problem solving using multiplication and division

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Word Problems
Multiplication & division

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Multiplication & division word problems

Mixed multiplication & division.

These grade 4 math worksheets have mixed multiplication and division word problems . All numbers are whole numbers with 1 to 4 digits. Division questions may have remainders which need to be interpreted (e.g. "how many left over"). In the last question of each worksheet, students are asked to write an equation with a variable for the unknown quantity.

problem solving using multiplication and division

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Multiplication Division Worksheets

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Welcome to the Math Salamanders Multiplication Division Worksheets area.

Here you will find our free worksheet generator for generating your own multiplication & division times table worksheets and answers.

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Using the random sheet generator will allow you to:

choose the number range and number of questions you wish the worksheet to have;
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Multiplication & Division Tables Worksheet Generator

Here is our random worksheet generator for free combined multiplication and division worksheets.

Using this generator will let you create your own worksheets for:

Multiplying and dividing with numbers to 5x5;
Multiplying and dividing with numbers to 10x10;
Multiplying and dividing with numbers to 12x12;
Multiply and divide a range of decimals and whole numbers by 10, 100 and 1000;
Multiplying and divide with 10s e.g. 4 x 30, 120 ÷ 4
Multiplying and divide with 100s e.g. 6 x 400, 800 ÷ 2
Multiplying and divde with tenths e.g. 3 x 0.7, 3.5 ÷ 5
Multiplying and dividing with a single times table;
Practicing multiplication and division with selected times tables;

To start creating your sheet, choose an option from the Number values box below.

Multiplication & Division Worksheet Generator

4 Steps to Your Worksheets...

Choose your multiplication and division tables
Choose the number of questions
View your sheet
Print your sheet

(Optional) Give your worksheet a title.

(Optional) Write out any instructions to go at the top of the sheet.

Select Multiplication & Division Tables:

Decimal Values:

Multiplier/dividend values:

Number of Questions:

Your worksheet will appear below.

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Other Recommended Worksheets

Here are some of our other related worksheets you might want to look at.

More Multiplication & Division Worksheets

We also have some more multiplication and division worksheets suitable for 5th and 6th graders.

Topics covered include multiplying and dividing by 10 and 100, and also multiplying and dividing negative numbers.

Multiply and Divide by 10 100 Worksheets
Multiply and Divide Negative Numbers (randomly generated)

Multiplication Worksheet Generator

Here is our free generator for multiplication worksheets.

This easy-to-use generator will create randomly generated multiplication worksheets for you to use.

Each sheet comes complete with answers if required.

The areas the generators cover includes:

Multiplying with numbers to 5x5;
Multiplying with numbers to 10x10;
Multiplying with numbers to 12x12;
Multiply with up to 5 digits x 3 digits;
Practicing a single times table;
Practicing selected times tables;

The Times Table Worksheets Generator will help your child to learn and practice their times tables only.

The Free Multiplication Worksheets Generator will help your child practice a wider range of multiplication skills.

The Multi-Digit Multiplication Worksheet Generator will help your child practice long multiplication.

Times Tables Worksheets
Free Multiplication Fact Worksheets
Multi-Digit Multiplication Worksheet Generator

Division Worksheet Generator

Here is our free generator for division worksheets.

This easy-to-use generator will create randomly generated division worksheets for you to use.

The areas the generator covers includes:

Dividing with numbers to 5x5;
Dividing with numbers to 10x10;
Dividing with numbers to 12x12;
Dividing with a single times table;
Long division up to 5-digits by 2-digits
Practicing division with selected times tables;

These free printable math worksheets can be used in a number of ways to help your child with their division table learning.

Division Facts Worksheets (randomly generated)
Long Division Problems with Answers (randomly generated)
Multiplication Math Games

Here you will find a range of Free Printable Multiplication Games to help kids learn their multiplication facts.

Using these games will help your child to learn their multiplication facts to 5x5 or 10x10, and also to develop their memory and strategic thinking skills.

Math Division Games

Here you will find a range of Free Printable Division Games to help kids learn their division facts.

Using these games will help your child to learn their division facts, and also to develop their memory and strategic thinking skills.

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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

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.

