Vedic Mathematics

Vedic Mathematics is the name given to the ancient system of Indian 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 Sutras, 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.

Calculation At a very High speed and Mentally takes you almost half the way to your success in any competitive Exam.

 We start with

LESSONS ON SQUARING A NUMBER

We need to remember the squares of Numbers till 25,if you keep the squares in mind then you are capable to calculate the squares till 125 within seconds.

Q) Square of 42

What we do is ,we take the difference of 42 from 25 that is 17 and 42 is 8 less than 50 and square of 8 is 64,so the square of 42 is ( 1764),we just wrote 17 and 64 side by side and we get square or 42 that is 1764.

Q) Square of 72

In the numbers between 50-100,we find the difference of number from 100 that is in above case 28 ,we deduct 28 from 72 and get 44 and we know 28 square is 784 so the square will be (4 (4+7) 84)=(5184)

Q) Square of 125

In the numbers from 100 and above we find the difference of number from 100 that is 25 we add this to the number it becomes 150 then we add square of difference that is 25 square is 625 so the square is (15625) 

Q) Square of 45

In cases where ones digit is 5 in that case just take one more than the tens digit and write 5 square besides it like 45=(4*5) (5*5)=2025

                                    MULTIPLICATION OF A NUMBER FROM 11

Let Us say 52*11

To multiply 52 and 11,imagine there is a space between 52

52*11= 5_2 (Put an imaginary space in between)

Now,what to do with that space?

Just add 5 and 2 and put the result in the imaginary space

So, 52 * 11 =572 (which is your answer)

Isn't it great?

Lets try some more examples:

1) 35 * 11 = 3 (3+5) 5 = 385

2) 81 * 11 = 8 (8+1) 1 = 891

3) 72 * 11 = 7 (7+2) 2 = 792 

(Q) Is 456138 divisible by 9?

Now, it only takes 2 seconds for you to determine the answer.But if you go by the traditional way then it will take you 10 seconds.So you can see the difference.Those 8 extra seconds you win,you can spend on other question.Isn't it?

Now lets see the solution

(Answer) To test whether a certain large number is divisible by 9 or not,'just add all the digits of the number and if the end result is divisible by 9,then you can say that the entire large number will be divisible by 9 too'.

4+5+6+1+3+8=27

Now since 27 is divisible by 9 so 456138 will be divisible by 9 too.

Calculating Square of numbers quickly...

Lets calculate the square of 54

  

So (54)^2 = 5^2 +4 -- 4^2 = 25 +4 ----16 =29-------16= 2916

Similarly (55)^2 = 5^2 +5 --5^2=25+5------25=30---------25= 3025

Similarly (56)^2 = 5^2 + 6--6^2=25+6------36= 31--------36= 3136

Decimals Equivalents of Fractions

With a little practice, it's not hard to recall
the decimal equivalents of fractions up to 10/11!
First, there are 3 you should know already:
1/2 = .5
1/3 = .333...
1/4 = .25
Starting with the thirds, of which you already know one:
1/3 = .333...
2/3 = .666...
You also know 2 of the 4ths, as well, so there's only one new one to learn:
1/4 = .25
2/4 = 1/2 = .5
3/4 = .75
Fifths are very easy. Take the numerator (the number on top),
double it, and stick a decimal in front of it.
1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8
There are only two new decimal equivalents to learn with the 6ths:
1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...
What about 7ths? We'll come back to them
at the end. They're very unique.
8ths aren't that hard to learn, as they're just
smaller steps than 4ths. If you have trouble
with any of the 8ths, find the nearest 4th,
and add .125 if needed:
1/8 = .125
2/8 = 1/4 = .25
3/8 = .375
4/8 = 1/2 = .5
5/8 = .625
6/8 = 3/4 = .75
7/8 = .875
9ths are almost too easy:
1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...
10ths are very easy, as well.
Just put a decimal in front of the numerator:
1/10 = .1
2/10 = .2
3/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9
Remember how easy 9ths were? 11th are easy in a similar way,
assuming you know your multiples of 9:
1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...
As long as you can remember the pattern for each fraction, it is
quite simple to work out the decimal place as far as you want
or need to go!
Oh, I almost forgot! We haven't done 7ths yet, have we?
One-seventh is an interesting number:
1/7 = .142857142857142857...
For now, just think of one-seventh as: .142857
See if you notice any pattern in the 7ths:
1/7 = .142857...
2/7 = .285714...
3/7 = .428571...
4/7 = .571428...
5/7 = .714285...
6/7 = .857142...
Notice that the 6 digits in the 7ths ALWAYS stay in the same
order and the starting digit is the only thing that changes!
If you know your multiples of 14 up to 6, it isn't difficult to,
work out where to begin the decimal number. Look at this:
For 1/7, think "1 * 14", giving us .14 as the starting point.
For 2/7, think "2 * 14", giving us .28 as the starting point.
For 3/7, think "3 * 14", giving us .42 as the starting point.
For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:
For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.
Practice these, and you'll have the decimal equivalents of
everything from 1/2 to 10/11 at your finger tips!
If you want to demonstrate this skill to other people, and you know
your multiplication tables up to the hundreds for each number 1-9, then give them a
calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be
divided by a 1-digit number.
If they give you 96 divided by 7, for example, you can think,
"Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over.
So the answer is 13 and 5/7, or: 13.7142857!"