Vedic Mathematics: 16 Sutras and 13 Sub-Sutras

Vedic Mathematics, which has its roots in the ancient Vedas, can be defined as mathematical calculation systems, re-discovered in the early 20th century by Swami Bharati Krishna Tirthaji (Between 1911 and 1918). This ancient-rooted system of mathematics originating in India is popular for how it simplifies arithmetic operations and problem-solving. It is foundational on the techniques of Veda, ancient Indian scriptures and focuses on methods of mental calculations making computations quicker and more efficient. This ancient wisdom-rooted mathematical technique is popular among students and mathematics enthusiasts for its methods of transforming complex and difficult computations or calculations into a simple and easy process.  Swami Bharati Krishna compiled his re-discovery in a book called Vedic Mathematics, which has garnered international attention and research. This article will break down the major components of Vedic Mathematics: sutras and sub-sutras (Word formulae and sub-formulae). 

Before we dissect the Sutras and Sub-sutras that make up Vedic mathematics, let us explore how this ancient-based system of calculation is beneficial in the modern era of advanced computation and also dig into its key features.

 

Features of Vedic Mathematics

Integrity: The 16 Sutras in Vedic maths are all interrelated to facilitate better understanding. A single sutra can be used for solving multiple arithmetic calculations by following one rule.

Simplicity: Vedic mathematics is known for its simplicity which allows the solving of complicated multiplication problems by using only one single and simple step. This simple feature makes it a unique method, which has allowed saving time and increasing productivity. 

Creativity: Vedic maths takes into consideration all the perception that needs creativity and stress on understanding that there are multiple ways to solve a problem, allowing students to find their unique approach to solving any problem. 

Quick and Accurate Result: Vedic maths emphasizes mental calculation as the main strategy. The simple calculation allows time saving, increased productivity and fewer steps to solve problems leading to a higher probability of accurate results. 

Intuitional Capability: Vedic maths is characterized by speed and accuracy, which in turn boost the confidence of the students and enable them to be more competent, optimizing their intuition abilities.

Enhance memory and concentration: The mental exercises from the mental calculations involving only a few steps enable students to memorize and remember the basics easily, This further improves the student's concentration and memory. 

Algebraic Connection: Students can easily apply this Vedic maths method of calculation in solving any algebraic problem. 

Extensive application: Vedic maths formulae (Sutras) are applicable across all areas of arithmetic operations including geometry, trigonometry, differential and integral, analytical astronomy, etc.

Innovative: Vedic mathematics has garnered global recognition and interest for further research. It also encourages students and researchers across the globe to add creativity and innovate more tricks and hacks similar to the formulas it presents. 

 

16 Sutras and 13 Sub-Sutras: Word Formulae

 

Vedic Maths comprises 16 main sutras (word formulae). Let us outline each one of them along with the meanings and uses

 

1. Ekadhikena Parvenu

  • Meaning: By one more than the earlier one
  • Uses: Use for simplifying squaring numbers near to base values

2. Nikhilam Navatashcaramam Dashatah

  • Meaning: All from 9 and the last from 10
  • Uses: Used in subtraction, particularly when solving numbers close to multiples of 10

3. Urdhva Tiryagbyham

Meaning: Vertically and crosswise

Uses: Used in simplifying large numbers multiplication

4. Paraavartya Yojayet

  • Meaning:Transpose and adjust
  • Uses: Simplifies complex mathematical calculations that involve equations and variables

5. Shunyam Saamyasamuccaye

  • Meaning: When the sum is the same that sum is zero
  • Uses:  Used in algebraic equations having equal sums on both sides.

6. Anurupye Shunyamanyat

  • Meaning: If one is in ratio, the other is zero
  • Uses: Used in solving proportionality problems.

7. Yavadunam Tavadunikritya Varga Samam

  • Meaning:Whatever the extent of its deficiency, lessen that deficiency to form a square (if a number is a little less than a base number, subtract the deficiency from the base to find its square and then squaring the deficiency)
  • Uses: Used in simplifying division and finding square roots.

8. Vilokanam

  • Meaning: By mere observation
  • Uses: Used in solving problems requiring quick, intuitive solutions depending on patterns and observations.

