How to divide a number when the divisor ends in digit 8?


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. Here, we will discuss how to divide a number when the divisor ends in digit 8. This shortcut works only when the denominator has a unit digit of 8.

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 87÷128.

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

Division-denominator-8-1


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 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-8-2

Long Division Technique

Division-denominator-8-2

Shortcut Technique

Notice the first step, when 87/13, you get a quotient of 9 and reminder 6. In the second step, the reminder is appended to 9 to get 96 and add 6 to it.

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-8-5

 

So, Therefore,

Division-denominator-8-6

Notice that, it is much easier to divide a number from 13 than from 128. So, whenever the divisor ends in digit 8, it is easier to approximate it to next 10’th digit and divide the number using the above shortcut.

 

Example 2 : Let us consider another example. Divide 95÷158.

Solution : Step 1 :  Reduce 95÷158 as follows : 

Division-denominator-8-7


Step 2 :
Now divide 9.5 by 16  like normal division, instead of putting a zero in each step, the last quotient is appended to the reminder and the added to the resulting number to continue the division process as shown.

 

Division-denominator-8-8

So, therefore,

Division-denominator-8-9


Notice the carry-forward in the quotient. We have got a quotient of 10. However, we can keep only a single digit in the quotient and the rest of the digits are carry forward.

Very easy right 🙂

Try yourself :

Divide the following :

  1. 74/88
  2. 132/168
  3. 212/178
  4. 53/188
  5. 1/18

 

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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