Long division is a method for dividing multi-digit numbers. It involves repeatedly subtracting the divisor from the dividend. The number of times the divisor goes into the dividend gives the first digit of the quotient. The remainder is carried down and the process is repeated with the next digits until there is no remainder. For example, in dividing 13273 by 47, the steps are: 7 ÷ 4 = 1 remainder 3; 46 ÷ 4 = 11 remainder 2; 39 ÷ 4 = 9 remainder 3; and 47 ÷ 4 = 11 remainder 27/4 = 6 remainder 3. The answer is 13273/47 = 13273.5.

1. Long division

2. How to divide any number by 9 ?
Before we proceed to understand this shortcut, we need to remember the reciprocals of 9.
Number Fraction Reciprocal
1
1/9
0.1111
Find 13 / 9
2
2/9
0.2222
3
3/9
0.3333
Step 1 : Here 13 is the dividend and 9 is the
4
4/9
0.4444
divisor. In this example, divisor has 1 digit. So,
5
5/9
0.5555
set 1 digit from right as reminder.
6
6/9
0.6666
7
7/9
0.7777
Step 2 : The quotient is the sum of the digits
8
8/9
0.8888
on left. In our case, it is 1. So, the quotient is 1.
9
9/9
1
Step 3 : The reminder is the sum of all the digits. So, the reminder is 1+3 = 4.
Dividend is a 2-digit number
So, the quotient is 1 and reminder is 4.
From the above table, 4/9 = 0.4444. So 13/9 = 1.4444

3. How to divide any number by 9 ?
• Find 36 / 9
• Step 1 : Here 36 is the dividend and 9 is
the divisor. In this example, divisor has 1
digit.
• So, set 1 digit from right as reminder.
• Step 2 : The quotient is the sum of the
digits on left. In our case, it is 3. So, the
quotient is 3.
• Step 3 : The reminder is the sum of all
the digits. So, the reminder is 3+6 = 9.
• If the remainder is equal or more than
9(divisor), it is carry forward to the
quotient just like in multiplication.
• So, the quotient is 3+1 =4 and reminder
is 9-9 = 0.
3 6
3 9
4 0

4. How to divide any number by 9 ?
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Can you solve the following :
89 / 9
97 / 9
91 / 9
96 / 9
8 9
1
9 08
8 17

5. How to divide any number by 9 ?
• Dividend is a 3-digit number or more
• When the dividend is a 3-digit number or more, there is a slight variation
in the division steps.
• Find 425 / 9
• Step 1 : Here 425 is the dividend and 9 is the divisor. In this example,
divisor has 1 digit.
• So, set 1 digit from right as reminder.
• Step 2 : The quotient is the successive sum of the digits on left i.e., 4/4+2
= 46
• Step 3 : The reminder is the sum of all the digits i.e., 4+2+5 = 11.
• Notice, that the reminder is greater than 9. If the remainder is equal or
more than 9(divisor), it is carry forward to the quotient just like in
multiplication.
• So, the quotient is 46+1 =47 and reminder is 11-9 = 2.
• So, 421 /9 = 47.222
•

6. How to divide any number by 9 ?
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Can you solve the following :
12389 / 9
933347 / 9
1931 / 9
3631 / 9

7. How to divide a number by 99 ?
Before we proceed to understand this shortcut, we need to remember the reciprocals of 99.
Number Fraction Reciprocal
1
1/99
0.010101
2
2/99
0.020202
…
…
…
9
9/99
0.090909
10
10/99
0.101010
13
13/99
0.131313
56
56/99
0.565656
78
78/99
0.787878
89
89/99
0.898989

8. How to divide a number by 99 ?
• Dividend is a 3-digit number
• Find 732 / 99.
• Step 1 : Here 732 is the dividend and 99 is the
divisor.
• In this example, divisor(99) has 2 digit.
• So, set 2 digit from right as reminder.
• Group the digits on the left into groups of 2.
• Step 2 : The quotient is just the digit on the left.
In our case, it is 7. So, the quotient is 7.
• Step 3 : The reminder is the sum of all the digits
taken 2 digits at a time. So, the reminder is 7+32
= 79.
• So, the quotient is 7 and reminder is 39.
• From the above table, 39/99 = 0.393939. So
732/99 = 7.393939

