solution to division problem is called

Division in Math

Division is a math superpower that breaks down a whole — whether you’re cutting a pizza or divvying up some candy!

Author Christina Levandowski

Expert Reviewer Jill Padfield

Published: August 24, 2023

• Key takeaways
• Division is an opposite game – If you multiply numbers, you can “undo” them using division. It’s multiplication’s opposite function! 
• There’s a few signs to look for – There are three main symbols for division.
• You won’t always get “even Stevens” – Sometimes, you’ll have a little left over. That leftover number is known as the “remainder.”

Table of contents

What is division?

Common symbols and terminology, properties of division, how to divide in 6 easy steps, what is long division, working with remainders.

• Let’s practice together!

Practice problems

Division is one of the most important math skills you’ll practice, helping you to undo multiplication problems or break off parts of a “whole.” We know it looks complicated, but it really isn’t! You just need to know what signs to look for that tell you when division is needed. 

Like addition and subtraction, division uses a few special terms and symbols. Knowing these can help you to work out your problems quickly and correctly. 

We know it sounds complicated right now — but with a little practice and this handy guide, you’ll be flying through your math homework in no time!

Division is a process in math that lets you break down a number into multiple, equal parts. Sometimes, you can cut everything down into whole number parts, and, sometimes, you’ll be left with a little leftover, giving you a decimal or fraction for an answer rather than a whole number. 

You’ll often see division problems vertically, like this:

It can also be written horizontally: 10 ÷ 2, as 10/2 , or using a division bar: 2 ⟌ 10.

No matter how you see it, though, the use for it is always the same. You’re breaking down a number or quantity into smaller pieces. 

Let’s take a look at some key terms that’ll help you build your division skills.

Division is a simple mathematical operation, but there are still a few terms to know to help you find the correct solution. 

Here are the terms you need to know to solve division equations with ease:

➗ — This is known as a division sign, and it tells you that a number needs to be broken down into multiple pieces. 

⟌ — This is the division bar, and it also means to divide. On the outside of the bar, you’ll see the number determining how many pieces are needed from the whole (the divisor), and the dividend on the inside, which is what you’ll be dividing. The answer goes on the top of the bar. 

∕ — This is known as the division slash. Generally, the divisor comes first, and the dividend will appear second.

Important vocabulary

• Divisor – The divisor is the number that is determining how many pieces are needed from the whole. For example: in 15 ÷ 3, three would be the divisor. It’s also the number located outside of the bracket when you see a division bar.
• Dividend – The dividend is the number that’s being divided, and it’s found inside the division bar.
• Quotient – The quotient is your answer, which goes after the equals (=) sign or on the top of the division bar.
• Remainder – In some cases, you’ll have a remainder — which means that the divisor can’t be equally divided into the dividend. The remainder is written to the side of your equation next to the division bar.

Anytime you see the word “property” in math, know that it’s just a rule to remember as you work through your groups of problems. Here are some of the most important properties of division that you need to know: 

• The Division By 1 Property:  If a number is divided by 1, the quotient will always be the original number. 
• The Division By Itself Property: If a number is divided by itself, the quotient will always be 1. 
• The Division By 0 Property: If a number is divided by 0, it’s “undefined” and cannot be solved. 
• The Division Of 0 By (Any) Number Property: If a 0 value is divided by any number, you’ll have 0 as your quotient.

Knowing these helpful properties can help you to do basic operations (like division) confidently. Remember — these are division facts, so these properties will always be true…no matter what problem you’re working to find the quotient to!

Now that you know the terms and properties of your division operation, it’s time to practice your skills. Let’s work the problem below together. 

1. Prepare your equation

We know that the problem above can feel overwhelming — so we want to take this moment to remind you that what we’re doing is breaking down a number into smaller numbers (or smaller groups of numbers). 

First things first, we have to prepare the equation. Feel free to keep it horizontal,  write it vertically, or use a division bar if you’d like. Use whatever method you feel comfortable with. 

Remember: The dividend (15) belongs inside the division bar if you choose to use that method. 

2. Start with the first digit of the dividend from the left

As we begin to divide, we need to start from the first digit from the left (in this case, 1) and ask ourselves: Does the divisor (3) go into 1 at least once? 

The answer here is “no,” so we will then evaluate the first AND second integer (making 15) as a dividend. 

