DIVISION PROBLEMS - LONG DIVISION MADE EASY, SOLVED EXAMPLES, EXERCISES

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

There we explained the terms involved
in division namely Dividend, Divisor,
Quotient and Remainder
and the relation among them.

We also explained the process of
Long Division by Vertical Presentation.

That knowledge is a prerequisite here.

Here we see division of two or three
or four or more digit numbers
divided by single digit numbers.

As usual, Multiplication Tables
upto 9 times 9 is a prerequisite here.





Example 1 of Division Problems

Find the quotient and the remainder
when 97 is divided by 7.
Also check your result.

Solution to the division Problem:

Step1 :
Here, we first find a number which
when multiplied by 7 is near to 9
(not 97 because 9 is bigger than 7. ).
We know 1 x 7 = 7 is near 9. we write 1
in the right bracket and 7 below 9.
7 subtracted from 9 gives 2.


              Dividend
 Divisor   7 )   97   ( 1      
                 7
                 ---
                 2

You may note that
In division either at the end or
at any stage the remainder should
always be less than the divisor.

Step2 :
To the right of this 2, we descend
the next (last) digit 7 in the
dividend to make it 27.

Now we try to find a number which
when multiplied by 7 is near to 27.

We know 3 x 7 = 21 is near 27.
We write 3 in the right bracket to
the right of 1 and 21 below 27.
21 subtracted from 27 gives 6.

As there is no other digit left
in the dividend to descend,
6 is the remainder.

The long division process
is shown below.


              Dividend
 Divisor   7 )   97   ( 13   Quotient    
                 7
                 ---
                 27
                 21    
                 ---  
                  6   Remainder 
                 ---   

You may note that
In division either at the end or
at any stage the remainder should
always be less than the divisor.

Thus, quotient = 13 and remainder = 6
when 97 is divided by 7.

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

R.H.S. = Divisor x Quotient + Remainder
= 7 x 13 + 6 = 13 x 7 + 6

To Find 13 x 7 :

      13
       7                                  
     ----           2           
      91
     ----

R.H.S. = Divisor x Quotient + Remainder
= 7 x 13 + 6 = 91 + 6 = 97
= Dividend = L.H.S. (Verified. )

Example 2 of Division Problems

Divide 124 by 3.

Solution to the division Problem:

Step1 :
Here, first digit of dividend is 1
which is less than the divisor 3.
So we see the first two digits
of the dividend which is 12.
We find how many times 3 divides 12.
We know 4 x 3 = 12. We put 4 in the
right bracket and 12 below 12 of the
dividend. 12 subtracted from 12 gives 0.


              Dividend
 Divisor   3 )   124   ( 4       
                 12
                 ---
                  0

Step2 :
We descend the next (last) digit
of the dividend, 4 to the right of 0
to make it 04. We know 3 divides 4,
one time. 1 x 3 = 3. We write 1 in the
right bracket after 4 and 3 below 04.
3 subtracted from 4 gives 1
which is the remainder.


              Dividend
 Divisor 3 )   124   ( 41 Quotient    
               12
               ---
                04
                 3    
               ---  
                 1   Remainder 
               ---   

Thus 124 ÷ 3 gives quotient = 41
and remainder = 1. Ans.

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

R.H.S. = Divisor x Quotient + Remainder
= 3 x 41 + 1 = 41 x 3 + 1

To Find 41 x 3 :

      41
       3                                  
     ----           
     123
     ----

R.H.S. = Divisor x Quotient + Remainder
= 3 x 41 + 1 = 123 + 1 = 124
= Dividend = L.H.S. (Verified. )

Example 3 of Division Problems

Divide 2479 by 9.

Solution to the division Problem:


              Dividend
 Divisor 9 )   2479   ( 275 Quotient    
               18
               -----
                67
                63    
               -----  
                 49 
                 45   
               ----- 
                  4   Remainder
               ----- 

Step1 :
Here first digit of dividend is 2
which is less than the divisor 9.
So we see the first two digits
of the dividend which is 24.
We find how many times 9 divides 24.
We know 2 x 9 = 18.
(Note that 3 x 9 = 27 exceeds 24.)
We put 2 in the right bracket and
18 below 24 of the dividend.
18 subtracted from 24 gives 6.


                Dividend
 Divisor   9 )   2479   ( 2   
                 18
                 -----
                  6

Step2 :
We descend the next digit of the
dividend, 7 to the right of 6 to
make it 67. We know 9 divides 67,
seven times. 7 x 9 = 63.
(Note that 8 x 9 = 72 exceeds 67.)
We write 7 in the right bracket
after 2 and 63 below 67.
63 subtracted from 67gives 4.


                Dividend
 Divisor   9 )   2479   ( 27   
                 18
                 -----
                  67
                  63    
                 -----  
                   4 

Step3 :
We descend the next (last) digit of
the dividend, 9 to the right of 4
to make it 49. We know 9 divides 49,
five times. 5 x 9 = 45.
(Note that 6 x 9 = 54 exceeds 49.)
We write 5 in the right bracket
after 27 and 45 below 49. 45 subtracted
from 49 gives 4 which is the remainder.


                Dividend
 Divisor   9 )   2479   ( 275   Quotient    
                 18
                 -----
                  67
                  63    
                 -----  
                   49 
                   45   
                 ----- 
                    4   Remainder
                 ----- 

Thus 2479 ÷ 9 gives quotient = 275
and remainder = 4. Ans.

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

R.H.S. = Divisor x Quotient + Remainder
= 9 x 275 + 4 = 275 x 9 + 4

To Find 275 x 9 :

      275
        9                                  
     ----           4 6 
     2475
     ----
R.H.S. = Divisor x Quotient + Remainder
= 9 x 275 + 4 = 2475 + 4 = 2479
= Dividend = L.H.S. (Verified. )

Exercise on Division Problems

Find the quotient and the remainder
in the following Division Problems.

  1. 97 ÷ 2
  2. 138 ÷ 5
  3. 3791 ÷ 6
  4. 87341 ÷ 7
  5. 102109 ÷ 9
  6. 101 ÷ 3
  7. 3751 ÷ 4
  8. 30869 ÷ 8
  9. 98765 ÷ 9
  10. 4895 ÷ 8
For Answers see at the
bottom of the page.

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Answers to Exercise
on Division Problems

Answers to Division Problems :

  1. quotient = 48, remainder = 1;
  2. quotient = 27, remainder = 3
  3. quotient = 631, remainder = 5;
  4. quotient = 12477, remainder = 2
  5. quotient = 11345, remainder = 4;
  6. quotient = 33, remainder = 2
  7. quotient = 937, remainder = 3;
  8. quotient = 3858, remainder = 5
  9. quotient = 10973, remainder = 8;
  10. quotient = 611, remainder = 7

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