Applications of Vedic Mathematics in Algebra

Contributed by:
Harshdeep Singh
This PDF contains :
1. Introduction,
2. Vedic Sutras for solving simultaneous equations,
2.2.Anurupye Sunyamanyat,
2.3. Anurupye Sunyamanyat,
3. Conclusion
1. Volume 02 Issue 11S November 2020
Special Issue of First International Conference on Advancements in Engineering & Technology
(ICAET- 2020)
Applications of Vedic mathematics in Algebra
Sarita Devi 1.
Department of Applied Sciences and Humanities, Pillai HOC college of Engineering and Technology,
Rasayani. Raigad, Navi Mumbai, Maharashtra,, India.
sarita2009devi @gmail.com1.
Vedic mathematics is an interesting, speedy, simple logical & integral part of our ancient Indian culture
using traditional mathematics, which finds its origin in our Vedas especially “Atharva Veda” and is
mainly based on 16 principles called “Sutras” & 13 Sub-Sutras. Applied to almost every branch of
mathematics. The interesting part in Vedic mathematics is, you can mostly check your calculation and
know whether you are right or wrong in few seconds and that makes it more enjoyable. Here, discuss
some applications of Vedic mathematics in one of its field i.e. Algebra and see how it saves a lot of time &
efforts in solving the problems.
Keywords: Sutras, Sub –Sutras, Algebra, Atharva.
of the sixteen Sutras can be found in the different
1. Introduction branches of mathematics viz. geometry, calculus,
The Vedas & Upaveda are unlimited storehouse arithmetic’s, trigonometry etc. and these Sutras
of knowledge, which were probed extensively by make all the mathematical calculations easy, fast
and this led to the development of the sixteen and error free, which in turn, makes mathematics
Sutras and thirteen Sub-Sutras. Therefore, more joyful & is a great confidence booster for
developed methods & techniques, elaborating the students who fear mathematics. No wonder then,
principles contained in these Sutras & Sub- Sutras that, this Vedic mathematics is being adopted by
is called Vedic mathematics. various professionals, scientists, taught in some of
the most prestigious institutes worldwide &
Sutras, which are basically single line phrases, especially students preparing for various big
is based on a rational way of thinking, which competitions, to achieve better performance.[1-4]
improves intuition, creativity and emphasizes
on development of our mental abilities, which is 2. Vedic Sutras for solving simultaneous equation
the bottom-line of the mastery, that is seen, in
Vedic Sutras for solving simultaneous equation are
mathematical geniuses of the present and the
past. The Sutras are correlated. A single
 Paravartya Yojayet
Sutra/Formula can be used to perform various
arithmetic calculation, all the basic calculations  Anurupye Sunyamanyat
can be done using different available methods,  Sankalana Vyavakalana-bhyam
and it isup to the students to choose the method
they find to be more comfortable. Applications
International Research Journal on Advanced Science Hub (IRJASH) 61
2. Volume 02 Issue 11S November 2020
Here is an example to understand the entire concept
by this simple diagrammatical structure.
Numerator of x Numerator of y Denominator
This method is applicable for all sorts of linear
simultaneous equations. A simple idea for
finding value of x, start with y – coefficient and
independent terms and cross multiply them in b1 c1 a1 b1
the forward direction, the sign between the two
cross multiplication is minus (-). For y, start with
the independent term and x – coefficient and
cross-multiply them in the backward direction.
The sign between the cross-multiplication result b2 c2 a2 b2
is minus (-). For the result of the denominator,
take the coefficient of variable only and cross-
multiply then in backward direction.
Here is an example to understand this concept.
Suppose, have the following set of simultaneous
equations: -
a1x + b1y = c1 Example 1: Simplify for x and y, 3x + 4y = 10;
a2x + b2y = c2 4x - 2y = - 16
In order to get the numerator of x , leave the
coefficient of x and write the coefficient of y and
the independent term and cross multiply them Coefficient of y Independent term
with a minus sign in between the cross product 4 10
in rightward direction as shown here:-[4-6]
b1 c1
-2 -16
b2 c2
= b1 c2 - b2c1 x=
Again, to get numerator of y, leave the
coefficient of y and take only the coefficient of x Coefficient of x Coefficient of y
and the independent term into consideration. As
know the sutra moves in a cyclic order, so start
with independent term first. Cross multiplication 3 4
of the independent term and coefficient of x will
give the numerator of y.
c1 a1
4 -2
c2 a2
International Research Journal on Advanced Science Hub (IRJASH) 62
3. Volume 02 Issue 11S November 2020
Independent Term Coefficient of x 2.3. Anurupye Sunyamanyat:
This sutra simply says: Addition and subtraction.
10 3 When there is coefficient of x in 1st equation is
equal to the coefficient of y in 2nd equation and
vice versa. This sutra works well. To understand
this here is an example:
-16 4
Example3: Solve for x andy.
Coefficient ofx Coefficient of y 1955x – 476y=2482 ….(A)
3 4 476x – 1955y=-49131 ….(B)
Adding (A) and (B), equation becomes,
2431x - 2431y = - 2431;
x – y=-1 ….(C)
x = -2, y = 4 Subtract (B) from (A):
1479x – 1479y = 7395;
2.2.Anurupye Sunyamanyat:
x + y=5 … (D)
This Vedic sutra says – Add (C) and (D), value of x = 2 subtract (D)
If one is in ratio, the other one is zero, it means from(C), value of y =3.
when the ratio of x or y is equal to that of 3. Conclusion
independent term, put the ratio of y or x = 0. To Therefore, while applying Vedic mathematics one can
understand here is an example: versatility in solving problems and at the same time,
this helps to decide on the best method possible in
Example 2: Simplify for x and y solving a particular type of problem. The beauty of
Vedic mathematics is in its inventiveness, which one
7x + 6y = 70; experiences while applying. As one can see in the
14x+13y above methods that with good practice of the Vedic
mathematics one can do time consuming complex
Problems far more easily and faster.
The ratio of coefficients of x is 1:2 which is equal References
to the ratio of the independent term. So according [1]. Jagadguru Swami Sri Bharati Krisna Tirthaji (1986),
to above sutra, we put y = 0 in either of the Vedic Mathematics or Sixteen Simple Sutras from
equations to get the value of x. the Vedas. Motilal Banarasidas, Varanasi(India).
[2]. Rajesh Kumar Thakur: Advanced Vedic
For y=0, 7x=70, x =10 Mathematics.
[3]. Goel, A. (2006), Learn and teach mathematics, New
For x=10 y = 0, is the solution Delhi: Authors Press, Scholarly Books.
[4]. Rajesh Kumar Thakur – The essentials of Vedic
[5]. J.T. Glover - Vedic mathematics for
schools Book2.
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