9.Sankalana-vyavakalanabhyam

  • Meaning: By addition and by subtraction/ differences or similarities
  • Uses: Used for quick calculations both in addition and subtraction

10. Puranapuranabhyam

  • Meaning: By addition and by subtraction
  • Uses: Used in finding fractions and complements

11. Chalana-kalanabyham

  • Meaning: Differences and Similarities
  • Uses: Used in solving problems that involve ratios and proportions

12. Yaavadunam

  • Meaning: Partial Products
  • Uses: Used in simplifying multiplication of large numbers by breaking down the numbers into smaller and manageable parts

13.Vestanam

  • Meaning: Specific and General
  • Uses:  Used in solving problems that require deriving a specific value from a general one

14. Yavadvividham Vyashtih

  • Meaning: Separately the particular from the general
  • Uses: Used in finding individual component from a group

15. Samuccaye

  • Meaning: Collective addition
  • Uses: Used in quick summations that involve series of numbers

16. Ekanyunena Purvena

  • Meaning: By one less than the previous one
  • Uses: Used in division and simplifies finding quotients efficiently

13 Sub- Sutras

The 13 Sub-sutras are also known as corollaries that are often used as maths tricks. These tricks/ corollaries are derived from the main formulas (sutras) and offers short-cut or additional methods that facilitate faster and easier calculations and solving of problems. Let us dig into the 13 sub-sutras or better known as Vedic Maths tricks and learn their meanings and uses.

 

1. Antyayordashakepi

  • Meanings: The last digit remains the same
  • Uses:  Used in quick determination of the last digit of a product.

2. Sopantyadvayamantyam

  • Meanings: The last two of the last
  • Uses: Used in solving problems that require the last two digits 

3. Ekaadhikena Purvena

  • Meanings: One more than the previous
  • Uses: Used in squaring numbers nearer to the base

4. Paravartya Sutra

  • Meanings: Transposition and adjustment
  • Uses:  Used in problems of linear equations and balance

5. Calana-Kalanabhyam

  • Meanings: Differences and Similarities
  • Uses: Additional formula for problems involving ratio and proportion 

6. Gunakasamuccayah

  • Meanings: The product of the sum
  • Uses: Used in solving problems with product of two sums.

7. Gunita Samuccayah

  • Meanings:  The product of the sum is the sum of products
  • Uses: Used in simplifying algebraic expressions.

8. Yavadunam Tavatirekena Varga Yojayet

  • Meanings: By one less than the one so much is the square
  • Uses: Alternative method for finding squares.

9. Antyayordasake'pi

  • Meanings: The last digit is as it is
  • Uses: For quick calculations with the last digit of numbers

10. Antyayorekadhikaduhitayor

  • Meanings: On the last two digits
  • Uses: For efficient calculations with focus on the last two digits.

11. Ardhasamuccayah Samuccayoh

  • Meanings: The sum of the half-sums is the sum
  • Uses: Method for adding fractions with common denominators

12. Ardhasamuccayah Samuccayoh

 

  • Meanings: One less than the one followed by the last
  • Uses: Facilitates quick division.

13. Sesanyankena Caramena

  • Meanings:  The last by the last, and the ultimate by one less than the last
  • Uses: Used in division, especially when involving recurring decimals.

 

Fun Facts of Vedic Maths

 

  • Vedic Maths has well-constructed 16 sutras and 13 sub-sutras that aid in solving any complicated arithmetic problems.
  • Vedic Maths has its origin in the Ancient Indian Vedas.
  • Only minimal effort is required in Vedic Maths for any calculations and problems.
  • Promotes the use of  both the left and right sides of the brain, further enhancing innovative and intuitive mental development and exceptional problem-solving abilities
  • Users can improve and use their creativity to use formulas as it comes with recognition for intuitional abilities 
  • Users can attain quick and accurate results with a simple process
  • Vedic Maths enhances concentration and memory power
  • Vedic Maths facilitates quicker calculations
  • Vedic Maths offers more accurate and efficient calculations
  • It minimizes the need to use of finger-counting
  • Vedic maths transforms dull, dry and tedious maths into an interesting and fun subject, attracting students and children to enjoy learning. 

 

Key Benefits of Vedic Maths

 

Makes learning Mathematics interesting and Fun: Vedic maths breaks the traditional perception of it being a challenging and stressful subject. It makes learning maths easy fun and interesting as it brings out the creativity, and playfulness with numbers, making it an enjoyable subject.  

Enhances Mental Agility: With its profound scope of creativity and mental calculations, this new way of calculations provides substantial aid in cognitive development. It improves brain function, promotes logical thinking and enhances concentration, memory power and mental agility. 

Enhancing Calculation Speed: Imagine having the ability to solve complicated arithmetical problems within seconds. You can build this ability with Vedic Maths. It is all about easy and quick calculations without the need to do finger counting or elaborate calculations. 

Applications Beyond the Classroom: Vedic Maths application is not only limited to scholastic learning and classrooms. The quick tricks can be applied in personal and professional scopes like banking, shopping, budgeting, etc. Vedic Maths is a vital tool for calculations and can be effectively used in professions like research, banking, engineering, etc. 

 

Conclusion

 

From building the potential to solve complicated calculations to improving your memory power and mental agility, Vedic Education (Vedic Maths) can be the modern solution to massive complicated arithmetical calculations. Using easy and simple Vedic Maths tricks can make your life easier and even help you build interest in a subject that is considered taxing and stressful. 

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