can u tell me some tricks to calculate faster from vedic maths ?

Question

vedic maths is an ancient technique of calculating developed in india to calculate faster

Answer 1

Vedic mathematics is a system of mental calculation developed by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja in the middle 20th century which he claimed he had based on sutras he had found in an appendix of Atharvaveda, an ancient text of the Indian teachings known as the Vedas. He stated that these sutras only appeared in his personal copy of the appendix and not in the generally known appendices; his general editor noted that the style of language of the sutras "point to their discovery by Shri Swamiji himself".

It has some similarities to the Trachtenberg system in that it speeds up some arithmetic calculations. It has applications to more advanced mathematics, such as calculus and linear algebra. The system was first published in the book Vedic Mathematics ISBN 81-208-0164-4 in 1965. The system has since been developed further and there have been several other books released. Tirthaji claims in the book to have authored 16 volumes, one on each Sutra, and that they were subsequently lost in a fire in 1956.[1]

The system is based upon sixteen formulas and their corollaries, some of which are described below.

Contents [hide]
1 Sutras
1.1 Subsutras
2 All from nine and the last from ten
2.1 Corollary
3 By one more than the one before
3.1 Method 1: Using multiplication
3.2 Method 2: Using division
4 Multiplying by 11
5 Vertically and crosswise
6 Transpose and apply
7 When the samuccaya is the same, that samuccaya is zero
8 If one is in ratio, the other one is zero
9 Criticism
10 External links



[edit] Sutras
By one more than the one before
All from 9 and the last from 10
Vertically and crosswise
Transpose and apply
If the Samuccaya is the same it is zero
If one is in ratio the other is zero
By addition and by subtraction
By the completion or non-completion
Differential calculus
By the deficiency
Specific and general
The remainders by the last digit
The ultimate and twice the penultimate
By one less than the one before
The product of the sum
All the multipliers

[edit] Subsutras
Proportionately
The remainder remains constant
The first by the first and the last by the last
For 7 the multiplicand is 143
By osculation
Lessen by the deficiency
Whatever the deficiency lessen by that amount and set up the square of the deficiency
Last Totalling 10
Only the last terms
The sum of the products
By alternative elimination and retention
By mere observation
The product of the sum is the sum of the products
On the flag

[edit] All from nine and the last from ten
If you want to subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321.


[edit] Corollary
"Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency"

For instance, in computing the square of 9 we go through the following steps:

The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base.
Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer.
On the right hand side put the square of the deficiency that is 12. Hence the answer is 81.
Similarly, 82 = 64, 72 = 49.
For numbers above 10, instead of looking at the deficit we look at the surplus. For example:





and so on.
This is based on the fact that a2 = (a + b)(a − b) + b2.


[edit] By one more than the one before
"Eka Dikena Parvesam" is the Sanskirt term for "One more than the previous one". It provides a simple way of calculating values like 1/x9 (e.g 1/19, 1/29, etc). Let's take one 1/x9 and calculate. e.g., 1/19. In this case, x=1. The method is to write that x, then multiply it by 2 and keep that digit to its left. If the result of the multiplication is greater than 10, keep (value - 10) and keep the "1" as "carry over" which you'll add to the next digit.

The preposition "by" means the operations this formula concerns are either multiplication or division. [In case of addition/subtraction proposition "to" or "from" is used.] Thus this formula is used for either multiplication or division. It turns out that it is applicable in both operations.


Note: This applies to multiplication of numbers with the same first digit and the sum of their last unit digits is 10.


An interesting application of this formula is in computing squares of numbers ending in five. Consider:

35 × 35 = ((3 × 3) + 3),25 = 12,25
125 x 125 = ((12 x 12) + 12),25 = 156,25
The latter portion is multiplied by itself (5 by 5) and the previous portion is square of first digit or first two digit (3x3) or (12x12) and adding the same digit in that figure (3or12) resulting in the answer 1225.

This is a simple application of (a + b)2 = a2 + 2ab + b2 when a = 10c and b = 5, i.e.