We ask again: Does the divisor (3) go into 15 at least once? 

Now, the answer is “yes” — we just have to count how many times 3 can go into 15, starting our division process.* 

*NOTE: You can do this by using basic arithmetic operations (such as multiplication) to “undo” the problem (i.e., 3 x ? = 15) or counting by threes until you reach 15. 

In our case, 3 goes into 15 a total of five times.

3. Divide it by the divisor and write the answer on top as the quotient

Now that we know that 15 ÷ 3 = 5, it’s time to write it into our equation. Go ahead and write 5 behind the equals sign or standing tall at the top of your division bar. 

4. Subtract the product of the divisor and the digit written in the quotient from the first digit of the dividend

Now, we have to check our work. We have to ask ourselves: What is 5 x 3? Does it equal our dividend? If it does, you’re golden — you’ve done it! 

Do the multiplication, and then subtract your product to ensure that there’s no other steps remaining (like you’d see in the case of a remainder). 

In our example, 15 – 15 = 0…so no remainder or further action is needed.

5. Bring down the next digit in the dividend (if possible)

In other problems, if you did have a three or four digit dividend, you might need to bring down the next digit in the dividend, and determine if your divisor divides that number cleanly. 

You would then repeat the division process, putting your answer over the third or “next” place above the division bar as part of the quotient. 

Next, yo would repeat step 4 to determine if more steps in the division process are needed.

In our example, we don’t have to do this, so we will leave it as is. Good work!

Congratulations! You just broke a large number down into equal, separate parts. It’s time to repeat the process for your other problems. 

Long division is a form of division that’s used to break down larger numbers and will generally repeat steps 1-6 above at least three or more times. 

We’ll work on that stuff later — for now, let’s just focus on mastering the basics!

What happens when you wind up with a little extra left over, you might ask? While it can look pretty scary, it’s simple to solve.

To do this, you’ll repeat steps one through five above until you get a number that cannot continue to be divided evenly. At this point, you’ll do a few additional steps:

• Determine how many times the divisor goes in to the product of your current answer and the divisor. This won’t be a clean number, and that’s OKAY — that’s what your remainder process is for.
• Complete the subtraction steps. After you get your number, complete the subtraction steps and write your answer below the subtraction bar.
• For example: In the case of 16 ➗ 3, we would write the quotient as: 5R1.

When you see that there’s zero left over, or if there is no way for the divisor to divide into the dividend, that means that your problem is solved!

Let’s practice together

• We ask: “How many times can 6 go into 2?” 
• 6 is greater than 2, so we will not be able to put a number over the 2. We then consider, “How many times can 6 go into 20?”
• Well, this is a bit of a challenge! 6 does not go into 20 evenly. 6 x 3= 18, and 6 x 4= 24. So, 6 can go into 20 three times, but it won’t go evenly.
• So, we add the 3 over the 0, above the division bar.
• We put the product of 6 x 3 (our divisor x our quotient) under the dividend and subtract to determine if the a remainder in our difference. 
• There is a remainder of 2. We write our quotient as: 3R2 .

• We know that our divisor is going to be 1, and our dividend (the number being divided) is 5. We identify them, and we put them properly into a division bar. 
• We ask: “How many times can 1 go into 5?” 
• Instead of working the problem counting or using multiplication, we remember the Division By 1 Property. 
• We put 5 at the top of our division bar, since any integer that is divided by 1 will always be itself. 
• There is no remainder for these types of Division By 1 Property problems. We can move on to the next problem.

• We know that our divisor is going to be 2, and our dividend (the number being divided) is 0. We identify them, and we put them properly into a division bar. 
• We ask, “How many times can 2 go into 0?” 
• Instead of working the problem counting or using multiplication, we remember the Division Of 0 By (Any) Number Property. 
• We put 0 at the top of our division bar, since any integer that attempts to divide 0 as a dividend will always result in a quotient of zero. 
• There is no remainder for these types of Division Of 0 By (Any) Number Property problems. We move on to the next problem.

Ready to give it a go?

You’ve done great so far — and you’re well on your way to mastering the art of division. Don’t be afraid to keep trying and make mistakes. 

Practice makes perfect, so we’ve given you a few more problems to practice as you work to perfect your skills. Remember: You can always scroll up to walk through the tutorials and refresh yourself on the terms, placement, and properties you’ll need to solve these correctly. 

