problem solving involving multiplication and division

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This worksheets combine basic multiplication and division word problems. The division problems do not include remainders. These worksheets require the students to differentiate between the phrasing of a story problem that requires multiplication versus one that requires division to reach the answer.

Mixed Multiplication and Division Word Problems 1

Mixed Multiplication and Division Word Problems 2

Practicing the operations separately is a good start for each operation, but an important word problem skill is also figuring out which math operation is needed to solve a specific question. The worksheets in this section combine both multiplication word problems and division word problems on the same worksheet, so students not only need to solve the problem but they need to figure out how to do it.

By moving into these worksheets quickly, it avoids the crutch where students learn that they always need to add or always need to subtract the two values in a problem to get the answer. This forces students to really understand the intent of the problem, not just scan the text looking for numbers.

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Helping with Math

Multiplication and Division Word Problems

Word problems are fun and challenging to solve because they represent actual situations that happen in our world. As students, we are always wondering why we should learn one skill or another, and word problems help us see the practical value of what we are learning.

Read the tips and guidance and then work through the multiplication and division word problems in this lesson with your children. Try the three worksheets that are listed within the lesson (you will also find them at the bottom of the page.)

What is multiplication?

The process of finding out the product between two or more numbers is called multiplication . The result thus obtained is called the product . Suppose, you bought 6 pens on one day and 6 pens on the next day. Total pens you bought are now 2 times 6 or 6 + 6 = 12.

This can also be written as 2 x 6 = 12

Not the symbol used for multiplication. The symbol (x) is generally used to represent multiplication. Other common symbols that are used for multiplication are the asterisk (*) and dot (.)  

Important terms in the multiplication

Some important terms used in multiplication are – 

Multiplicand – The number to be multiplied is called the multiplicand. 

Multiplier – The number with which we multiply is called the multiplier.

Product – The result obtained after multiplying the multiplier and the multiplicand is called the product.

The relation between the multiplier, multiplicand and the product can be expressed as – 

Multiplier  ×  Multiplicand = Product

Let us understand this using an example.

Suppose we have two numbers 9 and 5. We wish to multiply 9 by 5.

So, we express it as 9 x 5 which gives us 45.

Therefore, 9 x 5 = 45

Here, 9 is the multiplicand, 5 is the multiplier and 45 is the product.

What is division?

• Division is the equal sharing of a given quantity.

For example, Alice wants to share 6 bananas equally with her friend Rose. So, she gives 3 of her bananas to Rose and she is also left with 3 bananas. This means that when we divide 6 by 2 we get 3.

Mathematically, we can write this as 

Symbol for Division

In mathematics, there is a symbol for every operation. The symbol for division is (÷). Other than the forward-slash (/) is also used to denote the division of two numbers , where, the dividend comes before the slash and the divisor after it. For instance, if we wish to write 15 is being divided by 3, we can write it as 15 ÷ 3 or 15 / 3. Both mean the same.

Important terms in Division

The number that is to be divided is called the Dividend .  Here, 6 is the dividend.

The number by which the dividend is being divided is called the Divisor . 

The result obtained by the process of division is called the Quotient .

The number that is left over after finding the quotient is called the Remainder .

Let us understand these by an example. 

Suppose, we have a pack of 65 chocolates and we want to divide them equally among 7 children while keeping the remaining chocolates with us. How many chocolates does each child get and how many chocolates are we left with after dividing these chocolates?

Using multiplication tables , we have 7 x 9 = 63

Therefore, 7 x 9 + 2 = 65

This means that the quotient when 65 is divided by 7 will be 9 and the remainder will be 2.

As per the definition of the four terms of division, we have

Divisor = 7

Dividend = 65

Quotient = 9

Remainder = 2

Remember: The remainder is always smaller than the divisor.

Formula for Division

There are four important terms in the division, namely, divisor, dividend, quotient, and the remainder. The formula for divisor constitutes all of these four terms. In fact, it is the relationship of these four terms among each that defines the formula for division. If we multiply the divisor with the quotient and add the result to the remainder, the result that we get is the dividend. This means,

Dividend = Divisor x Quotient + Remainder

What are word problems?

A word problem is a few sentences describing a ‘real-life’ scenario where a problem needs to be solved by way of a mathematical calculation. In other words, word problems describe a realistic problem and ask you to imagine how you would solve it using math. Word problems are fun and challenging to solve because they represent actual situations that happen in our world.

How to Solve Word Problems involving multiplication and division?

The following steps are involved in the process of solving word problems involving multiplication and division of numbers – 

• Read through the problem carefully, and figure out what it is about. This is the most important step as it helps to understand two things – what is given in the question and what is required to be found out.
• The next step is to represent unknown numbers using variables. Usually, these unknown numbers are the values that are required to be solved for.
• Once the numbers have been represented as variables, the next step is to translate the rest of the problem in the form of a mathematical expression.
• Once this expression has been formed, the last step is to solve this expression for the variable and obtain the desired result. 

Let us understand it through an example.

A hawker delivers 148 newspapers every day. How many newspapers will he deliver in a non-leap year?

We have been given that a hawker delivers 148 newspapers every day. We need to find out the total number of newspapers that he will deliver in a non-leap year. Let us summarise the given information as

Number of newspapers delivered by the hawker in a day = 148

Number of newspapers that he will deliver in a non-leap year = ?

Now, we know that a non-leap year consists of 365 days. This means that we need to find out the total number of newspapers that the hawker will deliver in 365 days. Therefore,

Total number of days on which hawker delivers the newspapers = 365

Now, to find the total number of newspapers delivered by the hawker in 365 days we will have to multiply the Number of newspapers delivered by the hawker in a day by the total number of days in a year. So, we have,

Number of newspapers that he will deliver in a non-leap year = (Number of newspapers delivered by the hawker in a day ) x (total number of days in a year ) ……….. ( 1 )

Substituting the given values in the above equation, we have

Number of newspapers that he will deliver in a non-leap year = 148 x 365

Now, 148 x 365 = 54020 

Hence, the number of newspapers that he will deliver in a non-leap year = 54020

Let us consider another example.

Example 

In a school, a fee of £ 345 is collected per student. If there are 240 students in the school, how much fee is collected by the school?

We have been given that in a school a fee of £ 345 is collected per student. Also, there are 240 students in the school. We need to find out the total fee collected by the school from all students. Let us first summarise this information

Amount of fee collected by the school from each student = £ 345

Number of students in the school = 240

Total amount of fee collected by the school = ?

This can be calculated by multiplying the fee collected for each student by the number of students in the school. Therefore we have,

Total amount of fee collected by the school = (Amount of fee collected by the school from each student ) x (Number of students in the school ) …….. ( 1 )

Substituting the given information in the above equation, we get

Total amount of fee collected by the school = £ ( 345 x 240 )

Now, 345 x 240 = 82800

Hence, Total amount of fee collected by the school = £ 82800

Solving Multiplicative Comparison Word Problems

Multiplication as comparing.

In multiplicative comparison problems, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set.

Any two factors and their product can be read as a comparison. Let’s look at a basic multiplication equation:  4 x 2 = 8.

What Operation to Use: Multiply? Divide? Add? Subtract?

The hardest part of any word problem is deciding which operation to use. There can be so many details included in a word problem that the question being asked gets lost in the whole situation. Taking time to identify what is important, and what is not, is essential.

