Vedic Mathematics is the mathematics of the ancient Vedic tradition of India. It has many definitions and many aspects, ranging from the governing intelligence of the universe to the familiar procedures of practical calculation.
Vedic Mathematics is an ancient knowledge comprising of 16 sutras or aphorisms related to Mathematics. This set of sutras was extracted from the Hindu Vedas which were written around 1500-900 BC. The founder of Vedic Mathematics was Swami Sri Bharati Krishna Tirthaji Maharaja, a Hindu scholar and mathematician.
It is also believed that this knowledge laid down the foundation of algorithm, square roots, algebra, the concept of zero and various methods of calculations. If you master all the Sutras or aphorisms in the vedic mathematics, you can solve any mathematical problem be it - arithmetic, algebra, geometry, or trigonometry and that too ORALLY !!.
The concept is very useful for all students who are 16 years and above and it will help them for competitive exams, which involve a mathematics paper, for example in solving the Maths section of the GMAT exam, as it speeds up problem solving and also helps to maintain accuracy thus saving time.
Let's see some very simple examples and compare them with traditional Mathematical techniques:
MULTIPLICATION
Obtaining the product of two 2-figure numbers
Using the Sutra Vertically and Crosswise we can multiply any two numbers together in one line using this general Vedic method.Suppose we want to multiply 45 by 63:
4            5
6            3
-------------------------
2     8      3     5
-------------------------
4     2
a) Vertically on the left, 4×6 = 24, write down 2 and carry 4 to the right.
b) Crosswise we get 4×3 + 5×6 = 42 (as before), add the carried 4, as 40, to get 82, write down 8 and carry the 2.
c) Finally, vertically on the right 5×3 = 15, add the carried 2, as 20, to get 35 which we write down.
We always add a zero to the carried figure as shown because the first product here, for example, is really 40×60 = 2400 and the 400 is 40 tens.
So when we are gathering up the tens we add on 40 more. This does not seem so strange when you realise that a similar thing occurs when calculating from right to left: in the first calculation above the first vertical product (on the right) was 15, and although the 1 in 15 stands for 10 it was counted as one unit in the next column.
The simple pattern used makes the method easy to remember and it is very satisfying to get the answer in one line. It is also easy to see why it works: the three steps find the number of units, the number of tens and the number of hundreds - and there, you have the answer!
Let us compare this with the usual method of ‘long multiplication’.
4            5
6            3
---------------------------
1       3     5
2      7       0
-------------------------
2       8     3     5
Here we have two lines of working before we get the answer. BUT, we also have to remember to put the zero down on the right on the second line and there is no memorable pattern as there is with the Vedic method.
These Vedic techniques can be extended to products of numbers of any size. The second method, from left to right, is useful for mental calculation because we write and pronounce numbers from left to right and so it is easier to get our answers the same way. Another advantage of calculating from left to right is that we may only want the first one, two or three figures of an answer, but working from the right we must do the whole sum and get the most significant figure last. In the Vedic system all arithmetic operations can be carried out from left to right and this means we can combine operations:
Obtain two products and sum them for example, or obtain two squares, sum them and take the square root. So we get answers digit by digit from left to right. We can extend this further to the calculation of sines, cosines, tangents and their inverses and the solution of polynomial and transcendental equations.