How to divide any number by 9 ?


This is a very interesting mathematical shortcut. In this tutorial, we are going to see how to divide any number by 9 ? We will see how to obtain the quotient and the reminder when a number is divided by 9. The same concept can be used to find when the number is divided by 99, 999 or any series of 9’s. This Mathematical shortcut has its origin from Vedic Maths. We have already seen how to check how to multiply a given 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

2

2/9

0.2222

3

3/9

0.3333

4

4/9

0.4444

5

5/9

0.5555

6

6/9

0.6666

7

7/9

0.7777

8

8/9

0.8888

9

9/9

1

As you can see from the table, it is so easy to memorize the 9’s reciprocals of all the numbers from 1 to 9.

With this understanding, let us understand this mathematical shortcut with a simple example. To begin with, let us consider a 2-digit number.

Dividend is a 2-digit number

Example 1: Find 13 / 9

Solution : Step 1 : Here 13 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 1. So, the quotient is 1.

Step 3 : The reminder is the sum of all the digits. So, the reminder is 1+3 = 4.

So, the quotient is 1 and reminder is 4.

From the above table, 4/9 = 0.4444. So 13/9 = 1.4444


Example 2 :
Find 36 / 9

Solution : 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.

Very easy right 🙂

 

Try Yourself

Can you solve the following :

  1. 89 / 9
  2. 97 / 9
  3. 91 / 9
  4. 96 / 9


Dividend is a 3-digit number

When the dividend is a 3-digit number or more, there is a slight variation in the division steps. Let me explain considering an example.

Example 3 : Find 425 / 9

Solution : 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

 

Example 4 : Find 321 / 9

Solution :

Quotient = 3/3+2 = 35

Reminder = 3+2+1 = 6

So, 321 / 9 = 35.6666

 

Dividend is a 4 or More number


When the dividend is a number having 4 or more digits, the steps remains the same as explained in the shortcut to divide a 3-digit number by 9.

Let us consider an example.


Example 4 :
Find 63894 / 9

Solution : Step 1 : Since we are dividing the number by 9(1 digit), set 1 digit from right as reminder.

Step 2 : Quotient is the successive sum of the numbers on the left.

When the numbers are added, make sure that that carry’s are forwarded.

Step 3 : Reminder is obtained by obtaining the sum of all the digits.

Reminder = 6 + 3 + 8 + 9 + 4 = 30

Since, 30 is greater than 9, it is subtracted by 9 successively till it is less than 9 and the rest is carry forward.

So, Quotient = 7096 + 3 = 7099

Reminder = 3

So, 63894 / 9 = 7099.33333


Try Yourself

Can you solve the following :

  1. 12389 / 9
  2. 933347 / 9
  3. 1931 / 9
  4. 3631 / 9

 

I hope you find the tutorial very useful. Please leave a comment or contact me, if you have any doubts or any comments on this topic. I would be glad to answer.

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

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