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. This article will give you an overview of the long division method along with its steps and examples.
1.  What is Long Division Method? 
2.  Parts of Long Division Equation 
3.  How to Do Long Division? 
4.  FAQs on Long Division 
What is Long Division Method?
In math, 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 to see the divisor, the dividend, the quotient, and the remainder.
Parts of Long Division Equation
As you have seen above, while performing the steps of long division, there is an equation formed which is known as the long division equation. For example, while dividing 75 by 4, we get 75 = 4 × 18 + 3 where 75 is the dividend, 4 is the divisor, 18 is the quotient, and 3 is the remainder. The general form of a long division equation is “Dividend = Divisor × Quotient + Remainder”. Here are the terms related to a division which are also considered as the parts of long division. They are the same terms that are used in the regular division.
Have a look at the table given below in order to understand the terms related to the long division with reference to the example shown above.
Dividend  The number which has to be divided.  75 

Divisor  The number which will divide the dividend.  4 
Quotient  The result of division.  18 
Remainder  The leftover part or the number left after certain steps and cannot be divided further.  3 
How to Do Long Division?
The 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.
Long Division Steps
To perform division requires the construction of a tableau. 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 steps of the long division 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’s have a look at the examples given below for a better understanding of the concept.
Case 1: When the first digit of the dividend is equal to or greater than the divisor.
Let’s consider an example: Divide 435 ÷ 4. The steps of long division are given below:
 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.
 Subtract: 4 – 4 = 0.
 Bring the second digit of the dividend down and place it besides 0.
 Now, 3 4. 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
Practice Questions on Long Division
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 we divide into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value got after doing the division is the quotient, and the number left after the division is called the remainder.
How to do Long Division?
The following steps explain the process of long division:
 Write the dividend and the divisor at 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. 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 – 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. It follows the steps 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 tens place digit.
 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.
What is Long Division Symbol Called?
The divisor and the dividend are separated by a right parenthesis 〈)〉 or a vertical bar 〈〉 whereas, the dividend and the quotient are separated by a vinculum or an overbar. The combination of these two symbols is referred to as long division symbol or division bracket.
What is the Remainder in Polynomial Long Division?
While dividing polynomials, sometimes there is a value left that is lesser in degree as compared to the divisor, that value is known as remainder. It can be in the form of an expression or a number.
This long division tutorial section demonstrates some examples of how to do LONG division.
Despite being a bit tedious at times, LONG division is actually fairly similar to SHORT division in principle.
It really doesn’t have to be as intimidating as some people often believe.
Long Division Tutorial,
How to do Long Division Examples
We start out setting up the same way as with Short Division .
21 798
Firstly, 21 does not go into 7, so like with short division, a 0 goes above.
0
21 798
Now, we look at dividing 79 by 21.
At this point, forget the remainder, just establish how many times 21 will go into 79.
21 × 3 = 63 , LESS THAN 79
21 × 4 = 84 , MORE THAN 79
So ignoring any remainder just now, 21 goes into 79 three times.
So 3 goes above now.
03
21 798
Next we take 21 × 3, which is 63 , and place it under the 79 in the “DIVIDEND”.
03
21 798
63
Then, subtract this 63 from 79, and place the result below 63 .
03
21 798
− 63
16
Now the next number in the “DIVIDEND” is brought down, and written on the end of 16 , here this is 8.
03
21 798
− 63
168
Then, we divide 168 by 21, and place the result above in the answer.
168 ÷ 21 = 8 038
21 798
− 63
168
Now lastly, we subtract 21 × 8 from 168 , which just gives 0,
and with no more numbers left to bring down in the DIVIDEND,
this means that the long division is complete.
038
21 798
− 63
168
− 168
0
798 &div 21 = 38
This example will feature a “remainder”.
Firstly, 18 does not go into 8, so a 0 goes above the 8.
0
18 806
Now, ignoring any remainder at this stage, 18 goes into 80 four times, so 4 goes above.
04
18 806
Now, subtract 18 × 4 from 80.
18 × 4 = 72
04
18 806
− 72
8
Next, the 6 is brought down beside the 8, to make 86 .
04
18 806
− 72
86
Ignoring remainders again at this point, 18 goes into 86 four times, so another 4 is placed above in the answer.
044
18 806
− 72
86
Then, the final step is to subtract 18 × 4 from 86 .
18 × 4 = 72
044
18 806
− 72
86
− 72
14
With no more numbers left to bring down from the “DIVIDEND”, our remainder left over is 14.
806 &div 18 = 44 r14
More division help information on Long Division can be seen at mathsonline.org .
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A polynomial looks like this:
example of a polynomial this one has 3 terms 
Dividing
Polynomials can sometimes be divided using the simple methods shown on Dividing Polynomials.
But sometimes it is better to use “Long Division” (a method similar to Long Division for Numbers)
Numerator and Denominator
We can give each polynomial a name:
 the top polynomial is the numerator
 the bottom polynomial is the denominator
If you have trouble remembering, think denominator is downominator.
The Method
Write it down neatly:
 the denominator goes first,
 then a “)”,
 then the numerator with a line above
Both polynomials should have the “higher order” terms first (those with the largest exponents, like the “2” in x 2 ).
It is easier to show with an example!
Write it down neatly like below, then solve it stepbystep (press play):
Check the answer:
Multiply the answer by the bottom polynomial, we should get the top polynomial:
Remainders
The previous example worked perfectly, but that is not always so! Try this one:
After dividing we were left with “2”, this is the “remainder”.
The remainder is what is left over after dividing.
But we still have an answer: put the remainder divided by the bottom polynomial as part of the answer, like this:
“Missing” Terms
There can be “missing terms” (example: there may be an x 3 , but no x 2 ). In that case either leave gaps, or include the missing terms with a coefficient of zero.
Write it down with “0” coefficients for the missing terms, then solve it normally (press play):
See how we needed a space for “3x 3 ” ?
More than One Variable
So far we have been dividing polynomials with only one variable (x), but we can handle polynomials with two or more variables (such as x and y) using the same method.
