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    16 Sutras Of Vedic Math


    16 sutras of Vedic Math


    Emerging as a rich crucible of knowledge, India has etched a glorious legacy of intellectual progression that spans countless epochs. Integral to this vast academic tapestry is the science of mathematics, whose importance has been recognized and revered since the era of the ancient Vedas.

    This complex discipline has been tenaciously honed and refined over millennia, with each generation meticulously preserving, enhancing, and bequeathing this priceless repository of knowledge to the succeeding generation. This relentless dedication to mastering and propagating mathematical principles delineates India’s continual role as a thriving hub of intellectual exploration and academic discourse.

    Among the many mathematical contributions, Vedic mathematics stands out as a unique collection of efficient and expedient techniques for resolving mathematical arithmetic. This system is underpinned by 16 sutras or principles, each being a word formula encapsulating a natural approach to solving a broad spectrum of mathematical problems.

    The inception of this remarkable technique can be credited to the esteemed scholar Shri Bharathi Krishna Tirthaji Maharaj, a luminary in the realms of Sanskrit, Mathematics, History, and Philosophy. His transformative work imbues mathematical solutions with simplicity and speed, adding a fresh dimension to the discipline and reflecting the ingenious mathematical spirit of India.

    Below are the 16 Vedic Maths Sutras with brief explanations:

    1. Ekadhikena Purvena (One more than the previous one): This sutra is useful for cases where the number is close to the base, like 10, 100, 1000, etc. It is mainly used in finding squares of numbers near these bases.

    2. Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10): This sutra is helpful when you are subtracting a number from a large round number like 10, 100, 1000, etc.

    3. Urdhva-Tiryakbhyam (Vertically and crosswise): This sutra is useful for multiplication of numbers where the multipliers are more than the number 10. It can also be applied for the multiplication of numbers close to bases (10, 100, 1000, etc).

    4. Paravartya Yojayet (Transpose and adjust): This sutra is used in division. It makes any type of division simple.

    5. Shunyam Saamyasamuccaye (When the sum is the same that sum is zero): This sutra is used in solving simultaneous linear equations where the coefficients of the variables are the same. The sum (or, difference) of the coefficients in the variables of these equations is zero.

    6. Anurupye – Sunyamanyat (If one is in ratio, the other one is zero): Used in solving simultaneous linear equations, this sutra comes into play when the coefficients of one variable are in the same ratio to each other as the independent terms.

    7. Sankalana-vyavakalanabhyam (By addition and by subtraction): This sutra is used to solve a special type of simultaneous linear equations where the coefficients of ‘x’ and ‘y’ are interchanged.

    8. Purana Puranabhyam (By the completion or non-completion): When the given data is incomplete, this method helps us to find the complete data first and then solve the problem.

    9. Chalana-Kalanabhyam (Differences and Similarities): This sutra is mainly used for solving the problems where differentiation is involved.

    10. Yaavadunam (As much as the extend): This sutra is useful in the operations involving ‘0’. It helps in case of multiplication.

    11. Vyashtisamanstih (Part and Whole): This is applied to find the product of two numbers when one number is far away from the base. It is also useful in solving complex numbers and statistics.

    12. Shesanyankena Charamena (The remainders by the last digit): This one helps in finding the remainders of division problems. It’s used when we divide a number by 9.

    13. Sopaantyadvayamantyam (The ultimate and twice the penultimate): Applicable when the multiplication of numbers whose last digits together make 10 and the remaining digits are identical.

    14. Ekanyunena Purvena (One less than the previous one): This sutra is used for the multiplication of numbers whose last digits add up to 10 and the preceding numbers are the same.

    15. Gunitasamuchyah (The product of the sum is the sum of the product): This sutra is used in solving problems related to algebra and geometry.

    16. Gunakasamuchyah (The factor of the sum is the sum of the factor): This sutra can be applied in factorization and solving algebraic equations.

    Remember, these are the basic ideas for each sutra, but each one can be applied to various types of calculations depending on the specific situation and needs to be practiced to get a hold of.

