Word Problems on Division
Word problems on division for fourth grade students are solved here step by step.
Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. How much money will each person get? Solution: Money received by 26 men = 5876 So, money received by one man = 5876 ÷ 26 = 226
Each man will get $226.
2. If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?
Since 95 bags contain wheat 9975 kg Therefore, 1 bag contains wheat (9975 ÷ 95) kg = 105 kg
Each bag contains wheat = 105 kg In a problem sum involving division, we have to be careful about using the remainder.
3. 89 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 12 people. How many tables are needed? Solution: To answer this question, we need to divide 89 by 12 89 ÷ 12
Quotient - 7
Remainder - 5
If the caterer arranges 7 tables, then 5 people will have no place to sit. So he needs to arrange 7 + 1 = 8 tables.
4. How many hours are there in 1200 minutes?
Solution: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20
So there are 20 hours in 1200 minutes.
Answer: 20 hours.
5. A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
Solution: Total number of passengers = 108
There are 12 rows of seats on the bus.
To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.
We get, divide 108 by 12
108 ÷ 12 = 9
Therefore, there are 9 seats in each row.
Answer: 9 seats.
6. Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends?
Solution: Total number of apples = 63
There are 9 friends of seats on the bus.
To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.
We get, divide 63 by 9
Therefore, Tom gives 7 apples to each of his friends.
Answer: 7 Apples
7. Mark baked 195 cookies and divided them equally into 13 packs. How many cookies did Mark put in each packet?
Solution: Total number of cookies = 195
There are 13 packs.
To find how many cookies did Mark put in each packet, divide the total number of cookies by the number of packs.
We get, divide 195 by 13
195 ÷ 13 = 15
Therefore, Mark put 15 cookies in each pack.
Answer: 15 cookies.
9. Nancy needs 5 lemons to make a glass of orange juice. If Nancy has 250 oranges, how many glasses of orange juice can she make?
Solution: Total number of oranges = 250
She needs 5 lemons to make a glass of orange juice.
To find how many glasses of orange juice can Nancy make, divide the total number of oranges by the number of oranges needed for each glass of orange juice.
We get, divide 250 by 5
250 ÷ 5 = 50
Therefore, Nancy can make 50 glasses of orange juice.
Answer: 50 glasses of orange juice.
10. In your classes you counted 120 hands. How many students were at the class?
Solution: Total number of hands = 120
We have 2 hands.
To find how many students were at the class, divide the total number of hands by the number of hands we have.
We get, divide 120 by 2
220 ÷ 2 = 60
Therefore, there were 60 students at the class.
Answer: 60 students.
11. The total train fare for 20 persons is 7540 rupees. What is the fare for 1 person.
These are the basic word problems on division.
Questions and Answers on Word Problems on Division:
1. 92 bags of cement can be loaded in a truck. How many such trucks will be needed to load 2208 bags?
Answer: 24 trucks
2. The total train fare for 11 persons was $3850. What was the fare for one person?
● Word Problems on Addition
● Check for Subtraction and Addition
● Word Problems Involving Addition and Subtraction
● Estimating Sums and Differences
● Find the Missing Digits
● Multiply a Number by a 2-Digit Number
● Multiplication of a Number by a 3-Digit Number
● Multiply a Number
● Estimating Products
● Word Problems on Multiplication
● Multiplication and Division
● Terms Used in Division
● Division of Two-Digit by a One-Digit Numbers
● Division of Four-Digit by a One-Digit Numbers
● Division by 10 and 100 and 1000
● Dividing Numbers
● Estimating the Quotient
● Division by Two-Digit Numbers
● Word Problems on Division
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25 Division Word Problems for Grades 3 to 5 With Tips On Supporting Students’ Progress
Division word problems are important in building proficiency in division. Division is one of the bedrocks of math alongside addition, subtraction and multiplication. Therefore, it is vital that students have a deep understanding of division, its function within arithmetic and word problems, and how to apply both short division and long division with success.
Division itself is the mathematical process of breaking a number up into equal parts and then finding out how many equal parts you can have. It may be that you have a remainder following the division or you may have no remainder and so a whole number as your answer.
What are division word problems?
Introducing standard algorithm division, why are word problems important for childrens’ understanding of division, applying math to real life situations, building problem solving skills, developing mathematical language skills, deepening understanding of the inverse relationship between division and multiplication, how to teach division word problem solving in elementary school., example of a division word problem, how can we show this visually, examples of division word problems in the elementary setting, 3rd grade division word problems, 4th grade division word problems, 5th grade division word problems.
