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.
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?
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).
Long division steps for 74 \( \div \) 3
The same steps follow for long division problems related to long division polynomials and long division with decimals.
Here are a few long division problems:
Let us solve 435 \( \div \) 4
• 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
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
• 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.
Let's consider another example: 735 \( \div \) 9
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 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:
What Are the Parts of Long Division?
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.
You will come across more of long division problems in the sections below.
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?
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 \(3\)
Aarohi can make \(17\) glasses of juice with 51 apples.
|\(\therefore\) Number of glasses of juice = \(17\)|
\(75\) 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?
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.
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 = \(13\)|
Calculate the number of hours in \(2100\) minutes.
We know that,
\(1\) hour = \(60\) minutes.
To find the number of hours in \(2100\) minutes, we have to divide \(2100\) by \(60\).
There are \(35\) hours in \(2100\) minutes.
|\(\therefore\) Required number of hours = \(35\)|
Aayush planted \(75\) trees equally in \(3\) rows. How many trees did he plant in each row?
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.
\(\therefore\) The number of trees in each row = \(25\)
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.
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.
Each man will be given Rs. \( 160\)
\(\therefore\) Amount given = Rs. \(160\)
Here are a few activities for you to practice.
Select/Type your answer and click the "Check Answer" button to see the result.
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.
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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.