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## How to Do Long Division

Last Updated: November 29, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 3,856,025 times.

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals . This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life. [1] X Research source

- The quotient (answer) will eventually go on top, right above the dividend.
- Leave yourself plenty of space below the equation to carry out multiple subtraction operations.
- Here's an example: if there are six mushrooms in a 250-gram pack, how much does each mushroom weigh on average? In this case, we must divide 250 by 6. The 6 goes on the outside, and the 250 on the inside.

- In our example, you'd want to determine how many times 6 goes into 2. Since six is larger than two, the answer is zero. If you wish, may write a 0 directly above the 2 as a place-holder, and erase it later. Alternatively, you can leave that space blank and move on to the next step.

- If your answer to the previous step was 0, as in the example, expand the number by one digit. In this case, we'd ask how many times 6 can go into 25.
- If your divisor has more than two digits, you'll have to expand out even further, to the third or maybe even fourth digit of the dividend in order to get a number that the divisor goes into.
- Work in terms of whole numbers . If you use a calculator , you'll discover that 6 goes into 25 a total of 4.167 times. In long division, you always round down to the nearest whole number, so in this case, our answer would be 4.

- It is important in long division to make sure the columns of numbers remain correctly aligned. Work carefully, otherwise you may make an error that leads you to the wrong answer.
- In the example, you would place a 4 above the 5, since we're putting 6 into 25.

## Multiplying

- In the example, 6 times 4 is 24. After you've written a 4 in the quotient, write the number 24 beneath the 25, again being careful to keep the numbers aligned.

## Subtracting

- In the example, we'll subtract 24 from 25, getting 1.
- Do not subtract from the complete dividend, but only those digits you worked with in Parts One and Two. In the example, you should not subtract 24 from 250.

- In the example, because 6 can't go into 1 without exceeding it, you need to bring down another digit. In this case, you'll grab the 0 from 250 and place it after the 1, making it 10, which 6 can go into.

- In the example, determine how many times 6 can go into 10. Write that number (1) into the quotient above the dividend. Then multiply 6 by 1, and subtract the result from 10. You should end up with 4.
- If your dividend has more than three digits, keep repeating this process until you've worked through all of them. For example, if we we had started with 2,506 grams (88.4 oz) of mushrooms, we'd pull the 6 down next and place it next to the four.

## Remainders and Decimals

- In the example, the remainder would be 4, because 6 cannot go into four, and there are no more digits to bring down.
- Place your remainder after the quotient with a letter "r" before it. In the example, the answer would be expressed as "41 r4."
- You would stop here if you were trying to calculate something that would not make sense to express in partial units , for example, if you were trying to determine how many cars were needed to move a certain number of people. In a case such as this, it would not be useful think about things in terms of partial cars or partial people.
- If you plan to calculate a decimal, you can skip this step.

- In the example, since 250 is a whole number, every digit after the decimal will be 0, making it 250.000.

- In the example, determine how many times 6 can go into 40. Add that number (6) to the quotient above the dividend and after the decimal point. Then multiply 6 by 6, and subtract the result from 40. You should end up with 4 again.

- In the example, you could keep getting 4 out of 40-36 forever, and add 6's to your quotient indefinitely. Instead of doing this, stop the problem and round the quotient. Because 6 is greater than (or equal to) 5, you would round up to 41.67.
- Alternatively, you can indicate a repeating decimal by placing a small horizontal line over the repeating digit. In the example, this would make the quotient 41.6, with a line over the 6. [15] X Research source

- If you added a zero as a place-holder at the beginning, you should erase that now as well.
- In the example, because you asked how much each mushroom in a 250-gram pack of 6 weighs, you'll need to put your answer into grams. Therefore, your final answer is 41.67 grams.

## Practice Problems and Answers

## Community Q&A

- If you have time, it's a good idea to do calculations on paper first, then check with a calculator or computer. Remember that machines sometimes get the answers wrong for various reasons. If there is an error, you can do a third check using logarithms . Doing division by hand rather than relying on machines is good for your mathematical skills and conceptual understanding. [16] X Research source Thanks Helpful 2 Not Helpful 0
- Start by using simple calculations. This will give you the confidence and develop the necessary skills to move to more advanced ones. Thanks Helpful 11 Not Helpful 7
- Look for practical examples from everyday life. This will help learn the process because you can see how it is useful in the real world. Thanks Helpful 1 Not Helpful 1

## Tips from our Readers

- To remember the steps, use the mnemonic "Does McDonalds Sell Cheese Burgers Rare?" The D stands for "divide", M for "multiply", S for "subtract", C for "check" your work, B for "bring down" more digits, and R for "repeat" the whole process if needed. This little memory device covers all the key parts of long division.
- Be sure you have multiplication facts mastered before attempting long division. It will be painfully slow if you must stop to figure out what 7 x 7 is each time. Quick recall of times tables is essential. Consider practicing flash cards or math games to improve.
- To divide any number by a power of 10, simply move the decimal point leftward by the exponent on the 10. For example, to divide 20 by 1000 (which is 10^3), think "what times 20 equals 1000?" and move the decimal in 20 three places left to get 0.02.
- Long division works very similarly to dividing fractions. Set up the equation just like a fraction, with the number being divided (dividend) on top and divisor on bottom. Then divide the numerator by denominator using the long division process.
- Don't worry if you make mistakes at first! Long division takes practice. Check each step carefully as you work problems. Over time, you will get faster and more confident. Be patient with yourself and celebrate small successes along the way.

## You Might Also Like

- ↑ https://www.csun.edu/~vcmth00m/longdivision.pdf
- ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut36_longdiv.htm
- ↑ https://www.calculatorsoup.com/calculators/math/longdivision.php
- ↑ https://www.mathsisfun.com/long_division.html
- ↑ https://www.bbc.co.uk/bitesize/guides/z3kmpbk/revision/4
- ↑ https://flexbooks.ck12.org/cbook/ck-12-fifth-grade-math-resource-flexlet/section/1.1/primary/lesson/long-division-without-remainders/
- ↑ https://www.mathsisfun.com/long_division2.html
- ↑ https://www.calculatorsoup.com/calculators/math/longdivisiondecimals.php
- ↑ https://www.mathsisfun.com/definitions/recurring-decimal.html

## About This Article

To do long division, follow these seven steps: Step 1. Calculate how many times the number outside the division bar goes into the first number inside the bar. Step 2. Put the answer on top of the bar. Step 3. Multiply the number outside the division bar by the number at the top of the bar. Step 4. Write the answer below the number inside the division bar, so the first digits of both numbers are lined up. Step 5. Subtract the two numbers inside the division bar and write the answer below the two numbers. If there are any remaining digits inside the division bar, bring them down to the new answer. Step 6. Repeat the division process with the new number. Step 7: If you get to a point where the number outside the division bar can’t fit into the remaining number, write that number, also known as the remainder, next to your answer with an “r” in front of it. Did this summary help you? Yes No

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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 is splitting into equal parts or groups.

It is the result of "fair sharing"., example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates.

Answer: 12 divided by 3 is 4. They get 4 each.

We use the ÷ symbol, or sometimes the / symbol to mean divide:

Let's use both symbols here so we get used to them.

## More Examples

Here are some more examples:

## Opposite of Multiplying

Division is the opposite of multiplying . When we know a multiplication fact we can find a division fact:

Example: 3 × 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Why? Well, think of the numbers in rows and columns like in this illustration:

So there are four related facts :

Knowing your Multiplication Tables can help you with division!

## Example: What is 28 ÷ 7 ?

Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.

Answer: 28 ÷ 7 = 4

There are special names for each number in a division:

dividend ÷ divisor = quotient

## Example: in 12 ÷ 3 = 4:

- 12 is the dividend
- 3 is the divisor
- 4 is the quotient

## But Sometimes It Does Not Work Perfectly!

Sometimes we cannot divide things up exactly ... there may be something left over.

## Example: There are 7 bones to share with 2 pups.

But 7 cannot be divided exactly into 2 groups, so each pup gets 3 bones, but there will be 1 left over :

We call that the Remainder .

Read more about this at Division and Remainders

Try these division worksheets .

## 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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## Division Worksheets

Welcome to the division worksheets page at Math-Drills.com! Please give us your undivided attention while we introduce this page. Our worksheets for division help you to teach students the very important concept of division. If students have a good recall of multiplication facts, the division facts should be a breeze to teach. If you want your students to experience success in learning division, please make sure they know their multiplication facts to 81, how to multiply by 0 and how to multiply by 10. If they don't know these things, learning division will take a lot longer.