By the end of this session, we’re confident that you’ll be ready to claim that A+ on your next math test. You can do it!

Click to reveal the answer.

The answer is 2 .

The answer is 1R6 .

The answer is 4 . 

Parent Guide

The answer is 2.

How did we get here? 

• We identify 4 as the dividend and 2 as the divisor, and place them in the division bar. 
• We ask: “How many times can 2 go into 4?” We determine this using the “count by twos” method, which shows us that 2 goes into 4 a total of two times. 
• We put 2 at the top of our division bar as the quotient, and multiply it by our divisor (2). We then subtract the product of our multiplication from the number to get an answer of 0, which shows us that there is no remainder. You’re done!

The answer is 1R6.

• We identify 8 as our divisor and 14 as our dividend, and place them in the division bar. 
• We ask: “How many times can 8 go into 14?”, as 8 will not go into 1. We determine this using the “count by eights” method, which shows us that 8 goes into 14 just once. 
• We write a 1 in the quotient place above the 4 under the division bar. We then multiply 1 x 8 to get a product of 8, which is placed below the 14 under the division bar. 
• Now, we do the math and subtract 8 from 14. We’ll get 6 as our difference. 
• We then write our quotient as 1R6.

The answer is 4. 

How did we get here?

• We identify 5 as our divisor and 20 as our dividend, and place them in the division bar. 
• We ask: “How many times can 5 go into 20,” as 5 will not go into 2 at all. We determine this using the “count by fives” method, which shows us that 5 can go into 20 cleanly four times. 
• We place a “4” in our quotient place, and multiply 4 x 5 to get a product of 20. This is written under the division bar as a subtraction problem. 
• We subtract 20 – 20, resulting in a difference of 0. 
• This means that 4 is our final quotient with no remainder.

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FAQs about math strategies for kids

We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

Division is the mathematical process that breaks down a big value into smaller values. 

There are plenty of times you’ll use division in your everyday life. Some of the most common ways might be to break up an even quantity of something, determining how much of an ingredient to use, or grouping up items for use. 

Division is the inverse of multiplication. This means that it naturally undoes any sort of operation that’s done with multiplication. 

The three main parts of division are the divisor, dividend, and quotient. 

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Christina Levandowski

Christina has written for hundreds of clients from small businesses to Indeed.com. She has extensive experience working with marketing strategy and social media marketing, and has her own business creating assets for clients in the space. She enjoys being an entrepreneur and has also started pursuing investment opportunities as time permits.

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A quotient is the result of a division problem. It is one of three main parts of a division problem, with the other two being the dividend and divisor.

What is the quotient

A quotient is the solution to the question "how many times does a number (the divisor ) go into another (the dividend )?"

Parts of a division problem

The three main parts of a division problem are the quotient, divisor, and dividend.

• Dividend - the dividend is the number that is being divided.
• Divisor - the divisor is the number that the dividend is being divided by.
• Quotient - the quotient is the result of dividing the dividend by the divisor; it is the solution to the division problem.

Quotient and remainder

Depending on the divisor and dividend, and whether or not we are using decimals, we may end up with a remainder. A remainder is the number left over when we cannot evenly divide the divisor into the dividend such that the quotient is not an integer . For example, if we divide 10 by 4 we have a remainder of 2 because 4 goes into 10 twice (4 × 2 = 8), leaving 2.

10 ÷ 4 = 2 R2

How to write a division problem

A division problem can be structured in a number of different ways. The figure below shows three different ways to write a division problem, as well as the parts of the division problem. The quotient is shown in blue, the dividend in orange, and the divisor in blue.

There are other symbols used to indicate division as well, such as 12 / 3 = 4. In all the cases, the problem is the same, and the quotient is 4.

How to find the quotient

There are a few different ways to find the quotient. One of the most straightforward (but not very efficient) ways to do so is through repeated subtraction. Another more consistent but potentially tedious way is long division.

Repeated subtraction

To use repeated subtraction to find the quotient, use the following steps.

• Identify the dividend and divisor.
• Repeatedly subtract the divisor from the dividend until doing so results in 0, or would result in a negative number.
• If the result is 0, the dividend is evenly divided by the divisor, and the quotient is the number of times that the divisor was subtracted until this result was reached.
• If subtracting the divisor from the dividend will result in a negative number, stop subtracting. The number of times the divisor was subtracted is the quotient; the final non-zero result is the remainder.