Division word problems are an extension of the arithmetic method whereby they are word problems with division at the heart. Students will be expected to use the process of division to find a solution to the word problem.
Typically, word problems use a story as a scenario and are based on a real life situation where students are expected to interpret what the word problem is asking and then apply their division knowledge to find the answer. Division can also be introduced early through the idea of grouping before advancing to the formal method of long division.
To help you with the division journey, we have put together a collection of division word problems which can be used for children between 3rd grade to 5th grade.
Word Problems Grade 4 Fractions and Decimals
11 grade 4 fractions and decimals questions to develop reasoning and problem solving skills.
Division word problems in upper elementary
As children enter 3rd grade, they begin to develop their mental and written strategies for division. Students will begin to use their multiplication knowledge and times tables to assist in their solving of division problems and how they can use the corresponding division facts and multiplication facts to answer questions.
By the end of 3rd grade, students are expected to recall their multiplication and division facts for multiplication times tables up to 10 x 10. They should also use their knowledge of place value, and known and derived facts to assist with simple division such as dividing by 1 and halving.
Introducing partial quotients
Before being introduced to the standard algorithm, also known as long division, students learn the partial quotients method. Students practice their fluency of short division, in order to answer division word problems that have a whole number answer, and those with a remainder.
Before entering 4th and 5th grade, students encounter division word problems and multi step problems with increasingly harder numbers going from a simple division problem, such as, ‘If we have 30 students in our class and we are divided into groups of 5, how many students will be in each group?’ to ‘If there are 56 books in our library and they are shared among 7 children, how many books would each child get?
As our students enter 5th grade, the standard algorithm, or long division, is introduced. By the end of 5th grade, students should be fluent in both multiplication and division and the written strategies, and be able to apply knowledge in fraction word problems .
4th grade students work towards being able to divide up to 4 digit numbers by a one digit number using partial quotients and being able to interpret remainders in the correct context – even presenting the remainder as a decimal or fraction. Students should also be able to divide mentally and know how to divide by 10, 100 and 1,000 and how place value works alongside dividing a number so it is 10, 100 or 1,000 times smaller.
5th grade students are expected to consolidate on the above formal methods of division before being able to divide a four digit number by a two digit number using the formal method of standard algorithm division and to again be able to understand remainders within this and present them in the correct context.
This also flows into division word problems as children should be able to read a multi step problem and know how to correctly interpret it, apply their divisional knowledge and solve the problem successfully. The concept of multi step problems is built upon at each stage of your state math curriculum.
Word problems, alongside the use of concrete objects and visual representations, are important in helping children understand the complexities and possible abstract nature of division.
While children may understand that when we divide our answer will be smaller, before providing a child with word problem worksheets, just like with exploring arrays to support multiplication word problems , it is important to visually explore how division looks – from grouping and beyond.
Word problems are important because they provide a real life context for children to understand division and how we encounter it in real life. By allowing children to see how division is used in everyday situations, children will find it more meaningful and relevant which in turn develops a deeper understanding of the four operations as a whole.
Word problems are also vital to developing problem solving skills. First, they must read and understand the problem before being able to identify the relevant information within the contextual problem and apply their knowledge to find a solution. This naturally builds critical thinking and a child’s ability to reason, which is an important skill for any mathematician.
Finally, the importance of moving from simple division word problems to more challenging ones enhances students’ vocabulary and language skills. For children to develop an understanding of vocabulary such as divisors, quotient and remainders means they must first understand these key words and apply it to the process of division and be able to communicate clearly what they are aiming to do.
Division word problems also solidify the connection between multiplication and division. Understanding these inverse operations and being able to interchange the skills of multiplication and division will help make connections between different mathematical concepts and deepen students’ learning.
Having taught the concept of division to students using concrete examples, for example how to group or share counters and cubes, the next step is to advance to division word problems.
As with all word problems, it is important that students are able to read the question carefully and interpret it so they know what they are being asked. Do they need to add, subtract, multiply or divide? Are they solving a multi step problem and need to do more than one step? They may decide what operation to do, in this blogs’ case – division, and then choose to represent it visually.
There are 40 pieces of candy ready to go in the party bags for Laura’s birthday. They are to be shared between 8 friends. How many pieces of candy will each child get?
