problem solving using multiplication and division

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Mixed multiplication & division word problems

Multiply or divide think.

These math word problems may require multiplication or division to solve.  The student will be challenged to read the problem carefully and think about the situation in order to know which operation to use.

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Multiplication and division

Here you will learn about multiplication and division, including strategies on how to multiply and divide various types of rational numbers.

Students first learn about multiplication and division in the 3 rd grade and 4 th grade with their work with operations and algebraic thinking, as well as number and operations base ten and fractions.

What is multiplication and division?

Multiplication and division are two of the four basic operations. Multiplication is finding the product of two or more numbers, and division is finding the quotient of two numbers.

Multiplication is basically the repeated addition of equal groups.

For example, 4 equal groups of 3 :

In a multiplication equation, the answer to multiplying one number by another is called the product. The multiplicand is the quantity to be multiplied by the multiplier, which will give you a product.

The product will be 0 if either the multiplicand or multiplier is 0 .

Arrays are visual models that represent multiplication.

For example, this array shows 3 rows of 6 which is the same as 3 \times 6 .

3 \times 6=18

Step by step guide: Understanding Multiplication

Multiplication is commutative. The order in which the calculation is performed does not matter.

For example,

3\times{4}=4\times{3}=12

Multiplying multi-digit numbers

To multiply multi-digit numbers, you can use the algorithm or the area model.

The area model is a rectangular model where the product represents finding the area of the rectangle.

For example, multiply 42 \times 62 using an area model.

2400+120+80+4=2604

42 \times 62=2604

Step-by-step guide: Multiplying multi-digit numbers

Multiplicative comparisons

You can use multiplication to make comparisons between quantities. Multiplicative comparisons compare two quantities by showing that one quantity is how many times larger or smaller than another quantity.

Mike has 3 lollipops. Michelle has 4 times as many lollipops as Mike. How many lollipops does Michelle have?

Michelle has 4\times 3=12 lollipops.

Jillian has 24 inches of hair ribbon. Suzanne has half that amount. How long is Suzanne’s hair ribbon?

Suzanne’s ribbon is \cfrac{1}{2} \times 24=12 \text { inches }

Step by step guide: Multiplicative comparisons

[FREE] Multiplication and Division Worksheet (Grade 4, 5 and 7)

Use this quiz to check your grade 4, 5 and 7 students’ understanding of multiplication and division. 10+ questions with answers covering a range of 4, 5 and 7 grade multiplication and division topics to identify areas of strength and support!

Multiplying rational numbers

You can multiply rational numbers. Rational numbers include multi-digit numbers, integers, fractions, and decimals. When multiplying positive and negative numbers, the following rules apply:

For example, (-3) \times(-5)=15

Step by step guide: Multiplying and dividing integers

Division shares or breaks a number into equal sized groups.

For example, the number 12 can be divided into 4 equal groups of 3 .

In a division equation, the answer you get when you divide one number by another is called the quotient.

The word quotient comes from Latin and means ‘how many times.’ When dividing, you are finding out ‘how many times’ a number goes into another number.

The quotient will only be 0 if the dividend is 0 but the divisor is not.

8 \div 0=\text {Does not exist }

Step by step guide: Understanding division

Unlike multiplication, division is not commutative. If the order of the numbers within the calculation changes, the result will change.

12 \div 4 ≠ 4 \div 12

To solve division problems with larger numbers, you can use long division.

For example, 452.1 \div 3

Step-by-step guide: Long division

Step by step guide: Dividing multi-digit numbers

Division can also be done with positive and negative integers, fractions, and decimals. When dividing positive and negative numbers, the following rules apply:

For example, (-20) \div (-5)=4

Step by step guide: Multiplying and dividing rational numbers

Common Core State Standards

How does this relate to 4 th – 7 th grade math?