Below is a repeated subtraction example.

Find the quotient and remainder (if any) of 40 ÷ 12.

The dividend is 40 and the divisor is 12, so we subtract 12 from 40:

40 - 12 = 28

28 - 12 = 16

16 - 12 = 4

At this point, subtracting 12 from 4 would result in a negative number. Since we subtracted 12 from 40 three times, the quotient is 3, leaving 4 as the remainder. We can write our final solution as:

40 ÷ 12 = 3 R4

What is a partial quotient

A partial quotient is a division method similar to that of repeated subtraction. To use partial quotients to find the quotient of a division problem, use the following steps.

• Multiply the divisor by as large a factor as possible such that you know the product will still be less than the dividend.
• Subtract the product from step 1 from the dividend.
• Repeat steps 1 and 2 until the result is 0 or you have a remainder.
• If the division problem can be carried out such that the remainder is 0, the quotient is the sum of the factors by which we multiplied as well as the number of times (if any) we repeatedly subtracted. The quotient is the same even if the problem cannot be carried through to 0, but the non-zero result is the remainder.

Below is a partial quotient example.

Use the partial quotient method to find the quotient and remainder (if any) of 43 ÷ 2.

2 goes into 43 21 times such that the product of 2 × 21 = 42. Subtracting 42 from 43 gives us:

43 - 42 = 1

Since we cannot subtract 2 from 1 without getting a negative result, the quotient is 21 and the remainder is 1. In this example, we immediately knew that 21 was the largest factor we could multiply by. Even if this is not the case, we can still use partial quotients. For example, say that we know 2 × 10 = 20. We then subtract 20 from 43:

43 - 20 = 23

From here, we may notice that we can instead multiply by 11 to get 22, which we then subtract from 23:

23 - 22 = 1

Now we have arrived at the same point, where we cannot subtract 2 from 1. The quotient is the sum of the factors we multiplied by as well as any repeated subtraction (which we did not do in this case):

10 + 11 = 21

This gives us the same result as above: 43 ÷ 2 = 21 R1.

Long division

Long division is a process used to find the quotient in a division problem. Long division is written as follows:

The quotient is written above the dividend and radical symbol (the symbol around which a division problem is written).

To find the quotient using long division, we will use the above example as reference, as well as the following steps:

• Reading from left to right, we first want to find the smallest sequence of digits (in the dividend, 564) that the divisor, 6, can go into at least once. 6 cannot go into the 5 in 564. Since it can't, move on to the next number formed, which is 56. 6 can go into 56 a total of 9 times to equal 54.
• Write the first value of the quotient above the dividend. In this case, write 9 above the 6 in 56 to indicate that 6 goes into 56 a total of 9 times. The position that the number 9 is written in is important. When doing long division, make sure that the numbers align. The starting point of the quotient should be above the last digit (reading from left to right) in the smallest sequence of numbers that the divisor can go into; in this case above the 6 in 56. The next number that forms the quotient should be written directly to the right of the first.
• Write the product, in this case 6 × 9 = 54, below 56, and perform subtraction; in this case there is a remainder of 2.
• Bring the 4 in 564 down next to the remainder to form 24, keeping in mind that alignment is important.
• Repeat the process starting from step 1, treating 24 as the new dividend. Continue this process as long as necessary until the remainder is 0, or we find a repeating pattern. In this case, since 6 × 4 = 24, subtract 24 from 24 to get 0, and the long division is complete. If, on a different problem, the remainder is not 0, continue to step 6.
• If there is still a remainder and there are no more new numbers from the dividend to bring down, add a decimal point and a 0, then bring the 0 down to the remainder and continue the process above (including adding 0's) until there is no longer a remainder, or until a repeating pattern is found.

Since the remainder is 0, the quotient is 94. If, as an example, the remainder were 2, we could write the solution as 94 R2. If we wanted to continue the long division process to get a decimal quotient, we continue the division process, adding a decimal point, and bringing down a 0 for each subsequent place value in the dividend until we arrive at a solution, or find that the decimal repeats. Refer to the figure below:

Concept of division

It is important to understand the various parts of a division sentence (and equations in general) to be able to understand and communicate mathematics. However, it is also important to understand division as a concept. One way to conceptualize division is to think of it in terms of a given number of objects being broken up into a number of groups containing an equal number of objects. For example, in 8 ÷ 2 = 4, there are a total of 8 objects that are broken into 4 groups. In order for each group to have an equal number of objects, each group would have to have 2 objects, as in the figure below.