On this page you will find many Division Worksheets including division facts and long division with and without remainders. We start off with some division facts which are just the multiplication facts expressed in a different way. The main difference is that you can't divide by 0 and get a real number. If you really want your students to impress, say at their dinner table when their parents ask them what they learned today, you can teach them that division by zero is undefined.

The rest of the page is devoted to long division which for some reason is disliked among some members of the population. Long division is most difficult when students don't know their multiplication facts, so make sure they know them first! Oh, we already said that. What about a long division algorithm... maybe the one you or your parents or your grandparents learned? We adamantly say, yes! The reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals and whole numbers. Long division really isn't that hard.

## Most Popular Division Worksheets this Week

## Division Facts Tables

Like their counterparts on the multiplication facts page, these division facts tables can be used in a variety of ways to help students learn division facts. Students can memorize, look for patterns in the tables, compare them to multiplication tables, write answers on the versions with the answers omitted, or a variety of other learning activities. The tables come in gray, color and Montessori color depending on what fits you and your printer or school the best. For those that have already mastered the facts up to 12, they might be challenged to try the 13 to 24 versions.

- Division Facts Tables for Facts from 1 to 12 Division Facts Tables in Gray 1 to 12 Division Facts Tables in Gray 1 to 12 (Answers Omitted) Division Facts Tables in Color 1 to 12 Division Facts Tables in Color 1 to 12 (Answers Omitted) Division Facts Tables in Color 1 to 12 with Individual Facts Highlighted Division Facts Tables in Montessori Colors 1 to 12 Division Facts Tables in Montessori Colors 1 to 12 (Answers Omitted)
- Division Facts Tables for Facts from 13 to 24 Division Facts Tables in Gray 13 to 24 Division Facts Tables in Gray 13 to 24 (Answers Omitted) Division Facts Tables in Color 13 to 24 Division Facts Tables in Color 13 to 24 (Answers Omitted)

## Division Facts up to the 7 Times Table

If your students aren't quite ready for all of the division facts at once, this might be a good place to start. Perhaps they are really good at the multiplying up to 5; there is a worksheet to help them practice, and when they are ready, they can include 6 then 7. This section includes vertical questions with the traditional division symbol (aka bracket) and some arranged with a division symbol like you might see addition, subtraction or multiplication arranged.

- Division Facts up to the 7 Times Table with a Long Division Symbol Vertical Division Facts Up To The 5 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To The 6 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To The 7 Times Table With Long Division Symbol/Bracket (50 per page) ✎
- Division Facts up to the 7 Times Table with a Division Sign Vertical Division Facts Dividends to 25 With Division Sign Vertical Division Facts Dividends to 36 With Division Sign Vertical Division Facts Dividends to 49 With Division Sign

More worksheets with division facts up to 7, but these ones are arranged horizontally. This is a more natural arrangement for students who are used to reading things from left to right, allows them to practice recalling the answers and it is possible to fit 100 of these questions on the page without it getting too cluttered. If clutter is a problem though, there are also 50 and 25 question options.

- Horizontally Arranged Division Facts up to the 5 Times Table Horizontally Arranged Division Facts with Dividends to 25 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 25 ( 50 Questions ) ✎ Horizontally Arranged Division Facts with Dividends to 25 ( 25 Questions ; Large Print) ✎
- Horizontally Arranged Division Facts up to the 6 Times Table Horizontally Arranged Division Facts with Dividends to 36 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 36 ( 50 Questions ) ✎ Horizontally Arranged Division Facts with Dividends to 36 ( 25 Questions ; Large Print) ✎
- Horizontally Arranged Division Facts up to the 7 Times Table Horizontally Arranged Division Facts with Dividends to 49 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 49 ( 50 Questions ) ✎ Horizontally Arranged Division Facts with Dividends to 49 ( 25 Questions ; Large Print) ✎

Some students require chunking and more practice before they can handle the more complex pages with many different divisors. Here the worksheets only contain one divisor and there are several repetitions of the set on each page.

- Dividing by Individual Facts up to the 7 Times Table Vertically Arranged Dividing by 1 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 2 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 4 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 5 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 6 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7 with Quotients 1 to 7 ( 50 Questions ) ✎
- Dividing by Groups of Individual Facts up to the 7 Times Table Vertically Arranged Dividing by 1, 2 and 5 with Quotients 1 to 7 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3, 4 and 6 with Quotients 1 to 7 ( 50 Questions ) ✎

More individual division facts worksheets but with a horizontal arrangement. This section includes 50 and 25 question options with each set repeated on the page.

- Horizontally Arranged Dividing by Individual Facts up to the 7 Times Table (50 Questions per Page) Horizontally Arranged Dividing by 1 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 7 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 7 ( 50 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts up to the 7 Times Table (25 Large Print Questions per Page) Horizontally Arranged Dividing by 1 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 7 ( 25 Questions ; Large Print) ✎

## Division Facts up to the 9 Times Table

Manipulatives can help students "get" the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles. For the question 81 ÷ 9, students would start with eight ten blocks and one unit block. They would trade in the ten blocks for unit blocks and try to distribute all 81 of the unit blocks into nine piles. If they did it correctly, they would end up with 9 piles of 9 units and could say that 81 ÷ 9 = 9 as there are 9 units in each pile.

- Division Facts up to the 9 Times Table With a Long Division Symbol Vertical Division Facts Up To The 8 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To The 9 Times Table With Long Division Symbol/Bracket (50 per page) ✎
- Division Facts up to the 9 Times Table with a Division Sign Vertical Division Facts Dividends to 64 With Division Sign Vertical Division Facts Dividends to 81 With Division Sign Large Print Vertical Division Facts Dividends to 81 With Division Sign

If students learn up to the 9 times table and can do all the related division, they are likely to do well in later math studies. Long multiplication and long division, algebra, and many other math topics rely on students knowing these facts. Division facts worksheets up to the nine times tables can be used for students to practice, as a diagnostic test to see what gaps exist, or as a mastery test before moving on to the next topic. This section includes horizontally arranged questions which allows for a 100 per page option. Worksheets up to the 8 times table are also included to ensure a continual flow with the rest of this page, say, if you were adding one number at a time.

- Horizontally Arranged Division Facts up to the 8 Times Table Horizontally Arranged Division Facts with Dividends to 64 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 64 ( 50 Questions ) ✎ Horizontally Arranged Division Facts with Dividends to 64 ( 25 Questions ; Large Print) ✎
- Horizontally Arranged Division Facts up to the 9 Times Table Horizontally Arranged Division Facts with Dividends to 81 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 81 ( 50 Questions ) ✎ Horizontally Arranged Division Facts with Dividends to 81 ( 25 Questions ; Large Print) ✎

More individual facts where a single number is used as the divisor throughout the entire worksheet. The quotients end up being in the range 1 to 9. These are great for students that need more practice on one or more divisors. This might be identified using a diagnostic test of a worksheet that includes all the division facts. If students consistently get questions wrong with a certain divisor, these worksheets might help them.

- Dividing by Individual Facts up to the 9 Times Table Vertically Arranged Dividing by 1 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 2 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 4 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 5 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 6 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 8 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 9 with Quotients 1 to 9 ( 50 Questions ) ✎
- Dividing by Groups of Individual Facts up to the 9 Times Table Vertically Arranged Dividing by 1, 2 and 5 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3, 4 and 6 with Quotients 1 to 9 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7, 8 and 9 with Quotients 1 to 9 ( 50 Questions ) ✎

Same as the previous section except with horizontally arranged questions and more options for the number of questions per page.

- Horizontally Arranged Dividing by Individual Facts up to the 9 Times Table (100 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 9 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 9 ( 100 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts up to the 9 Times Table (50 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 9 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 9 ( 50 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts up to the 9 Times Table (25 Large Print Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 9 ( 25 Questions ; Large Print) ✎

## Division Facts up to the 10 Times Table

Ten is such an important number in math. Our entire numbering system is based on tens. There are ten digits and each lower place is a tenth (divided by 10) of the place before it. Although 10 is a two-digit number, it is almost always included in multiplication and division facts learning. Multiplying and dividing by 10 is so important there is a whole page (powers of ten) on Math-Drills dedicated to it.

If you jumped right to this section, you cannot be blamed! A lot of students learn their times tables all at once and that means including the most important 10! So, when they are ready for division worksheets, they are ready for this section. For students who might be struggling a bit though, please scroll up and start them off with something a little more at their pace.

