All right, this is an interesting way of multiplication.
In this method, you create a new number system, based on a common number near to both the numbers we need to multiply.
1: So, for a multiplication of 103 * 102, I would take a base of 100.
103 +3
102 +2
105 06
103*102=10506.
The method is simplicity itself. The base used here is 100, so write the distance from 100, i.e. +3 and +2 respectively. Once done, cross-add. Since the base is the same, the number, and the distance of the second number from hundred is the same. 103+2=102+3=105. So write 105 down. Then multiply the numbers of the right handed column, 3*2= 6. I write it as 06, so it corresponds to the number system. Behold!! The answer!!!
2: The interesting thing is that we can take any base we need. Still, it’s probably better if we take a good base, like a multiple of 10. Therefore 1003*998=
1003 +3
998 -2
1001 -006
1000 994
1003*998= 1000994
Again it’s pretty simple. I write the base thing again. However, the slight twist here is my second part is negative. So, I add it to my base, (1000 in this case) and subtract one from the left hand side.
3: As I said before, its particularly better if we use a good base. That, however is unnecessary, since all numbers can be expressed as a multiple of 10. So 20= 10*2, 45=4.5*10, 3=0.3*10 and etc.
So 21*23
21 +1
23 +3
24 +3
48 +3
21*23=483.
Simply assume that you would make a base of 10, but write the distance as from 20. At the end of it all, multiply your left-hand side with your multiple (in this case 2) and there you go!!!
4: 26*23
26 +6
23 +3
29 18
58 18
59 8
It’s as simple as it can get. The twist is that the right hand side contains more digits than possible, so we use the carry on method, adding one to the left hand side to give us the answer.
23*29= 598.
5: The last one. 47*41
47 +2
41 -4
43 -8
193.5 -8
192.5 2
192 7
47*41= 1927
This one is almost completely useless, since it is actually much faster to just use the normal way. The base here could be taken as 40 or 50 even, to give a much easier solution. However, here, multiply by 4.5. Subtract one to make the right hand side positive. The last step is just that you take the number in the decimal place and add it to your right hand side.
Notes: The whole way of solving has a mathematical solution to it. So if you know it, then please mail me the proof. However, experimentally this method seems to work on everything I have tried. Again, if you spot any mistake, then please mail.
I found this method in a Vedic math book, containing the heading of vertically and crosswise.
Vertically and crosswise has a whole bunch of applications from multiplication and division to finding equations of a line, valuation of logarithms, exponentials, trigonometrical functions and solutions of simultaneous, transcendental, polynomial and differential equations.
No comments:
Post a Comment