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.
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.
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:
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 |
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. |
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