- Division Facts up to the 10 Times Table With a Long Division Symbol Vertical Division Facts Up To The 10 Times Table With Long Division Symbol/Bracket (50 per page) ✎
- Division Facts up to the 10 Times Table with a Division Sign Vertical Division Facts Dividends to 100 With Division Sign

Even with its size, 10 is often the easiest divisor to use... well, besides 1. This section includes horizontally arranged practice questions for all the division facts from the 1 times to the 10 times table.

- Horizontally Arranged Division Facts up to the 10 Times Table Horizontally Arranged Division Facts with Dividends to 100 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 100 ( 50 Questions ) ✎

The worksheets in this section are included for students that need the facts one at a time with quotients from 1 to 10.

- Dividing by Individual Facts up to the 10 Times Table Vertically Arranged Dividing by 1 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 2 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 4 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 5 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 6 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 8 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 9 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 10 with Quotients 1 to 10 ( 50 Questions ) ✎
- Dividing by Groups of Individual Facts up to the 10 Times Table Vertically Arranged Dividing by 1, 2, 5 and 10 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3, 4 and 6 with Quotients 1 to 10 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7, 8 and 9 with Quotients 1 to 10 ( 50 Questions ) ✎

A horizontal repeat of the previous section.

- Horizontally Arranged Dividing by Individual Facts up to the 10 Times Table (100 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 10 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 10 ( 100 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts with up to the 10 Times Table (50 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 10 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 10 ( 50 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts up to the 10 Times Table (25 Large Print Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 10 ( 25 Questions ; Large Print) ✎

## Division Facts up to the 12 Times Table

Ah, twelve. Educators have a penchant for the the 12 times table likely because it is important in clocks, eggs, the Vendergood language, and definitely to the Dozenal Societies of America and Great Britain. In mathematics, it is seen mostly in the completion of both multiplication and division facts worksheets. Since Math-Drills is happy to support the base twelve system, we present worksheets with division facts up to the 12 times table in the unlikely event that the duodecimal (aka dozenal) system is ever adopted.

- Division Facts up to the 12 Times Table with a Long Division Symbol Vertical Division Facts Up To The 11 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To The 12 Times Table With Long Division Symbol/Bracket (50 per page) ✎
- Division Facts up to the 12 Times Table with a Division Sign Vertical Division Facts Dividends to 144 With Division Sign

Division is essentially asking the question, "How many _____'s are in _____?" For the question, 81 ÷ 9, the prompt would sound like, "How many 9's are in 81?" This prompt will benefit students in later math studies when there are more complex concepts such as dividing decimals or fractions. "How many thirds are in four?" or even better, "How many third cups are in four cups?" If necessary, get out the measuring cups.

This important section includes worksheets with division facts up to the 12 times table with a 100 question option.

- Horizontally Arranged Division Facts up to the 12 Times Table Horizontally Arranged Division Facts with Dividends to 144 ( 100 Questions) ✎ Horizontally Arranged Division Facts with Dividends to 144 ( 50 Questions ) ✎

So, if you are having your students learn division facts up to the 12 times table, it might be useful to have some worksheets with individual facts for a few students who might be overwhelmed with everything at once!

- Dividing by Individual Facts up to the 12 Times Table Vertically Arranged Dividing by 1 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 2 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 4 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 5 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 6 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 8 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 9 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 10 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 11 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 12 with Quotients 1 to 12 ( 50 Questions ) ✎
- Dividing by Groups of Individual Facts up to the 12 Times Table Vertically Arranged Dividing by 1, 2, 5 and 10 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 3, 4 and 6 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 7, 8 and 9 with Quotients 1 to 12 ( 50 Questions ) ✎ Vertically Arranged Dividing by 11 and 12 with Quotients 1 to 12 ( 50 Questions ) ✎

Same idea as the previous section, but with a horizontal arrangement and different numbers of questions on each page.

- Horizontally Arranged Dividing by Individual Facts up to the 12 Times Table (100 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 11 with Quotients 1 to 12 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 12 with Quotients 1 to 12 ( 100 Questions ) ✎
- Horizontally Arranged Dividing by Groups of Individual Facts up to the 12 Times Table (100 Questions) Horizontally Arranged Dividing by 1, 2, 5 and 10 (Quotient 1-12)
- Horizontally Arranged Dividing by Individual Facts up to the 12 Times Table (50 Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 11 with Quotients 1 to 12 ( 50 Questions ) ✎ Horizontally Arranged Dividing by 12 with Quotients 1 to 12 ( 50 Questions ) ✎
- Horizontally Arranged Dividing by Individual Facts up to the 12 Times Table (25 Large Print Questions) Horizontally Arranged Dividing by 1 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 2 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 3 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 4 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 5 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 6 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 7 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 8 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 9 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 10 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 11 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎ Horizontally Arranged Dividing by 12 with Quotients 1 to 12 ( 25 Questions ; Large Print) ✎

## Division Facts beyond the 12 Times Table

Scenario: you have some students that have aced the division facts up to the 12 times table and need more of a challenge. This section has got you covered. Is there an argument for learning division facts for times tables beyond 9? 10? 12? Sure, why not. Students are likely to apply their knowledge in future math studies by instantly recognizing that the square root of 625 is 25, for example.

- Division Facts up to the 25 Times Table With a Long Division Symbol Vertical Division Facts Up To the 13 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 14 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 15 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 16 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 17 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 18 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 19 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts Up To the 20 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts From 5 Up To the 21 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts From 5 Up To the 22 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts From 5 Up To the 23 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts From 5 Up To the 24 Times Table With Long Division Symbol/Bracket (50 per page) ✎ Vertical Division Facts From 5 Up To the 25 Times Table With Long Division Symbol/Bracket (50 per page) ✎
- Division Facts Up to the 15 Times Table With a Division Sign Vertical Division Facts Dividends to 169 With Division Sign Vertical Division Facts Dividends to 196 With Division Sign Vertical Division Facts Dividends to 225 With Division Sign

There are certainly a few questions on these worksheets that will be useful knowledge later on. If your students are interested in learning them, anything to do with 16, 20, 24, and 25 will certainly be useful, and likely someone could come up with a reason for learning the others. Sixteen is used in the base 16 (aka hexadecimal system), so converting hexadecimal numbers to decimal numbers involves dividing (and multiplying by 16). Twenty is a great number that is divisible by six different numbers and in turn is a factor of some important numbers. Twenty is also a coin unit in many countries. Twenty-four hours is the length of a day, so if you wanted to know how many days were in 288 hours, you might want to know your 24 times table division facts. Twenty-five, well that is the value of a quarter, isn't it? You could also calculate how many seconds of PAL video you have by dividing the number of frames by 25!

- Horizontally Arranged Division Facts up to the 20 Times Table Horizontally Arranged Division Facts Up to the 13 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 14 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 15 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 16 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 17 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 18 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 19 Times Table ( 100 Questions) ✎ Horizontally Arranged Division Facts Up to the 20 Times Table ( 100 Questions) ✎

If the previous two sections are a little tough to handle right out of the gates, perhaps start with these worksheets that only deal with one of the divisors at a time.

- Dividing by Individual Facts up to the 25 Times Table Vertically Arranged Dividing by 13 with Quotients 1 to 13 ( 50 Questions ) ✎ Vertically Arranged Dividing by 14 with Quotients 1 to 14 ( 50 Questions ) ✎ Vertically Arranged Dividing by 15 with Quotients 1 to 15 ( 50 Questions ) ✎ Vertically Arranged Dividing by 16 with Quotients 1 to 16 ( 50 Questions ) ✎ Vertically Arranged Dividing by 17 with Quotients 1 to 17 ( 50 Questions ) ✎ Vertically Arranged Dividing by 18 with Quotients 1 to 18 ( 50 Questions ) ✎ Vertically Arranged Dividing by 19 with Quotients 1 to 19 ( 50 Questions ) ✎ Vertically Arranged Dividing by 20 with Quotients 1 to 20 ( 50 Questions ) ✎ Vertically Arranged Dividing by 21 with Quotients 1 to 21 ( 50 Questions ) ✎ Vertically Arranged Dividing by 22 with Quotients 1 to 22 ( 50 Questions ) ✎ Vertically Arranged Dividing by 23 with Quotients 1 to 23 ( 50 Questions ) ✎ Vertically Arranged Dividing by 24 with Quotients 1 to 24 ( 50 Questions ) ✎ Vertically Arranged Dividing by 25 with Quotients 1 to 25 ( 50 Questions ) ✎

Even more of the previous section, but with 100 questions per page and a horizonal arrangement.