Use a highlighter on written problems to identify words that tell you what you are solving, and give you clues about which operations to choose . Make notes in the margins by these words to help you clarify your understanding of the problem.

Remember: If you don’t know what’s being asked, it will be very difficult to know if you have a reasonable answer.

Different Types of Problem

There are three kinds of multiplicative comparison word problems (see list below). Knowing which kind of problem you have in front of you will help you know how to solve it.

Product Unknown Comparisons

Set size unknown comparisons, multiplier unknown comparisons.

The rest of this lesson will show how these three types of math problems can be solved.

Multiplication Problems: Product Unknown

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the “multiplier” amount. The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in one set, and the multiplier are called “Product Unknown” comparisons, because the total is the part that is unknown.

In order to answer the question you are being asked, you need to multiply the number in the set by the multiplier to find the product.

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the “multiplier” amount. The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed. These problems in which you know both the number in one set, and the multiplier are called “Product Unknown” comparisons, because the total is the part that is unknown.

Mary is saving up money to go on a trip. This month, she saved three times as much as money as she saved last month. Last month, she saved £ 24.00. How much money did Mary save this month?

We have been given that Mary is saving up money to go on a trip. This month, she saved three times as much as money as she saved last month. Last month, she saved £24.00. we need to find out how much money did Mary save this month?

Now, as much as tells you that you have a comparison. Three times is the multiplier. 24 is the amount in the first set. The question being asked is how much money did Mary save this month? To find the answer, we multiply 24 by 3. Therefore, we have 24.00 x 3 = 72.

It is important to clearly show that you understand what your answer means. Instead of writing just 72, we will write it as Mary saved £ 72 this month.

Note that whenever we finish a math problem of any kind, we always go back to the original problem. Think: “What is the question we are being asked?” 

Make sure that our final answer is a reasonable answer for the question we are being asked.

We were asked, “How much money did Mary save this month?” 

Our answer is: Mary saved $72.00 this month. Our answer is reasonable because it tells how much money Mary saved this month. We multiplied a whole number by a whole number, so the amount of money Mary saved this month should be more than she saved last month. Seventy-Two is more than 24 . Our answer makes sense.

Multiplication Problems: Set Size Unknown

In some multiplicative comparison word problems, the part that is unknown is the number of items in one set. You are given the amount of the second set, which is a multiple of the unknown first set, and the “multiplier” amount, which tells you how many times bigger (or more) the second set is than the first. Remember, “bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in the second set, and the multiplier are called “Set Size Unknown” comparisons, because the number in one set is the part that is unknown.

In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is “partition” or “sharing” division. Dividing the number in the second set by the multiplier will tell you the number in one set, which is the question you are being asked in this kind of problem.

In some multiplicative comparison word problems, the part that is unknown is the number of items in one set. You are given the amount of the second set, which is a multiple of the unknown first set, and the “multiplier” amount, which tells you how many times bigger (or more) the second set is than the first. Remember, “bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed. These problems in which you know both the number in the second set and the multiplier are called “Set Size Unknown” comparisons because the number in one set is the part that is unknown.

Jeff read 12 books during the month of August. He read four times as many books as Paul. How many books did Paul read?

We have been given that Jeff read 12 books during the month of August. He read four times as many books as Paul. We need to find out how many books did Paul read?

“As many as “ tells you that we have a comparison. Four times is the multiplier. 12 books is the amount in the second set. How many books did Paul read? This is the question we are being asked. To solve, divide 12 by 4. Now 12 ÷ 4 = 3. It is important to clearly show that we understand what our answer means. Instead of just writing 3, we write complete sentence that Paul read three books.

Note that whenever we finish a math word problem, always go back to the original problem. Think: “What is the question we are being asked?”  Make sure that our final answer is a reasonable answer for the question you are being asked. We were asked, “How many books did Paul read?”  Our answer is: Paul read three books. Our answer is reasonable because it tells how many books Paul read. We divided a whole number by a whole number, so the number of Paul’s books should be less than the number of Jeff’s books. Three is smaller than 12. My answer makes sense.

Multiplicative Comparison Problems: Multiplier Unknown

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the number of items in the second set, which is a multiple of the first set. The “multiplier” amount is the part that is unknown.

The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in one set, and the number in the second set are called “Multiplier Unknown” comparisons, because the multiplier is the part that is unknown.

In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is called “measurement” division.

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the number of items in the second set, which is a multiple of the first set. The “multiplier” amount is the part that is unknown. The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed. These problems in which you know both the number in one set and the number in the second set are called “Multiplier Unknown” comparisons because the multiplier is the part that is unknown. In order to answer the question you are being asked, you need to use the inverse operation of multiplication: division. This kind of division is called “measurement” division.

The gorilla in the Los Angeles Zoo is six feet tall. The giraffe is 18 feet tall. How many times taller than the gorilla is the giraffe?

We have been given that the gorilla in the Los Angeles Zoo is six feet tall. The giraffe is 18 feet tall. We need to find out how many times taller than the gorilla is the giraffe?

Taller than tells us that we have a comparison. Six feet is the amount in the first set. 18 feet is the amount in the second set. How many times taller than the gorilla is the giraffe? This is the question we are being asked. To solve this we divide18 feet by six feet. Now, 18 ÷ 6 = 3. It is important to clearly show that we understand what our answer means. Instead of just writing 3, we write the complete sentence that the giraffe is three times taller than the gorilla.

Note that whenever we finish a math word problem , always go back to the original problem. Think: “What is the question we are being asked?”  Make sure that your final answer is a reasonable answer for the question you are being asked. We were asked, “How much taller than the gorilla is the giraffe?”  Our answer is: The giraffe is three times taller than the gorilla. Our answer is reasonable because it tells how much taller the giraffe is, compared to the gorilla. We divided a whole number by a whole number, so our quotient should be less than my dividend. Three is less than 18, so our answer makes sense.

Solved Examples

Example 1 There are 287 rows in a stadium. How many students can be seated in this stadium if each row has 165 seats to be occupied?

Solution We are given that,

Number of rows in a stadium = 287

Number of seats in each row = 165

Total number of students that can be seated in the stadium = 287 x 165 = 47335.

Example 2 Henry bought 15 packets of cookies. Each packet contains 35 cookies. How many cookies in all does Henry have?

Solution We are given that

Number of packets of cookies bought by Henry = 15

Number of cookies in each packet = 35

Total number of cookies that Henry has = 15 x 35 = 525

Key Facts and Summary

• The process of finding out the product between two or more numbers is called multiplication. The result thus obtained is called the product.
• A word problem is a few sentences describing a ‘real-life’ scenario where a problem needs to be solved by way of a mathematical calculation.

Recommended Worksheets

Fact Families for Multiplication and Division (Summer Themed) Math Worksheets Multiplication and Division of Fractions (Veterans’ Day Themed) Math Worksheets Multiplication and Division Problem Solving (Halloween Themed) Math Worksheets

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Unit 3: Multiplication and division

About this unit.

In this topic, we will multiply and divide whole numbers. The topic starts with 1-digit multiplication and division and goes through multi-digit problems. We will cover regrouping, remainders, and word problems.