    Learn Know About the Each Sutra in Detail: 

    1. Vedic Math Sutra 1- Ekadhikena Purvena
    2. Vedic Math Sutra 2- Nikhilam Navatashcaramam Dashatah
    3. Vedic Math Sutra 3– Urdhava – Tiryagbyham
    4. Vedic Math Sutra 4- Paravartya Yojayet 
    5. Vedic Math Sutra 5- Sūnyaṁ Samyāsamuccaya
    6. Vedic Math Sutra 6- Anurupye
    7. Vedic Math Sutra 7- Urdhava- Saṅkalana Vyavakalanābhyāṃ
    8. Vedic Math Sutra 8- Puranapuranabhyam 
    9. Vedic Math Sutra 9- Chalana-Kalanabhyam
    10. Vedic Math Sutra 10- Yavadunam
    11. Vedic Math Sutra 11- Vyastisamastih
    12. Vedic Math Sutra 12- Sesanyankena Caramena
    13. Vedic Math Sutra 13– Sopantyadvayamantyam 
    14. Vedic Math Sutra 14- Ekanyunena Purvena 
    15. Vedi Math Sutra 15- Gunitasamuccayah 
    16. Vedic Math Sutra 16– Gunakasamuccayah

               sixteen sutras of Vedic Math

    The concept of Vedic Math is based on sixteen sutras. So, we list all sixteen sutras with their meaning and uses in the table below.

    S.No. Sutras Name Meaning Where to use
    Sutra 1 Ekadhikina Purvena By one more than the previous one Squaring of a number ending with 5
    Sutra 2 Nikhilam Navatashcaramam Dashatah All from 9 and the last from 10 Multiplication of numbers, which are near to base like 10, 100, 1000
    Sutra 3 Urdhva-Tiryagbyham Vertically and crosswise It is the general formula, applicable to all cases of multiplication of two large numbers
    Sutra 4 Paraavartya Yojayet Transpose and adjust When the divisor greater than 10
    Sutra 5 Shunyam Saamyasamuccaye When the sum is the same that sum is zero If there is a common term in the equation and the sum of the equation is 0 then the common term can be equated to 0
    Sutra 6 Anurupyena- Sunyamanyat If one is in ratio, the other is zero To find out the product of two number when both are near the common base like 40, 40, etc. (multiples of powers of 10).
    Sutra 7 Sankalana-Vyavakalanabhyam By addition and by subtraction It is used to solve simultaneous simple equations which have the coefficient of the variables interchanged.
    Sutra 8 Puranapuranabyham By the completion or Non- completion Used to simplify or solve algebra problems.
    Sutra 9 Chalana-Kalanabyham Differences and Similarities To find the roots of a quadratic and to factorize expressions of the 3rd, 4th, and 5th degrees.
    Sutra 10 Yaavadunam Whatever the extent of its deficiency Applicable to obtain sq. of a number close to bases of powers of 10
    Sutra 11 Vyashtisamanstih Part and Whole Help in the factorization of the quadratic equation of types
    Sutra 12 Shesanyankena Charamena The remainders by the last digit It is to express a fraction as a decimal to all its decimal places
    Sutra 13 Sopaantyadvayamantyam The ultimate and twice the penultimate -
    Sutra 14 Ekanyunena Purvena By one less than the previous one This sutra is used in case of multiplication by 9, 99…
    Sutra 15 Gunitasamuchyah The product of the sum is equal to the sum of the product -
    Sutra 16 Gunakasamuchyah The factors of the sum are equal to the sum of the factors Used in the factorization of cubics, biquadratics

    We have tried to summarize all the invaluable sutras of Vedic Math in the simplest way possible. We hope the table above will help you solve complex problems in seconds and assist you in speed calculations. 

    Moonpreneur understands the needs and demands this rapidly changing technological world is bringing with it for our kids. Our expert-designed Advanced Math course for grades 3rd, 4th, 5th, and 6th will help your child develop math skills with hands-on lessons, excite them to learn, and help them build real-life applications. 

    Register for a free 60-minute Advanced Math Workshop today!

    Update: This article was last updated on 31st July 2023 to reflect the accuracy and up-to-date information on the page.

