Long Division: Division with Remainders

Contributor: Meghan Vestal. Lesson ID: 11810

When you buy something with cash and have change left over, that can be nice. When you divide numbers and have something left over, no problem! This lesson will teach you how to work with remainders!


Arithmetic, Whole Numbers and Operations

learning style
Auditory, Visual
personality style
Lion, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

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  • Can Sarah evenly divide 13 whole cookies among her four children?

Unfortunately, it is impossible for Sarah to evenly divide 13 cookies among four children without breaking one of the cookies.

Often, when solving long division problems, the divisor will not evenly divide into the dividend.

  • What do you think you should do in these situations?

As long as you know how to solve a long division problem, you can easily solve a problem where the divisor cannot evenly divide the dividend.

If you need a refresher on the steps to solving a long division problem, go back to the first Related Lesson in this Long Division series, found in the right-hand sidebar, to review. Make sure you know how to solve long division problems before proceeding any further with this lesson.

If you have a problem where the divisor will not evenly divide into the dividend, solve the same way you would normally solve a long division problem.

Look at the example below. You know the problem has been solved because there are no numbers left in the dividend to bring down, but there is still one left at the bottom.

  • What do you think you should do next?

It is impossible to divide 349 into six equal parts. Six equal parts can be created, but there is still one remaining. The number(s) that is left over is called the remainder. In this problem, 1 is the remainder.

To show that a number cannot be evenly broken into the number of parts specified, write an "R" and the number of parts remaining next to the quotient. The "R" stands for "Remainder."

Look at the completed example below:

Now, let's review!

Watch Long Division WITH Remainders! Dividing Numbers Fourth Grade Fractions from Math & Learning Videos 4 Kids:

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  • What do you do when solving a division problem that has a remainder?

In the previous Related Lesson (right-hand sidebar), you learned how to check your work when you are finished solving a long division problem.

  • How do you check your work at the end of a problem?

You may be wondering how you check your work when there is a remainder in the quotient. Know what? That remainder does not present a challenge when checking your work!

Do what you normally would do by multiplying the quotient by the divisor (58 x 6 = 348). Then, add the remainder to the product. (348 + 1 = 349).

When you add the remainder to the product, you should get the same number that is in the dividend. If you do not, go back and check your work.

Go back to the problem at the beginning of the lesson. Solve the problem on a separate piece of paper. Make sure to check your work.

  • How would you write the quotient with the remainder?
  • Did you say the answer to the problem is 3 R1?

That is correct!

When you are ready, move on to the Got It? section to continue solving long division problems with remainders.

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