When I found out I was going to have 5th class this year, I was delighted and I quickly thought of the Maths curriculum – I think there is a huge amount in the 5th class Maths curriculum and one of the most difficult areas to teach is long division. When I was on teaching practice, I was asked to teach long division at the beginning of September – to say the first lesson was a disaster would be an understatement and to make matters worse, the inspector was sitting at the back of the room. In my ‘Dip’ year, I had 5th class again and knew that long division was a challenging area so this time I was prepared.
Originally, I had planned to tackle long division after mid term but in a moment of madness I decided to get stuck in over the last two weeks and overall it has been a success so here are some of the strategies we used.
Honesty
I told the children that long division was a tricky topic and that it will take some time to get the hang of it. I find with maths that children can often switch off when it gets too difficult so making them aware at the beginning that this will be tricky and that most children find it difficult to grasp at the beginning. The children were then more open to the challenge and were listening extremely carefully to try to get the hang of it. (The more able children wanted to prove that they could quickly grasp the new concept, while the children who often struggle felt supported as I wasn’t expecting them to get it straight away.)
Subtraction Method
I spent less than 5 minutes on this. Previously, I have used this strategy for a few days before introducing long division and I’ve found that it confuses children. We made the link between subtraction and division and I did 3/4 examples on the board and I linked back to it when we started the long division method.
Long Division Family
This works brilliantly. It’s easy to remember and makes long division a really step by step process.
We broke the 3 digit number into hundreds and tens and kept the units separate. We focussed on hundreds and tens first and left the units digit.
Division Daddy – first we estimate and divide.
Multiplication Mammy – next we multiple the divisor by the estimate and try to get as close as possible to the number.
Subtraction Sister – next we subtract.
Bring Down Brother – then we bring down the units digit
Remainder/Repeat Rover – finally repeat the process, otherwise you are left with a remainder.
Examples
I did countless examples on the whiteboard showing the step by step process. Then we worked through a number of examples on whiteboards. I find whiteboards fantastic for maths as if there is a mistake it can be wiped away and the children can just continue with their work.
Avoid Copies
This was a piece of advice that my mentor gave me when I had fifth class for my dip. At that time, I made division notebooks for the children. This year, I gave each child an A3 piece of white paper which we folded into 8th’s. This created 8 spaces on the front and 8 on the back. I’m quite strict about how I like Maths copies to be laid out (ruled perfectly, one number per box etc.), with a new concept children often make more mistakes than usual so avoiding copies lessens the stress associated with learning something new.
Step by step
Some children found it helpful to write D, M, S, B to the side of their page (they then ticked each step to remind them of what to do next). We also found it helpful to write the answer with the remainder at the end of each sum – this made the answer very clear. I found it really useful to start with questions that had no remainders, the children knew very quickly if they had gotten the correct answer and they were very easy to correct too.
We used the division family to help us to remember each step. Some other useful reminders include;
Don’t Ever Munch Soggy Biscuits. (Divide, Estimate, Multiply, Subtract, Bring down)
Tricky areas
Questions like the one above proved a bit tricky for the children – when the children brought down the units digit, they were left with a number that was less than the divisor. We discussed what we could do. Was 1 remainder 31 correct? We could do the calculation 1×45 in our heads and knew the answer wasn’t close enough to 481. We then realised that 45 can’t divide into 31 so the answer was 0 and 31 was the remainder. We could then see that 45 x 10 = 450 and then add the remainder of 31 to get the answer 481.
Checking answers
We used calculators to check our answers. I let the children experiment to start with and they realised that when they tried to divide a 3 digit number by a 2 digit number and were left with a remainder then the answer on the calculator had a decimal point and wasn’t presented as ___ r ____. We then had to think of a different way to check our answers so we realised that if we multiply the divisor by our answer and add the remainder we should end up with the dividend.
Long division calculator displays the whole work for dividing the dividend by the divisor resulting in the quotient in less time. Simply put the dividend and divisor values in the input field and click on the calculate button provided next to the input box.
Long Division Calculator: Trying to do division for long numbers and don’t know how to do proper calculations in an easy manner. Then, we are here with you to assist in performing a long division method with an instant long division calculator. This long division tool helps you understand how to do long division with integers or decimals. This calculator also aids you out to do a long division with decimals or remainders. Want to learn more about the long division calculator then go with the below sections and get the complete details in detail.
What is meant by Long Division?
The long division method includes basic math operations. In order to find the division of two numbers using this method, a tableau is drawn. The divisor is written outside the right parenthesis, while the dividend is placed within. The quotient is written above the line on top of the dividend. If you want to learn how to do long division for a fraction or given numbers with long division method, please keep on reading.
Procedure for Division of Numbers using Long Division Method
In order to calculate the division for two numbers easily, one should know the process very well and must apply the steps properly. So, to master the division of numbers using the long division method, we have provided the detailed process here along with a solved example.
Long division with remainders has never been so simple! So accept it as a challenge and solve the problem on your own by referring to the below steps.
 To find the result which is the ratio of two numbers i.e, dividend and divisor we use the long division method.
 First, you need to identify the dividend and divisor and then use those values in the long division.
 In the given fraction numerator will be the dividend and denominator will be the divisor. Outline the dividend and divisor in the form of long division.
 Probably, you have to add a decimal and zeros if the dividend is smaller than the divisor. Continue long division until you get the proper result for the given numbers. It will give the remainder in both the whole number or in a decimal format.
 The result can be written in many ways as a quotient and a remainder, a fraction, and a decimal converted from the fraction.
For a better understanding of the long division method, we have provided the workedout example for a division of numbers using the long division method. Refer to the below example and learn the step by step process of solving long division.
Example:
Calculate division for 678/35 using a long division method?
Solution:
In the given input 678/35, 678 is the numerator i.e. dividend and 35 is the denominator i.e. divisor. As the dividend is greater than the divisor you can proceed with the long division process and get the result as such
Therefore, the Quotient is 19 and the Remainder is 13.
