Long division - Definition with Examples

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What is long division? 

In math, long division is a method used for dividing large numbers into groups or parts.
Long division helps in breaking the division problem into a sequence of easier steps. Just like all division problems, a large number, which is the dividend, is divided by another number, which is called the divisor, to give a result called the quotient and sometimes a remainder.
 
 
 
How do you do long division?
The long division method involves basic math operations. 

To divide two numbers using this method, a tableau is drawn. The divisor is written outside the right parenthesis, while the dividend is placed within. The quotient is written above the over bar on top of the dividend.

Long Division method to divide large numbers example

Long division involves 5 steps:

 D  Divide
 M  Multiply
 S   Subtract
 B  Bring down
 R  Repeat or Remainder
 

Here’s an example of long division with each step shown clearly. 

Long Division method to divide large numbers steps

The process begins with dividing or finding how many times the leftmost digit of the dividend can be divided by the divisor. 
Then, the result or answer from step 1, which becomes the first digit of the quotient, is multiplied by the divisor and written under the first digit of the dividend. 
Subtraction is carried out on the first digit of the dividend and the remainder is written. 
The next digit of the dividend is brought down and then, the process is repeated until all the digits of the dividend are brought down and a remainder is found. 
 
How to divide decimals using the long division method?
Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder. 

Here’s an example of long division with decimals. 

Long Division method to divide decimal numbers example

  Fun Facts

  • 123454321 when divided by 11111 gives a quotient of 11111 and remainder 0.

 

 

let's sing Let's sing!

When you have large numbers to divide,
draw a tableau for long division on the side.
Write the steps that will be your guide,
D, M, S, B and R – Abide by to long divide!
 

let's do it Let's do it!

Instead of showing videos for teaching long division or handing out practice worksheets to your 4th graders, cite real-life instances wherein they can use long division method to divide. 
Say, while preparing cupcakes and cookies for a bake sale in school, you can ask your child to calculate the number of batches in which cookies or cupcakes can be prepared (basis the number of molds in a tray) if the total number of cookies and cupcakes required is given. You can also ask them to calculate the total number of cartons required if each cookie carton packs 15 cookies and the cupcake carton packs 6 cupcakes. Ask them to calculate using the long division method. 
 

related math vocabulary Related math vocabulary

Division
 

Frequently Asked Questions

  • Is long division the same as division?

    Division is the process of distributing a set of objects into equal parts. Long division is a method used to divide large numbers into equal parts. Unlike division, it breaks down the division problem into a series of steps, making the calculation easier.

  • What are the steps of long division?

    Long division involves 5 main steps: 1. Divide: a) If the first digit is equal or greater than the divisor: Take the first digit of the dividend and divide it by the divisor. Write the answer as the quotient. b) If the first digit is less than the divisor: Take the first two digits (or more if the divisor is a large number) of the dividend and divide it by the divisor. Write the answer as the quotient, ignoring the remainder. 2. Multiply the quotient by the divisor. 3. Subtract the product obtained in step 2 from the first digit or the first two digits (depending on cases 1(a) or 1(b) of the dividend.) 4. Bring down the next digit(s) of the dividend. 5. Repeat till you find the remainder. The remainder can either be 0 or any other number less than the divisor.

  • How can we check the answer of a long division?

    We can check the long division answer using the following formula: Dividend = Divisor x Quotient + Remainder.

  • Can the long division method also be used to divide decimals?

    Yes, long division can also be used to divide decimal numbers. It follows the same steps as the long division of whole numbers.

Practice Problems on Long Division

Pick the correct answer
1.   In long division, what is the number you divide by called?
2.   What is the result of a division problem called?
3.   301 ÷ 3 = ?
4.   There are 60 cupcakes that need to be packed equally in 7 boxes. How many cupcakes will be left unpacked?
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