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- Multiplication and Division

## How to Do Division

Last Updated: February 10, 2023 References

## Long Division

- Sample problem #1 (beginner): 65 ÷ 5 . Place the 5 outside the division bar, and the 65 inside it. It should look like 5厂65 , but with the 65 underneath the horizontal line.
- Sample problem #2 (intermediate): 136 ÷ 3 . Place the 3 outside the division bar, and the 136 inside it. It should look like 3厂136 , but with the 136 underneath the horizontal line.

- In sample problem #1 ( 5厂65 ), 5 is the divisor and 6 is the first digit of the dividend (65). 5 goes into 6 one time, so place a 1 on the top of the divisor bar, aligned above the 6.
- In sample problem #2 ( 3厂136 ), 3 (the divisor) does not go into 1 (the first digit of the dividend) and result in a whole number. In this case, write a 0 above the division bar, aligned above the 1.

- In sample problem #1 ( 5厂65 ), multiply the number above the bar (1) by the divisor (5), which results in 1 x 5 = 5 , and place the answer (5) just below the 6 in 65.
- In sample problem #2 ( 3厂136 ), there is a zero above the division bar, so when you multiply this by 3 (the divisor), your result is zero. Write a zero on a new line just below the 1 in 136.

- In sample problem #1 ( 5厂65 ), subtract the 5 (the multiplication result in the new row) from the 6 right above it (the first digit of the dividend): 6 - 5 = 1 . Place the result (1) in another new row right below the 5.
- In sample problem #2 ( 3厂136 ), subtract 0 (the multiplication result in the new row) from the 1 right above it (the first digit in the dividend). Place the result (1) in another new row right below the 0.

- In sample problem #1 ( 5厂65 ), drop the 5 from 65 down so that it’s beside the 1 that you got from subtracting 5 from 6. This gives you 15 in this row.
- In sample problem #2 ( 3厂136 ), carry down the 3 from 136 and place it beside the 1, giving you 13.

- To continue 5厂65 , divide 5 (the dividend) into the new number (15), and write the result (3, since 15 ÷ 5 = 3 ) to the right of the 1 above the division bar. Then, multiply this 3 above the bar by 5 (the dividend) and write the result (15, since 3 x 5 = 15 ) below the 15 under the division bar. Finally, subtract 15 from 15 and write 0 in a new bottom row.
- Sample problem #1 is now complete, since there are no more digits in the divisor to carry down. Your answer (13) is above the division bar.

- For 3厂136 : Continue the process for another round. Drop down the 6 from 136, making 16 in the bottom row. Divide 3 into 16, and write the result (5) above the division line. Multiply 5 by 3, and write the result (15) in a new bottom row. Subtract 15 from 16, and write the result (1) in a new bottom row.
- Because there are no more digits to carry down in the dividend, you’re done with the problem and the 1 on the bottom line is the remainder (the amount left over). Write it above the division bar with an “r.” in front of it, so that your final answer reads “45 r.1”.

## Short Division

- In order to do short division , your divisor can't have more than one digit.
- Sample problem: 518 ÷ 4 . In this case, the 4 will be outside the division bar, and the 518 inside it.

- In the sample problem, 4 (the divisor) goes into 5 (the first digit of the dividend) 1 time, with a remainder of 1 ( 5 ÷ 4 = 1 r.1 ). Place the quotient, 1, above the long division bar. Place a small, superscript 1 beside the 5, to remind yourself that you had a remainder of 1.
- The 518 under the bar should now look like this: 5 1 18.

- In the sample problem, the number formed by the remainder and the second number of the dividend is 11. The divisor, 4, goes into 11 twice, leaving a remainder of 3 ( 11 ÷ 4 = 2 r.3 ). Write the 2 above the division line (giving you 12) and the 3 as a superscript number beside the 1 in 518.
- The original dividend, 518, should now look like this: 5 1 1 3 8.

- In the sample problem, the next (and final) dividend number is 38—the remainder 3 from the previous step, and the number 8 as the last term of the dividend. The divisor, 4, goes into 38 nine times with a remainder of 2 ( 38 ÷ 4 = 9 r.2 ), because 4 x 9 = 36 , which is 2 short of 38. Write this final remainder (2) above the division bar to complete your answer.
- Therefore, your final answer above the division bar is 129 r.2.

## Dividing Fractions

- In the sample problem, 5 goes into 6 one time with a remainder of 1. Therefore, the new whole number is 1, the new numerator is 1, and the denominator remains 5.
- As a result, 6/5 = 1 1/5 .

