Interpreting Remainders
Basics on the topic Interpreting Remainders
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.
Frequently Asked Questions about Division Word Problems
Transcript Interpreting Remainders
Mr. Squeaks is planning a surprise party to celebrate Imani’s Manufacture Date. He is working on decorations. Let's help Mr. Squeaks figure 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 can not be grouped equally. When we have a remainder in our quotient, 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. We can ignore it, use it, add it, or share it. Let’s use the party supplies to look at each way of interpreting a remainder. M.r. 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, which is four and we would IGNORE the remainder. 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 Mr. Squeaks have leftover? First, read the problem and highlight important information. There are seventy-two balloons and we are putting in bundles 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 the guests need to wear party hats! They come in packs of six, and there's forty-five attendees. He needs a party hat for each. How many packs of hats does he need? 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. Since there are three leftover and they come in packs of six, Mr. Squeaks would have to get an additional pack of party hats. In this problem, we would interpret the remainder by adding one to the quotient. 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 eighty-five feet. How long is each piece of streamer for each wall?' Based on the information, what is the division problem we need to solve? Eighty-five divided by four. What is eighty-five divided by four? Twenty-one remainder one. What does the problem want us to find? How much of the streamers are 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 get one-fourth of the streamer. Mr. Squeaks will put twenty-one and one-fourth feet of streamers on each wall. While everyone waits for Imani, let's review. Remember… When solving real word 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. Add one to the quotient 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
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What is a remainder?
HintsWhen 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?
SolutionWith 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."
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Define how remainders can be used.
HintsRead 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.
SolutionThese 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
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How can we interpret remainders?
HintsTo 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?
SolutionEach 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
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.
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Solve the division problem.
HintsThink, 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.
SolutionIn 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.
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Determine how the remainder will be used in this problem.
HintsAsk yourself, "what is the problem asking me?"
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?
SolutionIn 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.
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What meanings do numbers have in an equation?
HintsIn the equation 54 ÷ 4 = 13 R 2. The number 2 represents the remainder, or what is leftover.
Read the question carefully and think about what you are being asked.
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?
SolutionIt 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.