• Grade 3: Operations and Algebraic Thinking ( 3.OA.A.1) Interpret products of whole numbers, for example, interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
• Grade 3: Operations and Algebraic Thinking (3.OA.A.2) Interpret whole-number quotients of whole numbers, for example, interpret 56 \div 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.
• Grade 3: Operations and Algebraic Thinking (3.OA.C.7) Fluently multiply and divide within 100 , using strategies such as the relationship between multiplication and division.
• Grade 4: Operations and Algebraic Thinking (4.OA.2) Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
• Grade 4: Number and Operations – Fractions (4.NF.B.4) Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
• Grade 5: Number and Operations Base Ten (5.NBT.B.5) Fluently multiply multi-digit whole numbers using the standard algorithm.
• Grade 5: Number and Operations – Fractions (5.NF.B.7) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
• Grade 6: Number System (6.NS.C.6) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
• Grade 7: Number System (7.NS.A.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

How to do multiplication and division

There are several strategies to multiply and divide numbers. For more specific step-by-step guides, check out the individual pages linked in the “What is multiplication and division?” section above or read through the examples below.

In order to multiply using a visual model:

Draw the array.

• Count the objects in each row.
• Find the total .

In order to divide using a visual model:

Count the objects in each group.

• Write the answer .

In order to multiply and divide multi-digit numbers:

Perform the multiplication or division algorithm.

Write the answer.

In order to find multiplicative comparisons:

Draw a model.

Write an equation.

Solve the equation and label the answer.

Multiplication and division examples

Example 1: multiply using a model.

Use a visual model to multiply 5 \times 3.

5 x 3 is 5 rows of 3.

2 Count the objects in each row.

3 Find the total .

There are 3 chips in each row, 3+3+3+3+3=15

3 \times 5=15

Example 2: multiply using algorithm

Multiply 99 \times 7.

Using the algorithm,

99 \times 7=693

Example 3: multiply and divide rational numbers

Multiply 1.23 \times 3.2.

1.23 \times 3.2=3.936

Example 4: divide using a visual model

Divide: 9 \div 3

Example 5: dividing rational numbers

Divide: 15.4 \div 2

15.4 \div 2=7.7

Example 6: multiplicative comparison

Bobby has 3 baseball cards. Joey has five times as many cards as Bobby. How many cards does Joey have?

3 \times 5= \, ?

Joey has 15 baseball cards.

Teaching tips for multiplication and division

• Use manipulatives to reinforce the conceptual understanding of multiplication and division.
• Include real world scenarios so that students can connect the mathematical concepts to the world around them.
• Reinforce to students that the concept of multiplication and division is the same regardless if the numbers are whole numbers or rational numbers.
• Using the area model for multiplication and division can be a fun way for students to understand multiplication and division while also reinforcing math facts.
• To practice multiplication facts, consider using digital and non-digital games instead of flashcards. Game playing is a fun way for students to remember the times tables.

Easy mistakes to make

• Confusing the rules for multiplying and dividing positive and negative numbers For example, multiplying (-4)\times (-8) and getting a product of -32 instead of 32 .
• Misinterpreting the meaning of key words in word problems resulting in using the incorrect operation For example, thinking that the word “of” means to divide instead of multiply.

Practice multiplication and division questions

1) Which multiplication expression represents this array?

Count the number of objects in each row.

There are 5 objects in each row which is 5+5.

5+5 is the same as 2 \times 5.

So, 2 \times 5 is the correct expression.

2) Multiply 104 \times 3.

Use the algorithm for multiplying multi-digit numbers, regrouping when necessary.

104 \times 3=312

3) Multiply 53 \times 32.

You can use the area model to multiply 53 \times 32.

Add the products together: 1500+100+90+6=1696

53 \times 32=1696

4) Use the array to find the quotient of 16 \div 4 .

Divide the array into 4 equal groups and then count how many objects are in each group.

16 \div 4 = 4

5) Divide 128 \div 4.

Divide the numbers using the algorithm for long division.

128 \div 4= 32

6) Chris has 3 pencils. Pam has four times as many pencils as Chris. How many pencils does Pam have?

Draw a picture.

4 \times 3=12

Pam has 12 pencils.

Multiplication and division FAQs

Yes, the rules for multiplying and dividing positive and negative numbers hold true regardless if the numbers are whole numbers or rational numbers. Step-by-step guide : Negative numbers

Knowing your multiplication facts and division facts helps when solving problems.

Repeated subtraction is a way for students to begin to develop an understanding of division.

There is not one best strategy to use when multiplying multi-digit numbers. Some strategies, can be quicker than others, but not better.

Knowing your multiplication tables helps to answer questions faster than when you do not know them.

The commutative property of multiplication is: 5 \times 3=3 \times 5 , the order of the numbers does not matter.