Multiplication intro

• Multiplication as equal groups (Opens a modal)
• Intro to multiplication (Opens a modal)
• Basic multiplication (Opens a modal)
• Multiplication with arrays (Opens a modal)
• Worked example: Whole numbers on the number line (Opens a modal)
• More ways to multiply (Opens a modal)
• Ways to represent multiplication (Opens a modal)
• Understand multiplication using groups of objects 7 questions Practice
• Multiply with arrays 7 questions Practice
• Represent multiplication on the number line 4 questions Practice

Multiplication facts

• Multiplication tables for 2-9 (Opens a modal)
• Multiplication tables for 10, 11, 12 (Opens a modal)
• Multiply by 0 or 1 14 questions Practice
• Multiply by 2 7 questions Practice
• Multiply by 3 7 questions Practice
• Multiply by 4 7 questions Practice
• Multiply by 5 7 questions Practice
• Multiply by 6 7 questions Practice
• Multiply by 7 14 questions Practice
• Multiply by 8 14 questions Practice
• Multiply by 9 14 questions Practice
• Basic multiplication 7 questions Practice

Properties of multiplication

• Properties of multiplication (Opens a modal)
• Properties and patterns for multiplication (Opens a modal)
• Associative property of multiplication (Opens a modal)
• Commutative property of multiplication review (Opens a modal)
• Associative property of multiplication review (Opens a modal)
• Distributive property review (Opens a modal)
• Commutative property of multiplication 7 questions Practice
• Associative property of multiplication 7 questions Practice
• Distributive property 4 questions Practice

Multiplying by tens

• Multiplying by multiples of 10 (Opens a modal)
• Multiplying by tens word problem (Opens a modal)
• Multiply by tens 7 questions Practice
• Multiply by tens word problems 4 questions Practice

Multiplication by 10s, 100s, and 1000s

• Multiplying 10s (Opens a modal)
• Multiplying 1-digit numbers by multiples of 10, 100, and 1000 (Opens a modal)
• Multiplying 1-digit numbers by 10, 100, and 1000 (Opens a modal)
• Multiplying 10s 7 questions Practice
• Multiply 1-digit numbers by a multiple of 10, 100, and 1000 7 questions Practice
• Multiply 1-digit numbers by 10, 100, and 1000 7 questions Practice

Multiplication: place value and area models

• Using area model and properties to multiply (Opens a modal)
• Multiplying with distributive property (Opens a modal)
• Multiplying with area model: 6 x 7981 (Opens a modal)
• Multiplying with area model: 78 x 65 (Opens a modal)
• Lattice multiplication (Opens a modal)
• Why lattice multiplication works (Opens a modal)
• Multiply 2-digits by 1-digit with distributive property 4 questions Practice
• Multiply 2-digit numbers with area models 4 questions Practice

Multi-digit multiplication

• Multiplying 2-digit by 1-digit (Opens a modal)
• Multiplying 3-digit by 1-digit (Opens a modal)
• Multiplying 3-digit by 1-digit (regrouping) (Opens a modal)
• Multiplying 4-digit by 1-digit (regrouping) (Opens a modal)
• Multiplying 2-digit numbers (Opens a modal)
• Multiplying 2-digit by 2-digit: 36x23 (Opens a modal)
• Multiplying 2-digit by 2-digit: 23x44 (Opens a modal)
• Multiplying multi-digit numbers (Opens a modal)
• Multiply without regrouping 7 questions Practice
• Multiply with regrouping 7 questions Practice
• Multiply 2-digit numbers 7 questions Practice
• Multi-digit multiplication 4 questions Practice

Relating multiplication and division

• Relating division to multiplication (Opens a modal)
• Multiplication word problem: parking lot (Opens a modal)
• Division word problem: school building (Opens a modal)
• Relate division to multiplication 7 questions Practice
• Relate division to multiplication word problems 4 questions Practice

Division intro

• The idea of division (Opens a modal)
• Intro to division (Opens a modal)
• Ways to represent division (Opens a modal)
• Division with groups of objects 7 questions Practice
• Divide with visuals 7 questions Practice

Division facts

• No videos or articles available in this lesson
• Divide by 1 11 questions Practice
• Divide by 2 10 questions Practice
• Divide by 3 10 questions Practice
• Divide by 4 10 questions Practice
• Divide by 5 10 questions Practice
• Divide by 6 10 questions Practice
• Divide by 7 10 questions Practice
• Divide by 8 10 questions Practice
• Divide by 9 10 questions Practice
• Divide by 10 10 questions Practice
• Basic division 7 questions Practice

Division problems that work out nicely

• Quotients that are multiples of 10 (Opens a modal)
• Canceling zeros when dividing (Opens a modal)
• Divide multiples of 10, 100, and 1,000 by 1-digit numbers 7 questions Practice
• Cancel zeros when dividing 7 questions Practice

Division: place value and area

• Division using place value (Opens a modal)
• Division with area models (Opens a modal)
• Divide using place value 4 questions Practice
• Divide by 1-digit numbers with area models 4 questions Practice

Multi-digit division (no remainders)

• Intro to long division (no remainders) (Opens a modal)
• Long division: 280÷5 (Opens a modal)
• Divide multi-digit numbers by 2, 3, 4, and 5 (remainders) 7 questions Practice
• Zeros in the dividend (no remainders) 4 questions Practice
• Zeros in the quotient (no remainders) 4 questions Practice
• Intro to remainders (Opens a modal)
• Understanding remainders (Opens a modal)
• Interpreting remainders (Opens a modal)
• Long division with remainders: 3771÷8 (Opens a modal)
• Long division with remainders: 2292÷4 (Opens a modal)
• Divide with remainders (2-digit by 1-digit) 4 questions Practice
• Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) 4 questions Practice
• Multi-digit division 4 questions Practice

Multi-digit division (remainders)

• Intro to long division (remainders) (Opens a modal)
• Dividing by 2-digits: 6250÷25 (Opens a modal)
• Dividing by 2-digits: 9815÷65 (Opens a modal)
• Dividing by 2-digits: 7182÷42 (Opens a modal)
• Partial quotient method of division: introduction (Opens a modal)
• Partial quotient method of division: example using very large numbers (Opens a modal)
• Divide by taking out factors of 10 4 questions Practice
• Basic multi-digit division 7 questions Practice
• Division by 2-digits 4 questions Practice

Multiplication and division word problems

• Multiplication word problem: carrots (Opens a modal)
• Division word problem: row boat (Opens a modal)
• Multiplication word problem: pizza (Opens a modal)
• Division word problem: field goals (Opens a modal)
• Multiplication, division word problem: pedaling (Opens a modal)
• Multiplication and division word problems 7 questions Practice
• Multi-step word problems with whole numbers 4 questions Practice

3rd Grade Worksheets - Represent and solve problems involving multiplication and division.

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 / 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 / 8.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ / 3, 6 x 6 = ?

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25 Division Word Problems for Grades 3 to 5 With Tips On Supporting Students’ Progress

Steven Eastes

Division word problems are important in building proficiency in division. Division is one of the bedrocks of math alongside addition, subtraction and multiplication. Therefore, students must have a deep understanding of division, its function within arithmetic and word problems, and how to apply short division and long division successfully.

Division is the mathematical process of breaking a number up into equal parts and 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, just a whole number as your answer.

What are division word problems?