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

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

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November 27, 2019

Multiplication and Division Word Problems

With these steps, you will never resent multiplication and division word problems again! Using these strategies for solving word problems will help your students master mixed word problems. Multiplication and Division Word Problems are so challenging for many students. It doesn’t matter whether they are in elementary school or high school. Word problems in general cause students to have to first read a problem and then comprehend what it is asking. Lastly, they have to actually choose the correct operation and get the arithmetic correct. As teachers, the first time we hand out multiplication and division word problems worksheets we immediately see how many students get them wrong. Don’t even get me started on mixed multiplication and division word problems. This is where the resentment begins!

Multiplication and Division Word Problems Grade 3

As teachers, we all know that this is a challenge! Whether you are a first-year teacher or even a veteran teacher, it is obvious that this math skill proves to be a very difficult one. 3rd grade word problems become very challenging because they are no longer basic addition and subtraction word problems like in kindergarten through second grade. Our students are now being exposed to mixed multiplication and division word problems.

When students were in the primary grades they had a 50 percent shot of getting the operation correct because they only had two options to choose from. Also, many of the problems had a keyword like total, altogether, left or combine that helped them know what to do. But in 3rd grade, we introduce two step addition, subtraction, multiplication and division word problems. These include all the operations so their chances of guessing correctly have now gone from 50 percent down to 25 percent. Then when you add in the addition of two-step word problems that percent goes down to less than 7 percent.

Wow! Have you ever even thought about that? This why as teachers we start to notice that students are struggling with word problems. Because in lower grades they have a better chance of just guessing and getting the problems correct. As they get in the upper elementary grades they start getting more word problems wrong which makes that red flag go up that these students do not really understand word problems. This is why many teachers resent 3rd grade multiplication and division word problems.

Numberless Word Problems

Starting in first grade, or maybe even kindergarten, our students should be exposed to word problems without numbers. This will help them start developing an understanding of the word problem scenarios and not just guessing the operation. If you have not already checked out numberless word problems then you need to do that now. These have been in a game-changer in my classroom at getting students to understand the scenarios rather than just guessing the operation, that’s why I created FREE videos and a step by step guide to start using them in your classroom. In addition to everything I am telling you in the paragraph below, I use numberless word problems a couple of times a week as my number talks. When using numberless word problems, I am sure to go over one and two step multiplication and division word problems as well.

It’s more than just Multiplication and Division Word Problems Worksheets

So what strategies do I use to teach multiplication and division word problems? Well, to be honest, there are many. Word problems are not one of those skills that you will be able to teach in one day. Heck, you won’t even be able to have them master this skill in one week. They are a skill that you will need to practice for months before your students will ever have the chance to fully master this skill. Teaching word problems involves using many different strategies and interventions, not just one.

The first strategy I always use is taking out the numbers. I have them look at the scenario of the multiplication and division word problems. As they are looking at the scenarios, I have them act out what is happening in the problems. This means that I split my students into groups and give each group a word problem without any numbers. Then I give them time as a group to come up with a skit to show what is happening in their problem. After a few minutes, I then will display that group’s word problem on the board. They will read the problem to the class and then act out the skit. We do this strategy one day every couple of weeks, just to get in that repetition.

Finding keywords for multiplication and division word problems helps, but should not be the only way.

The next strategy I use is to CUBE the multiplication and division word problem. If you do not know what CUBES is then here is a short version. It is an acronym where each letter stands for a different thing to do in the word problem.

C-circle the numbers.

U-underline the question.

B-Box the keywords or math action words.

E-eliminate extra information or silly answer choices.

S-show your work to solve the problem.

This strategy is only beneficial if the students are doing it while actually thinking about what is happening in the problem. For instance, when I first taught this strategy as a first-year teacher I kept thinking this doesn’t work. Well, that was because the students were just going through the motions doing the steps, rather than actually thinking about the word problem.

Oh and also a quick tip is to have your students identify the keywords. Do not just make a list of keywords and put them on the wall. It is more helpful for them to identify them on their own throughout the year and you just add to the chart each time!

The key ingredient for teaching word problems

Lastly, I provide many opportunities to practice with word problems as a class, with partners, and independently. You can do this through games, task cards, small group work, or even exit tickets. I have heard many many teachers looking for ways to get their students to become successful at word problems, but I have found that consistency is the key ingredient. You have to consistently practice word problems with and without numbers in order to help your student master this skill.

You can find many many multiplication and division word problems practice worksheets on Teachers Pay Teachers. This resource not only included multiplication and division worksheets, but it also includes multiplication and division games as well. I have an entire Multiplication and Division Bundle that covers everything from 1 step two-step problems, as well as strip diagrams, input-output tables, and equations.