The next lessons are

• Types of numbers
• Rounding numbers
• Factors and multiples

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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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Multiplication and Division Word Problems

Here are some examples of multiplication and division word problems. The videos will illustrate how to use the block diagrams (Singapore Math) method to solve word problems. Go to Math Word Problems for more examples.

The following diagram shows how to use bar models for multiplication and division. Scroll down the page for more examples and solutions on using the multiplication and division part-whole model.

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Multiplication Word Problem Worksheets

This page hosts a vast collection of multiplication word problems for 3rd grade, 4th grade, and 5th grade kids, based on real-life scenarios, practical applications, interesting facts, and vibrant themes. Featured here are various word problems ranging from basic single-digit multiplication to two-digit and three-digit multiplication. Another set of printable worksheets hone children's multiplication skill by multiplying large numbers. Free worksheets are included.

Single-digit Multiplication Word Problems

The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios.

• Download the set

Multiplication Word Problems: Two-digit times Single-digit

The word problems featured here require a grade 3 learner to find the product by multiplying a two-digit number by a single-digit multiplier.

Multiplication Word Problems: Two-digit times Two-digit

The worksheets presented here involve multiplication of two-digit numbers. Read the word problems and find the product. Apply long multiplication (also known as column multiplication) method for easy calculation.

Theme Based Word Problems

Our engaging theme-based pdf worksheets help young minds understand the fundamentals of multiplication. Answer the word problems based on three fascinating themes - Winter Season, Ice rink and Library.

Multiplication Word Problems: Three-digit times Two-digit

Read the word problems featured in these printable worksheets for grade 4 and find the product of three-digit and two-digit numbers. Write down your answers and use the answer key below to check if they are right.

Three-digit Multiplication Word Problems

Solve these well-researched word problems that involve three-digit multiplication. Perform multiplication operation and carry over numbers carefully to find the product.

Multiplication: Three or Four-digit times Single-digit

The word problems featured here are based on practical applications and fact-based situations. Multiply a three or four-digit number by a single-digit multiplier to find the correct product.

Multi-digit Word Problems: Multiplying Large Numbers

Sharpen your skills by solving these engaging multi-digit word problems for grade 5. Apply long multiplication method to solve the problems. Use the answer key to check your answers.

Related Worksheets

» Addition Word Problems

» Subtraction Word Problems

» Division Word Problems

» Word Problems

» Multiplication

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1.7: Solving Equations by Multiplication and Division

• Last updated
• Save as PDF
• Page ID 23213

• David Arnold
• College of the Redwoods

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In Section 1.6, we stated that two equations that have the same solutions are equivalent . Furthermore, we saw that adding the same number to both sides of an equation produced an equivalent equation. Similarly, subtracting the same the number from both sides of an equation also produces an equivalent equation. We can make similar statements for multiplication and division.

Multiplying both Sides of an Equation by the Same Quantity

Multiplying both sides of an equation by the same quantity does not change the solution set. That is, if

\[ a = b\nonumber \]

then multiplying both sides of the equation by c produces the equivalent equation

\[ a \cdot c = b \cdot c\nonumber \]

provided c ≠ 0.

A similar statement can be made about division.

Dividing both Sides of an Equation by the Same Quantity

Dividing both sides of an equation by the same quantity does not change the solution set. That is, if

then dividing both sides of the equation by c produces the equivalent equation

\[ \frac{a}{c} = \frac{b}{c},\nonumber \]

In Section 1.6, we saw that addition and subtraction were inverse operations. If you start with a number, add 4 and subtract 4, you are back to the original number. This concept also works for multiplication and division.

Multiplication and Division as Inverse Operations

Two extremely important observations:

The inverse of multiplication is division . If we start with a number x and multiply by a number a, then dividing the result by the number a returns us to the original number x . In symbols,

\[ \frac{a \cdot x}{a} = x.\nonumber \]

The inverse of division is multiplication . If we start with a number x and divide by a number a , then multiplying the result by the number a returns us to the original number x . In symbols,

\[ a \cdot \frac{x}{a} = x.\nonumber \]

Let's put these ideas to work.

Solve the equation 3 x = 24 for x .