Division word problems are an extension of the arithmetic division method whereby they are word problems with division at the heart. Students are expected to use the division process to find a solution to the word problem.

Typically, word problems use a real-life or real-world scenario and students are expected to interpret what the word problem is asking and apply their division knowledge to find the answer.

Division can be introduced through grouping before advancing, in higher-grade math, to the formal long division method.

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.

If you’re looking for more division word problems, explore the collection of division word problem worksheets for elementary school students.

Word Problems Grade 4 Fractions and Decimals

Download grade 4 fractions and decimals word problems to develop your students' reasoning and problem solving skills. Includes 11 questions and answers!

Division word problems in upper elementary

As children enter 3rd grade, they begin to develop their mental and written strategies for division.

Students begin to use their multiplication and times tables knowledge to assist them when solving division problems alongside their knowledge of the corresponding division and multiplication facts. 

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 learning the standard algorithm, also known as long division, students learn the partial quotients method. They practice their short division fluency to answer division word problems with whole number or integer answers, and those with a remainder.

Before entering 4th and 5th grade, students encounter division word problems and multi step problems . These use increasingly harder numbers, more than a single digit. Students move from simple division problems, such as:

‘If we have 30 students in our class and are divided into groups of 5, how many students will be in each group?’

‘If there are 56 books in our library and they are shared among 7 children, how many books would each child get?

Introducing standard algorithm division

4th grade students work towards dividing 4 digit numbers by a one digit number using partial quotients. They must interpret remainders in the correct context and present 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 introduced to the standard algorithm, or long division method. By the end of 5th grade, students should be fluent in multiplication and division, and written strategies. They must be able to apply knowledge in fraction word problems .

In addition to the 4th grade requirements, 5th grade students are expected to consolidate these formal division methods before dividing a four digit number by a two digit number using the formal method of standard algorithm division.

Again, they should understand remainders within this and present them in the correct context. 

This also flows into division word problems as children must read a multi-step problem and know how to interpret it, apply their divisional knowledge and solve the problem step-by-step.

The concept of multi-step problems builds up at each stage of your state math curriculum.

Why are word problems important for childrens’ understanding of division?

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 dividing results in a smaller answer, it is important to explore how division looks visually before providing them with word problem worksheets. This is the same when exploring arrays to support multiplication word problems .

Applying math to real life situations

Word problems are important because they provide a real-life context to help children understand division and where we encounter it in real life.

Allowing children to see how division is used in everyday situations, makes it more meaningful and relevant. In turn, this develops a deeper, more well—rounded understanding of the four operations.

Building problem solving skills

Word problems are vital to developing problem solving skills. First, students must read and understand the problem before identifying the relevant information within the contextual problem and apply their knowledge to find a solution.

This naturally builds critical thinking and a child’s reasoning ability, an important skill for any mathematician.

Developing mathematical language skills

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 vocabularies such as digit divisors, quotient and remainders, they must first understand these key words and apply them to the process of division and communicate clearly what they are aiming to do.

Deepening understanding of the inverse relationship between division and multiplication

Division word problems solidify the connection between multiplication and division. Understanding these inverse operations and the ability to interchange the skills of multiplication and division will help make connections between different mathematical concepts and deepen students’ learning. 

How to teach division word problem solving in elementary school.

Having taught the concept of division to students using concrete examples, for example, grouping or sharing counters and cubes, the next step is to advance to division word problems. 

As with all word problems, students must carefully read the question and decipher what is 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 use and then represent it visually.

Example of a division word problem

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
• Students must divide the total number of candies by the number of friends

To solve this problem we could use the partial quotient method and divide the dividend by the the divisor which would be 40 / 8.

If we do this, we would get the quotient of 5. 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.

How can we show this visually?

We could show 8 circles, each representing a child, and place a piece of candy in each circle until all 40 pieces of candy are placed equally in the circles. Each child should have 5 candies.

Students could also represent the division word problem as a bar model:

• Split the bar model into 8 sections
• Each section of the bar should have 5 pieces of candy
• Divide the 40 candies between the 8 sections

How these visual representations look:

Word problems are an important aspect of learning in Third Space Learning’s one-on-one tutoring programs.

Tutors work with students to break down word problems and identify the correct operation and strategy needed to solve the problem.

Examples of elementary division word problems

Below are examples of what can be expected in each grade with Third Space Learning’s tutoring programs from grades 3 to 5.

Students become familiar with word problems throughout their learning. They encounter word problems regularly throughout each personalized lesson.

Scaffolded and independent practice of word problems increases students’ confidence, familiarity with vocabulary and mathematical understanding.

3rd grade division word problems

Word problems for 3rd grade students, particularly division word problems, should encourage:

• Recall of their times table facts
• Division of two digit numbers by one digit numbers using mental and partial quotients
• Word problems may also involve multi-step problems

Question 1:

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

Question 2:

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.

Question 3:

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

Question 4:

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.

Question 5:

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:

4th grade division word problems

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?

Answer: 117cm

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?

Answer: 208

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?

Answer: $28.

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?

Answer: 426m

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.

5th grade division word problems

Word problems for 5th grade should prepare students for the end of elementary school. Students are familiar with the concept of standard algorithm division and dividing 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?

Answer: 674m

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
• Subtraction word problems
• 2nd grade 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 tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring 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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Multiplication and Division word problems: 3 Easy ways to master

• Author: Noreen Niazi
• Last Updated on: September 30, 2023

You’re not alone if word problems make you want to tear your hair out. 

But don’t worry; you’ve got this! You’ll quickly break through multiplication and division word problems with a few easy tricks.

Forget the confusion and frustration – it’s time to build your confidence from the ground up. Rather than seeing word problems as intimidating, consider them an exciting challenge to flex your mathematical muscles. 

With regular practice, these brain teasers will become second nature. Stay positive, believe in yourself, and keep your eyes on the prize. Conquer each problem one step at a time, and before you know it, you’ll be the word problem whiz you were always meant to be! 

Ready to get started? Let’s do this!

Multiplication and division word problems – they can seem tricky, but don’t worry, you’ve got this! These useful math skills are easier to master than you might think.

What Are Multiplication and Division Word Problems?

Multiplication and division word problems are just math problems described using words instead of numbers and symbols. They challenge you to take a wordy description of a situation, figure out what numbers are involved, and calculate the solution.

Solving them helps build valuable real-world skills. You’ll improve comprehension, critical thinking, and applying logic in new contexts. With regular practice, these word problems will become second nature!

Here are a few tips to get started:

• Read through the whole problem carefully. Identify what is being asked and what information you have been given.
• Look for keywords and phrases that indicate an operation like multiplication or division, such as ‘times,’ ‘product,’ ‘ratio,’ ‘per,’ or ‘shared equally.’ Underline or highlight them.
• Figure out what numbers correspond to what is being asked. You may need to substitute numbers for words or break longer phrases into shorter ones.
• Set up the problem using the numbers and indicated operation (x for multiplication or ÷ for division). Then solve!
• Check that your solution makes sense in the context of the original problem. Make sure all the details in the wording match your final answer.

You’ll solve multiplication and division word problems quickly with enthusiasm and practice! Stay positive, break big problems into small steps, and keep at it. You’ve got the skills – now put them to use! Before you know it, these will feel like a breeze.