The dividend in the figure above is represented by the 8 red circles.

Terms for Addition, Subtraction, Multiplication, and Division Equations

Terms for Addition

Terms for Subtraction

Terms for Multiplication

Terms for Division

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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..

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Long Division

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too. Let us learn how to divide using the long division method , along with long division examples with answers, which include the long division steps in this article.

What is Long Division Method?

Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division . Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder.

The above example also showed us how to do 2 digit by 1 digit division.

Parts of Long Division

While performing long division, we need to know the important parts of long division. The basic parts of long division can be listed as follows:

The following table describes the parts of long division with reference to the example shown above.

How to do Long Division?

Division is one of the four basic mathematical operations, the other three being addition , subtraction , and multiplication . In arithmetic, long division is a standard division algorithm for dividing large numbers, breaking down a division problem into a series of easier steps. Let us learn about the steps that are followed in long division.

Long Division Steps

In order to perform division, we need to understand a few steps. The divisor is separated from the dividend by a right parenthesis 〈)〉 or vertical bar 〈|〉 and the dividend is separated from the quotient by a vinculum (an overbar). Now, let us follow the long division steps given below to understand the process.

• Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
• Step 2: Then divide it by the divisor and write the answer on top as the quotient.
• Step 3: Subtract the result from the digit and write the difference below.
• Step 4: Bring down the next digit of the dividend (if present).
• Step 5: Repeat the same process.

Let us have a look at the examples given below for a better understanding of the concept. While performing long division, we may come across problems when there is no remainder, while some questions have remainders. So, first, let us learn division in which we get remainders.

Division with Remainders

Case 1: When the first digit of the dividend is equal to or greater than the divisor.

Example: Divide 435 ÷ 4

Solution: The steps of this long division are given below:

• Step 1: Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1. So, 1 is written on top as the first digit of the quotient.
• Step 2: Subtract 4 - 4 = 0. Bring the second digit of the dividend down and place it beside 0.
• Step 3: Now, 3 < 4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it beside 3.
• Step 4: So, we have 35 as the new dividend. We can see that 35 > 4 but 35 is not divisible by 4, so we look for the number just less than 35 in the table of 4 . We know that 4 × 8 = 32 which is less than 35 so, we go for it.
• Step 5: Write 8 in the quotient. Subtract: 35 - 32 = 3.
• Step 6: Now, 3 < 4. Thus, 3 is the remainder and 108 is the quotient.

Case 2: When the first digit of the dividend is less than the divisor.

Example: Divide 735 ÷ 9

Solution: Let us divide this using the following steps.

• Step 1: Since the first digit of the dividend is less than the divisor, put zero as the quotient and bring down the next digit of the dividend. Now consider the first 2 digits to proceed with the division.
• Step 2: 73 is not divisible by 9 but we know that 9 × 8 = 72 so, we go for it.
• Step 3: Write 8 in the quotient and subtract 73 - 72 = 1.
• Step 4: Bring down 5. The number to be considered now is 15.
• Step 5: Since 15 is not divisible by 9 but we know that 9 × 1 = 9, so, we take 9.
• Step 6: Subtract: 15 - 9 = 6. Write 1 in the quotient.
• Step 7: Now, 6 < 9. Thus, remainder = 6 and quotient = 81.

Case 3: This is a case of long division without a remainder.

Division without Remainder

Example: Divide 900 ÷ 5

Solution: Let us see how to divide step by step.

• Step 1: We will consider the first digit of the dividend and divide it by 5. Here it will be 9 ÷ 5.
• Step 2: Now, 9 is not divisible by 5 but 5 × 1 = 5, so, write 1 as the first digit in the quotient.
• Step 3: Write 5 below 9 and subtract 9 - 5 = 4.
• Step 4: Since 4 < 5, we will bring down 0 from the dividend to make it 40.
• Step 5: 40 is divisible by 5 and we know that 5 × 8 = 40, so, write 8 in the quotient.
• Step 6: Write 40 below 40 and subtract 40 - 40 = 0.
• Step 7: Bring down the next 0 from the dividend. Since 5 × 0 = 0, we write 0 as the remaining quotient.
• Step 9: Therefore, the quotient = 180 and there is no remainder left after the division, that is, remainder = 0.