- Horizontally Arranged Dividing by Individual Facts up to the 25 Times Table Horizontally Arranged Dividing by 13 with Quotients 1 to 13 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 14 with Quotients 1 to 14 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 15 with Quotients 1 to 15 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 16 with Quotients 1 to 16 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 17 with Quotients 1 to 17 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 18 with Quotients 1 to 18 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 19 with Quotients 1 to 19 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 20 with Quotients 1 to 20 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 21 with Quotients 1 to 21 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 22 with Quotients 1 to 22 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 23 with Quotients 1 to 23 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 24 with Quotients 1 to 24 ( 100 Questions ) ✎ Horizontally Arranged Dividing by 25 with Quotients 1 to 25 ( 100 Questions ) ✎

## Long division Worksheets

Need an easier way to divide large numbers? Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder. Example: 1458 ÷ 54. Note 54 × 1 = 54, 54 × 10 = 540 (nothing greater is needed). 1458 - 540 - 540 = 378. Note that 540 was subtracted twice, so the number of times that 54 "goes into" 1458 so far is 20 times. Continuing, 378 - 54 - 54 - 54 - 54 - 54 - 54 - 54 = 0. Since 54 was subtracted seven times, the quotient increases by seven for a total of 27. In other words, 54 "goes into" 1458, 27 times.

We might also mention that this method can be even more sophisticated by using multiples of powers of ten. In the above example, using 54 × 5 = 270 would have helped to get to the quotient quicker.

- Long Division Worksheets with No Remainders Long Division with No Remainders with a Multiple of Ten Divisor and a 2-Digit Quotient Long Division with No Remainders with a 1-Digit Divisor and a 1-Digit Quotient Long Division with No Remainders with a 1-Digit Divisor and a 2-Digit Quotient Long Division with No Remainders with a 1-Digit Divisor and a 3-Digit Quotient Long Division with No Remainders with a 2-Digit Divisor and a 2-Digit Quotient Long Division with No Remainders with a 2-Digit Divisor and a 3-Digit Quotient Long Division with No Remainders with a 2-Digit Divisor and a 4-Digit Quotient Long Division with No Remainders with a 3-Digit Divisor and a 3-Digit Quotient Long Division with No Remainders with a 3-Digit Divisor and a 4-Digit Quotient Long Division with No Remainders with a 3-Digit Divisor and a 5-Digit Quotient
- European Format Long Division Worksheets with No Remainders European Format Long Division with No Remainders with a 1-Digit Divisor and a 1-Digit Quotient European Format Long Division with No Remainders with a 1-Digit Divisor and a 2-Digit Quotient European Format Long Division with No Remainders with a 1-Digit Divisor and a 3-Digit Quotient European Format Long Division with No Remainders with a 2-Digit Divisor and a 2-Digit Quotient European Format Long Division with No Remainders with a 2-Digit Divisor and a 3-Digit Quotient European Format Long Division with No Remainders with a 2-Digit Divisor and a 4-Digit Quotient European Format Long Division with No Remainders with a 3-Digit Divisor and a 2-Digit Quotient European Format Long Division with No Remainders with a 3-Digit Divisor and a 3-Digit Quotient European Format Long Division with No Remainders with a 3-Digit Divisor and a 4-Digit Quotient

Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders? It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient. For example 19 ÷ 3 is 6 with a remainder of 1 which is more precisely 6 1/3. Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise (e.g. compare 6 1/3 with 6.3333....).

- Long Division Worksheets with Remainders Long Division with Remainders with a Multiple of Ten Divisor and a 2-Digit Quotient Long Division with Remainders with a 1-Digit Divisor and a 2-Digit Dividend Long Division with Remainders with a 1-Digit Divisor and a 3-Digit Dividend Long Division with Remainders with a 1-Digit Divisor and a 4-Digit Dividend Long Division with Remainders with a 2-Digit Divisor and a 3-Digit Dividend Long Division with Remainders with a 2-Digit Divisor and a 4-Digit Dividend Long Division with Remainders with a 2-Digit Divisor and a 5-Digit Dividend Long Division with Remainders with a 3-Digit Divisor and a 4-Digit Dividend Long Division with Remainders with a 3-Digit Divisor and a 5-Digit Dividend Long Division with Remainders with a 3-Digit Divisor and a 6-Digit Dividend
- European Format Long Division Worksheets with Remainders European Format Long Division with Remainders with a 1-Digit Divisor and a 2-Digit Dividend European Format Long Division with Remainders with a 1-Digit Divisor and a 3-Digit Dividend European Format Long Division with Remainders with a 1-Digit Divisor and a 4-Digit Dividend European Format Long Division with Remainders with a 2-Digit Divisor and a 3-Digit Dividend European Format Long Division with Remainders with a 2-Digit Divisor and a 4-Digit Dividend European Format Long Division with Remainders with a 2-Digit Divisor and a 5-Digit Dividend European Format Long Division with Remainders with a 3-Digit Divisor and a 4-Digit Dividend European Format Long Division with Remainders with a 3-Digit Divisor and a 5-Digit Dividend European Format Long Division with Remainders with a 3-Digit Divisor and a 6-Digit Dividend
- Long Division Worksheets with Decimal Quotients Long Division with Decimal Quotients with a 1-Digit Divisor; 2-Digit Dividend Long Division with Decimal Quotients with a 1-Digit Divisor; 3-Digit Dividend Long Division with Decimal Quotients with a 1-Digit Divisor; 4-Digit Dividend Long Division with Decimal Quotients with a 2-Digit Divisor; 3-Digit Dividend Long Division with Decimal Quotients with a 2-Digit Divisor; 4-Digit Dividend Long Division with Decimal Quotients with a 2-Digit Divisor; 5-Digit Dividend Long Division with Decimal Quotients with a 3-Digit Divisor; 4-Digit Dividend Long Division with Decimal Quotients with a 3-Digit Divisor; 5-Digit Dividend Long Division with Decimal Quotients with a 3-Digit Divisor; 6-Digit Dividend
- European Format Long Division Worksheets with Decimal Quotients European Format Long Division with Decimal Quotients with a 1-Digit Divisor; 2-Digit Dividend European Format Long Division with Decimal Quotients with a 1-Digit Divisor; 3-Digit Dividend European Format Long Division with Decimal Quotients with a 2-Digit Divisor; 2-Digit Dividend European Format Long Division with Decimal Quotients with a 2-Digit Divisor; 3-Digit Dividend European Format Long Division with Decimal Quotients with a 2-Digit Divisor; 4-Digit Dividend European Format Long Division with Decimal Quotients with a 3-Digit Divisor; 3-Digit Dividend European Format Long Division with Decimal Quotients with a 3-Digit Divisor; 4-Digit Dividend European Format Long Division with Decimal Quotients with a 3-Digit Divisor; 5-Digit Dividend

We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school. Learning this algorithm by itself is sometimes not enough as it may not lead to a good conceptual understanding. One tool that helps students learn the standard algorithm and develop an understanding of division is a set of base ten blocks. By teaching students division with base ten blocks first then progressing to the standard algorithm, students will gain a conceptual understanding plus have the use of an efficient algorithm for long division. Students who have both of these things will naturally experience more success in their future mathematical studies.

- Long Division with 1-Digit Divisors with the Steps Shown on the Answer Key 2-Digit by 1-Digit Long Division with Remainders with the Steps Shown on the Answer Key 3-Digit by 1-Digit Long Division with Remainders with the Steps Shown on the Answer Key 4-Digit by 1-Digit Long Division with Remainders with the Steps Shown on the Answer Key 5-Digit by 1-Digit Long Division with Remainders with the Steps Shown on the Answer Key 6-Digit by 1-Digit Long Division with Remainders with the Steps Shown on the Answer Key
- Long Division with 2-Digit Divisors with the Steps Shown on the Answer Key 3-Digit by 2-Digit Long Division with Remainders with the Steps Shown on the Answer Key 4-Digit by 2-Digit Long Division with Remainders with the Steps Shown on the Answer Key 5-Digit by 2-Digit Long Division with Remainders with the Steps Shown on the Answer Key 6-Digit by 2-Digit Long Division with Remainders with the Steps Shown on the Answer Key
- Long Division with 3-Digit Divisors with the Steps Shown on the Answer Key 4-Digit by 3-Digit Long Division with Remainders with the Steps Shown on the Answer Key 5-Digit by 3-Digit Long Division with Remainders with the Steps Shown on the Answer Key 6-Digit by 3-Digit Long Division with Remainders with the Steps Shown on the Answer Key

Some students find it difficult to get everything lined up when completing a long division algorithm, so these worksheets include a grid and wider spacing of the digits to help students get things in the right place. The answer keys include the typical steps that students would record while completing each problem; however, slight variations in implementation may occur. For example, some people don't bother with the subtraction signs,some might show steps subtracting zero, etc.

