As a child i used to do multiplication through this method. Now i want to understand the logic behind its working. Help! please As a child i used to do multiplication through this method. Now i want to understand the logic behind its working. Help! please
As you can see from the image, i lined numbers and subtract them from their nearest 10th number and multiply the difference and add the original numbers put them together and cancel the first digit. it worked always but how?
!http://i.imgur.com/ct1kami.jpg?1

It is quite simple. 
Let we have two numbers. Say, $a$ and $b$.
Now, comsider the product - 
 $(100-a)(100-b)$ ...[We are considering this product because firstly you have subtracted given two numbers from 100.]
Now, $(100-a)(100-b) = 10000-100b-100a+ab$
In the above expression, we only want $ab$[We want to find product of numbers $a$ and $b$]
So, we have to subtract $10000-100b-100a$ from above expression to get final result $ab$.
Now, subtracting $10000-100b-100a$ means adding $-10000+100b+100a=-10000+100(a+b)$ in the expression . Note that you put $a+b$ in the hundread's place which means to add $100(a+b) $ in the expression,  and removed $1$ from last, which means to subtract $10000$ from the expression.
