28 Nov 2010

Transpose and Apply

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Transpose and Apply is also known as " Parāvartya Yojayet".This method can be applied to solve Horner's process of Synthetic Division ( polynomial divisions ) and is useful in cases where the divisor consists of small digits.

Example :
Polynomial Divisions
x3+4x2+5x+1 by x-2
Here we have four terms of x3 , x2, x and an integer.We take each term separately and solve using four steps

Step 1 :
The x3 divided by x gives us x2 which is our first part of our result.
Result :
x2+......

Step 2:
x2 multiplied with -2 from (x-2)divider gives us the answer of -2x2.Now note that we have an integer of 4 in the above equation for x2.And so we add them together to get 6x2.Now divide this by x again ,we get answer 6x.
Result: 
x2 + 6x+.....

Step 3:
Now for the third term ,we take the result from step two and multiply it with the divider (-2) .We get the answer as 6x multiply -2 = -12x.We already have an co-efficient of   5 in the x -term and so adding them both ,we get 12+5 =17x.Now divide this by x again, we get answer 17.
Result :
x2 + 6x +17

Step 4:
Now the last term 17 from the above step  is multiplied by -2 .We get - 34 as answer.But we have 1 in the co-efficient and so adding them both we get 34+1 =35.This 35 is the Remainder.

Therefore for the polynomial equation  x3+4x2+5x+1 by  x-2 , we have
Quotient Q = x2 + 6x +17 and Remainder R =35

Note that the above method complements "All from nine and the last from ten", which is useful in divisions by large numbers.

This Sutra also has great use in dividing large Numbers by any number of digits .
Click here for its Continuation.


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12 Nov 2010

Predict the Gender of your baby

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What is the gender of my unborn baby? Is is wrong to know it before the baby is born. In countries like US and UK, it is fine to know the gender of your unborn baby and every parent has the right to know it in their 5th month Ultra-scan report.

In some countries like India, it is not permissible for good. But every mother likes to guess her baby - is it a prince or princess. We have our good old grandma or relatives guessing the sex of the baby, "Look at your bump! it must be a girl :)". Their guesses rely mainly with their experiences in human behavior and physical appearance of the mom-to-be. Here are some assumptions which is thought to be true. Why don't you try this to find out yourself?
Table to predict the gender of your Baby
predict baby gender

FOR A GIRL BABY
FOR A BOY BABY
Mum-to-be craving more sweet itemsMum-to-be craving cheese and red meat
The Mum's bump is big and noticeable from behindThe bump is small and not much noticeable
The Mom has lost her good looks The Mom is quite cheerful with her good-looks
The Mom has gained a lot of weight than beforeThe Mom has lost some weight than before
Mum-to-be sleep more on the Right side Mum-to-be sleep more on the Left side 
Spring and summer season favour GirlsFall - October and November favour Boys
Look at the mirror and your pupil don’t dilatesLook at the mirror and your pupil dilates
You are moody and are not much cheerfulYou are quite cheerful
Your baby moves activelyYour baby does not  move actively
You have thin,dull hair and your shin is softYou have full,shiny hair and your skin is dry
Chinese Chart to calculate the gender of your baby before or  after Conception.
Click the image to get a bigger picture.


predict baby gender

Disclaimer:
The above post is created just for awareness or planning your next birth of the child. It is believed to be 90% accurate and is a source of ancient knowledge. It can be used for the purpose for fun as well. Share it if you like it!



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9 Nov 2010

VERTICALLY AND CROSSWISE close to 100

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VERTICALLY AND CROSSWISE for multiplying numbers close to 100
Now let us see another simple form of vertically and crosswise method for numbers close to 100.This method will amuse you with its simplicity.


(a) For numbers below 100


Example 1 :  82 * 94
The above numbers are close to 100
82  is 18 below 100 and 94 is 6 below 100.