Instructions to use Long Division Calculator
Here are the simple steps that you should follow while using the long division calculator with remainders or decimals. Just have a look at them and learn how to use this long division method calculator to calculate lengthy division problems and get the quotient and remainders in a fraction of seconds.
 First of all, enter the input dividend and divisor values in the input box provided on the screen.
 Next, click on the Arrow symbol button beside the input field.
 Now, it will find the quotient of the division and display an interactive, stepbystep illustration of the long division.
Make all your math problems easier and faster with our Onlinecalculator.guru site provided free online calculators for various mathematical & statistical concepts.
FAQs on Long Division Calculator with Remainders
1. What is Long Division with Remainders?
A long division with remainders is a method for dividing multidigit numbers by hand. It splits the division into a series of simpler steps. One number, called the dividend is divided by another number called the divisor and gives the result as quotient and remainder.
2. What is Quotient in Long Division?
The quotient is the outcome of dividing one number by another using a long division method.
3. What is Remainder in the division?
The remainder is the left out value after multiplying the whole number portion of the quotient by the divisor and then subtracting that result from the dividend.
4. How do you do long division easily by hand?
Simply refer to the abovementioned steps on how to do long division and follow them correctly to calculate the long divisions by hand. Or else, use our free online Long Division Calculator with or without Remainder and get the outcome within no time.
What is long division?
Long division is a way to solve division problems with large numbers. These are division problems that you can’t do in your head.
How to Write it Down
First you have to write the problem down in long division format. The typical division problem looks like this:
To write this down in long division format it looks like this:
Let’s try a fairly simple example: 187 ÷ 11 = ?
1) First step is to put the problem into long division format:
2) The second step is to determine the smallest number to the left of the dividend, in this case 187, that can be divided by 11. The first number “1” is too small, so we look at the first two numbers “18”. 11 can fit into 18 so we can use that.
In this step, we write down how many times 18 can be divided by 11. In this case the answer is 1. If we tried 2 that would be 22, which is bigger than 18.
Next, we write 11 underneath the 18 because 1×11 = 11. Then we subtract 11 from 18. This equals 7, which we write down.
3) Since we had a remainder of 7, the problem isn’t finished. We now move the 7 down from the end of the 187 (see the picture).
4) In this step we determine how many times 11 will divide into 77. That is exactly 7 times. We write down the 7 next to the 1 in the answer area. We also write down 77 underneath the 77 because 7 x 11 = 77.
5) Now we subtract 77 from 77. The answer is zero. We have finished the problem. 187 ÷ 11 = 17.
A few tips for long division:
 Write down a multiple table for the divisor before you start the problem. For example, if the divisor is 11 you write down 11, 22, 33, 44, 55, 66, 77, 88, 99, etc. This can help you to avoid mistakes.
 Put a “0” in the left positions of the quotient that you aren’t using. Make sure you keep all your numbers lined up. Writing neatly and keeping the numbers lined up can really help you to make fewer mistakes.
 Double check the problem with multiplication. Once you have your answer, do the problem in reverse using multiplication to make sure you got the correct answer.
Below are a few more examples of long division. Try to work through these problems yourself to see if you get the same results.
LONG DIVISION: METHOD AND EXAMPLES
Long division is probably one of the most difficult things to learn in maths. Many students struggle with the concept of long division.
Unlike other school subjects, maths require a strong level of accuracy. There is a definitive answer, and therefore you need to be able to know the process of how to reach the correct answers.
LONG DIVISION VIDEO
Watch our video on how to work out long division calculations. Our Careervidz channel on Youtube is a highly popular educational channel, which has lots of videos ranging from Maths and English, and ventures out into Science and History!
Subscribe to our channel to be updated with regular uploads of our educational videos!
LONG DIVISION WORKSHEETS
The best way to understand how to use long division correctly is simply via example. I am going to provide you with one example and a video. These will show you the stepbystep process of how to use the long division method to work out any division calculation.
Calculate 3312 ÷ 24
STEP 1 = write the numbers in the correct division format:
STEP 2 = how many times does ‘24’ go into ‘3’?
Answer = 0.
So write 0 above the line, above the number 3.
STEP 3 = how many times does ‘24’ go into ‘33’?
Answer = 1.
So write 1 above the line, above the second number 3.
You need to subtract 24 from 33.
STEP 4 = Now you have the number ‘9’. You need to bring the number ‘1’ down from the large number, and place it next to the ‘9’.
How many times does ‘24’ go into ‘91’?
Answer = 3
So write 3 at the top of the line.
You need to subtract three lots of 24 from 91.
STEP 5 = Now you have the number ‘19’. You need to bring the number ‘2’ down from the large number, and place it next to the ‘19’.
How many times does ‘24’ go into ‘192’?
Answer = 8
So write 8 at the top of the line.
STEP 6 = Because ‘24’ goes into ‘192’ exactly, that means we have completed the calculation.
So, 3312 ÷ 24 = 138
LONG DIVISION AND OTHER USEFUL RESOURCES
Click on the link for more of my other useful maths resources, guaranteed to improve your maths skills and knowledge.
This resource is packed full of maths videos, and each video focuses on a certain aspect of maths, including:
• Long division
• How to multiply
• Mean, mode, median and range
• BIDMAS
• Area, perimeter and volume
• Fractions, decimals and percentages and many more!
Learn to divide using dots and lines
If you’ve ever seen the Japanese trick for multiplying using lines, you know that doing math by hand doesn’t have to mean doing it the oldfashioned way. If long division always confused you or you simply want to try something new, this trick might be for you.
Start by choosing a number to divide by another: We’re going to try 145,824 divided by 112. The first step is to draw dots on a piece of paper in columns where each column has a number of dots that represents a digit in the number you are dividing. So here, we have a column with one dot, a column with four dots, a column with five dots and so on.
Next, we are going to trace lines between the dots. Since we are dividing by 112, we’re going to connect one dot from a column to one dot from the next column to two dots from a third column. You always start as far left as you can (where there are empty dots).