- Long Division Worksheets with Grid Assistance and Prompts (No Remainders) 2-Digit by 1-Digit Long Division with Grid Assistance and Prompts and NO Remainders 3-Digit by 1-Digit Long Division with Grid Assistance and Prompts and NO Remainders 3-Digit by 2-Digit Long Division with Grid Assistance and Prompts and NO Remainders 4-Digit by 1-Digit Long Division with Grid Assistance and Prompts and NO Remainders 4-Digit by 2-Digit Long Division with Grid Assistance and Prompts and NO Remainders 5-Digit by 1-Digit Long Division with Grid Assistance and Prompts and NO Remainders 5-Digit by 2-Digit Long Division with Grid Assistance and Prompts and NO Remainders 6-Digit by 1-Digit Long Division with Grid Assistance and Prompts and NO Remainders 6-Digit by 2-Digit Long Division with Grid Assistance and Prompts and NO Remainders
- Long Division Worksheets with Grid Assistance Only (No Remainders) 3-Digit by 1-Digit Long Division with Grid Assistance and NO Remainders 3-Digit by 2-Digit Long Division with Grid Assistance and NO Remainders 4-Digit by 1-Digit Long Division with Grid Assistance and NO Remainders 4-Digit by 2-Digit Long Division with Grid Assistance and NO Remainders 5-Digit by 1-Digit Long Division with Grid Assistance and NO Remainders 5-Digit by 2-Digit Long Division with Grid Assistance and NO Remainders 6-Digit by 1-Digit Long Division with Grid Assistance and NO Remainders 6-Digit by 2-Digit Long Division with Grid Assistance and NO Remainders
- Long Division Worksheets with Grid Assistance and Prompts (Some Remainders) 2-Digit by 1-Digit Long Division with Grid Assistance and Prompts and some Remainders 3-Digit by 1-Digit Long Division with Grid Assistance and Prompts and some Remainders 3-Digit by 2-Digit Long Division with Grid Assistance and Prompts and some Remainders 4-Digit by 1-Digit Long Division with Grid Assistance and Prompts and some Remainders 4-Digit by 2-Digit Long Division with Grid Assistance and Prompts and some Remainders 5-Digit by 1-Digit Long Division with Grid Assistance and Prompts and some Remainders 5-Digit by 2-Digit Long Division with Grid Assistance and Prompts and some Remainders 6-Digit by 1-Digit Long Division with Grid Assistance and Prompts and some Remainders 6-Digit by 2-Digit Long Division with Grid Assistance and Prompts and some Remainders
- Long Division Worksheets with Grid Assistance Only (Some Remainders) 3-Digit by 1-Digit Long Division with Grid Assistance and some Remainders 3-Digit by 2-Digit Long Division with Grid Assistance and some Remainders 4-Digit by 1-Digit Long Division with Grid Assistance and some Remainders 4-Digit by 2-Digit Long Division with Grid Assistance and some Remainders 5-Digit by 1-Digit Long Division with Grid Assistance and some Remainders 5-Digit by 2-Digit Long Division with Grid Assistance and some Remainders 6-Digit by 1-Digit Long Division with Grid Assistance and some Remainders 6-Digit by 2-Digit Long Division with Grid Assistance and some Remainders

Divisibility by 2, 5 and 10

A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2. A number is divisible by 5 if the final digit is a 0 or a 5. A number is divisible by 10 if the final digit is a 0.

Divisibility by 3, 6 and 9

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3. A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules). A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.

Divisibility by 4, 7 and 8

A number is divisible by 4 if the last two digits of the number are divisible by 4. For 7, there are a couple of strategies to use. Please see Divisibility Tricks for Learning Math for more information. A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.

- Divisibility Rules Worksheets with 2-Digit Numbers Divisibility of 2, 5 and 10 (2-digit) Divisibility of 3, 6 and 9 (2-digit) Divisibility of 4, 7 and 8 (2-digit) Divisibility of Numbers 2 to 10 (2-digit)
- Divisibility Rules Worksheets with 3-Digit Numbers Divisibility of 2, 5 and 10 (3-digit) Divisibility of 3, 6 and 9 (3-digit) Divisibility of 4, 7 and 8 (3-digit) Divisibility of Numbers 2 to 10 (3-digit)
- Divisibility Rules Worksheets with 4-Digit Numbers Divisibility of 2, 5 and 10 (4-digit) Divisibility of 3, 6 and 9 (4-digit) Divisibility of 4, 7 and 8 (4-digit) Divisibility of Numbers 2 to 10 (4-digit)

Dividing numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

- Worksheets for Long Division in Other Base Number Systems Dividing Binary Numbers (Base 2) Dividing Ternary Numbers (Base 3) Dividing Quaternary Numbers (Base 4) Dividing Quinary Numbers (Base 5) Dividing Senary Numbers (Base 6) Dividing Octal Numbers (Base 8) Dividing Duodecimal Numbers (Base 12) Dividing Hexadecimal Numbers (Base 16) Dividing Vigesimal Numbers (Base 20) Dividing Hexatrigesimal Numbers (Base 36) Dividing Various Numbers (Various Bases)

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Breadcrumbs

## Step by Step Guide for Long Division

What is long division.

Long division is a way to solve division problems with large numbers. Basically, these are division problems you cannot do in your head.

## Getting started

One of the problems students have with long division problems is remembering all the steps. 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 .

Write D M S B in the corner of your worksheet to remember the sequence you’re about to use.

## How to write it down

First, you have to write down the problem in long division format. A typical division problem looks like this:

Dividend ÷ Divisor = Quotient

To write this down in long division format it looks like this:

Let’s try a fairly simple example:

Now, let’s write that problem down in the long division format:

We’re ready to start using the acronym: D M S B

## Step 1: D for Divide

How many times will 5 go into 65? That’s too hard to work out in your head, so let’s break it down into smaller steps.

The first problem you’ll work out in this equation is how many times can you divide 5 into 6. The answer is 1. So you put 1 on the quotient line.

## Step 2: M for Multiply

You multiply your answer from step 1 and your divisor: 1 x 5 = 5. You write 5 under the 6.

## Step 3: S for Subtract

Next you subtract. In this case it will be 6 – 5 = 1.

## Step 4: B for Bring down

The last step in the sequence is to bring down the next number from the dividend, which in this case is 5. You write the 5 next to the 1, making the number 15.

Now you start all over again:

How many times can you divide 5 into 15. The answer is 3. So you put 3 on the quotient line.

You multiply your answer from step 1 and your divisor: 3 x 5 = 15. Write this underneath the 15.

Now we subtract 15 from 15. 15 – 15 = 0.

There is no need for step 4. We have finished the problem.

Once you have the answer, do the problem in reverse using multiplication (5 x 13 = 65) to make sure your answer is correct.

K5 Learning has a number of free long division worksheets for grade 4 , grade 5 and grade 6 . Check them out in our math worksheet center .

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## Long Division Calculator – with Steps to Solve

Enter the divisor and dividend below to calculate the quotient and remainder using long division. The results and steps to solve it are shown below.

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## How to Do Long Division with Remainders

Parts of a long division problem, steps to calculate a long division problem, how to get the quotient and remainder as a decimal, how to do long division without division, frequently asked questions.

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

Learning long division is a crucial milestone in understanding essential math skills and a rite of passage to completing elementary school. It strikes fear in elementary school students and parents alike.

A recent study found that the understanding of long division and fractions in elementary school is directly linked to the student’s ability to learn and understand algebra later in school. [1]

Have no fear!

Learning long division can be easy, and in just a few easy steps, you can solve any long division problem. Follow along as we break it down, but first, we need to cover the anatomy of a long division problem.

There are a few parts to a long division problem, as shown in the image above.

The dividend is the number being divided and appears to the right and under the division line.

The divisor is the number being divided by and appears to the left of the division line.

The quotient is the solution and is shown above the dividend over the division line. Often in long division, the quotient is referred to as just the whole number part of the solution.

The remainder is the remaining part of the solution, or what’s leftover, that doesn’t fit evenly into the quotient.

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process.

## Step One: Set up the Expression

The first step in solving a long division problem is to draw the equation that needs to be solved. If the problem is already in long division form, then skip along to step two.

If it’s not, this is how to draw the long division problem.

Start by drawing a vertical bar to separate the divisor and dividend and an overbar to separate the dividend and quotient.

