Multiply a number by 11

Multiplying a one digit number by 11, is easy. For example, 2 x 11 = 22. We just repeat the number back twice.

What if we have 1334 x 11? This strategy could help us to multiply any greater than 2 digits number by 11.



The best way to explain this strategy is by using examples.

Example 1: 243 x 11.

1. 2 _ _ 3   (3 digits - put extra 2 blanks in the middle)


2. 2 2+4 _ 3   (add the 1st 2 numbers)


3. 2 6 4+3 3   (add the last 2 numbers)


4. 2 6 7 3

Therefore, 243 x 11 = 2673

Example 2: 1435 x 11.

1. 1 _ _ _ 5  (4 digits - put extra 3 blanks in the middle)


2. 1 1+4 4+3 3+5 5 = 15785

Therefore, 1435 x 11 = 15785

Note:

If the addition of the 2 numbers would gives 2 digits number, add that number's left digit to the left digit of the original number.

Example 3: 99x 11.

Wrong: 99 x 11 = 9 9+9 9 = 9189

Note that 9 + 9 = 18 (a 2 digits number).

1. 9 _ 9


2. 9 9+9 9


3. 9 18 9 ---> 9 + 1 8 9


4. 1089

Example 4: 46 x 11.

46 x 11 = 4 4+6 6 = 4 10 6 = 4 +1 0 6 = 506

As a conclusion, to multiply a number by 11, add the digits of a 2 digits number, and place the sum between them. If the addition produce a more than 1 digit number, carry the tens column to the left.