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Solving Word Problems Using Diagrams

Using diagrams makes solving word problems involving multiplication and division a breeze[ 1 ]. Why diagrams? Because they help you visualize what’s going on in the problem so you can figure out how to solve it.

Let’s walk through an example, shall we? Say you have this problem: 

“24 students are going on a field trip. If each bus holds 8 students, how many busses are needed?”

• First, draw a box representing the total number of students, 24. 
• Then, draw smaller boxes inside it to represent groups of 8 students for each bus. 
• Keep adding boxes of 8 students until you’ve used up all 24 students. 
• Count the number of small boxes – that’s how many buses you need! 
• For this problem, you’ll end up with 3 boxes of 8 students, so the answer is 3 buses.

See how visualizing the problem made it so much easier to solve? Now you try one: “ A bakery made 96 cupcakes. If they put 12 cupcakes in each box, how many boxes will they need? ” Draw it out and you’ll get the answer in no time!

The key to mastering word problems is practicing. Try using diagrams to solve word problems involving multiplication and division each day. Start with simpler problems and work your way up to more complex ones. Before you know it, these problems will seem like a piece of cake! Stay enthusiastic – you’ve got this! With regular practice, you’ll be solving word problems in your sleep.

Read more about Word Problems

An easy way to Translating Words into Algebraic Expressions

The Importance of Keywords

Multiplication and division word problems can seem tricky but don’t worry—with a few easy strategies, you’ll solve them quickly! The key is identifying important keywords that indicate what operation to use. Spotting these keywords is the first step to mastery.

Look for Multiplication Triggers

Keep an eye out for words like “times,” “product,” “twice,” “triple,” or “groups of.” These words signal that multiplication is needed to solve the problem. For example:

• “Sally has 3 times as many dolls as Jenny. Jenny has 12 dolls. How many dolls does Sally have?” 3 (times as many) = multiply

“The product of 7 and 8 is what number?” Product = multiply

Watch for Division Hints

Pay attention to words such as “divided by,” “split into,” “shared equally,” or “per.” These words indicate division is required. For example:

• “42 students were divided into 6 equal groups. How many students were in each group?” Divided into = divide
• “Tom earned $84 in tips which he shared equally among 7 coworkers. How much did each coworker receive?” Shared equally = divide

Look at the Question!

The question itself frequently contains clues about whether to multiply or divide. Questions with “How many in each group?” or “How much each?” usually involve division. Questions with “How many totals?” or “What is the product?” often require multiplication.

With practice, spotting these keywords will become second nature. Look for language that implies multiplying groups or dividing a whole into parts. Soon you’ll be solving multiplication and division word problems confidently and easily! Keep at it, and don’t get discouraged—you’ve got this!

Read the Problem Carefully

The most important step to mastering word problems is reading the problem carefully. Seriously, slow down and read each word problem thoroughly. You should dive right in and start solving, but take a deep breath and read it over a few times. Look for keywords that indicate what operation to use, like ‘times’, ‘product’, ‘divided by’ or ‘quotient’. Circle numbers and variables. Draw diagrams or models if it helps make the problem clearer.

Once you’ve read it over, ask yourself some questions. What are you trying to figure out? What information do you have? What additional info do you need? Solve word problems one step at a time instead of trying to do it all simultaneously. Think about what makes sense based on the context of the problem . How many are left if Sally has 8 apples and eats 3 of them? Well, Sally started with 8 apples, so if she ate 3 of them, there must be 8 – 3 = 5 apples left. See how thinking it through logically can help.

Read more about Proportion.

Mastering Proportion Word Problems: A Step-by-Step Guide

Make Educated Guesses

Don’t be afraid to make an educated guess. Use what you know to make an estimate and see if the answer choices make sense. Eliminate options that are clearly too large or too small. Guessing strategically can increase your odds of choosing the right answer.

Draw a Diagram or Act It Out

For tricky problems, drawing a diagram, picture, or model can be extremely helpful. You can also solve the problem with blocks, coins, or a number line. Manipulating concrete objects allows you to visually represent what’s happening in the word problem, and often the solution becomes clear as day.

Check Your Work

Double-check that your solution makes sense within the context of the original problem. Do all the numbers add up? Did you use the correct operation? Plug your solution back into the problem to ensure it’s the logical answer. Carefully checking your solution will allow you to catch any silly mistakes before moving on.

With practice, these word problems will become second nature. Stay enthusiastic and remember to read carefully, think it through step-by-step, make educated guesses when needed, and always double-check your work. You’ve got this! Keep at it, and word problems will no longer seem so problematic.

Identify What the Problem Is Asking

You’ve got this! Word problems involving multiplication and division can seem tricky, but you’ll solve them quickly with some practice. The most important first step is to determine exactly what the problem is asking. Read the problem carefully and look for keywords and phrases to determine the question.

Once you know what is being asked, you can work through the problem step-by-step. The key is not to feel overwhelmed – take it slowly and be methodical. Look for numbers, quantities, and values in the problem to determine what needs to be multiplied or divided. Pay close attention to units of measurement as well, like feet, pounds, etc.

Some common keywords to look out for include:

• Times (x): Indicates multiplication, e.g. “Bob had 3 times as many apples as Jenny.”
• Product: The multiplication result, e.g., “What is the product of 4 and 6?”
• Divided by (/): Indicates division, e.g. “The class was divided into 6 groups.”
• Quotient: The result of division, e.g. “What is the quotient of 12 divided by 3?”
• Per: Can indicate either multiplication or division, e.g. “Bob earns $10 per hour” or “There are 3 boxes per crate.”

Once you’ve determined the operation, write out the numbers, values, and units of measurement given in the problem. Set up the multiplication or division problem and solve it! Double-check your work to make sure the answer makes sense. If it seems off, re-read the original problem to set it up properly.

With regular practice, these word problems will become second nature. Stay enthusiastic and remember to go slowly. You’ve got the skills – now put them to work! Keep at it; before you know it, you’ll be a word problem-solving master!

Read more about decimal and fractions

Converting Mixed Numbers to Improper Fractions: A Step-by-Step Guide

Choose the Correct Operation: Multiplication or Division

Choosing between multiplication and division can be tricky in word problems, but you’ll solve them quickly with some practice! Here are a few tips to help determine which operation you need:

Think about the question

Read the word problem carefully. Is it asking you to find a total amount, like the number of apples if you have 3 bags with 4 apples each? That’s multiplication – you need to calculate 3 x 4 = 12 apples total. Or is it asking you to find how many groups, like figuring out how many 4-apple bags you can fill if you have 12 apples? That would be 12 / 4 = 3 bags.

Look for keywords

Certain words indicate you should multiply, like ‘each’, ‘every’, ‘altogether,’ ‘total’, or ‘product’. Words like ‘share’, ‘divide’, ‘distribute’, or ‘per’ usually mean you should divide. Underline or highlight these keywords to help determine the right operation.

Figure out the unknown.

Decide what the question asks you to find – the total, number of groups, and amount in each group. Set up the problem by writing what you know, leaving the unknown blank. For example, if you have 3 bags with 4 apples in each, you know:

4 apples in each bag

? total apples

So you fill in the blank with 3 x 4 = 12. For division, do the opposite:

Then solve: 12 / 4 = 3 bags

Check your work

Make sure the answer makes sense in the context of the original problem. If you calculated 12 total apples but the question asked how many apples were in each bag, go back and try again – you used the wrong operation! With regular practice, these word problems will become second nature. Keep at it, and don’t get discouraged if you make a mistake. You’ve got this!

