Brain Exercise Through Mental Maths - Multiplying by 11

Using pen and paper, this would not be too difficult.  However, trying to do it in the head, you may find it hard to align the numbers as you do it on paper.

For a two-digit number, the idea is simply to add the 2 digits and place the answer in the middle. Example:  32 x 11  >   3 + 2 = 5 >  place 5 in the middle  >  352.

It gets a little more tricky if there is a carry-over from the sum.  Example:  67 x 11  >  6 + 7 = 13.  In such cases, you have to add 1 to the digit on the left and place the unit digit of the sum in the middle like before.  In the example, you add 1 to 6 and you place 3 in the middle, to arrive at the answer 763.

This method can be extended to any number of digits, by repeating the process of adding two adjacent digits starting from the left and placing the result next to the left digit.  Example:  123 x 11 >  1+ 2 = 3, 2 +3 = 5 > result = 1355.  With carry-overs, you add 1 to the number on the left as before.  Example: 678 x 11  >  6 + 7 = 13 >  add 1 to 6 to give 7 as the first digit of the answer and 3 as the 'interim' second digit,  >  7 + 8 = 15  > add 1 to the interim second digit (3) and that gives you 4 for the second digit and 5 as the next digit >  final answer = 7458.

The description may sound complicated, but as you do it yourself for different numbers, you will find that you will be able to arrive at the answer almost instantaneously.  The fact that you have to look ahead for carry-overs will exercise your brain to be more alert.  This 'look ahead' exercise will also prepare your brain for more exercises to come.

Now, you can exercise on your own.  Do try longer numbers.  As you do, you will come across combinations of numbers that force you to look two steps ahead.  Examples are given below:

456 x 11
637 x 11
2729 x 11

Next, we will explore more combinations of numbers using 'multiplying by 11' approach....