Dividing With a Remainder

Instructor: Jaimee Arnold

Jaimee has worked in elementary school and has her Master's +30.

In this lesson you will learn what to do when you are dividing and you have a number leftover. We will be using basic division steps and learning all about remainders.

Division Reminder

Division is when you take a total and divide it, or break it into equal groups. It's like the brother of multiplication, so you can use what you already know in multiplication to help you solve division problems. For example, 3 x 2 = 6, so if you take 6 and divide it by 2, it will be 3. It is a fact family. (Remember, a fact family is a group of related facts.) This picture helps to show you how division and multiplication are related.

Sometimes when you are dividing, the number doesn't go equally and there is something left over called a remainder. After today's lesson, you will know what to do when you have a division problem that ends up with a remainder.

This fact family shows the relationship between multiplication and division.

Math Vocabulary

In today's lesson, we will be using two important math vocabulary words: division and remainder.

Division, as we just discussed, is the math process of taking a total number and breaking it or dividing it into smaller equal parts.

A remainder is the extra left over when you divide. You will not always have a remainder when you divide. In some cases the division problem will end up with nothing left over, so in that case there would be NO remainder. For example, 4 divided by 2 equals 2 and there is nothing left over.

When you're writing out math problems, the abbreviation for remainder is 'R' with the number next to it and it is placed directly next to the quotient, or answer to the problem. This picture shows how the remainder is written in a math problem.

dividing with a remainder

Dividing with a Remainder

When you divide, you are taking a total number and breaking into smaller equal parts. Let's see this in action.

We'll begin with a total of 10 and break it into 3 parts. The first step is to set up the division problem, so you need to take a total of 10 and see how many groups of 3 are in it. Hint: This is where knowing multiplication facts will be helpful. (3 x ? = 10, or something close to 10.) But if you are not great at multiplication, you can always draw a picture on the side of your paper or list the multiples of the number to help determine the answer. Look at the illustration to see these other strategies.

dividing with a remainder set up

In this problem, 3 x 3 = 9, so 3 is the quotient since 9 is the highest number divisible by 3 that fits into 10. However, it's not quite 10, is it? That's right: 10 - 9 = 1. There is 1 left over, which becomes the remainder. So this problem solved would be: 10 ÷ 3 = 3 R1.

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