Show Your Work

Showing your work is one of the best ways to master multiplication and division word problems. Why? Because it helps you organize your thoughts and break down the problem into easy-to-understand steps. When you write out each step, you’ll gain confidence in solving these tricky problems.

So grab your pencil and some scrap paper – it’s time to show your work! Follow these three simple techniques:

1. Read the entire problem.

This problem has gone viral on YouTube due to two versions of the order of operations. There needs to be more clarity in which the multiplication sign is omitted. There are two different ways to approach this.

2. Identify what needs to be found.

What exactly are you trying to figure out? Circle or underline key phrases in the problem that indicate what needs to be calculated or solved. This could be a total amount, difference, product, or quotient. Knowing what you need to find will guide setting up your work.

3. Set up the problem visually.

Use addition, subtraction, multiplication, or division to represent the relationships described in the word problem. For example, if the problem refers to “groups of 6,” you would likely use multiplication (6 x ? = ?). If it refers to “sharing 12 apples among 3 friends,” you would set up 12 / 3 = ?. Setting up the mathematical operations visually is the key to solving word problems confidently!

By reading carefully, identifying what needs to be found, and setting up the problem visually with the appropriate operations, you’ll be solving multiplication and division word problems in no time. Showing your work in an organized way builds understanding and mastery. Keep practicing and stay enthusiastic – you’ve got this! Before you know it, word problems will be a breeze.

Check Your Answer

You’ve set up the problem, worked through all the steps, and now comes the moment of truth—check your answer! This is a crucial final step to build confidence in your math skills. Here are three ways to verify you nailed that multiplication or division word problem.

Double Check Your Work

Go back through each work step to ensure you made no silly mistakes. Check that numbers are in the right place value, signs are correct, and units are properly labeled. One small error could throw off your final answer, so take the time to double-check. You’ll be glad you did!

Plug In Your Answer

Pull your answer into the original problem to ensure it works out. For example, if the problem stated, “35 students are going on a field trip. Busses hold 8 students each. How many busses are needed?” and you answered 5 busses, plug that back in: 35 students / 5 busses = 7 students per bus. Perfect, your answer checks out! This strategy works for most multiplication and division word problems.

Estimate First

Before starting the problem, guess what the answer might be. Then, once you’ve worked through all the steps, compare your estimate to your actual answer. If they’re close, that’s a good sign you’re on the right track! Estimating builds number sense and helps detect unreasonable answers.

Keep practicing these useful techniques, stay enthusiastic, and you’ll be a word problem whiz before you know it! Multiplication and division problems won’t stand a chance against your math mastery. You’ve got this! Keep up the good work.

Conclusion: Mastering the art of graphing piecewise functions

You’ve got this! Armed with these three simple strategies, you’ll solve multiplication and division word problems in no time. Practice makes perfect, so keep at it. Before you know it, you’ll be breezing through these problems and impressing everyone with your math skills. Remember, take it step by step, visualize what’s happening, and check your work. With consistency and persistence, you’ll build up your confidence and competence. Soon, you’ll realize you’ve gained a valuable life skill that will serve you well for years. Stay positive, believe in yourself, and keep working at it. You’ve got this! Now get out there and show the world what you can do.

[1] Mixed multiplication and division word problems for grade 4 | K5 Learning

FAQs About Multiplication and Division Word Problems

You’ve got this! Multiplication and division word problems may seem tricky initially, but with some practice, you’ll solve them in no time. Here are some of the most frequently asked questions to help boost your confidence.

The secret is translating the words into an equation. Circle key numbers and determine what operation to use—multiplication or division. Arrange the numbers in the correct order, then solve! The more you practice, the better you’ll learn how to translate word problems into equations.

Don’t panic! Re-read the problem slowly and look for clues. Ask yourself some questions:

• What are the numbers in the problem?
• What is the question asking you to find?
• Do keywords indicate multiplication (times, product) or division (share, split)?

Work through the problem step-by-step. You can do this! Even if you make a mistake, you’ll learn from it and be better equipped for the next problem.

Here are a few tips to keep in mind:

• Pay attention to units like feet, pounds, dollars, etc. They determine what number goes where in the equation.
•  If the problem involves groups or sets, think of multiplication. If it involves splitting or sharing, think division.
•  Draw a diagram or model to represent the problem. This can help make the relationships between the numbers clearer.
• Check that your answer makes sense in the context of the original problem. Make sure the units match, and the numbers are reasonable.
• Practice regularly! The more word problems you solve, the more natural the process feels.

Believe in yourself and keep at it. You have all the skills to master multiplication and division word problems. Stay positive, translate each problem carefully, and check your work. You’ve got this! Keep practicing, and don’t hesitate to ask a teacher or parent if you have any other questions. Happy problem-solving!

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These grade 5 math word problems involve the 4 basic operations : addition, subtraction, multiplication and division. Some questions will have more than one step. The last question on each worksheet asks students to write an equation with a variable representing the unknown quantity.

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Multiplication or Division Word Problems (Grade 4)

Suggested learning targets.

• I can explain the difference between multiplicative (as many times as) and additive (more) comparisons.
• I can determine when to multiply or divide in word problems.

Additive and Multiplicative Comparison Problems

Using Bar Models

Using Drawings

Using Multiplicative Equations

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• Preparatory

Lesson Plan: Word Problems: Multiplication and Division Mathematics • Third Year of Primary School

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve one- and two-step problems where one of the steps involves multiplying or dividing numbers using multiplication facts up to 10 × 10.

Students will be able to

• identify whether a word problem can be solved by using multiplication or division,
• write equations to represent word problems,
• solve one- and two-step word problems involving multiplication and division,
• use multiplication or division to check the answer to a word problem.

Prerequisites

Students should already be familiar with

• multiplication facts up to 1 0 × 1 0 ,
• addition and subtraction of two-digit numbers,
• using bar models to model word problems,
• the fact that multiplication and division are inverse operations.

Students will not cover

• using fractions or decimals,
• solving problems with more than two steps.

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Multiplication and Division KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

One Wasn't Square

All the Digits

Cycling squares.

Multiplication Square Jigsaw

Shape Times Shape

What Do you Need?

How do you do it?

Table patterns go wild!

Journeys in Numberland

Ordering cards

Let us divide!

Word Problems on Multiplication

Word problems on multiplication for fourth grade students are solved here step by step.

Problem Sums Involving Multiplication: 1.  24 folders each has 56 sheets of paper inside them. How many sheets of paper are there altogether?

We can add 56 sheets 24 times

Since multiplication is repeated addition we can multiply 56 and 24 to get the answer.

[Sometime, more than one calculation is required.]  Therefore, altogether there are 1344 sheets.  

2. A carton holds 24 packets of biscuits. Each packet has 12 biscuits. How many biscuits can be packed in 45 cartons? 

In one carton we can pack 24 × 12 biscuits.

In 45 cartons, we can pack 24 × 12 × 45 biscuits.

24 × 12 = 288

Therefore, altogether there are 12,960 biscuits.

