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Mathematics Made Easy – III


by NS Murty  
Now let us move a bit further and find out the products of different numbers. Suppose you need to multiply 95 and 97 or 51 and 59 or 35 and 39 etc. We have a wonderful system in place which helps us find the product of any pair of multiplicands. Let us start with 95 and 97. The rule says that whenever you come across pairs of multiplicands like above, write the multiplicands one below the other and follow the procedure detailed below:
Yes. The process looks so long and cumbersome. But in reality it is damn easy and has a self check for the value obtained. Put 95 and 97 one over the other
The difference of the numbers with base looks like this:
You can see by cross adding the multiplicands and the differences, here 975=92 as also 953=92. Since we have taken 100 as base what we got this value is 100s. Then multiplying (5) and (3) we get 15. Thus the product of 95 and 97 is 9215. There is another interesting cross check. You add 95 and 97 and subtract 100 from it. You get 92. You add 5 and 3 the differences and subtract from 100, you still get 92. Thus when we take any base, remember clearly that the value we get in these operations is that many times the base we have chosen. So when you remember it you will make necessary adjustments to get 10s or 100s. Let us go to the second example: The process reads as follows: Take 50 as base. Write the given numbers 51 and 59 as follows:
and as already explained the 50 on the left side is 50s as such the real value in 10s is 50X5= 250 or 25 100s by adjustment . So the final value is 2500+ 09= 2509 Let us see one more: 35X39
Since the value 34 represents 40s the value in tens is 34X4 = 136 So the final value is 1365
Here base being 90, the value is (90X8 =720 in tens or 72 in hundreds) 7216
Since 120 is the base here the final value is (13X12 = 156 in hundreds) 15609 See this simple example:
Here no adjustment is necessary since 10 is the base. So 8x8= 64. Did you get it right? You see here another example;
Here gain no adjustment necessary since 10 is the base. What about this example?
You can clearly see that the product is 4 short of 10 square since 10 is our base. Hence the value is 100  4= 96. Now, do you get it right? 

16Apr2006  
Views: 8138  




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