Long division problems also include problems related to long division by a 2 digit number, long division polynomials and long division with decimals. Let us get an an idea about these in the following sections.

Long Division by a 2 Digit Number

Long division by a 2 digit number means dividing a number by a 2-digit number . For long division by a 2 digit number , we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend.

For example, if we need to divide 7248 by 24, we can do it using the long division steps. Let us see how to divide step by step.

• Step 1: Since it is a long division by a 2 digit number, we will check for the divisibility of the first two digits of the dividend. The first 2 digits of the dividend are 72 and it is greater than the divisor, so, we will proceed with the division.
• Step 2: Using the multiplication table of 24, we know that 24 × 3 = 72. So we write 3 in the quotient and 72 below the dividend to subtract these. Subtract 72 - 72 = 0.
• Step 3: Bring down the next number from the dividend, that is, 4. The number to be considered now is 4.
• Step 4: Since 4 is smaller than 24, we will put 0 as the next quotient, since 24 × 0 = 0 and write 0 below 4 to subtract 4 - 0 = 4
• Step 5: Bring down the next number from the dividend, that is, 8 and place it next to this 4. The number to be considered now is 48.
• Step 6: Using the multiplication table of 24, we know that 24 × 2 = 48. So we write 2 in the quotient and 48 below the dividend to subtract these. Subtract 48 - 48 = 0. Thus, remainder = 0 and quotient = 302. This means, 7248 ÷ 24 = 302.
• Long Division of Polynomials

When there are no common factors between the numerator and the denominator , or if you can't find the factors, you can use the long division process to simplify the expression. For more details about long division polynomials, visit the Dividing Polynomials page.

Long Division with Decimals

Long division with decimals can be easily done just like the normal division. We just need to keep in mind the decimals and keep copying them as they come. For more details about long division with decimals, visit the Dividing Decimals page.

How to Divide Decimals by Whole Numbers?

When we need to divide decimals by whole numbers, we follow the same procedure of long division and place the decimal in the quotient whenever it comes. Let us understand this with the help of an example.

Example: Divide 36.9 ÷ 3

• Step 1: Here, the first digit of the dividend is 3 and it is equal to the divisor. So, 3 ÷ 3 = 1. So, 1 is written on top as the first digit of the quotient and we write the product 3 below the dividend 3.
• Step 2: Subtract 3 - 3 = 0. Bring the second digit of the dividend down and place it beside 0, that is, 6
• Step 3: Using the multiplication table of 3, we know that 3 × 2 = 6. So we write 2 in the quotient and 6 below the dividend to subtract these. Subtract 6 - 6 = 0.
• Step 4 : Now comes the decimal point in the dividend. So, place a decimal in the quotient after 12 and continue with the normal division.
• Step 5: Bring down the next number from the dividend, that is, 9. The number to be considered now is 9.
• Step 6: Using the multiplication table of 3, we know that 3 × 3 = 9. So we write 3 in the quotient and 9 below the dividend to subtract these. Subtract 9 - 9 = 0. Thus, remainder = 0 and quotient = 12.3. This means, 36.9 ÷ 3 = 12.3

Long Division Tips and Tricks:

Given below are a few important tips and tricks that would help you while working with long division:

• The remainder is always smaller than the divisor.
• For division, the divisor cannot be 0.
• The division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
• We can verify the quotient and the remainder of the division using the division formula : Dividend = (Divisor × Quotient) + Remainder.
• If the remainder is 0, then we can check our quotient by multiplying it with the divisor. If the product is equal to the dividend, then the quotient is correct.

☛ Related Articles

• Long Division Formula
• Long Division with Remainders Worksheets
• Long Division Without Remainders Worksheets
• Long Division with 2-digit Divisors Worksheets
• Long Division Calculator

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Long Division Examples with Answers

Example 1: Ron planted 75 trees equally in 3 rows. Use long division to find out how many trees did he plant in each row?

The total number of trees planted by Ron = 75. The number of rows = 3. To find the number of trees in each row, we need to divide 75 by 3 because there is an equal number of trees in each of the three rows. Let us also observe how to do 2 digit by 1 digit division here.

