How to divide the number when the divisor ends in digit 9?


In this tutorial on Mathematical shortcuts, and over the course of next few articles, we will focus on division. Here, we will discuss how to divide the number when the divisor ends in digit 9.  This shortcut works when the denominator has a unit digit of 9. The traditional method of long division technique would often take long time. With time constraints in competitive examinations, this technique would not be advisable.

We will break the discussion into 2 parts. The second part of the discussion is here.

Let us understand the shortcut with an example. Consider this simple division 87÷129.

Step 1 : The first step is to round the denominator to the next digit. 

 Division-denominator-9


Step 2 :
This is where the division steps changes. Notice the division is similar to long division. When 87 is divided by 13, we get a quotient of 6 and a reminder of 9. In a long division method, you would put a zero in-front of 9 to continue the division.

However, when using this shortcut, instead of putting a zero, you would put the last quotient to continue the division.  Notice the difference between the long division on the left and the shortcut on the right.

Division-denominator-9-2 Division-denominator-9-1

Long Division Method

Shortcut Technique

Step 3 : This step is continued and at each step, the last quotient is added to the reminder to continue the division process.

Division-denominator-9-3

So, therefore, we have

Division-denominator-9-4
Notice that, it is much easier to divide a number from 13 than from 129.


Example 2 :
Let us consider another example. Divide 95÷159.

Solution : Step 1 :  Reduce 95÷159 as follows :

Division-denominator-9-5

 Step 2 : Now divide 9.5 by 16  like normal division, instead of putting a zero in each step, you replace it with the last quotient to continue the division.

Division-denominator-9-6

So therefore,

Division-denominator-9-7

Very easy right 🙂

Try yourself :


Divide the following :

  1. 47/89
  2. 12/69
  3. 132/179
  4. 123/189

I hope, you find this article very useful. If you have any doubts or have any comments concerning this tutorial, Please leave a comment or contact me. I would be glad to help.

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.

One Comment

Leave a Reply

Your email address will not be published. Required fields are marked *

Protected by WP Anti Spam