So,
82 +18
    \/
    /\
94 + 6
----------------

(82-6) or (94-18) / (6 * 18) ,now by multipying the right side and subracting the left side
76 / 108   ....76+1 / 08 ,by carrying over '1' since it is a two digit number

Therefore ,82 * 94 =7708

Example 2: 88 * 95

88 +12
95 + 5             ------> gives 100
-------------
(88-5)/(12 * 5)
83 / 60

Therefore, 88 * 95 =8360


(b) For numbers above 100 


Example 1: 102 * 105

102  - 2
105  - 5    ........> gives 100
---------------
(105+2) / 5 * 2   ...here we have to add the opposite numbers
107/10

Therefore,102 * 105 =10710

Example 2: 111 * 108

111 - 11
108 -  8.......> gives 100
-------------
(111+8)  / 11 * 8
119 /88
Therefore , 111 * 108 = 11988

More on Vertically and Crosswire along with the Grid Method

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4 Nov 2010

Vertically and Cross wise

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Vertically and cross wise Sutra : It is also called as  Urdhva – tiryagbhyam  which is the general formula applicable to all cases of multiplication and also in the division of a large number by another large number.

(a) Multiplication of two 2 small digit numbers.

Lets take two  numbers,say 15 x 23
Here start the multiplication from Right to Left
vedic maths
Step :1 
1   5
      |
2   3
------
 5 x 3 =15 ......keep the last digit  '5' and carry over '1'

Step 2:
1  5
  \/
  /\
2  3
-------
(1 x 3 ) + (2x5) = 3+10 =13

With carry over '1' from step 1 ,we get 13+1 =14.....keep the last digit '4' and carry over '1'

Step 3:
1  5
|
2  3
--------
1 x 2=2

With carry over '1' from step 2, we get 2+1=3

So our result from step 1 to step 3 = 345
Therefore, 15 x 23 =345

(b) Multiplication of two 2  large digit numbers

 With the number 72 x 88 ,We do all the above three steps from (a)

   7  2
   | \/ |
   | /\ |
   8  8
-------------
7x8 / ( (7x8)+(2x8)) / 2x8

56 / ( 56 +16) /16
56 / 72 / 16
 =  6336   , by keeping the last digits and carrying over the rest
Therefore, 72 x 88 = 6336

Algebric Proof :
(ax + b) (cx + d)  =  ac.x2 + adx + bcx + b.d
                            =  ac.x2 + (ad + bc)x + b.d

where in our example  15 x 23 , a=1 ,b=5 ,c=2,d=3
and so ac.x2 + (ad + bc)x + b.d = 2 x2  +13 x +15  where x=10 meaning the place value
                                                 =   345 
 by  keeping the last digits and carrying over the rest.

Now consider the multiplication of two 3 digit numbers.
Let the two numbers be (ax2 + bx + c) and (dx2 + ex + f). Note that x=10
Now the product is
                            ax2 + bx + c    multiply
                            dx2 + ex + f

          ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
         ad.x4+bd.x3+cd.x2+ae.x3+be.x2+ce.x+af.x2+bf.x+cf

=       ad.x4 + (bd + ae). x3 + (cd + be + af).x2 + (ce + bf)x + cf

From the above expression,  we see that we multiply from left to right as per the expression

Example :
Find the result of  234 x 615 ?

ad.x4 + (bd + ae). x3 + (cd + be + af).x2 + (ce + bf)x + cf  where  a= 2,b=3,c=4 and d=6 ,e=1,f=5

=2x6 +( 3x6 +2x1 ) +(4x6+3x1 +2x5) +(4x1+3x5)+ 4x5...lets keep X's outside
=12 +(18+2) +(24+3+10)+(4+15)+20
=12x4+20x3+ 37x2 +19x+20  ..inserting X's now

And so keeping the last digits and carrying over the rest, we get   143910

Therefore,  234 x 615 =143910

Nice ,as the proverb "Practicing keeps a Man perfect " ,practicing the above sutras makes your multiplication easier .Keep practicing..that's the Veda of Vedic Maths


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