Therefore, the number of trees in each row = 25 trees.

Example 2: $4000 needs to be distributed among 25 men for the work completed by them at a construction site. Calculate the amount given to each man.

The total amount is $4000. The number of men at work = 25. We need to calculate the amount given to each man. To do so, we have to divide 4000 by 25 using the long division method. Let us see how to work with long division by a 2 digit number and also see how to do long division step by step.

Each man will be given $160. Therefore, $160 is the amount given to each man.

Example 3: State true or false with respect to long division.

a.) In the case of long division of numbers, the remainder is always smaller than the divisor.

b.) We can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

a.) True, in the case of long division of numbers, the remainder is always smaller than the divisor.

b.) True, we can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.

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Practice Questions on Long Division

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FAQs on Long Division

What is long division in math.

Long division is a process to divide large numbers in a convenient way. The number which is divided into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value received after doing the division is the quotient, and the number left after the division is called the remainder.

The following steps explain the process of long division. This procedure is explained with examples above on this page.

• Write the dividend and the divisor in their respective positions.
• Take the first digit of the dividend from the left.
• If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient.
• Write the product below the dividend and subtract the result from the dividend to get the difference. If this difference is less than the divisor, and there are no numbers left in the dividend, then this is considered to be the remainder and the division is done. However, if there are more digits in the dividend to be carried down, we continue with the same process until there are no more digits left in the dividend.

What are the Steps of Long Division?

Given below are the 5 main steps of long division. For example, let us see how we divide 52 by 2.

• Step 1: Consider the first digit of the dividend which is 5 in this example. Here, 5 > 2. We know that 5 is not divisible by 2.
• Step 2: We know that 2 × 2 = 4, so, we write 2 as the quotient.
• Step 3: 5 - 4 = 1 and 1 < 2 (After writing the product 4 below the dividend, we subtract them).
• Step 4: 1 < 2, so we bring down 2 from the dividend and we get 12 as the new dividend now.
• Step 5: Repeat the process till the time you get a remainder less than the divisor. 12 is divisible by 2 as 2 × 6 = 12, so we write 6 in the quotient, and 12 - 12 = 0 (remainder).

Therefore, the quotient is 26 and the remainder is 0.

How to do Long Division with 2 Digits?

For long division with 2 digits, we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend. If the first 2 digits of the dividend are less than the divisor, then consider the first three digits of the dividend. Proceed with the division in the same way as we divide regular numbers. This procedure is explained with examples above on this page under the heading of 'Long Division by a 2 Digit Number'.

What is the Long Division of Polynomials?

In algebra , the long division of polynomials is an algorithm to divide a polynomial by another polynomial of the same or the lower degree. For example, (4x 2 - 5x - 21) is a polynomial that can be divided by (x - 3) following some defined rules, which will result in 4x + 7 as the quotient.

How to do Long Division with Decimals?

The long division with decimals is performed in the same way as the normal division. This procedure is explained with examples above on this page under the heading of 'How to Divide Decimals by Whole Numbers'? For more details, visit the page about dividing decimals . The basic steps of long division with decimals are given below.

• Write the division in the standard form.
• Start by dividing the whole number part by the divisor.
• Place the decimal point in the quotient above the decimal point of the dividend.
• Bring down the digits on the tenths place, i.e., the digit after the decimal.
• Divide and bring down the other digit in sequence.
• Divide until all the digits of the dividend are over and a number less than the divisor or 0 is obtained in the remainder.

Division Basics

• Dividend - The dividend is the number you are dividing up
• Divisor - The divisor is the number you are dividing by
• Quotient - The quotient is the answer

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21.3: Interpreting Division Situations

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Let's explore situations that involve division.

Exercise \(\PageIndex{1}\): Dot Image: Properties of Multiplication

Exercise \(\PageIndex{2}\): Homemade Jams

Draw a diagram and write a multiplication equation to represent each situation. Then answer the question.

• Mai had 4 jars. In each jar, she put \(2\frac{1}{4}\) cups of homemade blueberry jam. Altogether, how many cups of jam are in the jars?
• Priya filled 5 jars, using a total of \(7\frac{1}{2}\) cups of strawberry jam. How many cups of jam are in each jar?
• Han had some jars. He put \(\frac{3}{4}\) cup of grape jam in each jar, using a total of \(6\frac{3}{4}\) cups. How many jars did he fill?

