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 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|