Teachers would you like a strategy that will help your students finally understand how to solve word problems rather than guessing?

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[FREE] Fun Math Games & Activities Packs

Always on the lookout for fun math games and activities in the classroom? Try our ready-to-go printable packs for students to complete independently or with a partner!

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Adding and subtracting

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.

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
Multiplication and division within 100

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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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1.7: Solving Equations by Multiplication and Division

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Page ID 23213

David Arnold
College of the Redwoods

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.

$Screen Shot 2019-08-12 at 5.22.30 PM.png$

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.

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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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Multiplication and Division - Long Division

Multiplication and division -, long division, multiplication and division long division.

Multiplication and Division: Long Division

Lesson 5: long division.

/en/multiplicationdivision/introduction-to-division/content/

Long division

When you divide a number, you are splitting it equally . In Introduction to Division , you learned that division can be a way to understand real-life situations. For example, imagine a car dealership has 15 cars. The manager wants the cars parked in three equal rows.

You could write the situation like this and use a times table to solve it:

After the cars are divided, counting them shows that each row should have five cars. Now, let's say the car dealership has 42 cars and the manager wants to park them in three rows. The situation would look like this:

This problem is harder to solve. It would take a lot of time to divide that many cars into three groups. Plus, there's no 42 in the 3's column on the times table. Fortunately, there is a way to set up the problem that makes it easy to solve one step at a time. It's called long division .

Let's learn how to set up these problems. We'll look at the problem we discussed above: 42 / 3 .

In the last lesson, we learned how to write division expressions.

However, dividing a larger number is easier when the expression is written in a different way.

Instead of writing the numbers side by side with a division symbol...

Instead of writing the numbers side by side with a division symbol... we'll use a different symbol called a division bracket .

The number you're dividing goes under the division bracket. That's 42 .

To the left of the division bracket, write the number you're dividing by. In our problem, it's 3 .

The division bracket is also an equals sign. The quotient , or answer, is written above it.

Let's try setting up another expression, 125 / 5 . First, write the division bracket.

Next, write the number being divided, 125 .

Finally, write the number we're dividing by, 5 .

Remember, you should be careful to set up long division problems correctly.

The number you're dividing goes under the division bracket...

The number you're dividing goes under the division bracket... and the number you're dividing by goes to the left of it.

Solving long-division problems

To solve long division problems, you'll use three math skills you've already learned: division , multiplication , and subtraction . It's a good idea to make sure you feel comfortable with all three skills. If you think you might need more practice, take some time to review those lessons first.

When solving a long division problem, the number under the division bracket is split into smaller numbers. This makes division easier. Plus, you can use a familiar tool, like a times table, to help.

Let's see how solving a long division problem works.

Remember the manager of the used car dealership who wanted to divide 42 cars among 3 rows? Let's find out how many cars he should put in each row.

We'll use long division to solve this problem: 42 / 3 .

Long division follows a pattern . You follow the same basic steps again and again until the problem is complete. If this seems confusing, don't worry. We'll go through it step by step.

We'll begin with the left digit under the division bracket. That means we'll start with the 4 ...

We'll begin with the left digit under the division bracket. That means we'll start with the 4 ... and we'll figure out how many times it can be divided by 3 .

Now it's time to solve 4 / 3 .

We can use the times table . We'll look at the 3's column.

Since 4 is the number we're dividing, we need to locate the number that is the closest to 4. The number can't be any larger than 4 .

3 is the closest to 4 .

Next, we'll find the row 3 is located in. It's the 1's row.

That means 3 goes into 4 one time.

We'll write 1 above the 4 and the division bracket.

The next step is to multiply the 1 and 3 .

Whenever you multiply a number by 1, that number stays the same. So 1 x 3 is 3 .

We'll write 3 below the 4 .

The next step is to subtract .

Now we solve 4 - 3 .

4 - 3 is 1 . We'll write 1 below the 4 and 3 .

Since our answer is 1 , we're not done yet. We'll know our problem is complete when the answer to our subtraction problem is zero. Plus, there's still another digit under the bracket: 2 .

We'll bring the 2 down and rewrite it next to the 1 .

See how the 1 and 2 look like the number 12 ? That's the next number we need to divide.

12 is large enough to be divided, so we'll figure out how many times it can be divided by 3 .