How to solve this:
First, we need to interpret the question. Laura has invited 8 friends to her party and she has 40 pieces of candy to share equally between her friends. So we know:
- There are 40 pieces of candy in total
- They are to be divided among 8 friends in total
- We will need to divide the total number of candies (40) by the number of friends (8). To solve this problem we could put the total number of candies (the dividend – 40 ) using the partial quotient method and divide by the total number of friends (the divisor – 8). If we do this, we would get the answer of 5 – the quotient. Each friend would get 5 pieces of candy each as 40 divided by 8 is 5.
- Alternatively, we could use the inverse – multiplication – to solve this problem. We may not know the division fact that 40 divided by 8 = 5 but if we look to the inverse we may know what number multiplied by 8 equals 40. If we did our 8 times table we would get the answer of 5 – the correct answer.
We could show 8 circles – each circle to represent a child – and place a piece of candy in each circle until we have placed all 40 candies. This would mean we have shared the candies equally between the friends and would result in each child having 5 candies.
We could represent the division word problem as a bar model. We could split the bar model into 8 sections. There are 40 candies and so we share them between the 8 sections. We will see that each section will get 5 pieces of candy.
The below visuals show how this would look:
Word problems are an important aspect of our learning at Third Space Learning’s one-to-one tutoring program. Tutors will work with our tutees to break down the word problems and identify the correct operation needed to solve the word problem.
Below are examples of what can be expected at each year group from grades 3 to 5. Through our tutoring program at Third Space Learning, our tutees will become familiar with word problems throughout their learning. They will encounter word problems on a regular basis with each lesson personalized to develop the learning our tutees need. The word problems will increase their confidence, familiarity with vocabulary and mathematical understanding.
Division word problems are essential to developing problem solving skills and mathematical reasoning.
Word problems for 3rd grade, students should begin using their recall of the times table facts they have learned to help with division word problems and be able to divide two digit numbers by one digit numbers using mental and partial quotients. Word problems may also involve multi step problems.
If a school has 90 students in 2nd grade and there are 3 classes in 2nd grade, how many students are in each class?
90 shared equally into 3 classes = 30 children per class
Every day a school gets a delivery of milk in a crate. There are 96 cartons of milk in the crate. If there are 8 milk cartons in a pack, how many packs will be in the crate?
96 divided by 12 = 8.
There are 8 cartons of milk in a pack.
A delivery of 96 footballs arrives at school for sports day. They are to be shared equally between 4 classes. How many footballs does each class get?
96 divided by 4 = 24 footballs per class
3rd grade is going to the beach on a school trip. If there are 100 children in 3rd grade and only 10 children can go on one mini bus, how many mini buses does Mr. Pearson need to book?
100 children divided 10 = 10 mini buses.
If you have 60 flowers and divide them into four flower pots, how many flowers are in each pot? Are there any left over?
Answer: 15 flowers in each pot.
If we divide 60 into 4 equal groups then we can use the partial quotient method.
When using the partial quotients method, students rely on what multiplication facts they can use.
Because we are dividing 60 by 4, we may ask ourselves, what number can I multiply 4 by, to get close to 60 without going over? Students should be familiar with their 10s time tables, and 4 x 10 = 40. We place the 10 above the quotient line, and then subtract 40 from 60, leaving 20 remaining.
We will now start the process all over again. What number can I multiply 4 by to get close to 20 without going over? We know that 4 x 5 = 20, so again, place 5 above the 10 in the quotient line and subtract 20 – 20. Because there is nothing left over, we are done dividing.
So the answer to 60 divided by 4 = 15.
This would look like:
Word problems for 4th grade center around dividing a 4 digit number by a 1 digit number using the partial products method or area model method of division. They will also be introduced to remainders and be expected to interpret remainders correctly depending on the context.
Ronan has a ball of string that is 819 cm long. He cuts it into 7 equal pieces. How long is 1 piece of string?
819 divided by 7 = 117
In upper elementary there are 1,248 colored pencils. If there are 6 classes in upper elementary, how many pencils would each class receive?
We use the division method to divide 1,248 by 6 and we get 208 as the result.
Mia buys three computer games for $84. How much is one computer game?
We divide $84.00 by 3 and we get $28.00.
The area of the school hall is 1,704m and needs to be split into four quadrants. What would be the area of each quadrant?
We take the total area of the school and divide it by 4 to represent each quadrant. In doing so, we would have 426m for each quadrant.
To check this is the correct answer, we could do the inverse and multiply 426 by 4 and we would get 1,704m.
