Division by 9…

As we read earlier, 9 is a magic number.

And there must be something unique when we divide any number by 9. We are going to learn a method with which we can easily and quickly find the quotient and remainder in one line.

Let’s learn this with few examples. Example 1 and Example 2 covers simple examples and Example 3 covers special case where there are carries while finding the answers.

To find remainder:

Step 1: Find the digit sum of all digits of dividend. Digit Sum.

Remainder is this digit sum.

To find quotient : We move from left to right.

Step 1: The left most digit of quotient is the leftmost digit of dividend itself.

Step 2: The next right digit of quotient is the sum of above number in step 1 and 2nd next digit in dividend.

Repeat this pattern till you reach rightmost digit in dividend. The rightmost digit in dividend is not part of this pattern.

Example 1:

Example 2:

Example 3: Special Case – When there are carries:

This method can be extended to any length of number divided by 9.

Let us practice with more examples:

Divide the following by 9:

a. 74	b. 578	c. 764
d. 32	e. 45781	f. 456789999