# Interpreting Remainders Rating

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Interpreting Remainders
CCSS.MATH.CONTENT.4.NBT.A.3

## Interpreting Remainders in Division

In this learning text, we're going to learn about division and how to understand remainders. You might already know about division from things like cutting fruits in half, or splitting a pizza into equal slices. These everyday activities are actually math problems, which we call division. Division can be a bit tricky, so we're going to start by learning about division and remainders.

## Division and Interpreting Remainders – Definition

Let’s look at the meaning of the terms “division” and “remainders”:

Division is when we split things into equal groups, but sometimes we have some left over, which we call remainders. The remainder is what's left after we divide. In real life, there are many different ways that we can understand the remainder. We can: ignore it, use it, add it or share it.

In this learning text, we will be looking at different scenarios and learn how we can interpret the remainder. ## Interpreting Remainders – Word Problems

Now, let's look at some word problems to show different ways of understanding remainders. Depending on the situation, we will treat the remainder in different ways. The first example is about sharing treats: we have thirty (30) treats divided into seven (7) bags. We want to know how many treats are in each bag. So, we're going to share all treats equally into those seven bags. We divide thirty (30) by seven (7) and we find out there are four (4) treats in each bag with two (2) left over.

Let's look at the question again and decide what we're going to do with the two (2) left over. The question asks: How many treats will go into each bag? So, we just need to know the equal groups, so this time we will ignore the remainder. There are four (4) treats in each bag!

Let's look at our second example. First, read the problem and highlight the important information. There are seventy-two (72) balloons in a bag, and we need to make groups with seven (7) balloons each. So, if we divide the seventy-two (72) by seven (7), we have ten (10) with two (2) left over.

Then, after you do the math, make sure you read the question again and decide what you're going to do with the remainder.

This time, the question asks: How many balloons will NOT be used for the inside decorations?

We know the remainder after our division was two (2), so the answer is also two (2) because the remainder represents the NOT used balloons.

Our next example is about party hats: we have forty-five (45) guests at a party. Everyone must wear party hats. In one pack is six (6) hats, and we need to figure out how many packs of hats we need for the party. So, let's divide forty-five (45) by six (6). We get seven (7) with three (3) left over. This time the remainder tells us that we must add one (1) to the seven (7) which is eight (8) because we can't order three (3) extra hats separately. For this question, the answer is eight (8).

The interpretation of the remainder, as we mentioned before, can be different from question to question. That is why we are showing in this learning text different scenarios and learning how we interpret remainder word problems for 4th grade.

Let’s take a look at one more example word problem. We have to divide eighty-five (85) feet of streamers around the four (4) walls. When we do the math for this problem, we get twenty-one (21) with one (1) left over. Because we have to find out how long each piece of streamer for each wall is, we can't give our answer with the remainder. We must write the remainder as a fraction. To do that, we write the remainder one (1) over the divisor four (4), which will be the bottom number.

## Division Word Problems and Interpreting Remainders – Summary

When solving real word division problems that have remainders, we need to understand the remainder by figuring out what the problem is asking.

• Ignore remainder - if the question asks for equal or whole amounts.

• Use remainder - if the question asks how much is left over.

• Include remainder - meaning, add one to the answer if the question asks for everything to be included.

• Make the remainder a fraction - when the remainder can be divided into even smaller parts.

Now you should be able to solve the division word problem with the remainder in any form. If you need more help, please watch the video explaining each problem and complete the worksheets which are available for this topic.

What is division?
What is the remainder?

## Interpreting Remainders exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Interpreting Remainders .
• ### What is a remainder?

Hints

When dividing, we are looking for equal groups.

Think, can all numbers be divided equally?

If a number can't be divided equally, what would you do?

Solution

With division, we are splitting up a number into equal groups. Sometimes, a number cannot be divided equally, so we get a remainder. A remainder is " leftovers that cannot be grouped equally."

• ### Define how remainders can be used.

Hints

Read the question carefully and think about what you are trying to find.

Once you determine what you are trying to find, then you can determine what to do with the remainder.

Think about what it means to share something. You are further dividing something to make it equal. This applies to sharing remainder too.

When you don't have enough of something; you need to include the remainder.

Solution

These are the ways remainders can be used based on what the question is asking you to solve:

The remainder is needed to answer the question "how much is leftover?" Use it

The question is asking you to find equal or whole amounts. Ignore It

The question is asking you to determine how many of something you will need. Include it

The remainder needs to be divided up and made into a fraction. Share it

• ### How can we interpret remainders?

Hints

To determine what to do with the remainder, reread the question.

Ask yourself, "what am I trying to solve?"

There are 28 kids going on a field trip. The buses can seat 8 kids. How many buses will be needed for the field trip. In this example you would need to add the remainder. Which problem would we also need to add the remainder?

Mr. Squeaks needs 40 balloons. Balloons come in packs of 3. How many packs does he need to buy? In this example, we would ignore the remainder because it is not needed. Which problem would we also need to ignore the remainder?

Solution

Each question is asking you to do something different with the remainders. Here are the solutions based on what is being asked:

• Ignore it means you don't use the remainder
• Use it means you need to know how much is leftover
• Add it means everything needs to be included
• Share it or make a fraction means the remainder can be divided into
small parts

For the question about the lollipops, we would ignore the remainder because we need to know the whole number of lollipops that Mr. Squeaks can purchase. The remainder would just be what is leftover.

In the question about the goody bags, we would need to include the remainder because we wan to make sure we have enough for everyone.

We use the remainder in the question about the wrapping paper because it is specifically asking us about what is leftover.

We share or make a fraction for the question about the balloon string because we need equal amounts and will have to divide up the remainder to do so.

• ### Solve the division problem.

Hints

Think, what is the question asking me to find?

Ask yourself, "how is the remainder being used?"

Draw a picture with 7 groups and see how many could equally fit.

17 groups of 7 equals 17 remainder 6.

Solution

In this question, we are being asked to find "how many stickers." This means that we want equal groups with no remainder. So here, you would ignore the remainder and just focus on the whole number because we cannot have part of a sticker.

Divide 125 ÷ 7 = 17 R 6

Since we are ignoring the remainder, there are 17 stickers for each guest.

• ### Determine how the remainder will be used in this problem.

Hints

Think, "how am I going to use the remainder?"

Here you can see that when we divide 50 by 6, we end up with 8 in each group. But there are 2 that don't belong to a group. That is our remainder. What should we do with the remaining 2?

Solution

In the problem, we need to add the remainder. We need to add it because the question is asking for everything to be included. Mr. Squeaks needs to make sure he purchases enough packs of noise makers so that everyone can have one, so the remainder is included. Since the answer is 8 R 2, we would add one to 8 which give us 9 packs.

• ### What meanings do numbers have in an equation?

Hints

In the equation 54 ÷ 4 = 13 R 2. The number 2 represents the remainder, or what is leftover.

In the equation 84 ÷ 5; 84 is the total amount we have. How does that relate to the problem given here?

Sam has 12 boxes of toys. Each box can only fit 5 toys. How many toys cannot fit in a box? The remainder would be the answer which is 2. Where is the remainder in the story problem given here?

Solution

It is important to understand what the numbers in equations represent in order to correctly solve the problem. In the equation 75 ÷ 8 = 9 R 3, the representation of each number is as follows:

75 is the total number of guests.

8 is the number of seats at each table.

9 is the number of full tables.

3 is the number of guests at the extra table.