Let's look at the 3's column. Since 12 is the number we're dividing, we'll find the number closest to 12 . Remember, the number can't be any larger than 12 .

The 3's column has a 12 . It would be impossible to get closer than that!

Now we find the row 12 is located in.

It's the 4's row. 3 goes into 12 four times.

We'll write 4 above the 2 and the division bracket.

Now it's time to multiply the 4 and 3 .

4 x 3 is 12 .

Write the 12 beneath the 12 .

We'll set up our subtraction problem.

Now it's time to solve 12 - 12 .

12 - 12 is 0 . Write 0 beneath the line directly below the 2 and 2 .

The answer to our subtraction problem is 0 . That means we're done! 42 / 3 = 14 .

Solve these long division problems. Then, check your answer by typing it in the box.

Problems with remainders

In Introduction to Division , you learned that some numbers can't be equally divided. When that happens, there will be an amount left over. This is called a remainder . For instance, let's say you want to share 8 treats equally among your 3 dogs. The answer is that each dog would get two treats with a remainder of two .

The remainder is written as part of the quotient: 8 / 3 = 2 r2 .

Long division problems can have remainders too. Watch the slideshow to see how.

Let's try this problem, 49 / 4 .

As always, start by dividing the left digit. This means we'll solve for 4 / 4 .

4 / 4 is 1 .

Next, we'll multiply the answer we just got, 1 , by the number we're dividing by, 4 . So 4 x 1 .

4 x 1 is 4 .

Next, subtract 4 - 4 . Whenever you subtract a number from the same number, the answer is 0 . So 4 - 4 = 0 .

Our problem's not done. The next digit in the number we're dividing is 9 . We'll solve for 9 / 4 .

9 / 4 is 2.

Again, we'll multiply the number we just wrote by the number we're dividing by.

2 x 4 is 8 .

We'll subtract that number, 8 , from the number we were dividing.

9 - 8 is 1 .

Since 1 is smaller than 4, we can't divide it any further. 1 is our remainder . We'll write it next to the rest of the answer.

We're done! 49 / 4 = 12 , with a remainder of 1 .

Solve these division problems with remainders. Then, check your answer by typing it into the boxes.

Decimal quotients

On the last page, you learned how to find the remainder for a long division problem that can't be solved evenly. Remainders can be useful if you need to know how much is left over when you divide something, but they might not be very useful in every situation. For example, what if you wanted to divide a 9- foot-long board into 4 equal pieces ? That problem could look like this:

9 / 4 = 2 r1

In other words, when you divide a board that's nine feet long into four pieces , each piece will be two feet long . There will be one foot left over.

What if you don't want to waste any wood? In that case, you can continue to divide until there is no longer a remainder. That way, you'd have four equal pieces of wood, with none left over. That problem would look like this:

9 / 4 = 2.25

The answer, 2.25, is a decimal number. You can tell, because it includes a symbol called a decimal point (.) . The number to the left of the decimal point , 2 , is the whole number. The rest of the answer, .25 , shows the part of the number that didn't divide evenly.

Click through the slideshow below to learn how to find the decimal answer to a division problem.

Let's say we have 62 treats to divide equally among 4 dogs. The problem we're solving is 62 / 4 . Let's find out how many treats each dog should get.

As always, we'll begin with the left digit under the division bracket. That means we'll start with the 6 ...

As always, we'll begin with the left digit under the division bracket. That means we'll start with the 6 ... and we'll figure out how many times it can be divided by 4 .

Now it's time to solve 6 / 4 . We'll use the times table.

We'll look at the 4's column. Since 6 is the number we are dividing, we need to find the number that is closest to 6 . Remember, it can't be any larger than 6 .

4 is the closest to 6 .

Next, we'll find the row 4 is located in. It's the 1's row.

That means 4 goes into 6 one time. We'll write 1 above the 6 .

Next, we'll multiply the 1 and 4 .

Remember, whenever you multiply a number by 1, that number always stays the same. So 1 x 4 is 4 .

We'll write 4 below the 6 .

The next step is to subtract.

Now we solve 6 - 4 .

6 - 4 is 2 . We'll write 2 below the line.

Since 2 is more than zero, we know we're not done with our problem.

We'll bring the 2 down and rewrite it next to the 2 .

22 is large enough to be divided, so we'll figure out how many times it can be divided by 4 .

