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Mathematics Made Easy – VI


by NS Murty  
Dear friends, I must apologize to you for this long break. Now let us start from where we left off. We were discussing about using both hands for calculations without making use of any calculator.
Recap
You might have already mastered it and even otherwise think it is not a problem. Now comes the vantage over calculator. Let us suppose we want products between 11x11s to 15x15s. Remember we skipped in between products 6x11s to 6x15s. I will come to it after this to make a point clear to you. So bear with me for few minutes. Now, let us turn to our problem of 11x 11s to 15x15s. As we have only ten fingers, and as we go up we associate larger values to each finger, correspondingly we have to change the values of fingers joined and below, as also the values of the free fingers. How we change is all that you need to pay your attention for. If you got it, the answer is very very simple. Just look. When we are multiplying figures from 6x6 to 10x 10, we started with values above 5 for each hand. Then the sum of these two is 10. so we assigned to the fingers joined and below them a value of 10. Now for values between 11x11 and 15 x15, we start giving to each finger on the right and left a value above 10. So what value should we give by analogy to the fingers joined and below them now? Right. 10+10= 20. And what about the values of free fingers? You must add 5 to the number of free fingers on the right as well as left. Let us do it by example. Example 1. Suppose you want 12x12 What you join? Example 2. Take for example 14x 12 Let us get back to the problem I left out deliberately. That is from 6x11s to 6x15s. In the cases I described above, the range of multiplication in both the hands is same. That means, we are assigning the same set of values, say from 6 to 10 or 11 to 15 for the fingers of both hands. There by they are evenly matched. But when you multiply 6 by 11, you have to take care while assigning values to the joined fingers and below them, and the free fingers. (Following the order that the order of multiplication that the left number is represented by the left hand and the right number by the right hand I am giving the following explanation.) Whenever a large number is multiplied by a small number, we can say that the large number is pulled down or the small number is pulled up. Applying the same thing, we assign the values as follows:
Let us do by example to be very clear. Example 3: Take for example 7x 13. As usual we join LR and RM. Example 4: 6x14 We join LL and RI. Image under license with Gettyimages.com 

13Aug2006  
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