3. There are 226 pencils in a packet. How many pencils are there in 212 such packets?

4. A bag contains 289 apples. How many apples A will 72 such bags have?

Solution: 1 bag contains = 289 apples

72 bags contain = 289 ×  72 apples

                          2 8 9

                         × 7 2   

                          5 7 8

                +   2 0 2 3 0     

                    2 0 8 0 8  

Hence, 72 bags will contain 20,808 apples.

5. A car travels a distance of 345 km every day.  What distance will it travel in a year?

Distance travelled by the car in one day = 345 km

There are 365 days in a year.

Distance travelled by the car in 365 days = 345 km × 365

                       3 4 5                       × 3 6 5

                    1 7 2 5

                 2 0 7 0 0

          +  1 0 3 5 0 0

               1 2 5 9 2 5

Hence, the car will travel  1,25,925 km in a year.

Consider the following Examples on Word Problems Involving Multiplication:

1. A book costs $ 67. How much will be paid for 102 such books?  Solution:

The cost of one book            = $ 6 7                   6 7 Number of books                  = 1 0 2              × 1 0 2 The cost of 102 books          = $ 67 × 102        1 3 4                                           = $ 6834          + 6 7 0 0                                                                    6 8 3 4

Therefore, cost of 102 books = $ 6834  

2. A bicycle costs $ 215. How much will be paid for 87 such bicycles? 

Solution: 

The cost of one bicycle            = $ 2 1 5                   2 1 5 Number of bicycle                    = 8 7                        × 8 7 The cost of 87 bicycles            = $ 2 1 5 × 8 7        1 5 0 5                                              = $ 6834             + 1 7 2 0 0                                                                           1 8 7 0 5 Therefore, cost of 87 bicycles = $ 18705

3. The monthly salary of a man is $ 2,625. What is his annual income by salary? 

Monthly income               = $2,625                   2 6 2 5 Annual income                 = $2,625 × 12              × 1 2                                          = $31,500                 5 2 5 0                                                                  + 2 6 2 5 0                                                                      3 1 5 0 0

Therefore, annual income = $ 31,500

4. A chair costs $ 452 and a table costs $ 1750. What will be cost of 15 chairs and 30 tables? 

(i) Cost of one chair         = $ 452 Cost of 15 chairs             = $ 452 × 15                                     = $ 6,780 (ii) Cost of one table        = $ 1,750 Cost of 30 tables             = $ 1,750 × 30                                     = $ 52,500 Therefore, cost of 15 chairs and 30 tables = $ 6,780 + $ 52,500

Worksheet on  Word Problems on Multiplication:

1. Each student of class IV $ 75 for the flood victims. If there are 368 students in class IV, what is the total amount of money collected?

Answer: $ 27600

2. An orchard has 46 rows of mango trees. If there are 150 trees in each row. What is the total number of mango trees in the orchard?

Answer: 6900

3. A showroom has 165 bicycles. Each bicycle costs $ 4500. What is the total cost of all the bicycles? 

Answer: $ 742500

4. The teller in the bank received 814 notes today. If the value of each note is $ 500, what is the total amount of money collected by the teller?

Answer:  $ 407000

5. A car factory manufactures 75 cars each month. How many cars will be manufactured in the factory in one year?

Answer:  900

6. The National Library has 502 book shelves. In each shelf there are 44 books. What is the total number of books in the library?

Answer:  22088

7. Our heart beats about 72 times in a minute. How many times will it beat in an hour?

Answer:  4320

8. Shyam works for 10 hours in a day and Ram works for 9 hours in a day. Ram works for 6 days in a week and Sham works for 5 days in a week. Who works for more hours in a week and by how much?

Answer:  Ram, 4 hours

9. There are 100 baskets of fruit. Each basket has 24 kg of fruit. If half of the baskets are kept on the weighing machine, then what weight will be shown by the weighing machine?

Answer:  1200

10. A truck has 673 boxes of candies. Each box has a dozen candies in it. What is the total number of candies on the truck?

Answer:  8076

11. A packet consists of 600 chocolates. How many chocolates are there in 248 such packets?

Answer:   148800

12. A book contains 543 pages. How many pages are there in 22 such books?

Answer:   11946

13. A boat can carry 635 people. How many people can travel in 240 such boats?

Answer:   152400

14. A farmer produced 735 quintals of rice. He told it at the rate of 1,525 per quintal How much money did he get?

15. A transistor costs 2,492. Find the cost of 64 such transistors.

16. A rack can hold 1,850 books. How many books can be kept in 82 such racks.

17. A cartoon can hold 15 dozen of oranges. How many oranges are there in 924 cartons.

18. The cost of a doll is $ 524. What is the east of 680 such dolls?

19. The capacity of a water tank is 6450 litres. In a city, there are 250 such tanks. What is the storage capacity of the city?

20. A weaving machine makes 4148 m of cloth in a week. How much cloth will it in 48 weeks?

21. The water capacity of a tank is 1325 litres. Find the total capacity of such 174 tanks

22. In a village, there are 1265 farmers. Each farmer has 329 sheep. How many shees are there in all? 23. Nairitee reads 12 pages of a book in one hour How many pages are there in that book if she reads 5 hours in a day and finishes the book in 30 days?

24. A bus can carry 52 passengers in one tip. How many passengers will it carry in the month of July if it makes 5 trips in a day?

25. The monthly fee of a student a Rs. 530. There are 142 students in a class. How much fee is collected from that class?

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Related Concept

● Word Problems on Addition

● Subtraction

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Find the Missing Digits

● Multiplication

● 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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Multiplication Word Problem Area 2nd Grade

Welcome to our Multiplication Word Problems page for Second Grade. Here you will find our range of printable multiplication problems which will help your child apply and practice their multiplication and times tables skills to solve a range of 'real life' problems.

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• 2nd Grade Multiplication Problems Worksheets
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Multiplication Word Problems 2nd Grade Online Quiz

Multiplication word problems, 2nd grade multiplication problems.

Here you will find a range of problem solving worksheets involving multiplication.

Each sheet involves solving a range of written multiplication problems.

There are 3 levels of difficulty for each worksheet below: A,B and C.

Worksheet A is the easiest level, suitable for children at the beginning of their grade.

Worksheet B is a medium level worksheets for children who are working at the expected level in their grade.

Worksheet C is set at a harder level, suitable for children who are more able mathematicians.

The problems in each worksheet are similar in wording, but the numbers involved become trickier as the level gets harder.

To encourage careful checking and thinking skills, each sheet includes one 'trick' question which is not a multiplication problem. Children need to spot this word problem, and work out which operation they need to solve it.

Using these sheets will help your child to:

• apply their multiplication and times tables skills;
• apply their times table knowledge to work out related facts;
• recognise multiplication problems, and try to spot 'trick' problems;
• solve a range of 'real life' problems;
• solve multiplication problems with numbers up to 5x5;
• solve multiplicaiton problems for the 2, 5 and 10 times tables.

Some of the sheets have a UK version with spelling set for the UK.

2nd Grade Multiplication Problem Worksheets

Series 2 sheet 1 set.