Let's look at the 4's column to locate the number closest to 22 . The number can't be any larger than 22 .

20 is the closest to 22 .

Now we'll find the row 20 is located in. It's the 5's row. So 4 goes into 20 five times.

We'll write 5 above the 2 .

Now we need to multiply the 5 and 4 .

5 x 4 is 20 .

We'll write 20 beneath the 22 .

Now it's time to solve 22 - 20 .

22 - 20 is 2 . We'll write 2 beneath the line directly below the 2 and 0 .

The answer to the last subtraction problem is more than zero, so we'll look under the bracket to see if there is another digit we can bring down.

We've divided both of those digits. That means there are no more digits to bring down. But if we write another digit next to 62 , we could bring that digit down.

We don't want to make the 62 any larger. That would change our problem. We only had 62 bones to divide.

So next to the 62 , we'll write the number that means nothing: 0 .

But that changes 62 into a larger number: 620 . That won't work.

So to keep the value of 62 this same, we'll add a decimal point between the 62 and the 0 .

This means our quotient needs a decimal as well. So we'll write a decimal point next to the 15 directly above the other decimal.

Now we can continue to solve the problem. We'll bring the 0 down and rewrite it next to the 2 .

Let's figure out how many times 20 can be divided by 4 .

Look at the 4's column. 20 is the number we are dividing, so we'll find the number that is the closest to 20 but not larger than 20 .

The 4's column has a 20 . That's as close as we can get!

Now we find the row 20 is located in. It's the 5's row. 4 goes into 20 five times.

We'll write 5 above the 0 .

Now it's time to multiply the 5 and 4 .

Write 20 beneath the 20 .

Time to solve 20 - 20 .

20 - 20 = 0 . Write 0 below the line directly below the 0 and 0 .

The answer to the subtraction problem is 0 . That means we have completed the problem. So 62 / 4 = 15.5 .

Sometimes, you may notice that a decimal can start to repeat as you continue to add zeros under the division bracket. This is known as a repeating decimal. When this happens, you can place a horizontal line over the digit that repeats.

Look at the image below. A horizontal line has been placed over the repeating digit.

Another way to handle a repeating decimal is to round it. Rounding creates a new number that has a value close to the original number.

When rounding a repeating decimal, you'll reduce the number of digits that come after the decimal point. First, decide which digit you are rounding to. Then look at the digit to the right of it. If the digit is 5 or more, increase the rounded digit by 1. If it is 4 or less, the rounded digit stays the same. The other digits after the rounded digit are not written.

Look at the image below. In this case, each of these repeating decimals has been rounded to the second digit after the decimal point.

Find the decimal quotient for each of the long division problems below.

Checking your work

Checking your work after you divide is a good habit to develop. Checking helps you know that your answer is correct. To check the answer to a division problem, you'll need to use multiplication.

Let's look at this problem: 54 / 6 = 9 .

How do we know that 9 is the correct answer? We can check by multiplying.

Let's set up our multiplication problem. First, we'll write the quotient. That means we'll write 9 .

Next, we'll multiply the number that we divided by, 6 .

Time to multiply. 9 x 6 = 54 .

If we divided correctly, the answer will match the larger number in the division problem.

They are both 54 . We checked the problem, and it was correct!

Let's try checking another problem. This time, the quotient has a remainder: 20 / 3 = 6 r2 .

Let's set up our multiplication problem. First write the quotient without the remainder. That's 6 .

Then multiply the amount that the larger number was divided by, 3 .

Now it's time to multiply. 6 x 3 = 18 .

Let's check to see if our answer matches the larger number in the division problem — 18 and 20 . No, they aren't equal.

That may be because we haven't included the remainder, 2 .

Since the answer to the division problem has a remainder...

Since the answer to the division problem has a remainder... just multiplying should give you a number less than the original number.

We'll set up an addition problem to add the 2 to 18 .

Now add 18 and 2 .

18 + 2 is 20 .

Finally, check to see if 20 matches the larger number in the division problem. It does!

In the slideshow, we used multiplication to check our division. The answer to the multiplication problem should always be the same as the larger number in the division problem. If your two answers don't match, check to see if you added the remainder. If your answers are still different, you might have made a mistake the first time you were dividing. Try solving the problem again.

Long division with decimals

In this lesson, you also learned how to solve division problems that have a decimal in the answer. Checking your work for this type of problem is similar to checking other division problems. You'll follow the same steps.