To undo the effects of multiplying by 3, we divide both sides of the equation by 3.

\[ \begin{aligned} 3x= 24 ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{3x}{3} = \frac{24}{3} ~ & \textcolor{red}{ \text{Divide both sides of the equation by 3.}} \\ x = 8 ~ & \textcolor{red}{ \text{ On the left, dividing by 3 "undoes" the effect}} \\ ~ & \textcolor{red}{ \text{ of multiplying by 3 and returns to } x. \text{ On the right,}} \\ ~ & \textcolor{red}{ 24/3 = 8.} \end{aligned}\nonumber \]

To check, substitute the solution 8 into the original equation.

\[ \begin{aligned} 3x = 24 ~ & \textcolor{red}{ \text{ Original equation.}} \\ 3(8) = 24 ~ & \textcolor{red}{ \text{Substitute 8 for } x.} \\ 24 = 24 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \end{aligned}\nonumber \]

That fact that the last line of our check is a true statement guarantees that 8 is a solution of 3x = 24.

Solve for x : 5 x = 120.

Solve the following equation for x .

\[ \frac{x}{7} = 12\nonumber \]

To undo the effects of dividing by 7, we multiply both sides of the equation by 7.

\[ \begin{aligned} \frac{x}{7} = 12 ~ & \textcolor{red}{ \text{Original equation.}} \\ \frac{84}{7} = 12 ~ & \textcolor{red}{ \text{ Multiply both sides of the equation by 7.}} \\ x = 84 ~ & \textcolor{red}{ \text{ On the left, multiplying by 7 "undoes" the effect}} \\ ~ & \textcolor{red}{ \text{ of dividing by 7 and returns to } x. \text{ On the right,}} \\ ~ & \textcolor{red}{ 7 \cdot 12 = 84.} \end{aligned}\nonumber \]

To check, substitute the solution 84 into the original equation.

\[ \begin{aligned} \frac{x}{7} = 12 & \textcolor{red}{ \text{ Original equation.}} \\ \frac{84}{7} = 12 ~ & \textcolor{red}{ \text{ Substitute 84 for } x.} \\ 12 = 12 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \end{aligned}\nonumber \]

That fact that the last line of our check is a true statement guarantees that 84 is a solution of x /7 = 12.

Solve for x : x /2 = 19

Word Problems

In Section 1.6 we introduced Requirements for Word Problem Solutions . Those requirements will be strictly adhered to in this section.

Fifteen times a certain number is 45. Find the unknown number.

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions.

1. Set up a Variable Dictionary . We can satisfy this requirement by simply stating “Let x represent a certain number.”

2. Set up an equation . “Fifteen times a certain number is 45” becomes

\[ \begin{array}{c c c c} \colorbox{cyan}{15} & \text{times} & \colorbox{cyan}{a certain number} & \text{is} & \colorbox{cyan}{45} \\ 15 & \cdot & x & = & 45 \end{array}\nonumber \]

3. Solve the Equation . To “undo” the multiplication by 15, divide both sides of the equation by 15.

\[ \begin{aligned} 15x = 45 ~ & \textcolor{red}{ \text{ Original equation. Write 15 } \cdot x \text{ as 15}x} \\ \frac{15x}{15} = \frac{45}{15} ~& \textcolor{red}{ \text{ Divide both sides of the equation by 15.}} \\ x = 3 ~ & \textcolor{red}{ \text{ On the left, dividing by 15 "undoes" the effect}} \\ ~ & \textcolor{red}{ \text{ of multiplying by 15 and returns to } x. \text{ On the right,}} \\ ~ & \textcolor{red}{45/15 = 3.} \end{aligned}\nonumber \]

4. Answer the Question . The unknown number is 3.

5. Look Back . Does the solution 3 satisfy the words of the original problem? We were told that “15 times a certain number is 45.” Well, 15 times 3 is 45, so our solution is correct.

Seven times a certain number is one hundred five. Find the unknown number.

The area of a rectangle is 120 square feet. If the length of the rectangle is 12 feet, find the width of the rectangle.

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions .

1. Set up a Variable Dictionary . When geometry is involved, we can create our variable dictionary by labeling a carefully constructed diagram. With this thought in mind, we draw a rectangle, then label its length, width, and area.

The figure makes it clear that W represents the width of the rectangle. The figure also summarizes information needed for the solution.

