Multiplication of Numbers with a Series of 1’s

In this technique, we will see how to Multiplication of Numbers with a Series of 1’s. So, the multiplier will have numbers like 1, 11, 111, etc.

Let us begin with the multiplier 11

Ex-1. Multiply 72 by 11.
• In this example, first we write right-hand most digit 2 as it is. The answer at this stage is __2.
• Next, we add 2 to the number in left 7 (2+7 = 9) and write 9. The answer at this stage is _92.
• Last, we write the left hand most digit 7 as it is.
• So, the answer is 792.

Ex-2. Multiply 85 by 11.
• First we write right-hand most digit 5 as it is. The answer at this stage is __5.
• Next, we add 5 to the number in left 8 (5+8 = 13). Since 13 is a two-digit answer, we write down the 3 and carry over 1. The answer at this stage is _35.
• Now, left hand most digit 8, so we add carry 1 to 8 and make it (1+8) 9.
• The complete answer is 935.

Ex-3. Multiply 346 by 11.
The logic of 2-digit numbers can be expanded to a higher digit of numbers. Now, we have to multiply 346 by 11.
• We write right-hand most digit 6 as it is. The answer at this stage is ___6.
• Next, we add 6 to the number in the left 4 (6+4 = 10). Since 10 is a two-digit answer, we write down the 0 and carry over 1. The answer at this stage is __06.
• Next, we add 4 to the number in the left 3 (4+3 = 7). We get 7 and add carried over to make it (7+1) 8. The answer at this stage is _806.
• Last, we write the left hand most digit 3 as it is.
• The complete answer is 3806.

Similarly, When we multiply a number by 11 we write the last digit as it is. Then we move towards the left and continue to add 2-digits at a time till we reach the last digit which is written as it is. Since the multiplier 11 has two 1’s we add maximum 2-digits at a time. When the multiplier is 111 we will add maximum 3-digits at a time because the multiplier 111 has 3-digits. When the multiplier is 1111 we will add maximum 4-digits at a time since the multiplier 1111 has 4-digits and so on.
We have already seen how to multiply numbers by 11. Now we will see how to multiply numbers by 111.

Ex-4. Multiply 432 by 111.
• We write right-hand most digit 2 as it is. The answer at this stage is ____2.
• We move to the left and add 2 to the number in the left 3 (2+3 = 6). The answer at this stage is ___52.
• Next, we move to the left and add 4 to the number in the right 3 and 2 (4+3+2 = 9). The answer at this stage is __952. (Maximum 3 digits)
• We move to the left and add 3 to the number in the left 4 (3+4 = 7). The answer at this stage is _7952.
• Last, we write the left hand most digit 4 as it is.
• The complete answer is 47952.

Ex-5. Multiply 31232 by 111.
• We write right-hand most digit 2 as it is. The answer at this stage is ______2.
• We move to the left and add (2 + 3) and the answer at this stage is _____52.
• We move to the left and add (2 + 3 + 2) and the answer at this stage is ____752.
• We move to the left and add (3 + 2 + 1) and the answer at this stage is ___6752.
• We move to the left and add (2 + 1 + 3) and the answer at this stage is __66752. (Maximum 3 digits)
• We move to the left and add (1 + 3) and the answer at this stage is _466752.
• Last, we write the left hand most digit 3 as it is.
• The final answer is 3466752.

Ex-6. Multiply 21142 by 1111.
• We write right-hand most digit 2 as it is. The answer at this stage is _______2.
• We move to the left and add (2 + 4) and the answer at this stage is ______62.
• We move to the left and add (2 + 4 + 1) and the answer at this stage is _____762.
• We move to the left and add (2 + 4 + 1 + 1) and the answer at this stage is ____8762.
• We move to the left and add (4 + 1 + 1 + 2) and the answer at this stage is ___88762. (Maximum 4 digits)
• We move to the left and add (1 + 1 + 2) and the answer at this stage is __488762.
• We move to the left and add (1 + 2) and the answer at this stage is _3488762.
• Last, we write the left hand most digit 2 as it is.
• The final answer is 23488762.

This method is very simple as you see from the examples. In most cases, you will get the answer within a minute. In fact, this technique converts a process of multiplication to basic addition. Using this method, we can multiply any number by a series of 1’s.
In this method, we will add a maximum of 4 digits at a time (because there are four 1’s in 1111) and when the multiplier is 11111 we will be multiplying a maximum of 5 digits at a time. Now, if you any queries, please visit our YouTube Channel ‘Knowledge Gallery‘ and watch the detailed video.