Place the dividend to the right of the vertical bar and under the overbar. Place the divisor to the left of the vertical bar.

For example , to divide 75 by 4, the long division problem should look like this:

## Step Two: Divide

With the long division problem drawn, start by dividing the first digit in the dividend by the divisor.

You can also think about this as counting the number of times the divisor will evenly fit into this digit in the dividend.

If the divisor does not fit into the first digit an even number of times, drop the remainder or decimal portion of the result and write the whole number portion of the result in the quotient above the overline directly above the digit in the dividend.

For example , the divisor “4” goes evenly into the first digit of the dividend “7” one time, so a “1” can be added to the quotient above the 7.

## Step Three: Multiply

The next step is to multiply the divisor by the digit just added to the quotient. Write the result below the digit in the dividend.

This step forms the part of the expression for the next step.

Continuing with our example, multiplying the divisor “4” by “1”, which we found in the previous step, equals “4”. So, add a “4” below the first digit in the dividend.

## Step Four: Subtract

Now, add a minus sign “-” before the number added in the previous step and draw a line below it to form a subtraction expression.

Continuing the example above, add a “-” before the “4” and a subtraction line below it.

Now that you have created a subtraction problem, it’s time to solve it.

To solve, subtract “7” minus “4”, which equals “3”, so write a “3” below the subtraction line.

Note: if the resulting value of the subtraction problem is greater than the divisor, then you made a mistake in step 2 and should double-check your work.

If the long division problem has a dividend that is a single digit, then hooray, you’re done! The remaining number that is the result of the subtraction problem is the remainder , and the number above the dividend is the whole number quotient.

If more digits are remaining in the dividend, then proceed to the next step.

## Step Five: Pull Down the Next Number

At this point in the process, it’s time to operate on the next number in the dividend. To do this, pull down the next digit in the dividend and place it directly to the right of the result from the subtraction problem above.

The next digit in the dividend is “5”. So, pull “5” down and write it next to the “3” found in the previous step.

## Step Six: Repeat

At this point, you might be wondering where to go from here. Repeat steps two to five until all the digits in the dividend have been pulled down, divided, multiplied, and subtracted.

When dividing, use the result of the subtraction problem combined with the pulled-down digit as the dividend and divide the divisor into it.

Continuing the examples above, divide the result of the subtraction problem and the pulled-down digit by the divisor. Thus, the next step is to divide 35 by 4. The result is “8”, so add “8” to the quotient.

Next, multiply the quotient digit “8” by the divisor “4”, which equals 32. Add “32” to the long division problem and place a negative sign in front of it.

Next, repeat the subtraction process, subtracting 32 from 35, which equals 3. Add a “3” below the subtraction line. Since there are no longer any remaining digits in the dividend, this is the remainder portion of the solution.

Therefore, 75 divided by 4 is 18 with a remainder of 3. As you practice these steps, use the calculator above to confirm your answer and validate your steps solving long division problems.

If you’ve gotten this far, then you should have a good idea of how to solve a long division problem, but you might be stuck if you need to get the quotient as a decimal rather than a whole number with a remainder.

To calculate the quotient in decimal form, follow the steps above the get the whole number and remainder.

Next, divide the remainder by the divisor to get the remainder as a decimal. Finally, add the decimal to the quotient to get the quotient in decimal form.

For example , 75 ÷ 4 is 18 with a remainder of 3.

Divide 3 by 4 to get the decimal 0.75. 3 ÷ 4 = 0.75

Then, add 0.75 to 18 to get the quotient as a decimal. 0.75 + 18 = 18.75

Thus, the decimal form of 75 ÷ 4 equals 18.75.

While it defeats the purpose of actually learning how to do long division, there is technically a way to perform long division without actually doing any division. The way to do this is as follows.

Set up the long division expression the exact same way as you would normally.

## Step Two: Repeatedly Subtract the Divisor

Now, subtract the divisor from the dividend. Afterward, subtract the divisor again from the remaining value. Do this repeatedly until the remaining value is less than the divisor.

## Step Three: Count the Number of Subtractions

Finally, to find the quotient, simply count the number of times you subtracted the divisor. This is the whole number portion of the quotient, and the final remaining value is the remainder.

Note: While this method of solving long division problems may seem easier, it is often very impractical to do so. For example, in the above example of 75 divided by 4, you would need to repeat the subtraction 18 times!

Therefore, traditional long division is the vastly superior method.

## Why is long division important?

Long division is important not just because it is a tool that allows us to solve difficult division problems, but because it helps to teach logical thinking that will prepare students to excel in solving future mathematical problems.

## Why do we still teach long division?

We still teach long division because it teaches students how to think logically, a valuable skill that is shown not just to improve future understanding of algebraic concepts, but also to help solve problems in all aspects of their lives.

## How do you check a long division answer?

Just like subtraction is the opposite of addition, multiplication is the opposite of division. Therefore, to check a long division answer, multiply the quotient by the divisor, and if it equals the dividend, then the answer is correct!

## Can you do long division on a calculator?

While a calculator can solve division problems, it will not list out the steps used in evaluating a long division problem, and will therefore not improve your understanding of how to perform long division.

## Recommended Math Resources

- Vector Calculator
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- Carnegie Mellon University, Press Release: Carnegie Mellon-Led Research Team Finds Knowledge Of Fractions and Long Division Predicts Long-Term Math Success, https://www.cmu.edu/news/stories/archives/2012/june/june15_mathsuccess.html

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## 8 Long Division Examples And How To Solve Them: Explained For Elementary School

Sophie bartlett.

Long division examples are a great way to introduce and teach long division to 5th grade. Due to the number of steps involved, it can be tricky for students to get their head around the method. In this article, we provide you with long division examples to practice with upper elementary school students, plus expert guidance on how to solve them.

When teaching a new mathematical concept, worked examples are helpful in the same way that a ‘WAGOLL’, or model text, is helpful in writing lessons – children can see what the end result should look like. They can be used as a success criteria for mathematical problem solving- and long division is no exception.

## How to solve long division problems

Long division example step by step, 5th grade long division examples, easy long division examples, hard long division examples, top tips for working through long division examples, teaching long division worksheets.

Download this free pack of long division worksheets for grades 3-5.

In any division , the first number (the amount being divided) is called the dividend ; the second number (whatever the dividend is being divided by), is called the divisor ; the answer is called the quotient .

Long division is typically used when dividing larger numbers where the divisor is a two-digit number, although it can also be used with one-digit divisors.

There are five steps that can be used to simplify the long division method. These long division steps are:

- Bring the next digit down

Before beginning long division questions, it is helpful to list 9 multiples of the divisor to reduce the cognitive demand when working through the division method.

Listing multiples can be done through repeated addition or partitioning (partition the tens and ones, list the multiples of each and then add each constituent part).

See how the five division steps are then applied using this example below (this layout is also called the bus stop method ):

1. Divide : Starting with the first digit of the dividend, divide 4 ten thousands by 73. We cannot do this, so a 0 is placed above the 4 and instead we see the 4 ten thousands as 40 thousands alongside the 5 thousands (the next digit of the dividend).

Now, divide 45 thousands by 73, which also can’t be done, so we place another 0 above the 5 and see the 45 thousands as 450 hundreds. We can finally do 450 hundreds divided by 73, which is 6. This digit is placed above the 0 tens and becomes the first digit of the quotient.

2. Multiply : We need to calculate the remainder for this first step of the division – to do this, first multiply the first digit of the quotient, 6 hundreds, by the divisor, 73, to get 438 hundreds (this is where our list of multiples really helps). Place this underneath the dividend, making sure to align the place values correctly.

3. Subtract : To finish calculating the remainder for this first step of the division, finally subtract 438 hundreds from 450 hundreds to get 12 hundreds.

4. Bring the next digit down : In long division, we just bring the next digit of the quotient down – making sure to keep the numbers aligned when the digits above it.

5. Repeat: Now we start the division process again from…

Step 1: divide (divide 124 tens by 73 and place the answer, 1 ten, in the quotient);

Step 2: multiply (multiply the next digit of the quotient, 1 ten, by the divisor, 73, and place the answer, 73 tens, underneath the 124 tens);

Step 3: subtract (finish calculating the remainder to this next step by subtracting 73 tens ones from 124 tens to get 51 tens);

Step 4: bring the next digit down (51 tens plus 1 one becomes 511 ones)

Step 5: repeat (divide 511 ones by 73 to get 7 ones and place this in the quotient as the last digit; multiply 7 ones by 73 to get 511 ones; subtract this from 511 ones to calculate the remainder, which is 0; there is now no next digit to bring down so, as the remainder is now 0, the calculation is complete)

This example has a whole number quotient, but the long division method can be done with remainders .

