TEACHING LONG DIVISION - MADE EASY, SOLVED EXAMPLES, EXERCISES

Learn/Teach
Division through Fun Games
before Teaching Long Division,
For details, see near
the bottom of this page.

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

There, we studied a problem on
long division of a Three digit
number by a two digit number.

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

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Example 1

Divide 5892 by 37.

Solution :

Step1 :
Here the divisor is a
two digit number, 37.
So we see the first two digits
of the dividend which is 58.
We have to find how many
times 37 divides 58.

1 x 37 = 37; 2 x 37 is more than
2 x 30 i.e. 60 > 58.
So 37 divided 58 one time.

We have 1 x 37 = 37.
We put 1 in the right bracket
and 37 below 58 of the dividend.
37 subtracted from 58 gives 21.

              Dividend
 Divisor   37 )   5892   ( 1
                  37
                 -----
                  21

Step2 :
We descend the next digit
of the dividend, 9 to the
right of 21 to make it 219.
37 is near 40 and we know
5 x 40 = 200 which is near 219.
Let us find 5 x 37 and 6 x 37.

      37
       5                             
     ---           3
     185
     ---

      37
       6                             
     ---           4
     222
     ---

6 x 37 = 222 exceeds 219.
So 37 divides 219, five times
and 5 x 37 = 185.
We write 5 in the right bracket
after 1 and 185 below 219.
185 subtracted from 219 gives 34.

              Dividend
 Divisor   37 )   5892   ( 15
                  37
                 -----
                  219
                  185
                 -----
                   34

Step3 : Teaching Long Division
We descend the next (last) digit
of the dividend, 2 to the right
of 34 to make it 342.
37 is near 40 and we know
8 x 40 = 320 which is near 342.
Let us find 8 x 37 and 9 x 37.

      37
       8                             
     ---           5
     296
     ---

      37
       9                             
     ---           6
     333
     ---

9 x 37 = 333 is less than 342.
So 37 divides 342, nine times
and 9 x 37 = 333.
We write 9 in the right bracket
after 15 and 333 below 342.
333 subtracted from 342
gives 9 which is the remainder.

              Dividend
 Divisor   37 )   5892   ( 159   Quotient
                  37
                 -----
                  219
                  185
                 -----
                   342
                   333
                  -----
                     9    Remainder
                  -----

Thus 5892 ÷ 37 gives quotient
= 159 and remainder = 9. Ans.

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

R.H.S. = Divisor x Quotient + Remainder
= 37 x 159 + 9 = 159 x 37 + 9

To Find 159 x 37 :

      159
       37                            
     ----           6    4
     1113      2    1
     477
     ----
     5883
     ----

R.H.S. = Divisor x Quotient + Remainder
= 37 x 159 + 9 = 5883 + 9 = 5892
= Dividend = L.H.S. (Verified.)

As the number of digits of the
dividend increases, the number
of steps in the process
increases. Except for that
the procedure is same.

Teaching Long Division is done
by the above three steps.

Let us see another example in
which a six digit number is
divided by a three digit number.

Example 2 of Teaching Long Division

Divide 609182 by 463.

Solution :

Step1:Teaching Long Division
Here the divisor is a three
digit number 463.
So we see the first three digits
of the dividend which is 609.
We have to find how many times
463 divides 609.
1 x 463 = 463; 2 x 463 is more
than 800 > 609.
So 463 divides 609 one time.

We have 1 x 463 = 463. We put 1
in the right bracket and 463
below 609 of the dividend. 463
subtracted from 609 gives 146.

                  Dividend
 Divisor   463 )   609182   ( 1
                   463
                   ---
                   146

Step2: Teaching Long Division
We descend the next digit
of the dividend, 1 to the right
of 146 to make it 1461.
463 is near 500 and we know
3 x 500 = 1500 which is near 1461.
Let us find 3 x 463.

      463
        3                             
     ----           1
     1389
     ----

4 x 463 is more than 1600 which
exceeds 1461. So 463 divides 1461,
three times and 3 x 463 = 1389.
We write 3 in the right bracket
after 1 and 1389 below 1461.
1389 subtracted from 1461 gives 72.

                  Dividend
 Divisor   463 )   609182   ( 13
                   463
                   ---
                   1461
                   1389
                   ----
                     72           
                       

Step3: Teaching Long Division
We descend the next digit
of the dividend, 8 to the right
of 72 to make it 728.
1 x 463 = 463; 2 x 463
is more than 800 > 728.
So 463 divides 728 one time.

We have 1 x 463 = 463.
We put 1 in the right bracket
after 13 and 463 below 728.
463 subtracted from 728 gives 265.

                  Dividend
 Divisor   463 )   609182   ( 131
                   463
                   ---
                   1461
                   1389
                   ----
                     728
                     463
                   -----
                     265

Step4: Teaching Long Division
We descend the next (last) digit
of the dividend, 2 to the right of
265 to make it 2652.
463 is near 500 and we know
5 x 500 = 2500 which is near 2652.
Let us find 5 x 463 and 6 x 463.

      463
        5                             
     ----           1    3
     2315
     ----

      463
        6                             
     ----           1    3
     2778
     ----

6 x 463 = 2778 exceeds 2652.
So 463 divides 2652, five times
and 5 x 463 = 2315.
We write 5 in the right bracket
after 131 and 2315 below 2652.
2315 subtracted from 2652 gives
337 which is the remainder.

                  Dividend
 Divisor   463 )   609182   ( 1315   Quotient
                   463
                   ---
                   1461
                   1389
                   ----
                     728
                     463
                   -----
                     2652
                     2315
                     -----  
                      337   Remainder
                     -----  

Thus 609182 ÷ 463 gives quotient
= 1315 and remainder = 337. Ans.

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

R.H.S. = Divisor x Quotient + Remainder
= 463 x 1315 + 337 = 1315 x 463 + 337

To Find 1315 x 463 :

        1315
         463                            
      ------           1    
        3945      3    1
       7890       2    1
      5260
      ------
      608845
      ------

R.H.S. = Divisor x Quotient + Remainder
= 463 x 1315 + 337 = 608845 + 337
= 609182 = Dividend = L.H.S. (Verified.)

Thus, with any Dividend and any Divisor,
we can carry out the division by
following the same procedure.

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Exercise on Teaching Long Division

Solve the following problems on Teaching Long Division

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

1. 73651 ÷ 742
2. 827346 ÷ 876
3. 1642012 ÷ 1021
4. 47013 ÷ 271
5. 793097 ÷ 465

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Answers to Exercise
on Teaching Long Division

1. quotient = 99, remainder = 193
2. quotient = 944, remainder = 402
3. quotient = 1608, remainder = 244
4. quotient = 173, remainder = 130
5. quotient = 1705, remainder = 272