We'll try checking this problem: 57 / 5 = 11.4 .

Let's set up our multiplication problem.

We'll write the decimal quotient, 11.4 .

Next, we'll multiply the number that we divided by, 5 .

Now it's time to multiply: 11.4 x 5 .

Since the quotient had one digit to the right of the decimal point...

Since the quotient had one digit to the right of the decimal point... we write the answer with one digit to the right of the decimal point. 11.4 x 5 = 57.0 .

Finally, we'll check to see if 57.0 matches the larger number in our division problem. They are the same. Our answer was correct.

Practice division by solving these problems. There are 3 sets of problems. Each set has 5 problems.

Set 2: Type your answer using remainders.

Set 3: type your answer using decimals..

/en/multiplicationdivision/video-division/content/

Word Problems on Division

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

Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. How much money will each person get? Solution: Money received by 26 men = 5876 So, money received by one man = 5876 ÷ 26 = 226

$Word Problem on Division$

Each man will get $226.

2. If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?

Since 95 bags contain wheat 9975 kg Therefore, 1 bag contains wheat (9975 ÷ 95) kg = 105 kg

$Division Word Problem$

Each bag contains wheat = 105 kg In a problem sum involving division, we have to be careful about using the remainder.

3. 89 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 12 people. How many tables are needed? Solution: To answer this question, we need to divide 89 by 12 89 ÷ 12

$Division Word Problems$

Quotient - 7

Remainder - 5

If the caterer arranges 7 tables, then 5 people will have no place to sit. So he needs to arrange 7 + 1 = 8 tables.

4. How many hours are there in 1200 minutes?

Solution: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20

So there are 20 hours in 1200 minutes.

Answer: 20 hours.

5. A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?

Solution: Total number of passengers = 108

There are 12 rows of seats on the bus.

To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.

We get, divide 108 by 12

108 ÷ 12 = 9

Therefore, there are 9 seats in each row.

Answer: 9 seats.

6. Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends?

Solution: Total number of apples = 63

There are 9 friends of seats on the bus.

To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends.

We get, divide 63 by 9

Therefore, Tom gives 7 apples to each of his friends.

Answer: 7 Apples

7. Mark baked 195 cookies and divided them equally into 13 packs. How many cookies did Mark put in each packet?

Solution: Total number of cookies = 195

There are 13 packs.

To find how many cookies did Mark put in each packet, divide the total number of cookies by the number of packs.

We get, divide 195 by 13

195 ÷ 13 = 15

Therefore, Mark put 15 cookies in each pack.

Answer: 15 cookies.

9. Nancy needs 5 lemons to make a glass of orange juice. If Nancy has 250 oranges, how many glasses of orange juice can she make?

Solution: Total number of oranges = 250

She needs 5 lemons to make a glass of orange juice.

To find how many glasses of orange juice can Nancy make, divide the total number of oranges by the number of oranges needed for each glass of orange juice.

We get, divide 250 by 5

250 ÷ 5 = 50

Therefore, Nancy can make 50 glasses of orange juice.

Answer: 50 glasses of orange juice.

10. In your classes you counted 120 hands. How many students were at the class?

Solution: Total number of hands = 120

We have 2 hands.

To find how many students were at the class, divide the total number of hands by the number of hands we have.

We get, divide 120 by 2

220 ÷ 2 = 60

Therefore, there were 60 students at the class.

Answer: 60 students.

11. The total train fare for 20 persons is 7540 rupees. What is the fare for 1 person.

12. A milk container can store 8 litres of milk. How many containers are required to stare 6,408 litres of milk?

Capacity of one container = 8 lites of milk

Required number of containers = 6408 ÷ 8

Hence, 801 containers are required.

$Word Problems on Division$

13. A farmer produced 29800 kg of wheat. How many bags will be buy store the wheat if one bag can hold 70 kg?

Produced = 29890 kg

Number of bags needed = 29899 ÷ 70

Therefore, 427 bags are needed to hold 29890 kg of wheat.

$Division Word Problem$

These are the basic word problems on division.

Questions and Answers on Word Problems on Division:

1. 92 bags of cement can be loaded in a truck. How many such trucks will be needed to load 2208 bags?

