Vedic Maths: World's Fastest Mental Arithmetic System | What is Vedic Maths

What is Vedic Mathematics?

Author: Anbazhagan Devaraj

Aug 01.2011
தமிழில் படிக்க (Read in Tamil)

Vedic Mathss or Vedic Mathematics is a collection of Methods or Sutras to solve numerical computations quickly and faster. It consists of 16 Sutras called Formulae and 13 sub-sutras called Sub Formulae, which can be applied to the solving of problems in arithmetic, algebra, geometry, calculus, conics, etc. All the sutras and sub sutras of Vedic maths help to perform mathematical operations quickly and accurately.

Vedic Maths Benefits

Help to increase concentration.
You will be able to calculate 10-15 times faster than before!
Develop your left and right brain through visualization and concentration abilities.
Have fun with math! Get rid of your math phobia.
Become a human calculator yourself!

The importance of Vedic Maths can be explained in various ways. The application of Vedic maths in the simplification of numerical problems is many times faster than the modern methods of calculations. Sometimes, this way of simplifying numerical calculations does not require paper and pen also. Thus, learning Vedic maths saves time and improves the interest in learning more applications of maths.

Vedic Maths Sutras

The sixteen sutras (word-formulas), and thirteen sub-sutras that constitute the foundation of Vedic mathematics each offer precise solutions for a variety of mathematical problems.These approaches are applicable to addition, subtraction, multiplication, and division, as well as other mathematical operations. Here are all the main Sutras (word-formulae) and sub-Sutras from Vedic Mathematics discussed below:

Vedic Maths Main Sutras

There are sixteen main sutras in Vedic Maths. These Vedic Maths Sutras are discussed below in the tabular form.

No	Sutras	Meaning	Uses
1	Ekadhikena Purvena	By one more than the one before	This Sutra simplifies squaring numbers close to base values
2	Nikhilam Navatashcaramam Dashatah	All from 9 and the last from 10.	A powerful technique for subtraction, especially useful when dealing with numbers close to multiples of 10.
3	Urdhva Tiryak	Vertically and Crosswise.	This Sutra streamlines multiplication, especially useful for multiplying large numbers.
4	Paraavartya Yojayet	Transpose and adjust	This technique aids in simplifying complex mathematical problems involving equations and variables.
5	Shunyam Saamyasamuccaye	When the sum is the same, that sum is zero.	An effective approach for solving algebraic equations with equal sums on both sides.
6	Anurupye Shunyamanyat	If one is in ratio, the other is zero	This Sutra is indispensable for solving proportionality problems.
7	Yavadunam Tavadunikritya Varga Samam	Whatever the extent of its deficiency, lessen that deficiency to form a square	Simplifies division and finding square roots.
8	Vilokanam	By mere observation	A technique that encourages quick, intuitive solutions based on patterns and observations.
9	Sankalana-vyavakalanabhyam	By addition and by subtraction	This Sutra offers techniques for both addition and subtraction, enabling quick calculations
10	Puranapuranabhyam	By the completion or non-completion.	This Sutra aids in finding fractions and complements, simplifying various mathematical operations.
11	Chalana-kalanabyham	Differences and Similarities	Useful for problems involving ratios and proportions
12	Yaavadunam	Partial Products	This Sutra facilitates the multiplication of large numbers by breaking them down into smaller, more manageable parts
13	Vestanam	Specific and General	This Sutra helps in solving problems where a specific value is derived from a general one
14	Yavadvividham Vyashtih	Separately the particular from the general	This Sutra is handy for finding individual components from a group
15	Samuccaye	Collective addition.	Useful for quick summations, especially when dealing with a series of numbers
16	Ekanyunena Purvena	By one less than the previous one	This Sutra provides a technique for division and helps in finding quotients efficiently

Sub-Sutras of Vedic Maths

Vedic maths tricks are also known as sub-sutras or corollaries. They are derived from the main sutras and provide additional methods or shortcuts to solve problems faster and easier. There are 13 sub sutras. These sub sutras are discussed below in the table.

No	Sutras	Meaning	Uses
1	Antyayordashakepi	The last digit remains the same	This sub-Sutra aids in quickly determining the last digit of a product.
2	Sopantyadvayamantyam	The last two of the last	Useful for solving problems where the last two digits are required.
3	Ekaadhikena Purvena	One more than the previous	This sub-Sutra extends the “Ekadhikena Purvena” technique for squaring numbers closer to the base
4	Paravartya Sutra	Transposition and adjustment	Helps in solving linear equations and balance problems
5	Calana-Kalanabhyam	Differences and Similarities	Offers additional methods for solving ratio and proportion problems.
6	Gunakasamuccayah	The product of the sum	Useful for solving problems involving the product of two sums.
7	Gunita Samuccayah	The product of the sum is the sum of products	Aids in simplifying algebraic expressions.
8	Yavadunam Tavatirekena Varga Yojayet	By one less than the one so much is the square	Provides an alternative approach for finding squares.
9	Antyayordasake’pi	The last digit is as it is	Useful for quick calculations involving the last digit of numbers
10	Antyayorekadhikaduhitayor	On the last two digits	Enables efficient calculations when focusing on the last two digits.
11	Ardhasamuccayah Samuccayoh	The sum of the half-sums is the sum	A technique for adding fractions with common denominators
12	Ekanyunena Sesena	One less than the one followed by the last	Facilitates quick division.
13	Sesanyankena Caramena	The last by the last, and the ultimate by one less than the last	A technique for division, especially when dealing with recurring decimals.