It can also be applied in multiplications when the last digit is not 5 but the sum of the last digits is the base (10) and the previous parts are the same. Consider:

37 × 33 = (3 × 4),7 × 3 = 12,21
29 × 21 = (2 × 3),9 × 1 = 6,09
This uses (a + b)(a − b) = a2 − b2 twice combined with the previous result to produce:

(10c + 5 + d)(10c + 5 − d) = (10c + 5)2 − d2 = 100c(c + 1) + 25 − d2 = 100c(c + 1) + (5 + d)(5 − d).
We illustrate this formula by its application to conversion of fractions into their equivalent decimal form. Consider fraction 1/19. Using this formula, this can be converted into a decimal form in a single step. This can be done by applying the formula for either a multiplication or division operation, thus yielding two methods.


[edit] Method 1: Using multiplication
1/19, since 19 is not divisible by 2 or 5, the fractional result is a purely circulating decimal. (If the denominator contains only factors 2 and 5 is a purely non-circulating decimal, else it is a mixture of the two.) Each factor of 2 or 5 or 10 in the denominalor gives one fixed decimal digit.

So we start with the last digit

1
Multiply this by "one more", that is, 2 (this is the "key" digit from Ekadhikena)

21
Multiplying 2 by 2, followed by multiplying 4 by 2

421 → 8421
Now, multiplying 8 by 2, sixteen

68421
1 ← carry
multiplying 6 by 2 is 12 plus 1 carry gives 13

368421
1 ← carry
Continuing

7368421 → 47368421 → 947368421
1
Now we have 9 digits of the answer. There are a total of 18 digits (= denominator − numerator) in the answer computed by complementing the lower half (with its complement from nine):

052631578
947368421
Thus the result is 1/19 = 0.052631578,947368421 repeating.

1
21
421
8421
68421 (carry 1) - we got 16, so we keep 6 and carry 1
368421 (carry 1) - we get 6*2 + carry 1 = 13, so we keep 3 and carry one

do this to eighteen digits (19-1. If you picked up 1/29,
you'll have to do it till 28 digits). You'll get the following
1/19 = 052631578947368421
10100111101011000

Run this on your favorite calculator and check the result!

[edit] Method 2: Using division
The earlier process can also be done using division instead of multiplication. We divide 1 by 2, answer is 0 with remainder 1

.0
Next 10 divided by 2 is five

.05
Next 5 divided by 2 is 2 with remainder 1

.052
next 12 (remainder,2) divided by 2 is 6

.0526
and so on.

As another example, consider 1/7, this same as 7/49 which as last digit of the denominator as 9. The previous digit is 4, by one more is 5. So we multiply (or divide) by 5, that is,

...7 => 57 => 857 => 2857 => 42857 => 142857 => .142,857 (stop after 7 − 1 digits)

3 2 4 1 2

[edit] Multiplying by 11
11*35= 385

(1) The five in the ones place of the answer is taken from the five in 35.
(2) The eight in the answer is the sum of 35 (3+5=8).
(3) The three in the hundreds place of the answer is taken from the three in 35.
However, if in step #2 the sum is greater than 9, the sum's left digit is added the the first digit of the number multiplied by 11. For example:

11*59= 649

(1) The nine in the ones place of the answer is take from the nine in 59
(2) The four in the answer is the right digit in the sum of 59 (5+9=14)
(3) The six in the hundreds place of the answer is take from the sum of the five in 59 and the digit in the tens place from the sum of 59 (5+9=14) --> (5+1=6)

[edit] Vertically and crosswise
This formula applies to all cases of multiplication and is very useful in division of one large number by another large number.

For example, to multiply 23 by 12:

2 3
| × |
1 2
2×1 2×2+3×1 3×2
2 7 6
So 23×12=276.

When any of these calculations exceeds 9 then a carry is required.

This is just (10a+b)(10c+d)=100ac+10(ad+bc)+bd.

Video of a simple multiplication


[edit] Transpose and apply
This formula complements "all from nine and the last from ten", which is useful in divisions by large numbers. This formula is useful in cases where the divisor consists of small digits. This formula can be used to derive the Horner's process of Synthetic Division.


[edit] When the samuccaya is the same, that samuccaya is zero
This formula is useful in solution of several special types of equations that can be solved visually. The word samuccaya has various meanings in different applications. For instance, it may mean a term which occurs as a common factor in all the terms concerned. A simple example is equation "12x + 3x = 4x + 5x". Since "x" occurs as a common factor in all the terms, therefore, x = 0 is a solution. Another meaning may be that samuccaya is a product of independent terms. For instance, in (x + 7) (x + 9) = (x + 3) (x + 21), the samuccaya is 7 × 9 = 3 × 21, therefore, x = 0 is a solution. Another meaning is the sum of the denominators of two fractions having the same numerical numerator, for example: 1/ (2x − 1) + 1/ (3x − 1) = 0 means we may set the denominators equal to zero, 5x - 2 = 0.

