dividing tricks
Dividing any number by 9:
To divide any two digit number by 9 , the first digit is the quotient. To find the remainder add the two digits. If it is less than 9 then the answer is the remainder. However if it is more than 9 then subtract 9 from the remainder and add 1 to the quotient.
For example;
If we have to divide 42 by 9, the first digit 4 is the quotient. To find the remainder add 4 and 2, which is 6. Hence the remainder is 6.
Now let us take another example where the two digits sum up to be more than 9. Let us try and divide 85 by 9. The first digit is 8 which is the quotient. To find the remainder add 8 and 5 which equals to 13. Now since 13 is greater than 9 we subtract 9 from it to get the actual remainder which is 4. And subsequently we also add 1 to the quotient which will now become 9. Hence when 85 is divided by 9 the quotient is 9 and the remainder is 4.
Here’s another example to understand this better. Let us divide 64 by 9. The first digit, 6 is the quotient. And the reminder will be 6+4=10. Now since 10 is greater than 9 we subtract 9 from it to get the real remainder. 10-9=1. The remainder is 1 and we add one to the quotient. Hence the quotient is 7.
Similarly for a three digit number, the first digit of the dividend will act as the first digit of the quotient and add the first two digits of the dividend to get the next digit of the quotient. Now add up all the three digits as usual to get the remainder and if the remainder is greater than 9 then subtract 9 from it to get the actual remainder and add 1 to the quotient.
For example we try and divide 504 by 9.
The first digit 5 will act as the first digit of the quotient as well. Now add the first two digits i.e. 5+0= 5. Hence the quotient is 55. To derive the remainder, add all the three digits i.e. 5+0+4= 9. Hence the remainder is 9.
Let us try another example. Divide 867 by 9.
The first digit of the dividend, 8, acts as the first digit of the quotient as well.
Add the next digit of the dividend to the first digit, 8+6 = 14.
Carry over 1 and add it to the first digit of the quotient.
Hence the quotient now is 94
The remainder is [8+6+7] = 21 since 21 is greater than 9 we subtract 9 from it to get the real remainder, which is 21-9=12.
We shall also add 1 to the quotient for the same.
Hence to summaries the answer, on dividing 876 with 9 ,the quotient obtained is 95 and the remainder is 12.