How to divide a number when the divisor ends in digit 1?


In this tutorial on Mathematical shortcuts, and over the course of next few articles, we will focus on division. In the previous tutorial, we saw how to divide a number when the divisor ends in digit 9 and digits ending in 8. Here, we will discuss how to divide a number when the divisor ends in digit 1.

Again, we will break the discussion into 2 parts. You can refer to the second part of the discussion here.

Let us understand the shortcut with an example. Consider the simple division 42÷131.

Step 1 : The first step, subtract both the numerator and the denominator by 1.

Division-denominator-1-1

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 subtract the last quotient from 9 and append the difference to the reminder to continue the division.  Notice the difference between the long division on the left and the shortcut on the right.

Division-denominator-1-2

Long Division Method

Division-denominator-1-2-1

Shortcut technique

 

Notice the first step, when 41/13, you get a quotient of 3 and reminder 3. In the second step, the difference ( 9 – quotient) is appended to reminder 2  to get 26.

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

Division-denominator-1-3

Division-denominator-1-5

Very easy right  🙂

 

Example 2 : Let us consider another example, Divide 234/241

Solution : Step 1 :  Reduce 234÷241 as follows :

 Division-denominator-1-6

 Step 2 : Now divide 23.3 by 24  like normal division, instead of putting a zero in each step, the last quotient is subtracted from 9 and is appended to the reminder to continue the division process as shown.

Division-denominator-1-7

Division-denominator-1-8

Try yourself :

Divide the following:

  1. 51/131
  2. 132/151
  3. 162/251
  4. 21/31
  5. 53/321

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.

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