Vedic mathematics

[bhushanm]

Hi guys i am starting new thread for vedic maths.
may help to speed up the calculation.
so i hope u people will find it useful.

[bhushanm]

multiply 2 numbers close to 100,1000,10000,etc

Step 1) First, we multiply the offsets 2 and 3
We get 6.
Since our base is 100, which has 2 zeros, the product of offsets must also have 2 digits. Hence we write 6 as 06 and write it down as last 2 digits of our answer.

98 -2
97 3
-------------------------
06

Step 2) Now for the previous digits, just add any 2 numbers in the above figure crosswise i.e. either (98-3) or (97-2)
We get 95. This is written before 06 as follows: -

98 -2
97 3
---------------------------
95 / 06

That gives us 9506. That s our answer.
Hence 98 x 97 = 9506

[bhushanm]

Multiply 888 by 998: -

888 -112
998 -002
---------------------------
886 / 224

Here, the base is 1000 i.e. offsets are differences from 1000

-112 x 002 = 224 ( Simple enough )

And 888 002 = 886
Hence, 888 x 998 = 886224

[bhushanm]

method
1.Square the last digit (keep the carry) _ _ X
2.Multiply the last digit by 4, add the carry _ X _
3.The first digit will be 4 plus the carry: X _ _



Example:
If the number to be squared is 24:

1. Square the last digit (keep the carry):
4 × 4 = 16 (keep 1) _ _ 6
2. Multiply the last digit by 4, add the carry:
4 × 4 = 16, 16 + 1 = 17 _ 7 _
3. The first digit will be 4 plus the carry:
4 (+ carry): 4 + 1 = 5 5 _ _


So 24 × 24 = 576.

if number is 29

1. 9*9 =81 _ _ 1
2. 4*9 = 36, 36 + 8 = 44 _ 41
3. 4+4 =8 841

so answer is 29*29=841

[indapamod]

Hey BhushanM....great going man, keep up the good work...Badly need tricks like these for the CAT level maths...BTW< u tried your hand at any exams this year??

Keep Rockin....

Originally Posted by bhushanm

method
1.Square the last digit (keep the carry) _ _ X
2.Multiply the last digit by 4, add the carry _ X _
3.The first digit will be 4 plus the carry: X _ _



Example:
If the number to be squared is 24:

1. Square the last digit (keep the carry):
4 × 4 = 16 (keep 1) _ _ 6
2. Multiply the last digit by 4, add the carry:
4 × 4 = 16, 16 + 1 = 17 _ 7 _
3. The first digit will be 4 plus the carry:
4 (+ carry): 4 + 1 = 5 5 _ _


So 24 × 24 = 576.

if number is 29

1. 9*9 =81 _ _ 1
2. 4*9 = 36, 36 + 8 = 44 _ 41
3. 4+4 =8 841

so answer is 29*29=841

[bhushanm]

1.Square the last digit (keep the carry) _ _ _ X
2.Multiply the last digit by 6, add the carry _ _ X _
3.The first digits will be 9 plus the carry: X X _ _

Example:
If the number to be squared is 34:

1.Square the last digit (keep the carry):
4 × 4 = 16 (keep 1) _ _ _ 6
2.Multiply the last digit by 6, add the carry:
6 × 4 = 24, 24 + 1 = 25 _ _ 5 _
3.The first digits will be 4 plus the carry:
9 (+ carry): 9 + 2 = 11 1 1 _ _

So 34 × 34 = 1156.


over 2 example of 20s and 30s we can gernralize....squaring part.

genralized one:

LET digit be XY
1. square the last digit i.e. Y
2. multiply the last digit with 2X plus carry
3. add (square of X) plus carry



so guys u can easily sqaure 2 digit numbers.......so have fun....
in next mail i will talk abt 3 digits numbers.

till then
if u have any problem ...mail me...

[purple yogi]

25 * 35
in this case when ever the unit digit is same (5) and the tens digits are continous (2, 3) the product will always end in 75 and the fukk would be the square of the higher number (3) -1 .. complicated dont worry .. so the answer here is 875 --- 3^2-1=8

45*55 = 2475
75*85= 6375

have fun guys more to come

[bhushanm]

Originally Posted by purple yogi

25 * 35
in this case when ever the unit digit is same (5) and the tens digits are continous (2, 3) the product will always end in 75 and the fukk would be the square of the higher number (3) -1 .. complicated dont worry .. so the answer here is 875 --- 3^2-1=8

45*55 = 2475
75*85= 6375

have fun guys more to come

it will always....good...if we keep a generalize method....ur method is good to eliminate options.
keep mailing buddy.....

[bhushanm]

Question: Multiply 432 by 617.
Answer:
432
x 617
_______
3024
432
2592
_______
266544



the shortcut

More the number of digits in the numbers, more lines and time you consume. No more! Using the Sutra "Vertically and Crosswise", you have
Step 1 (mentally, don't write on notebook) : vertically (last digits) :
2x7=14; write 4 carry 1
Step 2 (mentally) : crosswise (last two digits) :
3x7 +2x1 = 23 +carry 1 = 24; write 4 carry 2
Step 3 : vertically and crosswise (three digits) :
4x7 + 3x1 +2x6 = 43 +carry 2 = 45; write 5 carry 4
Step 4 : (move left; first two digits) :
4x1 +3x6 = 22 +carry 4 = 26; write 6 carry 2
Step 5 : (move left; first digit of each number) :
4x6 = 24 +carry 2 = 26. End.
Write answer : 266544


No matter how big the numbers are, you will need to write only the final answer. All other steps are easily carried out mentally. If the two numbers have different number of digits, write smaller number below the other and pad it on left side with zeros. The theory behind above example is :

ax² +bx +c
dx² +ex +f
_____________________________________
adx4 +(ae+bd)x³ +(af+be+cd)x² +(bf+ce)x +cf

Observe that coefficient of x0 (units digit) is cf, which is obtained by multiplying last two coefficients (vertically). The coefficient of x1 (tens digit) is bf+ce, which is obtained by crosswise multiplication of last two coefficients. The coefficient of x² (hundreds digit) is af+be+cd, which is obtained by crosswise and vertical multiplication of last three coefficients. Now as all coefficients are used up, we leave last coefficients and use the remaining, and so on.

[bhushanm]

Method for multiplying numbers where the first figures are the same and the last figures add up to 10.

32 x 38 = 1216

Both numbers here start with 3 and the last
figures (2 and add up to 10.

So we just multiply 3 by 4 (the next number up)
to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to
get the last part of the answer.


ANOTHER EEXAMPLE

And 81 x 89 = 7209

8*9=72
1*9=09
SO ANSWER IS 7209