Yet another meaning is "combination" or total. This is commonly used. For instance, if the sum of the numerators and the sum of denominators are the same then that sum is zero. Therefore,


Therefore, 4x + 16 = 0 or x = −4.

This meaning ("total") can also be applied in solving quadratic equations. The total meaning can not only imply sum but also subtraction. For instance when given N1/D1 = N2/D2, if N1 + N2 = D1 + D2 (as shown earlier) then this sum is zero. Mental cross multiplication reveals that the resulting equation is quadratic (the coefficients of x2 are different on the two sides). So, if N1 − D1 = N2 − D2 then that samuccaya is also zero. This yields the other root of a quadratic equation.

Yet interpretation of "total" is applied in multi-term RHS and LHS. For instance, consider


Here D1 + D2 = D3 + D4 = 2x − 16. Thus x = 8.

There are several other cases where samuccaya can be applied with great versatility. For instance "apparently cubic" or "biquadratic" equations can be easily solved as shown below:

(x − 3)3 + (x − 9)3 = 2(x − 6)3.
Note that x − 3 + x − 9 = 2 (x − 6). Therefore (x − 6) = 0 or x = 6.
This would not work for the apparently quadratic (x − 3)2 + (x − 9)2 = 2(x − 6)2, which has no real or complex solutions.

Consider


Observe: N1 + D1 = N2 + D2 = 2x + 8. Therefore, x = −4.

This formula has been extended further.


[edit] If one is in ratio, the other one is zero
This formula is often used to solve simultaneous linear equations which may involve big numbers. But these equations in special cases can be visually solved because of a certain ratio between the coefficients. Consider the following example:

6x + 7y = 8
19x + 14y = 16
Here the ratio of coefficients of y is same as that of the constant terms. Therefore, the "other" variable is zero, i.e., x = 0. Hence, mentally, the solution of the equations is x = 0 and y = 8/7.

(alternatively:

19x + 14y = 16 is equivalent to:
(19/2)x +7y = 8.
Thus it is obvious that x has to be zero, no ratio needed, just divide by 2!)

Note that it would not work if both had been "in ratio". For then we have the case of coinciding lines with an infinite number of solutions.:

6x + 7y = 8
12x + 14y = 16
This formula is easily applicable to more general cases with any number of variables. For instance

ax + by + cz = a
bx + cy + az = b
cx + ay + bz = c
which yields x = 1, y = 0, z = 0.

A corollary says solving "by addition and by subtraction." It is applicable in case of simultaneous linear equations where the x- and y-coefficients are interchanged. For instance:

45x − 23y = 113
23x − 45y = 91
By addition: 68x − 68 y = 204 => 68 (x − y) = 204 => x − y = 3.

By subtraction: 22x + 22y = 22 => 22 (x + y) = 22 => x + y = 1.


[edit] Criticism
Critics in India have questioned whether this subject deserves the name Vedic or indeed mathematics. They point to the lack of evidence of any sutras from the Vedic period consistent with the system, the inconsistency between the topics addressed by the system (such as decimal fractions) and the known mathematics of early India, the substantial extrapolations from a few words of a sutra to complex arithmetic, and the restriction of applications to convenient, special cases. They further say that such arithmetic as is sped up by application of the sutras can be performed on a computer or calculator anyway, making their knowledge rather irrelevant in the modern world.

They are also worried that it deflects attention from genuine achievements of ancient and modern Indian mathematics and mathematicians, and that its promotion by Hindu nationalists may damage mathematics education in India. [1]

Additionally, the promotion of Vedic Maths as advanced mathematics has drawn critisism from Mathematicians. Although quite useful for practical calculations in daily life, the tricks involved have no connection to higher mathematics or mathematical research and can be explained very simply