This example shows how it would be laid out with a decimal remainder (when calculating the remainder, don’t forget to include the decimal point in the quotient as well as in the dividend).

## Long division examples

Providing worked examples is helpful when introducing new mathematical concepts to children. Children can use these as success criteria for their own work.

In Third Space Learning’s one-to-one tutoring sessions, tutors model new mathematical methods step by step to support and scaffold children’s learning. We find this is a great way to help students understand and practice the steps involved in long division.

Below, we provide a range of worked long division examples to suit your students’ needs. You can learn more about Third Space Learning and our math interventions for elementary school here.

For more support teaching the long division method , read our blog here.

Children aren’t required to do long division until 5th grade. Here are some worked examples of long division problems.

1. 8,051 ÷ 83

Don’t forget to list the first 9 multiples of 83 to help you solve it.

## Step by step long division

- We cannot divide 8 thousands by 83
- Write zero in the thousands place of your answer line
- 80 hundreds cannot be divided by 83
- Write zero in the hundreds place of your answer line
- 805 tens divided by 83 is 9 tens
- Write nine in the tens place of your answer line
- Subtract 747 tens (9 x 83) from 805 tens to get 58 tens
- Exchange the 58 tens for ones so now we have 581 ones
- 581 ÷ 83 = 7
- Write 7 in the ones place of your answer line
- Subtract 581 (7 x 83) from 581 to get zero. You have no remainders.
- Check your answer – 83 x 97 = 8051

2. Adam is making booklets. Each booklet must have 34 sheets of paper. He has 2 packets of paper. There are 500 sheets of paper in each packet. How many complete booklets can Adam make from 2 packets of paper?

Final answer is: 2 packets of 500 sheets = 1,000 sheets. 1,000 ÷ 34 = 29 complete booklets

1. Eggs are put in trays of 12. The trays are packed in boxes. Each box contains 180 eggs. How many trays are in each box?

You could use long division for 180 ÷ 12 as we’re dividing by two digits, but in this case it could be just as simple to use multiples of 12 to work it out. We know 12 x 5 = 60, and there are 3 lots of 60 in 180, so there must be 15 lots of 12 in 180. The answer is therefore 15 trays.

2. A lottery donates $504 to 21 different charities. How much does each charity get?

While 504 ÷ 21 may seem tricky at first glance, it’s actually fairly simple as the divisor is an ‘easy’ number to list multiples of – children may be able to complete it without having to list the multiples first and by calculating them mentally instead.

1. A grocer needs to order 1,176 apples. Apples are sold in boxes containing 28 trays, with 14 apples on each tray. How many boxes of apples does the grocer need to order?

28 trays each with 14 apples = 28 x 14 = 392 apples. We could then do 1,176 ÷ 392, but this is a pretty tricky calculation! It would be better to do the long division in two chunks – first dividing by 28, then by 14 (or the other way round – the answer would be the same!) 1176 ÷ 28 = 42, then 42 ÷ 14 = 3, so the grocer would need to order 3 boxes of apples.

2. A factory makes 4,923 teddy bears, and the bears are packed in boxes of 37. How many bears are left over?

4,923 ÷ 37 = 133r2, so there will be 2 bears left over.

3. 427 children visit a castle. They go in groups of 15. One group has less than 15. Every group of children has one adult with them. How many adults will need to go?

427 ÷ 15 = 28r7, as shown below. This means there are 28 ‘full’ groups (of 15 children) and one more group with only 7 children. There are therefore 29 groups overall, so 29 adults would be required to go. Read more here about how to complete division with remainders .

For more long division questions and long division worksheets to support your teaching, check out our blogs.

- List 9 multiples of the divisor before beginning the division to reduce cognitive load
- Ensure you align the place values correctly (each digit of the quotient going above the appropriate digit of the dividend)
- During the ‘divide’ step, if at any point your divisor will not fit into the dividend, don’t forget to include the 0!

In the example below, we’ve first correctly identified that 52 hundreds divided by 13 is 4 hundreds. This gives us a remainder of 0, but when we bring the next digit down it makes 9 tens.

We can’t divide 9 tens by 13, so here, we’ve incorrectly brought down the next digit as well to make 91 ones. 91 ones ÷ 13 is 7, but this 7 has been placed as the wrong digit in the quotient.

This is what the division should have looked like – after 52 hundreds ÷ 13 = 4 hundreds with 0 remainder, 9 tens divided by 13 = 0, so the 0 has to be placed as the next digit of the quotient (above the 9 in the dividend).

We can then continue with the method – multiply (0 tens x 13 = 0 tens), subtract (9 tens – 0 tens = 9 tens) and bring the next digit down (1 one, to make 91 ones). This takes us to the final step now (91 ones ÷ 13 to get 7 ones) which reaches the correct answer of 407, as opposed to 47 in the misconception above.

During the ‘subtract’ step, if the result of your subtraction (once you’ve brought down the next digit of the dividend) is bigger than 9 multiples of the divisor, something has gone wrong! In the example below, we’ve incorrectly calculated that 42 tens divided by 15 is only 1 ten.

This gave us a remainder of 27 tens + 7 ones, which is 277 ones – we can fit way more than 9 groups of 15 into 277 ones, so we have gone wrong somewhere!

The first digit of the quotient should actually be 2 as 42 tens divided by 15 is 2 tens with 12 tens remaining, as shown below.

- Use the inverse to check your answer at the end: in a division without a remainder, simply multiply the quotient by the divisor and you should get the dividend (e.g. if you calculate that 1,176 ÷ 28 = 42, then 42 x 28 should = 1,176). In division with a remainder, multiply the quotient by the divisor and then add the remainder – the result should, again, be the dividend (e.g. if you calculate that 427 ÷ 15 = 28r7, then 28 x 15 + 7 should = 427)

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

## Math Intervention Pack Operations and Algebraic Thinking [FREE]

Take a sneak peek behind our online tutoring with 6 intervention lessons designed by math experts while supporting your students with Operations and Algebraic Thinking.

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## Privacy Overview

## Long Division Calculator

Division is one of the basic arithmetic operations, the others being multiplication (the inverse of division), addition, and subtraction. The arithmetic operations are ways that numbers can be combined in order to make new numbers. Division can be thought of as the number of times a given number goes into another number. For example, 2 goes into 8 4 times, so 8 divided by 4 equals 2.

Division can be denoted in a few different ways. Using the example above:

8 ÷ 4 = 2

In order to more effectively discuss division, it is important to understand the different parts of a division problem.

## Components of division

Generally, a division problem has three main parts: the dividend, divisor, and quotient. The number being divided is the dividend, the number that divides the dividend is the divisor, and the quotient is the result:

One way to think of the dividend is that it is the total number of objects available. The divisor is the desired number of groups of objects, and the quotient is the number of objects within each group. Thus, assuming that there are 8 people and the intent is to divide them into 4 groups, division indicates that each group would consist of 2 people. In this case, the number of people can be divided evenly between each group, but this is not always the case. There are two ways to divide numbers when the result won't be even. One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 ÷ 4 = 2, this can be used to determine that 9 ÷ 4 = 2 R1. In other words, 9 divided by 4 equals 2, with a remainder of 1. Long division can be used either to find a quotient with a remainder, or to find an exact decimal value.

## How to perform long division?

To perform long division, first identify the dividend and divisor. To divide 100 by 7, where 100 is the dividend and 7 is the divisor, set up the long division problem by writing the dividend under a radicand, with the divisor to the left (divisorvdividend), then use the steps described below:

This is the stopping point if the goal is to find a quotient with a remainder. In this case, the quotient is 014 or 14, and the remainder is 2. Thus, the solution to the division problem is:

100 ÷ 7 = 14 R2

To continue the long division problem to find an exact value, continue the same process above, adding a decimal point after the quotient, and adding 0s to form new dividends until an exact solution is found, or until the quotient to a desired number of decimal places is determined.

## Division Word Problems with Remainders

Related Topics: Lesson Plans and Worksheets for Grade 4 Lesson Plans and Worksheets for all Grades More Lessons for Grade 4 Common Core For Grade 4

Examples, solutions and videos to help Grade 4 students learn how to solve division word problems with remainders.

Common Core Standards: 4.NBT.6, 4.OA.3

## New York State Common Core Math Grade 4, Module 3, Lesson 14

Worksheets for Grade 4

NYS Math Module 3 Grade 4 Lesson 14 Concept Development Problem 1: Divide a two-digit number by a one-digit number modeled with an array. There are 12 students in PE class separated into 4 teams. How many students are on each team?

