Another example

So,here is another example of multiplications using strings of 1.
1 2 3 4 5 6 7 8 9* 1 1 1 1 1 [here we have 5 ones]

1 2 3 4 5 6 7 8 9
* 1 1 1 1 1
---------------------------------------------------------------------------------------------
9 [putting the LMD ]
7 [adding the two LMDs,8+9=17,put 7,carry1]
5 [7+8+9=24+1(carry)=25,put 5,carry 2]
2 [6+7+8+9+2(carry)=32,put 2 carry 3]
8 [5+6+7+8+9+3(carry)=38,put 8 carry 3]
3 [5 digits has been added,so leaving out 9 to take
4,4+5+6+7+8+3(carry)=33,put 3 carry]
8 [leaving 8 to take 3,3+4+5+6+7+3(carry)=28,put 8,
carry 2]
2 [2+3+4+5+6+2(carry)=22,put 2,carry 2]
7 [1+2+3+4+5+2(carry) =17,put 7,carry 1]
1 [1+2+3+4+1(carry)=11,put 1,carry 1]
7 [1+2+3+1(carry)=7]
3 [2+1=3]
1
----------------------------------------------------------------------
1371728382579

So,this is the method to multiply any number with a string of 1's.Try it.Bye.

Calculations Made Easy.....

This is a shortcut for doing mathematical calculations easily।These are in use for a long time.I am just trying to gather them here. For this particular piece thanks to my friends Gulu and Tanuja,who helped me to understand this.So,lets start.

1>To multiply any number with a number having all 1's(e.g. 11,111,1111 etc.)

i>Count the number of 1's
ii>Start from right.
Put the right-most digit(RMD) in the right-most place of the answer
iii>Add the two RMDs and put the sum in the left of the already present digit in the answer.
iv>Keep on doing this until you add the same number of RMDs present in the multiplier
v>When this has been achieved, start to lessen the digits to add one by one.
vi>Always add the carry to the next addition.

Perhaps you did understand.So, here is an example.

4 3 5 2
* 1 1 1
------------------
2 [RMD,so placing it without change]
7 [The two RMDs,5+2=7]
0 [The three RMDs,2+5+3=10,placing 0 and carrying 1]
3 [As the multiplier has three 1s,so we are adding only three digits at most,
5+3+4=12+1=13,1 was carried over,so 3 is placed and 1 is carried]
8 [Adding the two Left-most digits,4+3=7+1=8]
4 [The LMD is placed as it is]
---------------------
483072 [This is the answer]

Is it clear enough.I would give some more examples on comming days...till then practice hard.Bye and take care