Multiply any number with 11

 

In this tutorial, we are going to learn, how to multiply any number with 11.  The idea can be extended to any multiplication where one of the number consists of series of 1’s.

For example, this shortcut can be used to multiply the numbers such as 32 x 11, 352 x 111,  201432 x 11 etc.

Let’s say, we want to multiply 34 x 11. The whole steps can be illustrated in the following figure.

Step 1 :  First we write the right most digit i.e., 4 as it.

Step 2 :  Next we add the last digit 4 and the digit 3 in the left and write 7.

Step 3 :  Now we write the left most digit i.e., 3 as it which gives the final answer as 374.

 

multiplication_11_1

Similarly, can you multiply  45 x 11 ?

multiplication_11_2

Similarly, can you compute what is 68 x 11 ?

multiplication_11_3

 

Notice the changes in the steps. When we add the digits 6 and 8, it results in 14. However, we can keep only 1-digit. So we keep 4 and carry forward the 1. This 1 is added to the left most digit 6. So the answer would be 748.

 

On the similar lines, can you multiply ?

  • 84×11
  • 78×11
  • 56×11

Very easy right  🙂

 

Let us now consider a 3 or more digit number and see how to multiply such number by 11. Let us consider the multiplication 652×11.

The entire steps can be illustrated in the following figure.

 

multiplication_11_4

 

Step 1 :  First we write the right most digit i.e., 2 as it.

Step 2 :  Next we add the number 2 and add it to the number 5 in the left and write 7.

Step 3 :  Now we number 5 and add it to the left-most number 6.  This step is continued, till we do not have any more digits left. The sum 11 is a 2-digit number. However, we can keep only 1-digit. So we keep 1 and carry forward the 1. This 1 is added to the left most digit 6.

Step 4 :  Now we add the left most digit i.e., 6 with the carry 1 which gives the final answer as 7172.

 

Similarly, the following figure, illustrates, the multiplication of a 4-digit 3802 by 11.  Notice, how 2-digits are taken at a time and added.

 

multiplication_11_6

Very easy right 🙂

On the similar lines, can you multiply ?

  • 8432 x 11
  • 17843 x 11
  • 56333 x 11
  • 345555 x 11

 

Please contact me if some point in the tutorial is not clear. 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.

7 Comments

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