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    Moonpreneur is an ed-tech company that imparts tech entrepreneurship to children aged 7 to 16. Its flagship offering, the Innovator Program, offers students a holistic learning experience that blends Technical Skills, Power Skills, and Entrepreneurial Skills with streams such as Robotics, Game Development, App Development, Advanced Math, and Book Writing & Publishing.
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    1 year ago

    Is Vedic math faster than Abacus?

    1 year ago
    Reply to  SarcasticSam

    It depends on the level of expertise and training. My son finds Vedic Math more intuitive and faster than Abacus.

    1 year ago

    I want to enroll my 5 year old daughter in vedic math class, am I rushing? What do you suggest?

    1 year ago
    Reply to  Murphy

    Basic Vedic Maths techniques can be introduced in early elementary school to kids ages 6-8.

    1 year ago

    Is speed math and Vedic math the same?

    1 year ago
    Reply to  Florence

    Vedic math and speed math have similarities but separate from one another. Vedic math is a specific system based on ancient Indian mathematics, focused on mental calculation methods and effective problem-solving approaches. Speed math is a general word for techniques to complete calculations quickly.

    1 year ago

    Vedic math is a rubbish concept as there are many drawbacks like limited applicability to advanced mathematics, lack of conceptual understanding, different from standardized methods, questionable historical origins, and its emphasis on speed over accuracy in calculations.

    1 year ago

    What was your experience like if you attempted to use these sutras in your own mathematical investigations?

    1 year ago
    Reply to  Olivia

    Vedic mathematics has left behind a long-lasting legacy of efficient problem-solving techniques with its sixteen sutras. Even though I haven’t utilized these sutras much in my mathematical research, I am aware of their advantages for mental math. They are a great resource for the mathematical community because they encourage creativity in mathematics and make complex problems easier to understand.

    1 year ago

    Could you provide an example of how to use “Ekanyunena Purvena” to quickly calculate the square of a number that is close to a base, like 98 squared, and explain the steps involved?

    1 year ago
    Reply to  Abigail

    The Vedic mathematics sutra “Ekanyunena Purvena ” is a useful tool for quickly calculating the square of a number that is close to a base, like 10, 100, or 1000. Let’s use square 98 as an example using this sutra:
    Start with the base, which is 100 in this case. We’ll start with 100 because 98 is two less than that number. Find the difference between the number (98) and the base (100) (98 – 100 = -2). The square of the difference is (-2)^2 = 4. Subtract this squared difference from the base squared (100^2 – 4 = 10,000 – 4 = 9,996).
    Therefore, we can use the “Ekanyunena Purvena” sutra to calculate that 98 squared equals 9,996. 

    1 year ago

    Could you provide an example of a challenging algebraic equation and demonstrate how to apply Gunitasamuchyah sutra to simplify and solve it, highlighting any specific challenges it helps with?

    11 months ago
    Reply to  Oliver

    For the solution of algebraic problems, the “Gunitasamuchyah” Vedic mathematics sutra provides a unique approach. Let’s look at a challenging algebraic equation and demonstrate how this sutra can be applied to simplify and solve it. 

    Now let’s tackle this difficult algebraic equation: (x + 4)(x – 3) = 25.

    How to Implement the “Gunitasamuchyah” Sutra:

    1. First, find the equation that may be applied to the “Gunitasamuchyah” sutra in the form (x + a)(x – b) = c.
    2. Multiply the two constants, a and b, to find the result: 4 * 3 = 12.
    3. Using “m” as half of the product of a and b, express the left side of the equation as a perfect square of (x ± m). In this instance, “m” equals six, or half of twelve.
    4. Write (x + 6)(x – 6) = 25 in its new form.
    5. On the left side of the equation, we now have the difference of two squares. The solution is (x^2 – 6^2) = 25.
    6. Reduce it even more to x^2 – 36 = 25.
    7. Lastly, isolate the variable and solve for “x”:
    • Add 36 to both sides: x^2 = 61.
    • Take the square root of both sides: x = ±√61.
    11 months ago
    Reply to  Oliver

    Thanks to the “Gunitasamuchyah” sutra, we were able to simplify and solve the challenging algebraic problem more quickly. In this case, it simplified the problem by transforming it into the difference of two squares. By eliminating the need for conventional algebraic factoring and quadratic equation approaches, this method reduces the time and effort required to solve quadratic equations.



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