Answer: 24 trucks

2. The total train fare for 11 persons was $3850. What was the fare for one person?

Answer: $350

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Real-World Multiplication and Division Problems

Educators in all grade levels must provide students with real-world problems to solve. Rather than discussing strategies students might use to multiply and divide in Grades K-8, we use this series of videos to: Describe different ways teachers can construct problems while ensuring students deeply understand multiplication and division concepts and Examine real-world contexts in which students apply their knowledge of multiplication and division. As we discuss the construction of contextualized problems, we also explore ways to make these problems real-world, realistic, and relevant to the lives of students. The K-2 standards in this series do not pertain to real-world problems. However, they are excellent precursors to preparing students to engage in this work in Grades 3-8.

Overview Real World Multiplication and Division with Ryan Flessner

Kindergarten Real World Multiplication and Division with Courtney Flessner

Grade 1 Real World Multiplication and Division with Courtney Flessner

GRADE 2—Real-World Multiplication and Division Problems with RyanFlessner

GRADE 3—Real-World Multiplication and Division Problems with Ryan Flessner

GRADE 4—Real-World Multiplication and Division Problems with Ryan Flessner

GRADE 5—Real-World Multiplication and Division Problems with Ryan Flessner

Grade 6 Real World Multiplication and Division with Ryan Flessner

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High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

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Multiplication and Division Word Problems

Subject: Mathematics

Age range: 7-11

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29 April 2016

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Common Core State Standards Initiative

Grade 3 » Operations & Algebraic Thinking

Standards in this domain:, represent and solve problems involving multiplication and division., understand properties of multiplication and the relationship between multiplication and division., multiply and divide within 100., solve problems involving the four operations, and identify and explain patterns in arithmetic..

1 See Glossary, Table 2.

2 Students need not use formal terms for these properties.

3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in conventional order when there are no parentheses to specify a particular order (Order of Operations).

Standards for Mathematical Practice
How to read the grade level standards
Introduction
Counting & Cardinality
Operations & Algebraic Thinking
Number & Operations in Base Ten
Measurement & Data
Number & Operations—Fractions¹
Number & Operations in Base Ten¹
Number & Operations—Fractions
Ratios & Proportional Relationships
The Number System
Expressions & Equations
Statistics & Probability
The Real Number System
Quantities*
The Complex Number System
Vector & Matrix Quantities
Seeing Structure in Expressions
Arithmetic with Polynomials & Rational Expressions
Creating Equations*
Reasoning with Equations & Inequalities
Interpreting Functions
Building Functions
Linear, Quadratic, & Exponential Models*
Trigonometric Functions
High School: Modeling
Similarity, Right Triangles, & Trigonometry
Expressing Geometric Properties with Equations
Geometric Measurement & Dimension
Modeling with Geometry
Interpreting Categorical & Quantitative Data
Making Inferences & Justifying Conclusions
Conditional Probability & the Rules of Probability
Using Probability to Make Decisions
Courses & Transitions
Mathematics Glossary
Mathematics Appendix A

Problem Solving: Multiplication and Division

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Keva Roberts

Problem Solving

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Solve problems involving multiplication and division
problem solving with division and multiplication
$problem solving using multiplication and division$
Multiplication And Division Word Problems Grade 4
Solving the Equation
Multiplication And Division Word Problems Year 4 : Maths Year 3 Autumn
Related Facts

VIDEO

Test Your Math! Quick Math: Simple Calculation Solutions #shorts
A Step-by-Step Guide to Solving One-Step Equations with Multiplication and Division
DIVISION USING MULTIPLICATION TABLES
solving equations using multiplication and division
3rd Grade STAAR Practice Multi-step Multiplication and Division Problems (3.4K
Use Multiplication to Solve Division Problems

