Multiply any number with 1111

 

Before understanding this shortcut, you might find the following tutorial helpful :

• how to multiply any number with 11
  
• how to multiply any number with 111

In the tutorial on Mathematical Shortcuts, we learnt,  how to multiply any number with 11 and how to multiply any number with 111.  In this tutorial, we will learn how to multiply any number with 1111 and any number with a series of 1’s. Let me explain with a simple example. Let’s say we want to multiply the number 345 x 111.

Let’s understand the steps involved.

 

 

Step 1:  First step, remains the same. We write the right most digit i.e., 2 as it is.

Step 2:  Next we start from the right and take the last 2-digits, 3 and 2 and we write 5.

Step 3:  Next we start from the right and take the last 3-digits, 6, 3 and 2 which gives us 11. So we write 1 and carry forward 1.

Step 4:  Since we are multiplying the number with 1111, in this step we need to take the last 4-digits at once and add them. So we need to add the digits, 4, 6, 3 and 2 which gives us 15. Add the carry-forward 1 from the previous addition.  So we write 6 and carry forward 1.  This step is continued till we no-longer have 4 digits to add.

Step 5 :  Since we do not have any more 4 digits to add, we will add the first 3-digits 4, 6 and 3 which gives us 13. Add the carry-forward 1 from the previous addition. So we write 4 and 1 is carry forward.

Step 6 :  We add the first 2-digits along with the carry forward from the previous addition which gives us 11.

Step 7 :  This is the last step. We write the left most digit i.e., 4 as it is the only digit left. This along the carry will give us 5.

Can you multiply 210432 x 1111 ?

 

The steps are illustrated in the figure.

 

 

Can you try multiplying 32 x 1111?

Notice that the number of digits in the number is 2( less the number of digits in 1111). In order that this shortcut works, the minimum number of digits should be same as in 1111. So, we append a 00 in 32  before we use this shortcut.

 

Very easy right 🙂

On the similar lines, can you multiply?

• 239959 x 1111
• 3999 x 1111
• 467 x 1111
• 33 x  1111

 

Multiplication with 11111 and other series of 1’s

So, the idea is,

• Starting from the right most digit, you take one-digit at a time and and them.
• You continue this process, till the number of digits is same as the number of 1’s.
• Continue this process, till you no longer have the digits as the number of 1’s
• Now, add the remaining digits till the left most digit.
• At every stage, make sure that you keep 1 digit in the answer and the rest of the digit is carry-forward.
• If the number of digits is less than the number of 1’s, then add 0’s to the beginning so that the number of digits is equal the number of 1’s.

 

Exercise : Can you multiply?

• 93939393 x 11111
• 3999 x 111111
• 4627 x 111111
• 22233 x  11111

 

Please leave a comment, if you have some doubts concerning this tutorial. I would be glad to help.