Problem 3: Divide a two-digit number by a one-digit number with a remainder modeled with a tape diagram. Kristy bought 13 roses. If she puts 6 roses in each vase, how many vases will she use? Will there be any roses left over?

Problem 4: Divide a two-digit number by a one-digit number, interpreting the remainder. Allison has 22 meters of fabric to sew dresses. She uses 3 meters of fabric for each dress. After how many dresses will Allison need to buy more fabric?

NYS Math Module 3 Grade 4 Lesson 14 Homework Solve the following problems. Use the RDW process.

- Linda makes booklets using 2 sheets of paper. She has 17 sheets of paper. How many of these booklets can she make? Will she have any extra paper? How many sheets?
- Linda uses thread to sew the booklets together. She cuts 6 inches of thread for each booklet. How many booklets can she stitch with 50 inches of thread? Will she have any unused thread after stitching up the booklets? If so, how much?
- Ms. Rochelle wants to put her 29 students into groups of 6. How many groups of 6 can she make? If she puts any remaining students in a smaller group, how many students will be in that group?
- A trainer gives his horse, Caballo, 7 gallons of water every day from a 57-gallon container. How many days will Caballo receive his full portion of water from the container? On which number day will the trainer need to refill the container of water?
- Meliza has 43 toy soldiers. She lines them up in rows of 5 to fight imaginary zombies. How many of these rows can she make? After making as many rows of 5 as she can, she puts the remaining soldiers in the last row. How many soldiers are in that row?
- Seventy-eight students are separated into groups of 8 for a field trip. How many groups are there? The remaining students form a smaller group of how many students?

NYS Math Module 3 Grade 4 Lesson 14 Problem Set Solve the following problems. Use the RDW process.

- There are 19 identical socks. How many pairs of socks are there? Will there be any socks without a match? If so, how many?
- If it takes 8 inches of ribbon to make a bow, how many bows can be made from 3 feet of ribbon (1 foot = 12 inches)? Will any ribbon be left over? If so, how much?
- The library has 27 chairs and 5 tables. If the same number of chairs is placed at each table, how many chairs can be placed at each table? Will there be any extra chairs? If so, how many?

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## Solving Problems on Division Worksheet

Put your skills to the test by practicing to solve problems on division..

## Know more about Solving Problems on Division Worksheet

Struggles with division can easily be overcome if students practice the concept in a fun and engaging way! Young learners will make connections between math and the real world as they solve a set of division word problems involving divide by scenarios. In these problems, they comprehend the scenarios and get to the result. This set of problems deals with numbers within 100.

## Your one stop solution for all grade learning needs.

## How to solve. 3.2 Synthetic Division/Factor Theorem Question 9 of 9...

Answer & explanation.

f(x) can linearly be factored as:

f ( x ) = ( x + 3 ) ( x + 3 ) ( x + 1 + 2 i ) ( x + 1 − 2 i )

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## Siemens Energy CEO to solve quality issues at onshore wind division

M UNICH, Germany: In a written statement published ahead of the group's annual general meeting (AGM), Christian Bruch, CEO of Siemens Energy, said the company is confident that it can solve quality issues at its onshore wind division, but that process could take several years.

"The losses we incurred in our wind business and the underlying problems are unacceptable. We will not tolerate them. We are resolutely tackling them and will ultimately solve them," Bruch said.

The problem is mainly due to quality issues with the group's newer generations of onshore wind turbines, the 4.X and 5.X platforms, he added, stressing that fixing the issues will probably take several years.

During its AGM scheduled on February 26, investors are expected to criticize AGM Siemens Energy for a share price decline caused by the turbine issues, which forced the group to seek billions of euros in state-backed guarantees.

"After eight months of intense analysis by an expert task force, no new causes of losses had been identified with the two models, meaning a Euro1.6 billion (US$1.7 billion) provision set aside to cover the problems was still seen as sufficient," Bruch said.

"We will solve these wind-power problems. We will win back your trust, the trust of our owners," he added.

## IMAGES

## VIDEO

## COMMENTS

Method 1 Long Division Download Article 1 Write out the problem using a long division bar. The division bar ( 厂 ) looks like an ending parentheses attached to a horizontal line that goes over the string of numbers beneath the bar.

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals.

This long division math youtube video tutorial explains how to divide big numbers the easy way. It explains how to perform long division with 2-digit diviso...

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).

How to Solve Division Problems Solving simple division problems is closely linked to multiplication. In fact, to check your work, you'll have to multiply the quotient by the divisor to see if it equals the dividend. If it doesn't, you've solved incorrectly. Let's try solving one simple division problem. For example: 12 ÷ 2 =

16 comments ( 60 votes) Upvote Downvote Flag VincentTheFrugal 11 years ago You would use the method at the end of the video. Sal provides some good examples of dividing two digit numbers in the level 4 division video: http://www.khanacademy.org/math/arithmetic/multiplication-division/v/level-4-division 4 comments ( 55 votes) Upvote Downvote

Solve division problems with tips from a math teacher in this free video on solving math problems. In math division problems, there are a number of formats for determining how many...

Looking to learn how to do long division? Learn with Mr. J!Whether you're just starting out, or need a quick refresher, this is the video for you if you're l...

Division Division Division is splitting into equal parts or groups. It is the result of "fair sharing". Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates? 12 Chocolates 12 Chocolates Divided by 3 Answer: 12 divided by 3 is 4. They get 4 each. Symbols ÷ /

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.

1. Division Problems: Repetition. This is the first type of division problem you are going to learn to do. For example: In my living room, there are 120 books in total, placed on 6 shelves. Knowing that each shelf has the same number of books, calculate how many books there are on each shelf. A total number of objects: there are 120 books in total.

Division problems nº 2. My town has a water supply beside the big gardens on the tallest hill, to make sure there is enough water for the irrigation, but there are only 56 gallons of water currently in the supply. If it is all shared with the recipients, 8 liters to each one, how many recipients are supplied with water?

Step-by-Step Set up the division problem with the long division symbol or the long division bracket. Put 487, the dividend, on the inside of the bracket. The dividend is the number you're dividing. Put 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.

Division worksheets including division facts and long division with and without remainders. ... reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals ...

Step 1: D for Divide How many times will 5 go into 65? That's too hard to work out in your head, so let's break it down into smaller steps. The first problem you'll work out in this equation is how many times can you divide 5 into 6. The answer is 1. So you put 1 on the quotient line. Step 2: M for Multiply

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process. Step One: Set up the Expression The first step in solving a long division problem is to draw the equation that needs to be solved.

How to solve long division problems. In any division, the first number (the amount being divided) is called the dividend; the second number (whatever the dividend is being divided by), is called the divisor; the answer is called the quotient.. Long division is typically used when dividing larger numbers where the divisor is a two-digit number, although it can also be used with one-digit divisors.

Solution: Step 1: Find how many marbles he had left. 700 - 175 = 525 He had 525 marbles left. Step 2: Find the number of marbles in each box. 525 ÷ 5 = 105 There were 105 marbles in each box. Example: Rosalind made 364 donuts. She put 8 donuts into each box. a) How many boxes of donuts were there? How many donuts were left over?

One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 ÷ 4 = 2, this can be used to determine that 9 ÷ 4 = 2 R1.

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Examples, solutions and videos to help Grade 4 students learn how to solve division word problems with remainders. Common Core Standards: 4.NBT.6, 4.OA.3. New York State Common Core Math Grade 4, Module 3, Lesson 14. Worksheets for Grade 4. NYS Math Module 3 Grade 4 Lesson 14 Concept Development

Struggles with division can easily be overcome if students practice the concept in a fun and engaging way! Young learners will make connections between math and the real world as they solve a set of division word problems involving divide by scenarios. In these problems, they comprehend the scenarios and get to the result. This set of problems deals with numbers within 100.

Improve your math knowledge with free questions in "Use arrays to solve division word problems" and thousands of other math skills.

How to solve. 3.2 Synthetic Division/Factor Theorem Question 9 of 9... How to solve . Math Algebra. Answer & Explanation. Solved by verified expert. Answered by mathsvinodmath on coursehero.com. f(x) can linearly be factored as:

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In this video, I demonstrate how to solve a simple division problem using base ten (place value). This correlates with the fourth grade standard for division...

532 likes, 7 comments - divisionofstudentwelfare on February 26, 2024: "Celebrating an epic win at Techfest Advitya organized by IIT Ropar, our brilliant students ...