The last step involves counting the number of groups of lines that start in each column. In our example, one group starts in the first column (red), three groups start in the next column (blue), then none and then two (green). That gives us our answer: 1302. You have to remember to put a zero for any column that doesn’t start new lines, but you can ignore the columns at the end — unless the answer ends in zeros. I recommend multiplying it back through to check whether or not you need them.
In some cases, this technique can get a little tricky when there aren’t enough dots in a particular column. In that case, you’ll have to transform one of the dots from a column into ten dots in the following column. Here’s one more example to see how that works: 3328/104. In this case, one of the dots from the second column is converted to 10 dots in the third column (shown in gray).
Watch the video below to see how this technique can be used for long division of polynomials as well!
Long division is a monumental skill for every elementary student! Some can’t wait to learn how to do it, and others are petrified at the thought. I could probably say the same for the teacher! Some teachers can’t wait to get to the long division unit, and others dread it like the plague! This post will hopefully get you excited by giving you some options! Learning the different styles of long division helps students build a good conceptual understanding and it provides student choice.
This post will help you understand how to teach each strategy and identify which students will benefit from the varying strategies. There are lots of examples, videos, and free printables that can help you get started today!
Click for your free copy of Division Resource Pages!
Which division strategy should you use to teach your students long division?
To decide which division strategy you should teach, you need to think about your students! Keep reading to see what I’ve learned over the years and download some useful resources you can use with your students.
Let me start by saying that there is no right or wrong strategy! Don’t spend too long teaching all the strategies! It’s best to introduce your students to all of them, and then let them choose which one they want to use. Don’t make students try and master every strategy. They simply need to pick a strategy and practice it until they are masters!
We will look at 4 different strategies and discuss which students would benefit for which strategies
Let’s start with the good ol’ fashioned long division algorithm. This is the strategy that most adults learned when they were in school and still use when the opportunity to do long division (without the use of a calculator) arises. Students that have parents that enjoy helping them with homework would appreciate their children using this strategy. This will be the strategy their parents will be the most comfortable helping them with. This strategy tends to be a good one for those teacherspetgonnagrowuptobeateacher type kids! These kids like showing their work, they’re usually neat with their handwriting, and they feel accomplished when they get to the end of a very long problem.
Using a checklist alongside this strategy can help students keep their thoughts in order as they work the problem.
Download a bunch of FREE student Resources Here!
The short division strategy is my favorite strategy! It works great for students that know their facts and can find remainders in their head. You can give them a quick quiz (grab it here!) to see how accurately they can find the quotient and remainder. If students are not able to do this, you should discourage them for using this strategy.
The short division algorithm is also good for students that have poor handwriting or lack the ability to keep their math neat and organized as they work. This strategy is not dependent on students keeping their work nice and lined up. It helps eliminate careless mistakes.
The drawback of this strategy is that it lacks concrete representation that helps students understand why the algorithm works. I tend to teach this strategy after I’m sure that students understand the concept of dividing big numbers.
if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps

Obtain the number whose square root is to be computed

place bars every pair of digits starting with the unit digits .Also place a bar on one digit if any not forming a on the extreme left. each pair and the remaining one digit (if any) on the extreme left is called a period

think of the largest number whose square is less than or equal to the first period . if this number as the divisor and the quotient

put the question above the period and write the product of divisor and question just below the first period.

subtract the product of divisor and quotient from the first period and bring down the next point to the right of the remainder this becomes the next dividend.

double the question as it appears and enter It to the blank on the right for the next digits, as the next possible divisor.

think of a digit to fill the blank in step 6 in such a way that the product of new divisor and its digit is equal to or just less than the new dividend obtained in the step 5 .

subtract the product of the digits chosen in steps 7 and the new division from the dividend obtained in step 5 and bring down the next period to the right of the remainder of this becomes new dividend .

repeat the steps 5 6 and 7 till all the periods have been taken up .

obtain the quotient as a square root of the given number .
Hope it helps “>]” datatest=”answerboxlist”>
Answer:
if you wanna do long division you have to simply just follow a procedure that is nice and easy so long division method is mainly need to find the square of a number with out using the prime factorization method the procedure is consisting of these of two steps
 Obtain the number whose square root is to be computed
 place bars every pair of digits starting with the unit digits .Also place a bar on one digit if any not forming a on the extreme left. each pair and the remaining one digit (if any) on the extreme left is called a period
 think of the largest number whose square is less than or equal to the first period . if this number as the divisor and the quotient
 put the question above the period and write the product of divisor and question just below the first period.
 subtract the product of divisor and quotient from the first period and bring down the next point to the right of the remainder this becomes the next dividend.
 double the question as it appears and enter It to the blank on the right for the next digits, as the next possible divisor.
 think of a digit to fill the blank in step 6 in such a way that the product of new divisor and its digit is equal to or just less than the new dividend obtained in the step 5 .
 subtract the product of the digits chosen in steps 7 and the new division from the dividend obtained in step 5 and bring down the next period to the right of the remainder of this becomes new dividend .
 repeat the steps 5 6 and 7 till all the periods have been taken up .
 obtain the quotient as a square root of the given number .
Here we will show you stepbystep with detailed explanation how to calculate 5 divided by 8 using long division.
Before you continue, note that in the problem 5 divided by 8, the numbers are defined as follows:
5 = dividend
8 = divisor
Step 1:
Start by setting it up with the divisor 8 on the left side and the dividend 5 on the right side like this:
8  ⟌  5 
Step 2:
The divisor (8) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:
0  
8  ⟌  5 
Step 3:
Multiply the divisor by the result in the previous step (8 x 0 = 0) and write that answer below the dividend.
0  
8  ⟌  5 
0 
Step 4:
Subtract the result in the previous step from the first digit of the dividend (5 – 0 = 5) and write the answer below.
0  
8  ⟌  5 
–  0  
5 
You are done.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 5 divided by 8 calculated using Long Division is:
0
5 Remainder
Long Division Calculator
Enter another problem for us to explain and solve:
More Information
If you enter 5 divided by 8 into a calculator, you will get:
The answer to 5 divided by 8 can also be written as a mixed fraction as follows:
Note that the numerator in the fraction above is the remainder and the denominator is the divisor.