Answer 2

Vedic maths requires much practice. Here perhaps it can not be explained because if I want to explain I will have draw arrows or underline the number to show which action is done. Any how I will eplain some examples.
Multiplication by 99, 999, 9999 the center " | " line in the answer show the two parts of answer
e.g. 42 × 99 answer is (42 – 1) |(99–42–1) = 41 58
42 × 999 answer is (42 – 1) | (999 – 42 – 1) = 41 958
428 × 999 answer is (428 – 1) | (999 – 428–1) = 427 572
4287 × 9999 answer is (4287 – 1) | (9999 – 4287 – 1) = 4286 5713
Square of numbers nearer to 100
e.g. sq. of 108
108 = 100 + 8 | (108 + 8)× 100 = 11600 + sq of 8 = 64
Ans. is 116 64
square or 96
96 = 100 – 4
(96 – 2)× 100 = 9200
9200 + sq. of 4 = 9216
Cube of number nearer to 100
e.g. 108 = 100 + 8
100 + 8 × 3 = 124
124 × 10000 = 1240000 ------------------(1)
3 × 8^2 = 192, 192 × 100 = 19200 ----(2)
cube of 8 = 512 ------------------------------(3)
Add 1+2+3
Answer is 1259712
Multiplications two digit numbers
e.g. 23 × 67 the method is called as | X | method
| = 3 × 7 = 21 --------------(1)
X = (2 × 7 + 6 × 3)×10 = 320 -------(2)
I = 2 × 6)× 100 = 1200
Add 1200 + 320+ 21 = 1541
There are so many it is not possible to explain here.
One of the method called Ganesh method in this multiplication can be done by using square or rectangle and joining all diagonals in it then one number is written above the side and another number is written along the adjacent side. sorry it is not possible to explain it here
Is there any method of attaching a file to this answer ? so the answers can be explained eaisily by drawing properly.

Answer 3

VEDIC MATHEMATICS IS EASY WAY OF FINDING DIFFICULT CALCULATIONS.

YOU CAN FIND TRICKS AT:

http://vedicmathsindia.blogspot.com/
http://vedicganita.org
http://www.sanbrosonline.com/Vedic_Math.cfm?pt=2&vid=1163109728_1X02X2189
http://www.vedamu.org/Mathematics/course.asp
http://www.ourkarnataka.com/vedicm/vedicms.htm
http://www.vedicsociety.org/vedic-maths-t-5.html?osCsid=802862edf8

Answer 4

Namasthe Asker ji. A real politician should know the people's mind, and will work for the people's welfare and also they will see the welfare of the future generation. Now a days our political bosses are much concerned on votes and they least to bother about people or children's future. They will not think this even in their dreams. They are much worried about their family only. what the politicians do now ? They commercialised the educational institutions. They are running schools and colleges. They are the real estate owners in bogus names. They are taking road contracts in bogus names. No commercial people hitherto done these works have opportunity since all ministers are doing all the government works. This is slowly spreading from tamilnadu to other states. Tamilnadu once showed in Rajaji garu, kamaraj ji, and others like venktraman ji, c. subramanianji, and they keep people in mind and worked. The tamilnadu once showed and guided best ways to other states. Now also the status quo maintained, but in other way not good way is the general view by all. Now, the political bosses too keeping in mind only their family. How can you expect when they thinking about freebees to people and making them to put on expectations and also they now poised with vote for money. i disagree one point with you sir, even they did not do correctly the westernised education. Eppodi erundha namo eppadi oittom..

Answer 5

i will tell you how to calculate perfect squares from 30 to 70 easily

for every calculation 50 is the base.
for example,if we want to calculate square of 47.
first we need to see by how much is the given number is less than 50 that is 3
now subtract 3 from 25
that would give 22.keep it aside.
find 3 sqaure.it is 09
now mix both of them.
square of 45 is 2209.

if the number is greater than 50,say 57.
see by how much it is greater than 50,that is 7
add it to 25.that would give us 32.keep it aside.
square 7.it is 49.now combine both
therefore square of 57 is 3249.


its too easy!!!!!!!!!it's it!!!!!!!!!!!!!!

Answer 6

can u explain " The Remainder Remains Constant " of vedic maths subsutra 2
/very urgent

Answer 7

Very easy. If you an orkutter became member of " VEDIC MATHS" community, if not enroll. All your problems will be solved.

Answer 8

if you want to know more about vedic math read the article in www. wikipedia.org

Answer 9

you can find some useful tricks here
http://www.vedicmathstricks.com/

Answer 10

using ABACUS you can calculate faster than calculator

Answer 11

make a cross and pray for the best