LONG DIVISION - METHOD OF LONG DIVISION MADE EASY, SOLVED EXAMPLES, EXERCISES

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Learn/Teach
Division through Fun Games
before Long Division

For details, see near
the bottom of this page.

Please study
Division,
if you have not already done so.

There we have covered division
as repeated subtraction.

We have also seen the concept of
division as sharing equally every
time and as making sets.

We have also seen the relation
between multiplication and division.

We also emphasized the need of
Multiplication Tables in division.

Here, we will proceed to explain the
standard procedure suitable for dividing
simple or complex multi-digit numbers.

It breaks down a division problem into
a series of easier steps. It enables
divisions involving arbitrarily large
numbers to be performed by following
this series of simple steps.

It is one of the most essential skills
to be learnt in elementary math.

This standard procedure
is called Long Division.

Terms involoved in Long Division :
Dividend, Divisor, Quotient and Remainder

Example 1

Suppose I ask you to find 21 ÷ 4.

You recall 4 times table and
realise that there is no number
which when multiplied by 4 gives 21.

Then, how to find 21 ÷ 4 ?

We will try to find a number
which when multiplied
gives a value near to 21.

From 4 times table, we know
4 x 5 = 20 and 20 is near 21.

The difference of 21 and 20 = 1
is called the Remainder
when 21 is divided by 4.

21 is called Dividend and
4 is called Divisor
and 5 is called the Quotient.

The Remainder (= 1) is less
than the Divisor ( = 4).

The number being divided
is called the Dividend.
The number that divides
is called the Divisor.
The number got after division
is called the Quotient.
The number that remains undivided
is called the Remainder.
The Remainder should always
be less than the Divisor.

Vertical Presentation

The process is shown below in vertical
presentation

Finding 21 ÷ 4 :


              Dividend
 Divisor   4 )   21   ( 5   Quotient    
                 20
                 ---
                  1   Remainder 
                 ---  

The vertical presentation
shown above is what we
follow in future division sums.

It is explained below.

First the Dividend (21 here) is
written. Then the Divisor (4 here)
with a bracket ')' is written
to the left of 21. and a bracket
'(' is written to the right of 21.

Now we recall 4 times table and find
a number such that the number x 4 is
near to 21. The number we know is 5.

This 5 (Quotient) is written
to the right side of 21 after
the bracket '(' already provided.

The value of 5 times 4 which is 20,
is written below the Dividend (21 here).

20 is subtracted from 21 to
get 1 (Remainder), which is
written below, between two lines.

Thus, we got the Quotient ( 5 here )
and the Remainder (1 here )
in the Division process.

The Remainder should always
be less than the Divisor.

In Division, either at the end or
at any stage, the Remainder should
always be less than the Divisor.















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Example 2

Find the quoitient and the remainder
when 89 is divided by 9.

Solution :
We know 9 x 9 = 81 which is near 89.


              Dividend
 Divisor   9 )   89   ( 9   Quotient    
                 81
                 ---
                  8   Remainder 
                 ---  

Thus, the quotient = 9 and
the remainder = 8. Ans.





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The relation among Dividend,
Divisor, Quotient and Remainder

We can see from Example 1
that 21 = 4 x 5 + 1.

Also, we can see from Example 2
that 89 = 9 x 9 + 8.

From these observations, we can say,

Dividend = Divisor x Quotient + Remainder.

If remainder is zero,
Dividend = Divisor x Quotient.

This is what we saw, (remainder = 0),
in examples and exercises of

Division as repeated addition

and

Division using Multiplication tables.

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Long Division Problems

For problems on long division
by a single digit number, go to

Division Problems.











For more problems and
introduction of long division
by two digit numbers, go to

More Division Problems.

For long division by two or
more digit numbers, go to

Division by Two
or more digit numbers.

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