2. Set up an equation . We know that the area of a rectangle is found by multiplying its length and width; in symbols,

\[ A = LW.\nonumber \]

We’re given the area is A = 120 ft 2 and the length is L = 12 ft. Substitute these numbers into the area formula (1.1) to get

\[120 = 12W.\nonumber \]

3. Solve the Equation . To “undo” the multiplication by 12, divide both sides of the equation by 12.

\[ \begin{aligned} 120 = 12W ~ & \textcolor{red}{ \text{ Our equation.}} \\ \frac{120}{12} = \frac{12W}{12} ~ & \textcolor{red}{ \text{ Divide both sides of the equation by 12.}} \\ 10 = W ~ & \textcolor{red}{ \text{ On the right, dividing by 12 "undoes" the effect}} \\ ~ & \textcolor{red}{ \text{ of multiplying by 12 and returns to } W. \text{ On the left,}} \\ ~ & \textcolor{red}{120/12 = 10.} \end{aligned}\nonumber \]

4. Answer the Question . The width is 10 feet.

5. Look Back . Does the found width satisfy the words of the original problem? We were told that the area is 120 square feet and the length is 12 feet. The area is found by multiplying the length and width, which gives us 12 feet times 10 feet, or 120 square feet. The answer works!

The area of a rectangle is 3,500 square meters. If the width is 50 meters, find the length.

A class of 23 students averaged 76 points on an exam. How many total points were accumulated by the class as a whole?

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. We can set up our variable dictionary by simply stating “Let T represent the total points accumulated by the class.” 2. Set up an equation. To find the average score on the exam, take the total points accumulated by the class, then divide by the number of students in the class. In words and symbols,

\[ \begin{array}{c c c c c} \colorbox{cyan}{Total Points} & \text{divided by} & \colorbox{cyan}{ Number of Students} & \text{equals} & \text{Average Score} \\ T & \div & 23 & = & 76 \end{array}\nonumber \]

An equivalent representation is

\[ \frac{T}{23} = 76.\nonumber \]

3. Solve the Equation . To “undo” the division by 23, multiply both sides of the equation by 23.

\[ \begin{aligned} \frac{T}{23} = 76 & \textcolor{red}{ \text{ Our equation.}} \\ 23 \cdot \frac{T}{23} = 76 \cdot 23 & \textcolor{red}{ \text{ Multiply both sides of the equation by 23.}} \\ T = 1748 & \textcolor{red}{ \text{ On the left, multiplying by 23 "undoes" the effect}} \\ ~ & \textcolor{red}{ \text{ of dividing by 23 and returns to } T. \text{ On the right, }} \\ ~ & \textcolor{red}{76 \cdot 23 = 1748.} \end{aligned}\nonumber \]

4. Answer the Question . The total points accumulated by the class on the exam is 1,748.

5. Look Back . Does the solution 1,748 satisfy the words of the original problem? To find the average on the exam, divide the total points 1,748 by 23, the number of students in the class. Note that this gives an average score of 1748 ÷ 23 = 76. The answer works!

Try it out!

A class of 30 students averaged 75 points on an exam. How many total points were accumulated by the class as a whole?

In Exercises 1-12, which of the numbers following the given equation are solutions of the given equation?

1. \(\frac{x}{6} = 4\); 24, 25, 27, 31

2. \(\frac{x}{7} = 6\); 49, 42, 43, 45

3. \(\frac{x}{2} = 3\); 6, 9, 13, 7

4. \(\frac{x}{9} = 5\); 45, 46, 48, 52

5. \(5x = 10\); 9, 2, 3, 5

6. \(4x = 36\); 12, 16, 9, 10

7. \(5x = 25\); 5, 6, 8, 12

8. \(3x = 3\); 1, 8, 4, 2

9. \(2x = 2\); 4, 8, 1, 2

10. \(3x = 6\); 2, 9, 5, 3

11. \(\frac{x}{8} = 7\); 57, 59, 63, 56

12. \(\frac{x}{3} = 7\); 24, 21, 28, 22

In Exercises 13-36, solve the given equation for x.

