Vedic Mathematics

INTRODUCTION

Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). According to his research all of mathematics is based on SIXTEEN SUTRA , or word-formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.

Perhaps the most striking feature of the Vedic system is its coherence. Instead of a hotch-potch of unrelated techniques the whole system is beautifully interrelated and unified: the general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. And these are all easily understood. This unifying quality is very satisfying, it makes mathematics easy and enjoyable and encourages innovation.

In the Vedic system 'difficult' problems or huge sums can often be solved immediately by the Vedic method. These striking and beautiful methods are just a part of a complete system of mathematics which is far more systematic than the modern 'system'. Vedic Mathematics manifests the coherent and unified structure of mathematics and the methods are complementary, direct and easy.

The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down). There are many advantages in using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one 'correct' method. This leads to more creative, interested and intelligent pupils.

Interest in the Vedic system is growing in education where mathematics teachers are looking for something better and finding the Vedic system is the answer. Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc.

But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the most refined and efficient mathematical system possible.

Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.

For example 1000 - 357 = 643
We simply take each figure in 357 from 9 and the last figure from 10.

So the answer is 1000 - 357 = 643

And thats all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
Similarly 10,000 - 1049 = 8951
For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 - 83 becomes 1000 - 083 = 917

Try some yourself:

1) 1000 - 777	=
2) 1000 - 283	=
3) 1000 - 505	=
4) 10,000 - 2345	=
5) 10000 - 9876	=
6) 10,000 - 1101	=
7) 100 - 57	=
8) 1000 - 57	=
9) 10,000 - 321	=
10) 10,000 - 38	=

Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.

Suppose you need 8 x 7
8 is 2 below 10 and 7 is 3 below 10.
Think of it like this:

The answer is 56.
The diagram below shows how you get it.

You subtract crosswise 8-3 or 7 - 2 to get 5,
the first figure of the answer.
And you multiply vertically: 2 x 3 to get 6,
the last figure of the answer.

That's all you do:

See how far the numbers are below 10, subtract one
number's deficiency from the other number, and
multiply the deficiencies together.
7 x 6 = 42

Here there is a carry: the 1 in the 12 goes over to make 3 into 4.

Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.

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.

You can imagine the sum set out like this:

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.

Try some:

1) 87
98 x

2) 88
97 x

3) 77
98 x

4) 93
96 x

5) 94
92 x

6) 64
99

7) 98
97 x

Multiplying numbers just over 100.

103 x 104 = 10712
The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),
and 12 is just 3 x 4.
Similarly 107 x 106 = 11342
107 + 6 = 113 and 7 x 6 = 42

Again, just for mental arithmetic

Try a few:

1) 102 x 107 =

1) 106 x 103 =

1) 104 x 104 =

4) 109 x 108 =

5) 101 x123 =

6) 103 x102 =

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