## Dividing Exponents

## Dividing Decimals

- In the sample problem, you only need to move the decimal point over one spot for both the divisor and dividend. So, 0.5 becomes 5, and 65.5 becomes 655.
- If, however, the sample problem used 0.5 and 65.55, you’d need to move the decimal point 2 places in 65.55, making it 6555. As a result, you’d also have to move the decimal point in 0.5 2 places. To do this, you’d add a zero to the end and make it 50.

- Divide 5 into the hundredths digit, 6. You get 1 with a remainder of 1. Place 1 in the hundredths place on top of the long division bar, and subtract 5 from 6 below the number six.
- Your remainder, 1, is left over. Carry the first five in 655 down to create the number 15. Divide 5 into 15 to get 3. Place the three above the long division bar, next to the 1.
- Carry down the last 5. Divide 5 into 5 to get 1, and place the 1 on top of the long division bar. There is no remainder, since 5 goes into 5 evenly.
- The answer is the number above the long division bar (131), so 655 ÷ 5 = 131 . If you pull out a calculator, you’ll see that this is also the answer to the original division problem, 65.5 ÷ 0.5 .

## Practice Problems and Answers

## Community Q&A

## Video . By using this service, some information may be shared with YouTube.

## You Might Also Like

- ↑ https://www.mathsisfun.com/long_division.html
- ↑ https://www.k5learning.com/blog/step-step-guide-long-division
- ↑ https://www.bbc.co.uk/bitesize/topics/znmtsbk/articles/zqpddp3
- ↑ http://www.mathsisfun.com/fractions_division.html
- ↑ https://www.ck12.org/arithmetic/divide-fractions/lesson/Quotients-of-Fractions-MSM6/?referrer=concept_details
- ↑ http://www.mathsisfun.com/algebra/variables-exponents-multiply.html
- ↑ https://www.mathsisfun.com/dividing-decimals.html
- ↑ https://www.bbc.co.uk/bitesize/topics/zh7xpv4/articles/zwdc4xs

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## How to Solve Division Problems

## What Is a Remainder in Math?

Trending Post : Teaching Fractions with Food

## 5 Fun Division Word Problems | Practice Multiple Ways of Solving | Free Printable

## Division Word Problems

## Division Problems

When we hit the division problem in his math book, he wasn’t quite as sure what to do.

## How to Solve Division Word Problems

Step 1: division word problem solving by grouping.

## Step 2: Solving Division Word Problems by Repeated Subtraction

## Step 3: Division Word Problem Solving with Arrays

They now have an array that is a 3 by 6. The answer to the division problem is 6.

Want to know how to use arrays to divide when the numbers are larger? Check out this POST !

## Step 4: Number Line to Solve Division Word Problems

## Step 5: Create an Equation

That number goes in the last box.

Get This Cut and Paste Division Assessment at my TpT Store .

## Division Word Problems Printable

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## Division Tips and Tricks

- Divide by 1 - Anytime you divide by 1, the answer is the same as the dividend.
- Divide by 2 - If the last digit in the number is even, then the entire number is divisible by 2. Remember that divide by 2 is the same as cutting something in half.
- Divide by 4 - If the last two digits divide by 4, then the entire number is divisible by 4. For example, we know that 14237732 can be divided evenly by 4 because 32 ÷ 4 = 8.
- Divide by 5 - If the number ends in a 5 or a 0, it is divisible by 5.
- Divide by 6 - If the rules for divide by 2 and divide by 3 above are true, then the number is divisible by 6.
- Divide by 9 - Similar to the divide by 3 rule, if the sum of all the digits is divisible by 9, then the entire number is divisible by 9. For example, we know that 18332145 is divisible by 9 because 1+8+3+3+2+1+4+5 = 27 and 27 ÷ 9 = 3.
- Divide by 10 - If the number ends in a 0, then it is divisible by 10.

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## Steps to Long Division Problems (With Examples)

- DESCRIPTION parts of long division problem
- SOURCE Created by Beth Wiggins for YourDictionary
- PERMISSION Owned by YourDictionary, Copyright YourDictionary

## What Is Long Division?

## Terms Used in Long Division

- dividend - the number that needs dividing
- divisor - the number you are dividing by
- quotient - the answer
- remainder - the leftover amount when dividend doesn't divide equally

## Simple Long Division Steps

1579 / 6 = x.