9. How to divide a number by 99 ?
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Find 498 / 99
Solution : Step 1 : Here 498 is the dividend and
99 is the divisor. In this example, divisor has 2
digit. So, set 2 digit from right as reminder.
Step 2 : The quotient is just the digit on the
left. In our case, it is 4. So, the quotient is 4.
Step 3 : The reminder is the sum of all the
digits taken 2 digits at a time. So, the reminder
is 4+98 = 102. If the remainder is equal or
more than 99(divisor), the difference is carry
forward to the quotient just like in
multiplication.
So, the quotient is 4+1 =5 and reminder is
102-99 = 3.
From the above table, 3/99 = 0.030303. So
498/99 = 5.030303.

10. How to divide a number by 99 ?
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Dividend is a 4-digit number
Find 5342 / 9
Solution : Step 1 : Here 5398 is the dividend and 99 is the
divisor.
In this example, divisor has 2 digit. So, set 2 digit from right
as reminder.
Step 2 : The quotient is just the digit on the left.
In our case, it is 53. So, the quotient is 53.
Step 3 : The reminder is the sum of all the digits taken 2
digits at a time.
So, the reminder is 53+98 = 151.
Since 151 is greater than 99(divisor), the difference is carry
forward to the quotient just like in multiplication.
So, the quotient is 53+1 =54 and reminder is 151-99 = 52.
From the above table, 52/99 = 0.525252 So 5392/99 =
54.5252

11. How to divide a number by 99 ?
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Can you solve the following :
898 / 99
2947 / 99
9451 / 99
9634 / 99

12. How to divide a number by 99 ?
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Dividend is a 5-DIGIT OR MORE
Example 4 : Find 777745 / 99
Solution : Step 1 : Since we are dividing the number
by 99(2 digit), set 2 digit from right as the
remainder. In our case it is 45.
Step 2 : The quotient is the successive sum taking 2digits at a time. So, the quotient was obtained by
taking the successive sum taking 1-digit on the right
at a time.
So, the quotient after the carry-forward is 7854.
Step 3 : The reminder is the sum of all the digits
taking 2-digits at a time.
i.e., 77 +77 + 45 = 199
Notice, that the reminder is greater than 99.
If the remainder is equal or more than 99(divisor),
the carry forward to the quotient is just like in
multiplication.
So, the quotient is 7854+2 =7856 and reminder is
199-99(2) = 1.
So, 777745 / 99 = 7856.0101

13. How to divide a number by 99 ?
• Find 3214675 / 99
Reminder = 115
So, the quotient is 32470+1 =32471 and reminder is 115-99 = 16.
So, 3214675 / 99 = 32471.161616

14. How to divide a number by 99 ?
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Can you solve the following :
4564564 / 99
679543 / 99
345346 / 99
45643 / 99

15. How to divide the number when the
divisor ends in digit 9?
• 87÷129 =?
• The first step is
to round the denominator
to the next digit.
Long Division Method Shortcut Technique

16. •
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Divide the following :
47/89
12/69
132/179
123/189

17. Divide 95÷159.
• Reduce 95÷159 as follows :
Now divide 9.5 by 16 like normal division,
instead of putting a zero in each step, you
replace it with the last quotient to continue
the division.

18. Divide 436÷159.
Reduce 436÷159 as follows :
Now, there is a small difference compared to
the previous 2 examples.
In the previous 2 examples, the numerator was
less than the denominator.
However, in this case, we have the numerator
which is greater than the denominator.
In this division, we need to add the quotient
with the rest of the digit (6) and put this digit
next to the reminder.

19. Divide 3462÷179.
Notice that numerator is greater
than the denominator.
There is a slight variation
compared to the previous example
Notice the carry-forward in step 2
of the division. So, therefore,

20. •
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Divide the following :
4347/149
1222/239
1349/179
2323/249