How to calculate 5 divided by 9 using long division
Here is the next division problem we solved with long division.
In today’s post we are going to explain how to solve double digit division.
Before beginning to learn how to solve double digit division, it is important that you become familiar with these terms, because we will use them later.
Dividend: the number that is being divided.
Divisor: the number by which the dividend is divided.
Quotient: the result of division.
Remainder: the amount that is left over after division.
Once you have seen this, you know where to place each number in the division. Now, we have to follow these steps:
 Take the first digits of the dividend, the same number of digits that the divisor has. If the number taken from the dividend is smaller than the divisor, you need to take the next digit of the dividend.
 Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient.
 Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it. If you cannot, because the dividend is smaller, you will have to choose a smaller number in the quotient until it can subtract.
 After subtraction, drop the next digit of the dividend and repeat from step 2 until there are no more remaining numbers in the dividend.
That’s the concept, but we are going to go through it with an example.
We are going to solve the following double digit division:
 Take the first digits of the dividend: in this case 57. But as 57 is smaller than 73, you have to take one more digit: 573.
 To divide 573 by 73, we take the first two digits of the dividend: 57 and divide them by the first digit of the divisor:
 Write the 8 in the quotient and multiply it by the divisor:
But 584 is bigger than 573; therefore, 8 “does not fit”. You have to choose the preceding number and multiply again:
511 is smaller than the dividend; therefore 7 “does fit”. We write 511 beneath the digits of the dividend and then divide and subtract:
 Drop the next digit of the dividend, which is 8. Now, you have to divide 628 by 73. Repeat the previous steps:
Divide the first two digits of the dividend by the first digit of the divisor and write it in the space of the quotient:
Multiply that digit by the divisor:
584 is less than 628; therefore, we can subtract:
The result of this division is 78 and a remainder of 44.
I hope that you have learned with this post how to do doubledigit division.
Do not hesitate to leave your comments!
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What is long division? Long division is a method of dividing larger numbers (3 or more digits) by numbers of 2 or more digits.
This is how to set out long division:
First, 15 does not go into 8, so look at the next digit.
15 goes into 86 five times, so write the number 5 above the 6.
(15 x 5 = 75)
Next, to work out the remainder take the 75 away from 86.
(86 – 75 = 11)
Then carry down the 1 to make 111.
15 goes into 111 seven times, so put a 7 above the 1.
(15 x 7 = 105)
Now take 105 away from 111 to get the remainder:
111 – 105 = 6
Finally, carry the 0 down to make 60.
15 goes into 60 exactly 4 times, so put a 4 above the 0.
(15 x 4 = 60)
This gives you the answer 574
When do children learn to do long division?
At the start of Key Stage 1 children will be taught the concept of division, teachers will probably introduce this by getting children to share out some objects amongst themselves. For example, some children might be given 6 coloured blocks and then asked to give half of them to the classmate sat next to them.
In Key Stage 2, after learning all their times tables and division facts, children will begin to use short division (called the ‘bus stop’ method) in Year 5. Short division is used to divide 3 or 4 digit numbers by a 1 digit number. Teachers will then introduce children to the long division method above so that they can use it to divide larger numbers by 2 digit numbers.
How to help children with long division?
Using the long division method will require that children are confident in their times tables and that they understand how multiplication relates to division, as there are a lot of calculations to work out as they go along. Therefore, if children are struggling it could be a good idea to go back over their times tables and make sure that they know their division facts. For example,
if 6 x 4 =24, then 24 ÷ 6 = 4.
It is also important that children understand the different terminology used in methods like long division. You may need to explain that a remainder is the number left over from a calculation. For example:
The number 27 does not divide exactly into 5, but we can divide 25 exactly by 5 (as 5 x 5 = 25). So, if Harriet had 27 sweets to share between her 5 friends, each friend would get 5 sweets and Harriet would have 2 sweets left over.
To remember which order to do calculations in long division, it can be helpful to create an acronym to make it more memorable. For example:
How does Learning Street help children with long division?
Similar to what they will be doing at school, Learning Street will begin with the basics of division in earlier courses, as without knowing the fundamentals, the child can’t learn long division. Through extension and revision, the child will slowly develop their knowledge of division before then being introduced to long division, followed up with extension and revision.
Tests could include SATs, competitive 11 Plus tests or selective Independent school exams.
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Here we will show you stepbystep with detailed explanation how to calculate 64 divided by 3 using long division.
Before you continue, note that in the problem 64 divided by 3, the numbers are defined as follows:
64 = dividend
3 = divisor
Step 1:
Start by setting it up with the divisor 3 on the left side and the dividend 64 on the right side like this:
3  ⟌  6  4 
Step 2:
The divisor (3) goes into the first digit of the dividend (6), 2 time(s). Therefore, put 2 on top:
2  
3  ⟌  6  4 
Step 3:
Multiply the divisor by the result in the previous step (3 x 2 = 6) and write that answer below the dividend.
2  
3  ⟌  6  4 
6 
Step 4:
Subtract the result in the previous step from the first digit of the dividend (6 – 6 = 0) and write the answer below.
2  
3  ⟌  6  4 
–  6  
0 
Step 5:
Move down the 2nd digit of the dividend (4) like this:
2  
3  ⟌  6  4 
–  6  
0  4 
Step 6:
The divisor (3) goes into the bottom number (4), 1 time(s). Therefore, put 1 on top:
2  1  
3  ⟌  6  4 
–  6  
0  4 
Step 7:
Multiply the divisor by the result in the previous step (3 x 1 = 3) and write that answer at the bottom:
2  1  
3  ⟌  6  4 
–  6  
0  4  
3 
Step 8:
Subtract the result in the previous step from the number written above it. (4 – 3 = 1) and write the answer at the bottom.
