Quick Eleven Times (II)


Let us try to find out 11 times of a number larger than the one considered in the last article. For example, we will now find out 11 times of 2314576. As a first step we will multiply 2314576 by 10. We get 23145760. Then we simply add 2314576 to 23145760. We will get the sum as 25460336. And this is the 11 times of 2314576. You may check the correctness of this answer by the method of direct multiplication.

Now we will examine the whole process once again with a view to make it more mechanical. When we examine the process our aim will be to avoid rewriting of any number, if possible or to avoid steps which require more mental work. This way we can shorten the time required for the whole calculation and also secure accuracy involved.

In the example above, as a first step we can simply add a 'zero' to the rightmost digit of the number to be multiplied by 11. This will give us 10 times the number, as a first step. Here we avoid complete writing of the number that is to be multiplied by 11. The next step involves addition of the two numbers, viz. ten times the number and the number itself. If you look at the vertical alignment of these two numbers you will realize that the nearby two digits get added. For example, the rightmost digit of the final sum (i.e. the digit in the unit's place) is obtained by adding 6 and 0. Thus in the unit's place we will have 6. The digit in the ten's place of the sum is obtained by adding the digits 7 and 6. In this case we get 13, a two-digit number. Obviously, we will be placing 3 in the ten's place and carry over 1 to the hundreds place, as we do in the case of normal addition. When you reach to the last digit, i.e. the leftmost, the addition is required only if there is a carryover from the earlier addition. Otherwise you have to just write down this digit as the leftmost digit of the final answer. You must not forget this! Look at the picture to the left-hand side.

All the above steps could now be linked with each other to make a smooth mechanically working pattern, as shown in the figure to the left.

Children are usually happy with the following kind of activities: