Long Division

Jane asked her teacher who gave the long division method we use today?

Her teacher said that the method we use today is an Italian method which was first described by Calandri in 1491

However, it was Henry Briggs, the first professor of Geometry, who named it as the 'long division method'.

Try this interactive calculator to get an idea about long division.

Enter the dividend and then the divisor.

Click on 'Calculate' to see the steps.

Lesson Plan


What Is Long Division Method?

In Math, long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps.


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.

It requires the constructs of a tableau.The divisor is separated from the dividend by a right parenthesis ⟨)⟩ or vertical bar ⟨|⟩ and the dividend is separated from the quotient by a vinculum (an overbar).

Method

Long division steps for 74 \( \div \) 3

Long division method

The same steps follow for long division problems related to long division polynomials and long division with decimals.

important notes to remember
Important Notes
  1. The dividend is always greater than the divisor and the quotient.
  2. The remainder is always smaller than the divisor.
  3. For division, the divisor cannot be 0

  4. When we divide a number by 10, the digit in the one's place is the remainder and the rest of the digits form the quotient. The same is the case with 100 and 100

Here are a few long division problems:

Example

Let us solve 435 \( \div \) 4

Step 1:

•    Here, the first digit is 4 and it is equal to the divisor.
•    So, \( 4 \div 4 =1 \); 1 is written on top, inside the yellow box below.
•    The result \( 4 \times 1 =4 \) is subtracted from the digit and 0 is written below.
•    Next, drop the second digit or the digit in the ten’s place beside 0

Long division sum

Step 2:

We can see that we have 03 as the result of step 1
•    Repeat the same step of checking if this number is greater or smaller than the divisor.
•    Since 03 is less than 4, we cannot divide this number.
•    Hence, we write a 0 on the top and drop the digit on the unit place beside 3
Now, we have 35

Step 3:

•    As 35 > 4, we can divide this number and write \( 35 \div 4 \) which gives 8 as the quotient.
•    Subtract the result \( 4 \times 8 = 32 \) from 35 and write 3 as the remainder.
3 is known as remainder and 108 is called the quotient.

long division sum

Let's consider another example: 735  \( \div \) 9

long division sum

In the above example, we can see that the first digit of the dividend is less than the divisor.
Hence, we add a zero and drop the next digit to proceed with the calculation.
We consider the first 2 digits to proceed with the division.

Let's solve one more example: 3640 \( \div \) 15

Long division sum

Long division problems also include problems related to long division polynomials and long division with decimals.

Long Division Polynomials

To have an understanding of long division polynomials, visit division of polynomials.

Long Division with Decimals

Here's the procedure for long division with decimals:

long division with decimals


What Are the Parts of Long Division?

  • Dividend

  • Divisor

  • Quotient

  • Remainder

The divisor is written outside the right parenthesis, while the dividend is placed within. The quotient is written above the overbar on top of the dividend.
The quotient in mathematics can be defined as the result of the division between a number and any divisor. It is the number of times the divisor is contained in the dividend without the remainder being negative.

long division sum

You will come across more of long division problems in the sections below.

tips and tricks
Tips and Tricks
  1. Division is repeated subtraction.
    So we can check our quotient by repeated subtractions as well.
  2. We can check the quotient and the remainder of division using the following formula:
    Dividend = (Divisor × Quotient) + Remainder
  3. 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.

Solved Examples

Example 1

 

 

Aarohi needs \(3\) apples to make a big glass of apple juice. If she has \(51\) apples, how many glasses of juice can she make?

Solution

The total number of apples with Aarohi = \(51\)

The number of apples needed for one glass of juice = \(3\)

To find the number of glasses of juice, we divide \(51\) by \(3\)

Division word problem: finding the quotient when 51 is divided by 3

Aarohi can make \(17\) glasses of juice with 51 apples.

\(\therefore\) Number of glasses of juice = \(17\)
Example 2

 

 

\(75\) people are invited to a birthday party. The suppliers have to arrange tables for the invitees. \(6\) people can sit around a table.

How many tables should the suppliers arrange for the invitees?

Solution

Total number of invitees = \(75\)

The number of people who can sit around one table = \(6\)

We divide \(75\) by \(6\) using the long division method.

long division word problem

Since \(12\) is the quotient, we need \(12\) tables.

With 12 tables, we will still have \(3\) (which is the remainder) people without a place to sit.

Hence, the suppliers should arrange one more table for them.

The total number of tables to be arranged by the suppliers = \(12+1=13\)

\(\therefore\) Required number of tables = \(13\)
Example 3

 

 

Calculate the number of hours in \(2100\) minutes.

long division word problem

Solution

We know that,

\(1\) hour = \(60\) minutes.

To find the number of hours in \(2100\) minutes, we have to divide \(2100\) by \(60\).

Division word problem: finding the quotient when 2100 is divided by 60

There are \(35\) hours in \(2100\) minutes.

\(\therefore\) Required number of hours = \(35\)
Example 4

 

 

Aayush planted \(75\) trees equally in \(3\) rows. How many trees did he plant in each row?

Solution

Total number of trees planted by Aayush = \(75\)

Number of rows = \(3\)

To find the number of trees in each row, we have to divide \(75\) by \(3\) because there are equal number of trees in each of the three rows.

long division word problem

\(\therefore\) The number of trees in each row = \(25\)

Example 5

 

 

Rs. \( 4000 \) are to be distributed among \(25\) men for the work completed by them at a construction site. Calculate the amount given to each man.

long division word problem

Solution

The total amount is Rs. \( 4000 \)

The number of men at work = \(25\)

We have to calculate the amount given to each man.

To do so, we have to divide \(4000\) by \(25\) using the long division method.

Division word problem: finding the quotient when 4000 is divided by 25

Each man will be given Rs. \( 160\)

\(\therefore\) Amount given = Rs. \(160\)


Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 

 
 
 
 
 
 
 
Challenge your math skills
Challenging Questions
  1. Anirudh has \(52\) cards. He arranges them into \(4\) groups. How many cards does each group contain?
  2. Shweta distributed \(32\) scoops of ice cream into \(8\) cones evenly. How many scoops of ice cream does each cone contain?

Let's Summarize

The mini-lesson targeted in the fascinating concept of long division.The math journey around long division starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favourite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we at Cuemath believe in.


Frequently Asked Questions (FAQs)

1.How do I do long division?

  • Take the first digit of the dividend.
  • If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top.
  • Subtract the result from the digit and write below and we get the difference. if it's not less than the divisor then it's not the final remainder.
  • Repeat the process.

2.What are the 5 steps of long division?

•    Step 1: D for Divide. 
•    Step 2: M for Multiply. 
•    Step 3: S for Subtract.  
•    Step 4: B for Bring down.
•    Step 5: Repeat till the time you get remainder less than the divisor.

3.How do you do long division with 2 digits?

Take up both the digits at divisor's place together as a number, proceed further following the long division procedure.

  
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