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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.

Refresher on Division

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 * 2 = 6, so if you take 6 and divide it by 2, the answer is 3. It is a fact family. Remember, a fact family is a group of related facts.

Sometimes when you're dividing, the number can't be broken into groups equally and there's something left over called a remainder. After this lesson, you will know what to do when you have a division problem that ends up with a remainder.

Math Vocabulary

To begin, let's talk about two important math vocabulary words: division and remainder. Division, as we just discussed, is the math process of taking a number and breaking it or dividing it into smaller equal parts. A remainder is any extra left over after you divide evenly. 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's nothing left over.

When you're writing out math problems, the abbreviation for remainder is 'R' with the number left over next to it, and it's placed directly to the right of the quotient, or answer to the division problem.

Dividing With a Remainder

When you divide, you're 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 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're 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.

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If you know that 3 * 3 = 9, you'll see that 3 will be 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.

To check your work, multiply the quotient (answer) by the divisor (number of groups you are dividing into), then add in the remainder. If your work was correct, you will get the dividend, or the total or largest number in the problem. So 3 (divisor) * 3 (quotient) = 9 +1 (remainder) = 10.

Here's another problem to practice. What is 19 divided by 4? Remember to use your multiplication facts to help you solve the problem. (4 * x = 19, or close to 19.) When you take 19 and divide it into groups of 4, you get 4 groups. 4 * 4 = 16, but 19 - 16 = 3, so there is a remainder of 3. Now let's check it: 4 * 4 =16 + 3 = 19.

Lesson Summary

The steps for dividing with remainders are the same as division in general: breaking a number into smaller equal groups. Using fact families for multiplication and division are helpful, but you can also use other strategies like writing multiples or drawing pictures to help. When a math problem has a remainder, it just means that there is a number left over after the division is done. To check your answer, just multiply your quotient and divisor and add your remainder. Your total should match the number you started with.

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