Packets of candy are put into multi packs of 4. Today, 7,800 packets of candy were packed. How many boxes of candy were packed?
Answer: 163 boxes
We then have to take the total packets of candy– 7,800 – and divide this by 4. If we do this we will get the answer 1,950 boxes were packed.
Word problems for 5th grade will be preparing for the end of elementary school. They would be familiar with the concept of standard algorithm division and needing to divide a 4 digit number by a 2 digit number using the formal method of standard algorithm division.
A school is selling tickets at $6 each to attend the Big Christmas Fair. Over 15 weeks it has earned an amazing $9,720! On average, how many tickets were sold each week?
Answer: 108 tickets per week
First, we need to use the formal method of standard algorithm division to divide the grand total – $9,720 by 15. If we do this correctly we will have the answer 648.
Then, we need to take this answer of 648, which is how much is earned each week, and then divide this by $6, the amount each ticket is.
This will result in the number of tickets sold each week – 108 tickets.
A square sports field has a perimeter of 2.696km. How long is each side of the field?
To answer this we need to be able to convert the 2.696km into meters. There are 1000 meters in a kilometer so that would be 2,696m. Then we divide this by 4 and get 674m for one side.
Keira is given a toy blocks kit containing 2,208 individual blocks. She wants to split the toy blocks evenly between 15 friends and herself to work on making a toy block city together. How many blocks should she give each of her friends?
Answer: 138 blocks
We need to use the formal method of standard algorithm division to solve this. We also need to ensure we include Keira and her 15 friends so we have the number 16 as the divisor.
When we divide 2,208 by 16 using long division we get the answer 138.
Wesleigh was running in the cross country race. He ran for a distance of 3,569m and it took him 11 minutes to complete the race. How many meters did he run per minute? Give your answer to the nearest whole meter.
Answer: 324 meters
We need to use standard algorithm division to divide 3,569 by 11. That will give us an answer of 324.45. As the decimal can be rounded down, the answer is 324 meters.
Sophia is preparing her candy stall for the fair. She can fit 18 tins of candy into one crate. How many crates will be needed to fit 153 tins of candy?
Answer: 9 crates
We divide 153 by 18 using standard algorithm division and we have an answer of 8, remainder 5. Therefore, having 8 crates would not be enough as we would have 85 tins left over and so we need a further tin to house the 5 tins left over. So, 9 crates are needed.
More word problems resources
Are you looking for more word problems resources? Take a look at our library of word problems practice questions including: time word problems , ratio word problems , addition word problems and subtraction word problems .
Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade – 3rd grade – 4th grade – 5th grade – 6th grade Why not learn more about how it works ?
The content in this article was originally written by former Deputy Headteacher Steven Eastes and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.
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Division word problems for 3rd grade
Simple division word problems.
After reading the word problem and understanding the 'real world scenario', the student must formulate the division equation to solve the problem. Only simple division is required.
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Division Word Problems — Examples & Practice - Expii
Division word problems — examples & practice, explanations (3).
Words to Math: Division
In this section, we will learn to translate phrases into a mathematical expression by identifying key words that indicate division.
When talking about division, you will most likely see the terms " divide ", " quotient ", " percent " ( divide by 100 ). There are other terms to indicate addition , multiplication, or subtraction .
Let’s take a look at an example.
Nicole has 20 cookies. She wants to divide the 20 cookies equally between 4 friends. How many cookies does each person receive?
We know that the term " divide " often refers to division, so the operator ‘÷ can be used. There is also an invisible equality sign. That's because we're looking for a number equal to how many cookies each person gets. Both sides of an equation are always equal. This problem is no different!
Nicole has 20 cookies and there are 4 people. So, we can rewrite this as a mathematical equation. Then perform the division of positive integers .
20 cookies ÷ 4 friends = 5 cookies each.
This problem is also illustrated with the following diagram.
Image source: By ryanmorrisonjsy CC0 , via pixabay.com
When talking about equality, you will most likely see the terms " equal to ", " is ", " the same as ", and " amounts to ".
These phrases describe division as a mathematical expression.
- 35 divided by 7 equals 5→35÷7=5
- The quotient of 6 and 3 is 2→6÷3=2
Word problems with division.
There is an important strategy for solving word problems. The key is to translate them into mathematical expressions. This is easier if you can pick out key phrases, called signal words . These that tell you what type of operation the problem is asking for. Each operation has its own set of signal words.