COMMENTS

Mixed Multiplication & Division Word Problems
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. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6. Similar:
Multiplication & division word problems
These grade 4 math worksheets have mixed multiplication and division word problems. All numbers are whole numbers with 1 to 4 digits. Division questions may have remainders which need to be interpreted (e.g. "how many left over"). In the last question of each worksheet, students are asked to write an equation with a variable for the unknown ...
Multiplication Division Worksheets
Using this generator will let you create your own worksheets for: Multiplying and dividing with numbers to 5x5; Multiplying and dividing with numbers to 10x10; Multiplying and dividing with numbers to 12x12; Multiply and divide a range of decimals and whole numbers by 10, 100 and 1000; Multiplying and divide with 10s e.g. 4 x 30, 120 ÷ 4.
Multiplication and division
Unit test. Test your understanding of with these NaN questions. Start test. 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 and Division Word Problems
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.
Multiplication and Division Word Problems
But in 3rd grade, we introduce two step addition, subtraction, multiplication and division word problems. These include all the operations so their chances of guessing correctly have now gone from 50 percent down to 25 percent. Then when you add in the addition of two-step word problems that percent goes down to less than 7 percent.
Multiplication And 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
Multiplication and division word problems (within 100)
Multiplication and division word problems (within 100) A roller coaster has 4 different cars. Each car holds 10 people. How many people are on the roller coaster when all the cars are full? Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a ...
One-step multiplication & division equations
Now for division, for the equation t/6=7, or 7=t/6 (they are the same thing, just put in a different format, keep that in mind), we use inverse operation, as shown in the Lesson, and we know what type of inverse operation it is because t/6 is division -because it's a fraction-, so we use multiplication instead so to solve for t in t/6=7, we ...
Problem Solving
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)
Lesson Plan: Word Problems: Multiplication and Division
Lesson Plan: Word Problems: Multiplication and Division. 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.
Represent and solve problems involving multiplication and division
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.
1.7: Solving Equations by Multiplication and Division
Solve the following equation for x. x 7 = 12 x 7 = 12. Solution. To undo the effects of dividing by 7, we multiply both sides of the equation by 7. x 7 = 12 84 7 = 12 x = 84 Original equation. Multiply both sides of the equation by 7. On the left, multiplying by 7 "undoes" the effect of dividing by 7 and returns to x.
Multiplication Word Problems Worksheets
The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios. 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 ...
Multiplication and Division: Long Division
Solving long-division problems. To solve long division problems, you'll use three math skills you've already learned: division, multiplication, and subtraction. It's a good idea to make sure you feel comfortable with all three skills. If you think you might need more practice, take some time to review those lessons first.
Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers
Analysis: To solve this problem, we will divide the first mixed number by the second. First, we will convert each mixed number into an improper fraction. Solution: Answer: The warehouse will have 2 and 2/25 pieces of tape. Summary: In this lesson we learned how to solve word problems involving multiplication and division of fractions and mixed ...
Examples on Word Problems on Division
Solution: Total number of apples = 63. There are 9 friends of seats on the bus. To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends. We get, divide 63 by 9. 63 ÷ 9 = 7. Therefore, Tom gives 7 apples to each of his friends. Answer: 7 Apples. 7.
» Real-World Multiplication and Division Problems
Educators in all grade levels must provide students with real-world problems to solve. Rather than discussing strategies students might use to multiply and divide in Grades K-8, we use this series of videos to: Describe different ways teachers can construct problems while ensuring students deeply understand multiplication and division concepts and Examine real-world contexts in which students ...
Multiplication/Division Word Problems Calculator
Free Multiplication/Division Word Problems Calculator - solve multiplication/division word problems step by step
Multiplication and Division Word Problems
Multiplication and Division Word Problems. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity. File previews. docx, 15.89 KB. A variety of multiplication and division word problems used for a year 5 class. Two versions for differentiation. Creative Commons "Sharealike".
Grade 3 » Operations & Algebraic Thinking
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and ...
Problem Solving by Using Multiplication to Solve Division Problems
Objectives. Students will investigate problem-solving situations in which problems involving division can be readily solved using multiplication. Students will: practice writing expressions and equations related to solving word problems as multiplication and division problems.
Problem Solving: Multiplication and Division worksheet
Problem Solving: Multiplication and Division. Loading ad... Keva Roberts. Member for 3 years 6 months Age: 9-10. Level: 5/6. ... School subject: Math (1061955) Main content: Multiplication and Division (2032048) Problem Solving. Other contents: Problem Solving Loading ad... Share / Print Worksheet. Google Classroom Microsoft Teams ...
Using abacus, you can solve both simple and complex math problems
Besides addition, subtraction, multiplication and division, we can als... | Instagram. 5 likes, 0 comments - coach_bounjoumDecember 21, 2021 on : "Using abacus, you can solve both simple and complex math problems.

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Multiplication and Division Word Problems

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Symbol for Division

Important terms in Division

Formula for Division

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

Different Types of Problem

Product Unknown Comparisons

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Multiplication Problems: Set Size Unknown

Multiplicative Comparison Problems: Multiplier Unknown

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Key Facts and Summary

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