Here is an applet to use if you choose to.

The toolbar includes buttons that represent 1 whole and fractional parts, as shown here. Click a button to choose a quantity, and then click in the work space of the applet window to drop it. When you're done choosing pieces, use the Move tool (the arrow) to drag them into the jars. You can always go back and get more pieces, or delete them with the Trash Can tool.

The jars in this applet are shown as stacked to make it easier to combine the jam and find out how much you have.

Here are the questions again.

Exercise \(\PageIndex{3}\): Making Granola

• Will the answer be more than 1 or less than 1?
• Write a multiplication equation and a division equation that represent this situation. Use “?” to represent the unknown quantity.
• Find the unknown quantity. If you get stuck, consider drawing a diagram.
• Write a mathematical question that might be asked about this situation.
• What might the equation \(14\div 4=?\) represent in Kiran’s situation?
• Find the quotient. Show your reasoning. If you get stuck, consider drawing a diagram.

If a situation involves equal-sized groups, it is helpful to make sense of it in terms of the number of groups, the size of each group, and the total amount. Here are three examples to help us better understand such situations.

• Suppose we have 3 bottles with \(6\frac{1}{2}\) ounces of water in each, and the total amount of water is not given. Here we have 3 groups, \(6\frac{1}{2}\) ounces in each group, and an unknown total, as shown in this diagram:

We can express this situation as a multiplication problem. The unknown is the product, so we can simply multiply the 2 known numbers to find it. \(3\cdot 6\frac{1}{2}=?\)

• Next, suppose we have 20 ounces of water to fill 6 equal-sized bottles, and the amount in each bottle is not given. Here we have 6 groups, an unknown amount in each, and a total of 20. We can represent it like this:

This situation can also be expressed using multiplication, but the unknown is a factor, rather than the product: \(6\cdot ?=20\)

To find the unknown, we cannot simply multiply, but we can think of it as a division problem: \(20\div 6=?\)

• Now, suppose we have 40 ounces of water to pour into bottles, 12 ounces in each bottle, but the number of bottles is not given. Here we have an unknown number of groups, 12 in each group, and a total of 40.

Again, we can think of this in terms of multiplication, with a different factor being the unknown: \(40\div 12=?\)

Likewise, we can use division to find the unknown:

Whenever we have a multiplication situation, one factor tells us how many groups there are, and the other factor tells us how much is in each group .

Sometimes we want to find the total. Sometimes we want to find how many groups there are. Sometimes we want to find how much is in each group. Anytime we want to find out how many groups there are or how much is in each group, we can represent the situation using division.

Exercise \(\PageIndex{4}\)

Write a multiplication equation and a division equation that this diagram could represent.

Exercise \(\PageIndex{5}\)

Consider the problem: Mai has $36 to spend on movie tickets. Each movie ticket costs $4.50. How many tickets can she buy?

• Write a multiplication equation and a division equation to represent this situation.
• Find the answer. Draw a diagram, if needed.
• Use the multiplication equation to check your answer.

Exercise \(\PageIndex{6}\)

Kiran said that this diagram can show the solution to \(16\div 8=?\) or \(16\div 2=?\), depending on how we think about the equations and the “?”.

Explain or show how Kiran is correct.

Exercise \(\PageIndex{7}\)

Write a sentence describing a situation that could be represented by the equation \(4\div 1\frac{1}{3}=?\).

(From Unit 4.1.2)

Exercise \(\PageIndex{8}\)

Noah said, “When you divide a number by a second number, the result will always be smaller than the first number.”

Jada said, “I think the result could be larger or smaller, depending on the numbers.”

Do you agree with either of them? Explain or show your reasoning.

(From Unit 4.1.1)

Exercise \(\PageIndex{9}\)

Mini muffins cost $3.00 per dozen.

• Andre says, “I have $2.00, so I can afford 8 muffins.”
• Elena says, “I want to get 16 muffins, so I’ll need to pay $4.00."

Do you agree with either of them? Explain your reasoning.

(From Unit 3.3.3)

Exercise \(\PageIndex{10}\)

A family has a monthly budget of $2,400. How much money is spent on each category?

• 44% is spent on housing.
• 23% is spent on food.
• 6% is spent on clothing.
• 17% is spent on transportation.
• The rest is put into savings.

(From Unit 3.4.6)