13. \(\frac{x}{6} = 7\)

14. \(\frac{x}{8} = 6\)

15. \(2x = 16\)

16. \(2x = 10\)

17. \(2x = 18\)

18. \(2x = 0\)

19. \(4x = 24\)

20. \(2x = 4\)

21. \( \frac{x}{4} = 9\)

22. \( \frac{x}{5} = 6\)

23. \(5x = 5\)

24. \(3x = 15\)

25. \(5x = 30\)

26. \(4x = 28\)

27. \( \frac{x}{3} = 4\)

28. \( \frac{x}{9} = 4\)

29. \( \frac{x}{8} = 9\)

30. \( \frac{x}{8} = 2\)

31. \( \frac{x}{7} = 8\)

32. \( \frac{x}{4} = 6\)

33. \(2x = 8\)

34. \(3x = 9\)

35. \( \frac{x}{8} = 5\)

36. \(\frac{x}{5} = 4\)

37. The price of one bookcase is $370. A charitable organization purchases an unknown number of bookcases and the total price of the purchase is $4,810. Find the number of bookcases purchased.

38. The price of one computer is $330. A charitable organization purchases an unknown number of computers and the total price of the purchase is $3,300. Find the number of computers purchased.

39. When an unknown number is divided by 3, the result is 2. Find the unknown number.

40. When an unknown number is divided by 8, the result is 3. Find the unknown number.

41. A class of 29 students averaged 80 points on an exam. How many total points were accumulated by the class as a whole?

42. A class of 44 students averaged 87 points on an exam. How many total points were accumulated by the class as a whole?

43. When an unknown number is divided by 9, the result is 5. Find the unknown number.

44. When an unknown number is divided by 9, the result is 2. Find the unknown number.

45. The area of a rectangle is 16 square cm. If the length of the rectangle is 2 cm, find the width of the rectangle.

46. The area of a rectangle is 77 square ft. If the length of the rectangle is 7 ft, find the width of the rectangle.

47. The area of a rectangle is 56 square cm. If the length of the rectangle is 8 cm, find the width of the rectangle.

48. The area of a rectangle is 55 square cm. If the length of the rectangle is 5 cm, find the width of the rectangle.

49. The price of one stereo is $430. A charitable organization purchases an unknown number of stereos and the total price of the purchase is $6,020. Find the number of stereos purchased.

50. The price of one computer is $490. A charitable organization purchases an unknown number of computers and the total price of the purchase is $5,880. Find the number of computers purchased.

51. A class of 35 students averaged 74 points on an exam. How many total points were accumulated by the class as a whole?

52. A class of 44 students averaged 88 points on an exam. How many total points were accumulated by the class as a whole?

53. 5 times an unknown number is 20. Find the unknown number.

54. 5 times an unknown number is 35. Find the unknown number.

55. 3 times an unknown number is 21. Find the unknown number.

56. 2 times an unknown number is 10. Find the unknown number.

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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Multiplication and Division KS2

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

One Wasn't Square

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Cycling Squares

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you replace the letters with numbers? Is there only one solution in each case?

Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

How Do You Do It?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Journeys in Numberland

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Ordering Cards

This problem is designed to help children to learn, and to use, the two and three times tables.

Let Us Divide!

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Find at least one way to put in some operation signs to make these digits come to 100.

Flashing Lights

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Four Goodness Sake

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Multiplication Squares

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

Cubes Within Cubes

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Which Is Quicker?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Odd Squares

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Up and Down Staircases

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

An Easy Way to Multiply by 10?

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

Multiples Grid

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Factors and Multiples Game

This game can replace standard practice exercises on finding factors and multiples.

Music to My Ears

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

What's in the Box?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Factor-multiple Chains

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Picture a Pyramid ...

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Which Symbol?

Choose a symbol to put into the number sentence.

Times Tables Shifts

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Counting Cogs

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Follow the Numbers

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Curious Number

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Factor Track

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

So It's Times!

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

Square Subtraction

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

This Pied Piper of Hamelin

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Multiply Multiples 2

Can you work out some different ways to balance this equation?

Multiply Multiples 3

Have a go at balancing this equation. Can you find different ways of doing it?

Division Rules

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Always, Sometimes or Never? Number

Are these statements always true, sometimes true or never true?

Satisfying Four Statements

Can you find any two-digit numbers that satisfy all of these statements?

Picture Your Method

Can you match these calculation methods to their visual representations?

Compare the Calculations

Can you put these four calculations into order of difficulty? How did you decide?