Image source: By Clker-Free-Vector-Images CC0 via pixabay.com
Image source: Clker-Free-Vector-Images CC0 via pixabay.com
Which signal word tells us that we'll be using division to solve this problem?
(Video) Solving Multiplication and Division Word Problems
by Ruth Erquiaga
Ruth Erquiaga has a great explanation and strategy on how to identify and approach word problems. This video focuses specifically on multiplication and division .
The key word that designates multiplication or division is " each ". " Each " indicates that the groups being combined or split up need to be equal in size. This is true of multiplication and division, but not necessarily of addition and subtraction.
Other words like " total ", " area ", " in all ", and " altogether " can designate multiplication or division. We need the context of the problem to allow you to work with equally sized groups.
The video covers a general strategy for translating word problems .
- Read the whole problem (in fact, read it twice, just in case).
- Find if the total is given. A given total means that the problem will be division or subtraction. No given total means the problem will be addition or multiplication. In the second case we usually want to find the total.
- Find if the groups are equal. Equal groups will mean multiplication or division. Unequal groups will mean addition or subtraction.
Difficulties with Division
Age 5 to 11.
Published 2011 Revised 2012
A lot of teachers struggle with teaching division to children and I have been thinking about this recently. I think there are a number of factors contributing to this. Firstly, by the middle of Stage 2 there is a huge range of level of understanding of the concept of division and secondly the concept itself can be thought of as building on children's understandings of addition, subtraction and multiplication. The spread of different levels of understanding is likely to make any class "mixed ability" for this topic. There are also difficulties with the written algorithm. Altogether, it is a complicated picture. Let us try to unravel this a little and find some interesting problems that might help us to help our pupils. We'll start with the different conceptions of division that are commonly used in schools. We basically have three different ideas that we use with children and we often switch between the languages of each without thinking about the confusions this might cause for the children. Division is often introduced as "sharing" and this is certainly one of the simplest approaches. We look at problems that involve sharing a number of items between a number of different people. We don't necessarily need to know how many items are in our original pile or how many people we are sharing them between to be talking about division in this way, and so this conception doesn't easily lead to the representation of the situation in the form of a mathematical expression such as $12\div 4=3$. At this stage children need lots of experience with sharing physical objects out and expressing what they are doing in words and then in symbols. An interesting problem that works with this idea is Lots of lollies .
A second conception of division is that of grouping and this links to ideas about successive subtraction. In this setting the problem is about how many groups of a given number you can make out of a pile of items - "How many groups of $3$ there are in $12$?" for instance. This links with ideas of division as inverse multiplication and children can be offered plenty of opportunities to explore patterns in the multiplication tables and to express them in all the different ways that are possible, in words and in symbols. For instance, our example of $3\times 4=12$ generates a whole lot of sentences and symbolic expressions: Three lots of four make twelve $4\times 3=12$ Four lots of three make twelve There are three groups of four in twelve $12\div 4=3$ There are four groups of three in twelve $12\div 3=4$ If you share twelve things between three people they will have four things each $12\div 3=4$ If you share twelve things between four people they will have three things each $12\div 4=3$ It is important that children grasp the equivalence of all these different expressions in order to develop their facility with division. In their delightful book Williams and Shuard outline three stages in understanding division as:
- Using grouping and sharing as different operations and solving problems using concrete apparatus
- Relating sharing to grouping
- Using their knowledge of multiplication to deal with both types of division by the same numerical procedure
These should be accomplished by working through the activities like the one above and encouraging children to communicate with one another about their understanding. Working on from using known facts, the next problem arises with the written algorithms for division. Unlike the other standard algorithms for addition, subtraction and multiplication, the standard algorithm for division is worked from left to right and the setting down seems totally different. Despite much advice about not introducing written algorithms too early, many children meet it before they are ready to understand it and without being given enough chance to develop their own strategies for dividing large numbers. Stuart Plunkett's comment made way back in 1978 still rings true: "Children should be helped to acquire sensible methods for calculating'' The value of informal jottings to record division calculations has been outlined by Julia Anghileri and she shows some interesting analysis in the book "Teaching Number Sense''. Before children embark on any formal recordings using the standard algorithm for division they need plenty of familiarity with tables and number patterns in them as well as practice with mental strategies such as chunking, doubling and halving. All of these activities do require a lot of practice and experience but once you are confident that your class have had a good grounding in these areas, why not try some of these problems?
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