LEARNING LONG DIVISION - MADE EASY, SOLVED EXAMPLES, EXERCISES

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Learn/Teach
Division through Fun Games
before Learning Long Division,

For details, see near
the bottom of this page.

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

There, we studied problems on
long division by a single digit number.

Here, we extend that study by solving
Long Division of a Five digit number
by a single digit number. We also
introduce long division by two digit
numbers.

Example 1 on Learning Long Division

Divide 79865 by 8.

Solution to Example 1 on Learning Long Division :

Step1 :
Here first digit of dividend is 7
which is less than the divisor 8.
So we see the first two digits
of the dividend which is 79.
We find how many times 8 divides 79.
We know 9 x 8 = 72. We put 9 in the
right bracket and 72 below 79 of
the dividend.
72 subtracted from 79 gives 7.


                Dividend
 Divisor   8 )   79865   ( 9   
                 72
                 -----
                  7

Step2:Learning Long Division
We descend the next digit of the
dividend, 8 to the right of 7 to
make it 78. We know 8 divides 78,
nine times. 9 x 8 = 72. We write
9 in the right bracket after 9
and 72 below 78.
72 subtracted from 78 gives 6.


                Dividend
 Divisor   8 )   79865   ( 99   
                 72
                 -----
                  78
                  72    
                 -----  
                   6 

Step3:Learning Long Division
We descend the next digit of the
dividend, 6 to the right of 6 to
make it 66. We know 8 divides 66,
eight times. 8 x 8 = 64.
(Note that 9 x 8 = 72 exceeds 66.)
We write 8 in the right bracket
after 99 and 64 below 66.
64 subtracted from 66 gives 2.


                Dividend
 Divisor   8 )   79865   ( 998
                 72
                 -----
                  78
                  72    
                 -----  
                   66 
                   64   
                 ----- 
                    2

Step4:Learning Long Division
We descend the next (last) digit
of the dividend, 5 to the right
of 2 to make it 25. We know
8 divides 25, three times. 3 x 8 = 24.
(Note that 4 x 8 = 32 exceeds 25.)
We write 3 in the right bracket
after 998 and 24 below 25.
24 subtracted from 25 gives 1
which is the remainder.


                Dividend
 Divisor   8 )   79865   ( 9983   Quotient    
                 72
                 -----
                  78
                  72    
                 -----  
                   66 
                   64   
                 ----- 
                    25
                    24
                 ----- 
                      1   Remainder
                 ----- 

Thus 79865 ÷ 8 gives quotient
= 9983 and remainder = 1. Ans.

Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.

R.H.S. = Divisor x Quotient + Remainder
= 8 x 9983 + 1 = 9983 x 8 + 1

To Find 9983 x 8 :

      9983
         8                                  
     ------           2 6 7
     79864
     ------

R.H.S. = Divisor x Quotient + Remainder
= 8 x 9983 + 1 = 79864 + 1 = 79865
= Dividend = L.H.S. (Verified. )





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Long Division
by two digit numbers

Here we see division of any
number by two digit numbers.

In addition to,
Multiplication Tables
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Example 2 of Learning Long Division

Divide 983 by 29.

Solution :

Step1: Learning Long Division
Here the divisor is a
two digit number, 29.
So we see the first two digits
of the dividend which is 98.
We have to find how many
times 29 divides 98.

Unlike in the previous sums
where the knowlegde of
Multiplication Tables was
sufficient to decide
how many times the divisor
divides the number,
here we have to calculate
to decide.

We don't remember (not supposed
to remember) 29 table.29 is near 30.
We know 3 x 30 = 90 which is near 98.
(To find 3 x 30, we simply find 3 x 3
and then put a 0 to the right of
the result.) So we try 3 x 29.

Here, we use the knowledge of

Multiplication.

      29
       3                             
     ---           2
     87
     ---

87 is less than 98 by 11 only.
So 4 times 29 is not required.
We have 3 x 29 = 87.
We put 3 in the right bracket and
87 below 98 of the dividend.
87 subtracted from 98 gives 11.


              Dividend
 Divisor   29 )   983   ( 3
                  87
                 -----
                  11

Step2: Learning Long Division
We descend the next (last) digit
of the dividend, 3 to the right
of 11 to make it 113.
We know 3 x 29 = 87.
Let us find 4 x 29:

      29
       4                             
     ---           3
     116
     ---

4 x 29 = 116 exceeds 113.
So 29 divides 113, three times
and 3 x 29 = 87.
We write 3 in the right bracket
after 3 and 87 below 113.
87 subtracted from 113 gives 26
which is the remainder.


              Dividend
 Divisor   29 )   983   ( 33   Quotient    
                  87
                 -----
                  113
                   87    
                 -----  
                   26   Remainder 
                 -----   

Thus 983 ÷ 29 gives quotient
= 33 and remainder = 26. Ans.

Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.

R.H.S. = Divisor x Quotient + Remainder
= 29 x 33 + 26

To Find 29 x 33 :

      29
      33                            
     ----           2
      87
     87
     ----
     957
     ----

R.H.S. = Divisor x Quotient + Remainder
= 29 x 33 + 26 = 957 + 26 = 983
= Dividend = L.H.S. (Verified. )

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Exercise on Learning Long Division

Find the quotient and the remainder
in the following divisions.
Also check your results.

  1. 987 ÷ 19
  2. 1928 ÷ 23
  3. 31829 ÷ 47
  4. 102460 ÷ 93
  5. 5734 ÷ 137

For Answers see at the
bottom of the page.

More Problems on Long Division
by two or more digit numbers

For more problems on
Learning Long Division by two or
more digit numbers, go to

Long Division by Two
or more digit numbers.

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Answers to Exercise
on Learning Long Division

  1. quotient = 51, remainder = 18
  2. quotient = 83, remainder = 19
  3. quotient = 677, remainder = 10
  4. quotient = 1101, remainder = 67
  5. quotient = 41, remainder = 117