2  1  
3  ⟌  6  4 
–  6  
0  4  
–  3  
1 
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 64 divided by 3 calculated using Long Division is:
21
1 Remainder
Long Division Calculator
Enter another problem for us to explain and solve:
More Information
If you enter 64 divided by 3 into a calculator, you will get:
The answer to 64 divided by 3 can also be written as a mixed fraction as follows:
Note that the numerator in the fraction above is the remainder and the denominator is the divisor.
How to calculate 64 divided by 4 using long division
Here is the next division problem we solved with long division.
Published on Dec 10, 2020
It’s remarkable how when you’re faced with helping children with their maths homework, much more comes flooding back to you than what you first thought.
The ‘bus stop’ method is a tried and tested way of doing long division when you’re asked to divide larger numbers by two or threedigit numbers, as well as when a number is being divided by a single digit, known as short division. Bus stop division is simply another name for a stepbystep long division method and is suitable for Key Stage 2 children but is typically introduced in Year 5.
If you need more Maths help for your Key Stage 2 children, you can check out our classes on Kidadl TV.
Why Is It Called The ‘Bus Stop’ Method?
The bracket you need to draw over the ‘dividend’, the number you’re being asked to divide, resembles a bus stop. The long edge shelters the dividend while the short edge, drawn towards the metaphorical ground, separates the ‘divisor’, the number you’re dividing by. This method differs from short division as here you need to draw the bracket on top and work out the sum using a slightly more complex process.
How To Do The Bus Stop Method With A 2Digit Divisor?
QUESTION: What is 1,722 ÷ 15?
Step A) 15 is too big to go into 1, so carry the 1 to the 7 to make 17. Cross out the big 1 and rewrite it smaller and closer to the 17 if that helps you visually.
Step B) 15 goes into 17 just once so write a 1 above the bracket over the 7. Now, what’s the difference between 15 and 17? The answer to that is 2 so write a small 2 alongside the next number which makes 22.
Step C) How many times does 15 go into 22? Just once so write a 1 above the bracket over the 2. Now, the difference between 15 and 22 is 7, so write a small 7 next to the following number.
What we have now is 72, so we must calculate 15 ÷ 72 and use our times tables.
Step D) 15 x 4 = 60 and that’s as close as we can get to 72 so now, write 4 above the 72. Now, we must work out the difference between 60 and 72, so do 72 – 60 = 12. But we’ve run out of numbers so where will we put the 12?
Immediately, add a decimal point after both the 114 and 1722, but after the decimal point below the bracket, put a 0.
Step E) Write a small 12 next to the 0 to make 120. Now, how many times does 15 go into 120? 15 x 8 = 120. Finally! Write 8 above the 120 and there you have it.
ANSWER: 1,722 ÷ 15 = 114.8!
Starting Out
Think you’ll never be able to master long division? Think about the acronym DMSB, which stands for Divide, Multiply, Subtract, Bring down. But isn’t it easier to remember: Dad, Mother, Sister, Brother or Does McDonalds Serve Burgers? Both of these phrases can help you remember the steps of a long division problem. Dad corresponds with divide; mother corresponds with multiply, and so on. If you can remember the four steps, you are half way to learning how to do one of these problems. Continue reading to learn how to do long division problems!
Step One: Divide
Let’s say your problem is 358/20. The first step is to divide. Remember 20 in this problem is called the divisor, and 358 is the dividend. The answer you write above the division symbol is called the quotient. So, how many times will 20 go into 358? That is too large of a problem to undertake, and so you break up the division problem into smaller steps. The first problem you would work in this example is: How many times can you divide 20 into 35? The answer is 1. So, you put a 1 above the 5 on the quotient line. You have now divided.
Step Two: Multiply
The next step is multiply. You are going to multiply your answer from step one and your divisor. In this example, you are multiplying 1 x 20, which equals 20. You write this 20 underneath the 35 (which is the first part of the dividend, 358 from step one).
Step Three: Subtract
Next you are going to subtract. You will work the problem 35 – 20. The answer in this example is 15.
Step Four: Bring Down
The last step in the long division process is to bring down. This means you are bringing down the next number from the dividend that hasn’t been used yet in the first small division problem. In this example, the number you are bringing down is 8. You are bringing it down and writing it next to the 15, which was the answer you got when you subtracted. Now, you have a new number 158 (which is also the new dividend. Your divisor is still 20.).
Starting All Over Again
Now, you are going to do the long division steps again with a new problem: 158/20. You will divide, multiply, subtract, and bring down. Divide: how many times does 20 go into 158? The answer is 7 times. Write the 7 on the quotient line above the 8 and next to where you wrote the 1. Now on the quotient line, you have 18. Multiply: Multiply the new answer you have from dividing, which is 7, with the divisor 20. You get 140. Write this underneath the 158. Subtract: Subtract the two numbers: 158140= 18. Bring down: There is nothing left to bring down. Check to make sure the 18, the answer you got when you subtracted, is less than the divisor. In this case, the divisor is 20, so 18 is less. This means the problem was done correctly and there is a remainder of 18. Next to the quotient of 17 write R18 for remainder of 18.
Putting it all together
Let’s put all the steps together to work one more problem. How about: 954/32? Divide: The first problem you would work is: 95/32. The answer would be 2. This 2 should be written above the 5 on the quotient line. Multiply: Next, you multiply the divisor and the quotient, which is 32 x 2 = 64. Subtract: Write the 64 below 95. This problem would be 95 – 64 = 31. Bring down: Bring down the 4 from 954. Bring it down next to the 31 you figured in the step above to make 314. Divide: The new problem you are working is 314/32. How many times does 32 divide into 314? The answer is 9. Write 9 on the quotient line above the 4 and to the right of 2. So, you have the answer, quotient, of 29. Multiply: Multiply 9 x 32, which equals 288. Write 288 below 314 at the bottom of the problem. Subtract: You are now subtracting 314 – 288. This equals: 26 Bring down: There is nothing left to bring down from the original dividend of 954, so the problem is completed. Your answer is 29 R 26. (29 with a remainder of 26)
Long Division Made Easy
You probably don’t want to hear this, but practice is the secret to remembering all the steps! You have to get used to the four steps, and remember that you may have to do them multiple times in one problem. Do you have any other suggestions or tips for how to do long division? Leave a comment below!
