Mathematical trick: multiply by 11

Wednesday, January 13, 2010

To multiply a number by 11 and add enough pairs of numbers from right within the given number except the numbers on the edges that should be repeated.

For example:

consider the following product: 324 x 11

* From the right type 4 (the last number to the right of 324) first digit of the product;
* Try the sum 4 +2 = 6 (the sum of 1 'and 2' figure), you get the second digit of the product;
* Try the sum 3 +2 = 5 (the sum of the 2 'and 3' figure), you get the second digit of the product;
* Repeat 3, last number of the product.

Summing up (*):

(3) (3 +2) (4 +2) (4) = 3564

(*) Groups are not intended parentheses multiplied together

Now let's see what happens when the sum of two numbers exceeds the internal ten.

Consider the product:

967 x 11

* Begin to write from right to left, the first digit of the product is the 7;
* Sum 6 +7 = 13 write 3 (2 'figure of the product) and over 1;
9 +6 = 15 * sum added to the carryover of the amount above 15: 15 +1 = 16 writing 6 with carryover of 1;
* Last figure 9 we add the carry of the sum above 9 +1 = 10 which is the last digit of the product;

and therefore:

967 x 11 = 10637

Simple right?
With a little 'training can become very fast and impress your classmates :-)