## Step 1: Divide

- DESCRIPTION long division example Step 1 divide
- PERMISSION Owned by YourDictionary, Copyright YourDictionary

## Step 2: Multiply

## Step 3: Subtract

## Step 4: Bring the Number Down

## Step 5: Repeat

## Long Division Examples

- 1204 / 4 4 goes into 1 zero times 1 - 0 = 1, 2 drops down 4 goes into 12 three times (first number in the answer is 3) 12 - 12 = 0, 0 drops down 4 goes into 0 zero times (second number in the answer is 0) 0 - 0 = 0, 4 drops down 4 goes into 4 one time (third number in the answer is 1), answer is 301 Check your answer: 301 * 4 = 1204
- 3024 / 24 24 goes into 3 zero times 3 - 0 = 3, 0 drops down 24 goes into 30 one time (first number in the answer is 1) 30 - 24 = 6, 2 drops down to make 62 24 goes into 62 two times (second number in the answer is 2) 62 - 48 = 14, 4 drops down to make 144 24 goes into 144 six times (last number is 6), answer is 126 Check your answer 24 * 126 = 3024
- 675 / 5 5 goes into 6 one time (first number in the answer is 1) 6 - 5 = 1, 7 drops down 5 goes into 17 three times (second number in the answer is 3) 17 - 15 = 2, 5 drops down 5 goes into 25 five times (last number in the answer is 5), answer is 135 Check your answer 5 * 135 = 675
- 679 / 5 5 goes into 6 one time (first number in the answer is 1) 6 - 5 = 1, 7 drops down 5 goes into 17 three times (second number in the answer is 3) 17 - 15 = 2, 9 drops down 5 goes into 29 five times (last number in the answer is 5) you have a remainder of 4, answer is 135 R4 Check your work (5 * 135) + 4 = 679

## Why Do Some Equations Have a Remainder

## How to Divide Decimals Using Long Division

## Keep Long Division Steps Simple

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## Long Division

## What is Long Division Method?

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

## Parts of Long Division

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

## How to do Long Division?

## Long Division Steps

- 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.

## Division with Remainders

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

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.

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

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 by a 2 Digit Number

- 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

## Long Division with Decimals

## How to Divide Decimals by Whole Numbers?

- 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:

- 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.

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

## Long Division Examples with Answers

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

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.

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

go to slide go to slide go to slide

## Practice Questions on Long Division

## FAQs on Long Division

What is long division in math.

- 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?

## What is the Long Division of Polynomials?

## How to do Long Division with Decimals?

- 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.

## How to Divide

## Introduction: How to Divide

## Step 1: Things You'll Need

## Step 2: Simple Division

The first method is simple division. Your answer will come out as a whole number.

## Step 3: Simple Division With Remainder

This is the same as simple division except we add in the remainder.

## Step 4: Long Division With Decimal

This is similar to dividing with a remainder except you go a step further and have a decimal.

## Step 5: Divide With More Than One Digit

## Step 6: Conclusion

First Prize in the Burning Questions: Round 6

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## 123 Comments

lol fr it be like that sometimes

i dont understand can someone ls help meh!

thank u i couldnt do it and now i can have my test friday let u know how i get on yhank u

hope you pass even tho this comment is from 11 years ago still waiting for update.

and how do you do 13 ÷ 3? it goes on forever

the answer is 4 and remainder 1

I don't know how to divide or long divide

can someone teach me how to divide and long division

What's with that brown paper? Recycled paper bag paper or something?

## IMAGES

## VIDEO

## COMMENTS

In this video, I'll show you a different way to solve division problems called "Short Division".Support Super Easy Math with a donation:

Complete list of Math Videos organized by State Standardshttp://www.moomoomathblog.com/2017/12/6th-grade-math-unit-1-math-videos.

Use a division bar to write out the problem. Place the divisor, the number you'll be dividing into, outside of (and to the left of) the division bar. Put the

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If you're just starting out with division, drawing a picture may help you to understand division problems better. First, draw the same number of boxes as the

Simple Long Division Steps · Step 1: Divide · Step 2: Multiply · Step 3: Subtract · Step 4: Bring the Number Down · Step 5: Repeat.

Another way to divide is to create equal groups with place value. Practice with 24 divided by 4. · Numbers can also be divided using

Long Division Steps · Step 1: Take the first digit of the dividend from the left. · Step 2: Then divide it by the divisor and write the answer on top as the

The first method is simple division. Your answer will come out as a whole number. 1) Setup the division problem (84/7). 2) Divide 8 by 7