Dicey Array

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

4 by 4 Mathdokus

Can you use the clues to complete these 4 by 4 Mathematical Sudokus?

Xavi's T-shirt

How much can you read into a T-shirt?

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Multiplication Word Problems 4th Grade

Welcome to our Multiplication Word Problems for 4th 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 at a 4th grade level.

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• 4th Grade Multiplication Problems Worksheets
• Easier & Harder Multiplication Worksheets
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Multiplication Word Problems 4th Grade Online Quiz

Multiplication word problems, 4th 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 at a 4th grade level;
• 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.

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

4th Grade Multiplication Word Problem Sheets

Series 4 sheet 1 set.

• Series 4 Sheet 1A (easier)
• Series 4 Sheet 1B (medium)
• Series 4 Sheet 1C (hard)

• PDF Series 4.1 (6 sheets)
• PDF Series 4.1 UK version (6 sheets)

Series 4 Sheet 2 Set

• Series 4 Sheet 2A (easier)
• Series 4 Sheet 2B (medium)
• Series 4 Sheet 2C (hard)
• PDF Series 4.2 (6 sheets)
• PDF Series 4.2 UK version (6 sheets)

Series 4 Sheet 3 Set

• Series 4 Sheet 3A (easier)
• Series 4 Sheet 3B (medium)
• Series 4 Sheet 3C (hard)
• PDF version Series 4.3 (6 sheets)
• PDF version Series 4.3 UK version (6 sheets)

Multiplication Word Problems Walkthrough Video

This short video walkthrough shows several problems from our Multiplication Problems Worksheet 4.3A being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

Looking for some easier Multiplication Problems?

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

The following areas are covered:

• basic multiplication fact sheets;
• multiplication facts to 10x10;
• 2 digits x 1 digit
• Multiplication Word Problem Worksheets 3rd Grade

Looking for some harder Multiplication Problems?

In our 5th Grade Multiplication word problem area, you will find a range of multiplication problems aimed at 5th graders.

• multiplication fact sheets;
• multiplication related facts to 10x10 e.g. 6 x 70, 8 x 0.6, etc;
• problems needing written multiplication methods to solve e.g. 2 digits x 2 digits, decimal multiplication
• Multiplication Problems Printable 5th Grade

More Recommended Math Worksheets

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

Looking for more 4th Grade Word Problems?

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

• 4th 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.

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at solving multiplication word problems by tens and hundreds.

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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

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• Subtraction Word Problems Subtraction Facts Word Problems With Differences from 5 to 12
• Multiplication Word Problems One-Step Multiplication Word Problems up to 10 × 10
• Division Word Problems Division Facts Word Problems with Quotients from 5 to 12
• Multi-Step Word Problems Easy Multi-Step Word Problems

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Course: 4th grade   >   Unit 5

• Division word problem: field goals
• Multiplication word problem: pizza

Multiplication and division word problems

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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Two Step Problems Addition, Subtraction, Multiplication & Division (All Basic Operators) Worksheets

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

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Two Step Problems Addition, Subtraction, Multiplication & Division (All Basic Operators) Worksheets Math Problems “Two-step Addition, Subtraction, Division & Multiplication Worksheets Problems” is a comprehensive resource designed to strengthen students’ proficiency in fundamental arithmetic operations. These worksheets offer a structured approach to mastering two-step problem-solving, integrating addition, subtraction, division, and multiplication. Varied Problem Types: Each worksheet presents a range of two-step problems, ensuring students encounter diverse scenarios that require different combinations of operations. Progressive Difficulty: Problems are organized by complexity, allowing students to gradually advance from basic to more challenging tasks. Answer Keys: Detailed answer keys accompany each worksheet, facilitating easy assessment and providing students with immediate feedback. Skill Reinforcement: Through repeated practice, students reinforce their understanding of addition, subtraction, division, and multiplication, building fluency and confidence. Whether used in the classroom, for homework assignments, or as supplementary practice, “Two-step Addition, Subtraction, Division & Multiplication Worksheets Problems” equips students with the skills they need to tackle multi-step mathematical problems with confidence and precision. Worksheets are made in 8.5” x 11” Standard Letter Size. This resource is helpful in students’ assessment, Independent Studies, group activities, practice and homework. This product is available in PDF format and ready to print as well.

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