This long division calculator divides two numbers: a dividend and a divisor and returns the number quotient along with a whole number remainder.
Other Tools You May Find Useful
■ Multiplying Fractions Calculator
■ Adding Fractions Calculator
Long division rules
The long division rules are explained in 12 steps for a case in which the dividend is a 3 length number, while the divisor is a 2 length one:
1st step: establish the dividend (the number to be divided) and the divisor (is the number “y” we often refer to in sentences like: divide the dividend x by the divisor y).
2 nd step: divide the first number of the dividend (meaning first number of the dividend from left to right) by the divisor and note the whole number that results from this first operation – this is the first number from the quotient.
3 rd step: the whole number from 2 nd step should be placed on top, right below the dividend in order to start the quotient. That whole number should be multiplied at this step by the divisor and the result should be placed under the number that was divided at step 2.
4 th step: Subtract the number obtained at step 3 from the number that got divided at step 2. Note below the result of the subtraction.
5 th step: Right next to the number obtained at step 4 by subtraction bring down the next number of the dividend (from left to right).
6 th step: divide the number that results from step 5 by the divisor.
7 th step: The whole number that results from step 6 should be placed in the second position of the quotient (right next to the first number of the quotient that was obtained at step 2) – this is the second number of the quotient. Multiply the whole number obtained at this step by the divisor and place the result under the number divided.
8 th step: Subtract the number obtained at step 7 from the number above it.
9 th step: Bring down the next number from the dividend (as in step 5 for instance) – this is the last number of the dividend from left to right.
10 th step: Divide the number from step 9 by the divisor.
11 th step: The whole number that results from step 10 is placed in the next position of the quotient and then multiply that number by the divisor and put the result under the number divided.
12 th step: Subtract the result of the 11 step from the number above it and this is the step where you get the remainder and the quotient.
In case you want to perform this calculation quicker than by hand you can use our long division calculator.
What is long division?
The long division method is used when you are dividing a large number (usually three digits or more) by a twodigit (or more) number. It is set out in a similar way to short division (the ‘bus stop’ method).
Long division: a stepbystep guide
Long division is set out in the following way.
When do children learn to use different division methods?
Children start learning about division in Year 1, where they may be asked to share an even number of objects between two people.
They start learning their times tables in Year 2, at which time they also learn their division facts (for example, they learn that if 4 x 5 = 20, then 20 ÷ 5 = 4).
They continue to learn the rest of their times tables, including division facts through Year 3 and Year 4.
In Year 5 they will learn to divide threedigit and fourdigit numbers by a onedigit number using short division (this is also known as the ‘bus stop’ method). They then move onto dividing larger numbers by twodigit numbers using long division, as shown above.
Teachers formerly used to teach children the method of chunking, however under the 2014 curriculum they are advised to use short division and long division.
Using division techniques in maths
It is very important that children are taught division in the context of problemsolving.
In Year 2 they may be asked to solve a word problem like this one:
I have 20 sweets. I share them between 4 people. How many sweets do they have each?
They may be encouraged to use counters to share out the ‘sweets’, but will be guided to move towards using their knowledge of division facts to work out this problem.
Children in Year 3 and 4 will answer questions using more difficult times tables, such as:
There are 42 children in a playground. They are divided into 6 groups, with an equal number of children in each. How many children are in each group?
In Year 5 and 6, they may be asked questions like:
There are 564 beads in a jar. They need to be divided equally into six small jars. How many beads will be in each jar?
I buy 23 cakes, each costing the same amount. The total comes to £11.04. How much does each cake cost?
It is really imperative that children get their heads around division in the context of their times tables, before they can go onto dividing bigger numbers. You can really help your child at home by asking them plenty of mental division questions in relation to their times tables.
It is also important that, in later KS2, they learn to divide numbers by 10 and 100 confidently and efficiently.
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Integration Using Long Division works best for rational expressions where the degree of the polynomial in the numerator is greater than or equal to the degree of the polynomial in the denominator.
Integration Using Long Division: Examples
Example question #1: Solve the following integral:
Step 1: Check to see if the degree in the numerator is greater than or equal to the degree in the denominator. For this example, it is, so we can continue.
Step 2: Divide the numerator by the denominator, using algebra:
Step 3: Rewrite the integral in the question with the new expression you got in Step 2:
Step 4: Solve the integral using the usual rules of integration:
 Apply the sum rule:
 Apply the common integral ∫ 1 ⁄_{x} dx = ln x + c: = 2x + 3 ln x – 2
 Add a constant: 2x + 3 ln x – 2 + C
Note: The sum rule states that the integral of the sum of two functions is the sum of their separate integrals:
∫[f(x) + g(x)] dx = ∫f(x)dx + ∫g(x) dx
Example question #2: Solve the following integral:
Step 1: Check to see if the degree in the numerator is greater than or equal to the degree in the denominator. For this example, it is, so we can continue.
Step 2: Divide the numerator by the denominator, using algebra:
We can’t actually divide this until we factor the denominator first:
Now we can perform the long division, dividing the numerator by the denominator:
The x – 1 is the quotient and 3x 2 is the remainder. Rewrite the solution above as “quotient + remainder/original factored denominator”:
Step 3: Solve the integral using the usual rules of integration: In addition to the sum rule and common integral ∫ 1 ⁄_{x} dx = ln x + c: = 2x + 3 ln x – 2, we also need to apply the power rule to the “x” in front. The solution is:
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Remember long division?
Do you remember doing long division? Now you probably use a calculator for most division problems. We’ll have to remember all those long division skills so that we can divide polynomials.
Think about dividing polynomials as long division, but with variables.
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Let’s review long division by dividing . 146. by . 13.
We start by thinking “How many times does . 13. go into . 14. ” It goes in . 1. time , so we write a . 1. above the long division sign and line it up with the . 4.