21. Divisors are different from 9’s but Close to TEN
7
1
1
9
3
17
2
1
8
3
3
0
–14
5
3

22. Divisors are different from 9’s but Close to TEN
7
8
6
3
24
90
0
93
11
0
93
+1
3
–91
12
3
2
3
8
3

23. Divisors are different from 99 but Close to 100
87
878
4
122
0
4
854
88
488
4
222
2
4
4
244
6
466
2
13
59
26
2
85

24. LONG DIVISION

25. 5
4
2
4
2
4
3
20
7
1
6
7
6
9
1
3
2
7
3
5
7 ÷ 5 = 1 remainder 2.
Put down the 7 and carry over the 4
Put the quotient 1, the first digit of the solution, 46 - 4 x 7 = 18 and then 18 ÷ 5 = 3 remainder 3.
in the first box of the bottom row and carry over Put down the 3 and carry over the 3
the remainder 2
39 - 4 x 3 = 27. Since the decimal point is reached
The product of the flagged number (4) and the
here, 27 is the raw remainder.
previous quotient (1) must be subtracted from
If decimal places are required, the division can
the next number (21) before the division can
proceed as before, filling the original number
proceed. 21 - 4 x 1 = 17. Then 17 ÷ 5 = 3
with zeros after the decimal point 27 ÷ 5 = 5
remainder 2.
remainder 2.
Put down the 3 and carry over the 2
Put down the 5 (after the decimal point) and
Again subtract the product of the flagged number carry over the 2
(4) and the previous quotient (3), 26 - 4 x 3 = 14 20 - 4 x 5 = 0. There is nothing left to divide, so
and then 14 ÷ 5 = 2 remainder 4. Put down the 2 this cleanly completes the division
and carry over the 4
Hence the answer is 13273.5
47 - 4 x 2 = 39 and then 39 ÷ 5 = 7 remainder 4.

26. Remarks: In the first step we have written that 4 ÷ 4 = 0 remainder 4 instead of 4 ÷ 4 = 1
remainder 0. Otherwise, in the following step, we would have to subtract 7*1=7 from 05
which is not possible.
45026 ÷ 47 4= 4958.0 4.
÷ = 0 remainder
4 9 7
5
4 5 0 2
6
Put the quotient 0, the first digit
of the solution, in the first box of
0
9
5
8
0 the bottom row and carry over the
Again subtract the product of the
remainder 4
flagged number (7) and the previous
The product of the flagged
quotient (9), 90 - 7 x 9 = 27 and then 27
number (7) and the previous
÷ 4 = 5 remainder 7.
quotient (0) must be subtracted
Put down the quotient 5 and carry
over the remainder 7.
from the next number (45) before
72 - 7 x 5 = 37 and then 37 ÷ 4 = 8
the division can proceed.
remainder 5.
45 - 7 x 0 = 45 and then 45 ÷ 4 = 9
Put down the quotient 8 and carry
remainder 9.
over the remainder 5.
Put down the quotient 9 and carry
56 - 7 x 8 = 0. There is nothing left to
divide, so this cleanly completes the
over the remainder 9.
47
division.
Hence the answer is 958.

27. To divide 716769 by 156:
Split divisor as 15 and 6
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------ 11
17
12
156 71
6
7
6
----- 4
5
9
4
Answer: 4594.673
12
15
9
6
9
0
7
0
3

28. 5
4
2
4
2
4
3
20
7
1
6
7
6
9
1
3
2
7
3
5
7 ÷ 5 = 1 remainder 2.
Put down the 7 and carry over the 4
Put the quotient 1, the first digit of the solution, 46 - 4 x 7 = 18 and then 18 ÷ 5 = 3 remainder 3.
in the first box of the bottom row and carry over Put down the 3 and carry over the 3
the remainder 2
39 - 4 x 3 = 27. Since the decimal point is reached
The product of the flagged number (4) and the
here, 27 is the raw remainder.
previous quotient (1) must be subtracted from
If decimal places are required, the division can
the next number (21) before the division can
proceed as before, filling the original number
proceed. 21 - 4 x 1 = 17. Then 17 ÷ 5 = 3
with zeros after the decimal point 27 ÷ 5 = 5
remainder 2.
remainder 2.
Put down the 3 and carry over the 2
Put down the 5 (after the decimal point) and
Again subtract the product of the flagged number carry over the 2
(4) and the previous quotient (3), 26 - 4 x 3 = 14 20 - 4 x 5 = 0. There is nothing left to divide, so
and then 14 ÷ 5 = 2 remainder 4. Put down the 2 this cleanly completes the division
and carry over the 4
Hence the answer is 13273.5
47 - 4 x 2 = 39 and then 39 ÷ 5 = 7 remainder 4.