Faster way to divide any number mentally by 9, 90, 900 and so on

The faster way to divide any number mentally by 9 is simply to reduce a complex division to a very simple addition. The technique follows the below steps:

Step-1:  Copy the first (left) digit from the dividend as it is and you have the first answer digit.

Step-2:   Add it to the next digit of the dividend and you have the 2^nd answer digit. Add this number to the next adjacent digit of the dividend and continue the step with the other digits. Write these numbers down as answer digit except the last set of digit(s) to get partial Quotient. Remember to add any carried numbers.

Step-3:   If last set of digits is = or >9; divide it by 9 and get the balance Quotient and final Remainder.

Step-4:   Add the partial and balance quotient to get the final quotient.

Here are some examples:

221013 ÷ 9 =?

Start putting the first (left) digit of the dividend as it is which is 2, and you have the first answer digit. ->2

The next one would be this answer digit plus the next digit of the dividend. So, 2 plus 2 is 4. ->2-4

The next answer digit would be this 4 plus 1 that is 5. ->2-4-5

Now, using the same logic, the next answer digit would be 5 plus 0, which is again 5. ->2-4-5-5

Next one would be 5 plus 1 that is 6. ->2-4-5-5-6

And then the last step would be 6 plus 3 that is 9. But do not write down 9, because this would be the remainder, if there is a remainder. In this case, there would be none, because 9 still goes 1 times in 9. This 1 would be added to the last findings i.e. 6 resulting 7. ->2-4-5-5-(6+1)

So, the answer would be 2-4-5-5-(6+1) that is 24557.

See the pattern?

So, 32142 ÷ 9 =?

The answer would be the first digit that is 3, ->3

3 plus the next digit 2 that is 5, ->3-5

5 plus the next digit 1 that is 6, ->3-5-6

6 plus the next digit 4 that is 10, now 10 is a 2 digit number so carry '1' (to be added with 6 making 7) and put 0 here. ->3-5-(6+1)-0

And 10 plus the last digit 2 would be 12, remember not to put 12 here. Now, 9 goes how many times in 12? Nine 1 times is 9. So, this 1 would be added to previous finding '0' and 3 is the remainder. ->3-5-(6+1)-(0+1)

So, the answer would be 3-5-(6+1)-(0+1) that is 3571 with 3 reminder.

8346425 ÷ 9 =?

The answer would be the first digit 8, ->8

8 plus 3 that is 11, put 1 and add 1 to the previous finding ->(8+1)-1

11 plus 4 that is 15, write 5 and add 1 to the previous finding ->(8+1)-(1+1)-5

15 plus 6 that is 21, write 1 and add 2 to previous finding ->(8+1)-(1+1)-(5+2)-1

21 plus 4 that is 25, write 5 and add 2 to previous finding ->(8+1)-(1+1)-(5+2)-(1+2)-5

25 plus 2 that is 27, write 7 and add 2 to the previous finding ->(8+1)-(1+1)-(5+2)-(1+2)-(5+2)-7

27 plus 5 that is 32. Now as it is the last digit, don’t write 27 down. See, 9 goes how many times in 32? Nine 3 times is 27 with 5 remainder. So, this 3 would be added to last finding that is 7 and 5 is the remainder. ->(8+1)-(1+1)-(5+2)-(1+2)-(5+2)-(7+3)

So, the answer would be ->(8+1)-(1+1)-(5+2)-(1+2)-(5+2)-(7+3)

that is 92737-10, Now again don’t write this 10 straightaway. 

Write ‘o’ and carry ‘1’ to add to previous finding that is 7 to get 8.

Therefore, the final answer is 927380 with a remainder of 5.

43967 ÷ 9 =?

Partial Quotient => 4, 7, 16, 22

=> 4, 7, (16+2), 2

=> 4, 7, 18, 2

=> 4, (7+1), 8, 2

=> 4, 8, 8, 2

Balance Quotient = 29/9 = 3, Remainder 2

Final Quotient = 4882 + 3 = 4885

Answer: Quotient 4885 Remainder 2

This way you can reduce a complex division to a very simple addition. And everyone is really very good at adding numbers.

For dividing by 90, shift the decimal point to 1 digit left and for dividing by 900, move the decimal point to 2 digits left after diving by 9 or following the above steps.