DECODING HINDUISM--Vedic math

Sanatan Dharma scriptures cover almost all the topics under the sun from Astrolonomy to Astrology , Science to Aeronautics ,Mathematics etc.Let us discuss about Ancient Vedic Mathematics techniques .

Vedic Mathematics : 'Vedic Mathematics' is the name given to the ancient system of mathematics, or, to be precise, a unique technique of calculations based on simple rules and principles, with which any mathematical problem - be it arithmetic, algebra, geometry or trigonometry - can be solved, hold your breath, orally!
Sutras: Natural Formulae

The system is based on 16 Vedic sutras or aphorisms, which are actually word-formulae describing natural ways of solving a whole range of mathematical problems.

Here are some of the techniques :

1) 75^2 = 5625

The answer is in two parts: 56 and 25.
The last part is always 25.
The first part is the first number, 7, multiplied by the number "one more", which is 8:
so 7 x 8 = 56

2)To Xply any number (should be more than 5*5)

Suppose you want to multiply 88 by 98.
Not easy,you might think. But with
VERTICALLY AND CROSSWISE you can give
the answer immediately, using the same method
as above.

Both 88 and 98 are close to 100.
88 is 12 below 100 and 98 is 2 below 100.

As before the 86 comes from
subtracting crosswise: 88 - 2 = 86
(or 98 - 12 = 86: you can subtract
either way, you will always get
the same answer).
And the 24 in the answer is
just 12 x 2: you multiply vertically.
So 88 x 98 = 8624
This is so easy it is just mental arithmetic.

3)Paravartya Yojayet Method to find Quotient and Remainder :

'Paravartya – Yojayet' means 'transpose and apply'

(i) Consider the division by divisors of more than one digit, and when the
divisors are slightly greater than powers of 10.
Example 1 : Divide 1225 by 12.
Step 1 : (From left to right ) write the Divisor leaving the first digit, write the
other digit or digits using negative (-) sign and place them below the divisor
as shown.
12
-2
‾‾‾‾
Step 2 : Write down the dividend to the right. Set apart the last digit for the
remainder.
42
i.e.,, 12 122 5
- 2
Step 3 : Write the 1st digit below the horizontal line drawn under
thedividend. Multiply the digit by –2, write the product below the 2nd digit
and add.
i.e.,, 12 122 5
-2 -2
‾‾‾‾‾ ‾‾‾‾
10
Since 1 x –2 = -2and 2 + (-2) = 0
Step 4 : We get second digits’ sum as ‘0’. Multiply the second digits’ sum
thus obtained by –2 and writes the product under 3rd digit and add.
12 122 5
- 2 -20
‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾
102 5
Step 5 : Continue the process to the last digit.
i.e., 12 122 5
- 2 -20 -4
‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾
102 1

Step 6: The sum of the last digit is the Remainder and the result to its left is
Quotient.
Thus Q = 102 andR = 1