# Interpreting Remainders

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## Interpreting Remainders in Division

In this learning text, we're going to learn more about division and how to understand interpreting remainders word problems. You might already know about division from things like cutting fruit in half or splitting a pizza into equal slices. These everyday activities are actually maths 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 about interpreting remainders in division word problems.

## Interpreting Remainders – Division 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 of the 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 continue to look at interpreting remainders (division word problems) with 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 maths, 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 work 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 more about interpreting remainders KS2.

Let’s take a look at one more division (interpreting remainders) example word problem.

We have to divide twenty-five (25) metres of streamers around the four (4) walls. When we do the maths for this problem, we get six (6) 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 so this time we are interpreting remainders as fractions. 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 world division problems that have remainders, we need to understand the remainder by working 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 division interpreting remainders worksheets which are available for this topic.

What is division?
What is the remainder?
Where can I have a go at division word problems?

### TranscriptInterpreting Remainders

Mr. Squeaks is planning a surprise party to celebrate Imani’s Manufacture Date. He is working on decorations. Let's help Mr. Squeaks work out what to do with the leftovers by "Interpreting Remainders" Division means we are putting items into equal groups. Sometimes when we divide, we have remainders, or leftovers, that cannot be grouped equally. When we have a remainder in our quotient, or answer, we need to interpret it or determine what to do with the leftovers based on what the problem is asking. There are several ways to interpret a remainder in real-world situations. Let’s use the party supplies to look at each way of interpreting a remainder. Mr. Squeaks is making goody bags for the little robot guests. He has thirty treats to divide up into seven bags. How many treats will go into each bag? Let’s look at the word problem and highlight the important information. We know that there are thirty treats we are dividing into seven bags, and the problem is asking us to find out how many treats go into each bag, so we will solve thirty divided by seven. Thirty divided by seven equals four with a remainder of two. To determine what we need to do with the remainder, let’s reread the question. How many treats will go into each bag? This tells us that we only need to know the equal groups, or how many treats will be in each bag, which is four.

So this time, we don't need to worry about the remainder, we have answered the question with four. There are four treats in each goody bag. Mr. Squeaks is also going to hang up balloons around the burrow. There are seventy-two balloons in a bag, and he wants to make bunches with seven balloons each. How many balloons will not be used for the inside decorations? First, read the problem and highlight important information. There are seventy-two balloons and we are putting them into bunches of seven. What is seventy-two divided by seven? Ten remainder two. Now, reread the question to determine how to interpret the remainder. How many balloons WILL NOT be used for the inside decorations?" This tells us that we only need to know how many balloons are leftover, which is two, so he has two balloons remaining. All of the guests need to wear party hats! They come in packs of six, and there are forty-five attendees. He needs a party hat for each. How many packs of hats does he need to get? Based on the information, what is the division problem we need to solve? Forty-five divided by six. What is forty-five divided by six? Seven remainder three. What does the problem say we need to find? How many packs of party hats he needs to get. Mr Squeaks needs seven whole packs, plus an extra three hats, meaning he must round up and buy eight packs.

In this problem, we would interpret the remainder by rounding up to get eight. Mr. Squeaks needs eight packs of party hats. Finally, Mr. Squeaks is going to hang up streamers around the four walls. The streamer roll measures twenty-five metres. How long is each piece of streamer for each wall?' "Based on the information, what is the division problem we need to solve?" "Twenty-five divided by four." What is twenty-five divided by four? "Six remainder one." What does the problem want us to find? The length of the streamer on each wall. In this problem, the remainder, one, represents a material that can be further divided into parts, so we write this remainder as a FRACTION. To write it as a fraction, we put the remainder, one, over the divisor, four, to show that each wall will also have one quarter. Mr. Squeaks will put six and a quarter metres of streamer on each wall. While everyone waits for Imani, let's review. Remember, when solving real world division problems with remainders, we need to Interpret remainders by identifying what the problem is asking. We can ignore the remainder if the question asks for equal or whole amounts. Use the remainder as your answer if the question asks how much is left over. Round up when the question asks for everything to be included. Or make the remainder a fraction when the quotient can be divided up into even smaller parts. "Shhh, Imani's coming." “SURPRISE!”

## Interpreting Remainders exercise

Would you like to apply the knowledge you’ve learnt? 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 remainders 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?"

In the question: There are 28 children going on a school trip. The buses can seat 8 children. How many buses will be needed for the field trip? You would need to add the remainder. Which problem would we also need to add 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:

• Mr. Squeaks went to the shop with £25 to buy lollipops for game prizes. The lollipops are £3 each. How many lollipops can he buy? Ignore it. Ignore it means we don't use the remainder.
• All the guests will receive a goody bag at the end of the party. There are 8 goody bags in a pack.There are 50 guests. How many packs of goody bags does Mr. Squeaks need to get? Add it. Add it means everything needs to be included.
• Mr. Squeaks is wrapping gifts for Imani. He has a total of 87ft of wrapping paper. Each present needs 10ft of wrapping paper. How many feet of wrapping paper will be leftover after he wraps the gifts? Use it. Use it means you need to know how much is leftover.
• There are 9 balloons that need to be hung. Mr. Squeaks is going to cut string to tie around each balloon. He has 37 feet of string. How long will each piece of string be? Share it or make a fraction. Share it or make a fraction means the remainder can be divided into small parts.
• ### 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.