Multiplication by numbers 11-19

Multiplication by numbers 11-19

Here we will see how we can multiply any number of any digits by 11-19. The method we follow is called “adding to neighbor”. Let us see how to do it. We will start with 11 and move to 12,13 etc

Step 1. Multiply unit digit of the given number by 1

Step 2. Add unit digit value with its neighbor (ten digit value)

Step 3. Add ten digit value to its neighbor (hundred digit value)

When we reach a digit where the value is 0, we stop the process. We will take few examples for a better understanding.

Multiplication by 11 

63 x 11

1. 3x1 = 3

2. 3+6 = 9 (unit digit value is 3, added to ten digit value 6)

3. 6+0 = 6 (ten digit value is 6, added to hundred digit value which is 0 here).

Steps	Carry	Answer
3x1	0	3
3+6	0	9
6+0	0	6

Combining the steps, the answer is 693.

794 x 11

1. 4x1 = 4

2. 4+9 = 13 (3 will go for answer and 1 as carry to next step)

3. 9+7=16+1(carry from previous step) = 17 (7 goes to answer and 1 is carry to next step)

4. 7+0=7+1(carry from previous step)=8

Steps	Carry	Answer
4x1	0	4
4+9	1	3
9+7	1	7
7+0	0	8

Combining the steps, answer is 8734

I have used tables to explain the steps above for clarity. If we have understood the steps, then method can be done in one step as below.

We will move on to the number 12.

Multiplication by 12

While multiplying by 11, starting from right most digit(unit) we used to add a digit with its previous digit successively. For multiplying with 12, we follow the same method of ‘adding with neighbour’ but instead of adding directly, we multiply the neighbouring number by 2 and then keep adding. Let us see with examples.

 648x12

1. Multiply unit digit by 2, 8x2 = 16. (6 goes to answer and 1 is carried to next digit)

2. Multiply 4 by 2 and add to 8, 4x2+8=16+1=17(carry from previous step).

3. Multiply 6 by 2 and add to 4, 6x2+4=116+1=17

4. Multiply 0 by 2 and add to 6,0+6=6+1=7

The sequence is stopped when we reach a 0 place value.

Steps	Carry	Answer
8x2	1	6
4x2+8	1	7
6x2+4	1	7
0x2+6	0	7

Answer is 7776

75492x12

Multiplication by 13-19

The same method can be extended to multiplication by numbers 13 to 19, with the multiplying factor being 3 to 9 respectively. We will see few more examples.