication:

We can apply this same relationship to the long division problem above.

First, let's make sure we can identify the parts of this division problem:

Now, let's plug what we know into the relationship with multiplication:

Last, check if the multiplication equation is true:

Now, go back and use your long division strategies to re-work and solve the division problem.

Once you solve for the quotient, check your answer using multiplication:

Good job! Now you are ready to check problems on your own!

Visit the *Got It?* section to see if you can find my mistakes!

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