• Series 2 Sheet 1A (easier)
• Series 2 Sheet 1B (medium)
• Series 2 Sheet 1C (hard)

• PDF version Series 2.1 (6 sheets)

Series 2 Sheet 2 Set

• Series 2 Sheet 2A (easier)
• UK version Sheet 2A
• Series 2 Sheet 2B (medium)
• UK Version Sheet 2B
• Series 2 Sheet 2C (hard)
• PDF version Series 2.2 (6 sheets)
• PDF version Series 2.2 (UK version) (6 sheets)

Series 2 Sheet 3 Set

• Series 2 Sheet 3A
• Series 2 Sheet 3B (medium)
• Series 2 Sheet 3C (hard)
• PDF version Series 2.3 (6 sheets)

Looking for some harder Multiplication Problems?

In our 3rd Grade Multiplication word problem area, you will find a range of multiplication word problems aimed at 3rd graders.

The following areas are covered:

• basic multiplication fact sheets;
• multiplication facts to 10x10;
• problems needing written multiplication methods to solve (TU x U)
• Multiplication Word Problem Worksheets 3rd Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Looking for more 2nd Grade Word Problems?

We have a range of real-life problems involving different measurements, such as the fastest insects, or the length of different dinosaurs!

There are a range of different skills covered, from rounding and place value, to using addition, subtraction and multiplication.

• 2nd Grade Math Word Problems

Multiplication Times Table Charts

Here you will find a selection of Multiplication Times Table Charts to 10x10 or 12x12 to support your child in learning their multiplication facts.

There is a wide selection of multiplication charts including both color and black and white, smaller charts, filled charts and blank charts.

Using these charts will help your child to:

• Learn their multiplication facts to 10x10 or 12x12;
• Practice their multiplication table.

All the free printable Math charts in this section are informed by the Elementary Math Benchmarks.

• Large Multiplication Chart
• Large Multiplication Charts Times Tables
• Multiplication Times Tables Chart to 10x10
• Times Table Grid to 12x12
• Blank Multiplication Charts to 10x10
• Blank Printable Charts to 12x12
• Multiplication Math Games

Here you will find a range of Free Printable Multiplication Games.

The following games develop the Math skill of multiplying in a fun and motivating way.

• learn their multiplication facts;
• practice and improve their multiplication table recall;
• develop their strategic thinking skills.

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Problem Solving - Multiplication and Division Worksheet

Updated:  19 Oct 2021

Practice solving word problems using one-step division and multiplication.

Editable:  Google Slides

Non-Editable:  PDF

Pages:  2 Pages

• Curriculum Curriculum:  CCSS, TEKS

Grades:  3 - 4

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This worksheet is best used as an independent practice to review one-step division and multiplication in word problems.

Multiplication and Division Word Problems Worksheet Scaffolding and Extension Tips 

In addition to individual student work time, use this multiplication and division problems worksheet as a:

• Math station/center activity
• Post-lesson exit ticket  
• Whole-class review (via smartboard)

Got fast finishers ? Students who need a challenge can create their own word problems.

For students who need extra support, provide manipulatives or encourage them to draw pictures to help solve the problems. You can also have students act out the problems in small groups to help visualize the operation.

A Variety of Ways to Prepare This Resource

Because this resource includes an answer sheet, we recommend you print one copy of the entire file. Then, make photocopies of the blank worksheet for students to complete.  

You can also turn this teaching resource into a sustainable activity! Print a few copies on cardstock and slip them into dry-erase sleeves. Students can record their answers with a dry-erase marker, then erase and reuse. 

Additionally, project the worksheet onto a screen and work through it as a class by having students record their answers in their math notebooks.

Before You Download

Use the dropdown icon on the Download button to choose between the PDF or Google Slides version of this resource. An answer key is also included with this download.

Get more handy worksheets here!  

This resource was created by Melissa McLaren, a teacher in Massachusetts and a Teach Starter Collaborator. 

Don’t stop there! We’ve got more operations activities we know your students will love:  

[resource:4704990]   [resource:678616]   [resource:46554]

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Multiplication and Division Fact Matchup Cards - Multiples of 1

A set of multiplication and division fact matchup cards for multiples of 1.

Multiplication and Division Fact Matchup Cards - Multiples of 2

A set of multiplication and division fact matchup cards for multiples of 2.

Multiplication and Division Fact Matchup Cards - Multiples of 3

A set of multiplication and division fact matchup cards for multiples of 3.

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Problems Involving Multiplication and Division Facts & Worksheets

By now, you have an understanding of the foundations of multiplication. in this lesson, we will try to understand how to interpret multiplication equations., search for worksheets, download the problems involving multiplication and division facts & worksheets.

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Table of Contents

By now, you have an understanding of the foundations of multiplication . In this lesson, we will try to understand how to interpret multiplication equations, how to interpret division equations, and how to solve problems involving multiplication and/or division.

See the fact file below for more information on the problems involving multiplication and division or alternatively, you can download our 33-page Problems Involving Multiplication and Division worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

Interpreting multiplication equations.

• Multiplication, in a basic sense, is just repeated addition .
• For example, let’s use 2 x 2 (two multiplied by two). Here, we have the value of 2 that we will add two times. Thus, 2 plus 2 gives us 4.
• Take the equation below as a sample multiplication equation.
• We can interpret the equation in two ways.
• The first way is to interpret it as the total number of objects in 5 groups with 3 objects each.
• The boxes represent the groups, while the circles are the objects.
• Therefore, if we count them all, we will get 15.
• The second way we can interpret it is as 3 groups of 5 objects each.
• Counting the objects , we will still get 15.
• Thus, we can think of the factors in a multiplication equation as a number of groups and a number of objects.

INTERPRETING DIVISION EQUATIONS

• Now, in this section we will try to understand division.
• Division is the process of splitting (or dividing) a set of objects into smaller equal subsets.
• The dividend is the larger number, the number that we will divide into smaller groups.
• The divisor is the smaller number. This number tells us “how many groups” we are going to make.
• The quotient is the answer of a division equation.
• The division symbol can also be expressed as “/”.
• Now, let’s move on to the representation. Using the equation provided, the divisor is 3. This means we need to divide the dividend (15) into 3 groups.

SOLVING PROBLEMS

• In this section, we will try to understand how to solve problems using multiplication and division.
• In the first scnario, we will solve problems involving equal groups.
• Andrea is planning to donate her old clothes to a foundation. She organized her clothes and put 4 pieces into each of her 3 small boxes.
• How many pieces of clothes is Andrea planning to donate?
• Now, read the word problem presented above. Do you have an understanding of what to do?
• What should we use? Multiplication or division?
• The answer is multiplication. This will be represented by the factors 4 and 3.
• We have another word problem presented below.
• Grace has 10 marbles. She is placing an equal number of marbles into 5 bags. How many marbles will be in each bag?
• Now, what are we going to use? Multiplication or division?
• The answer is division.

Problems Involving Multiplication and Division Worksheets

This is a fantastic bundle which includes everything you need to know about the problems involving multiplication and division across 33 in-depth pages. These are ready-to-use Problems Involving Multiplication and Division worksheets that are perfect for teaching students how to interpret multiplication equations, how to interpret division equations, and how to solve problems involving multiplication and/or division.

Complete List Of Included Worksheets

• Lesson Plan
• Problems Involving Multiplication and Division
• Complete The Equations
• Divide The Marbles
• Drawing Time
• Feed The Monkeys
• Transformation
• Show Everything

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