Then we multiply . 13\times 1. and get . 13. which means we subtract . 13. from . 14. and get . 1. Bring down the . 6.
How many times does . 13. go into . 16. It goes in . 1. time, so we write another . 1. above the long division sign, this time lined up with the . 6.
. 13\times1=13. which means we subtract . 13. from . 16. and get . 3. Since . 13. doesn’t go into . 3. and there’s nothing left to bring down, we have a remainder of . 3.
Our answer to . 146\div 13. is . 11. with a remainder of . 3. or
Now let’s look at the same problem using polynomial long division. This time we’ll divide . x^2+4x+6. by . x+3.
The leading term in the dividend (. x^2+4x+6. ) is . x^2. and the leading term in the divisor (. x+3. ) is . x. So we start by thinking, “What do I need to multiply . x. by to get . x^2. ” The answer is . x. so we write . x. above the long division sign and line it up with the . x^2.
Then we multiply . x+3. by . x. and get . x^2+3x. which means we subtract . x^2+3x. from . x^2+4x. and get . x. Bring down the . +6.
What do we need to multiply . x. by to get . x. We need to multiply by . 1. so we write . +1. next to the . x. above the long division sign.
. (x+3)\cdot1=x+3. so we subtract . x+3. from . x+6. and get . 3.
Our answer is . x+1. with a remainder of . 3. When we do polynomial long division, we should write the remainder as a fraction, with the remainder in the numerator and the divisor in the denominator, so we should write this answer as
Remember to always have placeholders for any “missing” terms (terms that have a coefficient of . 0. ) in the dividend. For example, if the problem above hadn’t had an . x. term, we would have needed to write . x^2+0x+6. under the long division sign.
Table of Contents
How do you calculate long division step by step?
How to Do Long Division?
 Step 1: Take the first digit of the dividend.
 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 number (if present).
 Step 5: Repeat the same process.
How do you divide equations on a calculator?
The procedure to use the dividing polynomials calculator is as follows:
 Step 1: Enter the numerator and denominator polynomial in the respective input fields.
 Step 2: Now click the button “Divide” to get the result.
 Step 3: Finally, the quotient of the polynomial division will be displayed in the new window.
How do you do algebraic division?
 Arrange the indices of the polynomial in descending order.
 Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor.
 Multiply the divisor by the first term of the quotient.
 Subtract the product from the dividend then bring down the next term.
How do you show division in an equation?
There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction.
What is the formula for long division?
Here’s a trick to mastering long division. Use the acronym DMSB, which stands for: D = Divide. M = Multiply. S = Subtract. B = Bring down. This sequence of letters can be hard to remember, so think of the acronym in the context of a family: Dad, Mother, Sister, Brother.
How do you explain long division?
Long division explained. In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps.
What is 3/24 simplified?
In the fraction 3/24, 3 is the numerator and 24 is the denominator. When you ask “What is 3/24 simplified?”, we assume you want to know how to simplify the numerator and denominator to their smallest values, while still keeping the same value of the fraction.
What is long division process?
long division. n. A process of division in arithmetic, usually used when the divisor is a large number, in which each step of the division is written out.
Want to improve this question? Add details and clarify the problem by editing this post.
Closed 7 years ago .
I am trying to divide a long(someValue) by a int. That must return a decimal value. I tried,
but to no avail. The result I get is a whole number. Please help.
5 Answers 5
This wont work because you are calculating the result and then do the cast.
But why didnt this work? For me it works fine, because you cast the values to double before calculating.
But there is no need for casting the result again! Or for casting both values to double. And its enough if you add an d to the end of the number to tell the compiler that this number should be a dobule value:
If you need precise floating point calculations, the recommended way to do it is to use BigDecimal . That is the truly platformindependent way to go (any other one will get you architecturedependent results).
This is quite a nice tutorial on BigDecimals and their usage
This won’t work because someValue/3600 will be calculated first, and it’ll be made with int calculations.
You should explicitly cast one side (the other will be cast implicitly):
Things to be aware when doing floating point arithematic:
You frist way, someValue/3600 is going to be calculated first, and that’s a integer division, and it will give you an integer, and then casted to a double, which doesn’t give you a correct answer.
You should have both of the value being a double. Therefore your second way should work. Just a bit of extra information here: you don’t really need to cast both number to double. During a division, if the compiler found that one of the value is an integer and the other is a double, the integer will be promoted to be a double for calculation, giving you the same result.
You may sometime find the result “inaccurate” even you are using second way. This is because floating point number is only a binary approximation which cannot present all decimal value accurately. You may consider using BigDecimal if you want an “accurate” decimal value, or learn to deal with floating point number properly.
It depends on your browser, some browsers support editing these symbols, some browsers do not support.
Different operating systems, different text editors, different ways to type Long Divisions, usually we do not need to remember how to type the Long Division(sign), just copy it when needed.
If you need to insert a Long Division in text, mail, or text message, facebook, twitter,etc. you can directly copy the Long Division in the above table.
Symbols are displayed in different shapes on different platforms (operating systems, browsers, text editors, websites) , so the same symbol (such as ⏱) in different browsers (such as Firefox and Google), different websites (facebook and twitter) ), different mobile phones (iphone and Samsung) display different shapes, these are normal. Some symbols, usually emoji, are not supported in word by default, because your system does not have the corresponding font installed, it is displayed as “tofu” this time.
If you need to insert a Long Division in a web page, please copy the HTMLcode corresponding to the Long Division in the above table.
Copy the Long Division in the above table (it can be automatically copied with a mouse click) and paste it in word, Or
 Select the Insert tab.
 Select Symbol and then More Symbols.
 Select the Long Division tab in the Symbol window.
Finding specific symbols in countless symbols is obviously a waste of time, and some characters like emoji usually can’t be found
There is no need to remember that because alt key does not seem so accurate always, copying is a more convenient method.
Because different webpage encodings are used, all encodings can be displayed normally on webpages.
These symbols are actually ideograms and smileys. Different platforms have designed different icons for these picture texts.
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