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Long Division

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What is Long Division?

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Long division in arithmetic is a common division algorithm suitable for multi-digit number splitting that is easy enough to do by hand. It breaks down a problem with a division into a set of easier measures.


One number, called the dividend, is split by another, called the divisor, producing a result called the quotient, as in all division issues. It makes it possible to perform computations involving arbitrarily large numbers by following a series of simple steps. Chunking (also referred to as the method of partial quotients or the hangman method) is a less mechanical type of long division prominent in the United Kingdom that leads to a more holistic understanding of the process of division.


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Define Long Division

When you divide a large number (typically three-digits or more) by a two-digit (or more) number, the long division method is used. Similar to short division (the 'bus stop' technique), it is set out. Long division does not use the division slash or division sign symbols in English-speaking countries but instead constructs a tableau. The divisor is separated by a right parenthesis from the dividend (or vertical bar); the dividend is separated by a vinculum from the quotient (i.e., an overbar). Long division is a mathematical operation which allows you to use a pencil and paper to perform complex division problems. The more complicated problem is broken down into simpler measures. With the advancements in computers and calculators, the need to know long division has faded. It is a valuable ability to have, however, and an outstanding way to exercise the brain.


Long Division Steps

In solving a long division problem, there are four main steps: 

  • Division.

  • Multiplying.

  • Minus.

  • Drop the last digit.

Long division is a method where the aim of each step is to simplify the next step, with each step we acquire one digit of the quotient and by the end of the process, we get the quotient.

Step 1: Divide the dividend of ten columns by the divisor.

Step 2: In the ten position column, multiply the divider by the quotient.

Step 3: Subtract the divider from the element.

Step 4: In the column, put the dividend down and repeat.

Step 5: To keep it simple, start with one-digit dividers and two-digit dividends.


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Division Types

  • Chunking: In primary school mathematics education, chunking (sometimes also referred to as the form of partial quotients) is an elementary approach to solving basic division issues by repeated subtraction. With the addition of a line separating the divisor, dividend, and partial quotients, it is also known as the hangman form. It also has a counterpart for multiplication in the grid method.

  • Formal Long Division: Long division helps to split the problem of division into a series of simpler steps. A large number, which is the dividend, is divided by another number, which is called the divisor, just like all division problems, to give a result called the quotient and sometimes a remainder.

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Long Division Examples

1. Using Long division, solve the following :

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FAQ (Frequently Asked Questions)

1. What are the Five Steps of Long Division?

Solution: Long division is a procedure for dividing one large multi-digit number into another large multi-digit number. It has 4 parts: Dividend, divisor, remainder and quotient. Dividend is the number that is divided by the divisor and the answer that we get after dividing is known as the quotient, in few cases, we are left with some remainders which happens only when the two numbers are not divisible with each other. It follows 5 steps, it starts with dividing, next step being multiplication, then subtracting, after that we bring down the next digit and then we repeat or find the remainder.

2. How to Perform a Long Division with Two Digits?

Solution: There are few things you must always remember while performing long division - the dividend is always greater than the quotient and the divider, the remainder should be smaller than the divisor. The value of divisor cannot be zero as division by zero is undefined. Whenever we perform long division, we follow the following steps:


Divide the first number of the dividend (or the first two numbers if another digit is taken from the previous step) by the first digit of the divisor. In the space of the quotient, write the outcome of this division. Multiply the quotient digit by the divisor, write and deduct the result below the dividend.