Vedic mathematics is an ancient system of mathematics that has its origin in the Athavarva Veda. It is a system of mathematics that provides quick calculation tricks that are different from traditional methods. These techniques are known as the Vedic Math Sutras.
There are 16 sutras and 13 sub-sutras of Vedic mathematics. The formulae and sub-formulae of Vedic mathematics can help you solve addition, subtraction, multiplication, division, square roots, and cube roots within seconds. With the help of the magical techniques of Vedic mathematics, you can solve any calculation in the fastest possible way.
In recent decades, students, teachers, and scholars have realized the importance of Vedic mathematics. In an era of competition, speed, and accuracy are the keys to success. Whether you are a budding engineer, an aspiring B-school student, or someone who wants to work in a government bank, Vedic mathematics will surely boost your chances in the selection process.
Vedic Mathematics is suitable for everyone, whether you are an exam aspirant, a student, a maths teacher, or someone who wants to learn this subject out of interest.
So, let us understand the sutras of Vedic mathematics.
What Are the 16 Sutras and 13 Sub Sutras of Vedic Maths?
Jagadguru Shankaracharya Swami Bharati Krishna Tirtha has compiled various sutras from ancient Vedic texts. The sixteen sutras and thirteen sub-sutras of Vedic mathematics can help you solve any problem in arithmetic, geometry, algebra, trigonometry, and calculus.
Let us have a look at the sutras and sub-sutras of Vedic mathematics.
Sixteen Sutras of Vedic Mathematics
The sixteen sutras with their applications are listed below:
| Serial Number | Sutras | Use of the sutra |
|---|---|---|
| 1 | Ekadhikina Purvena | This sutra is used to square a number ending in 5. |
| 2 | Nikhilam Navatashcaramam Dashatah | This sutra is used when multiplying numbers closest to the base numbers, such as 10, 100, 1000, etc. |
| 3 | Urdhva-Tiryagbyham | This sutra can generally be used to multiply two large numbers. |
| 4 | Paraavartya Yojayet | This sutra is used when the divisor is greater than 10. |
| 5 | Shunyam Saamyasamuccaye | This sutra is useful for getting the value of x in a linear equation. |
| 5 | Anurupyena- Sunyamanyat | This sutra is about calculating the product of two numbers that are close to the same base number. |
| 6 | Sankalana-Vyavakalanabhyam | It is used to solve simple equations with interchanged variable coefficients. |
| 7 | Puranapuranabyham | This sutra is used to solve algebra problems. |
| 8 | Chalana-Kalanabyham | This sutra is used to determine the roots of a quadratic equation. |
| 9 | Yaavadunam | This Sutra can be used to obtain the square of a number whose base is close to powers of 10. |
| 10 | Vyashtisamanstih | This sutra is used for the factorization of a quadratic equation. |
| 11 | Shesanyankena Charamena | With this sutra a fraction can be expressed in its decimal form. |
| 12 | Sopaantyadvayamantyam | With the help of this sutra you can find the solutions of equations like 1/ab + 1/ac + 1/ad + 1/bc, where a, b, c, and d are in arithmetic progression. |
| 13 | Ekanyunena Purvena | This sutra is used to multiply with9, 99 and so on. |
| 14 | Gunitasamuchyah | This sutra can help you verify multiplications, divisions, and factorizations. |
| 15 | Gunakasamuchyah | This sutra is helpful in solving cubic and biquadratic equations. |
Thirteen Sub-Sutras of Vedic Maths
The thirteen sub-sutras are listed below:
| Serial Number | Sub-Sutras | Meaning |
|---|---|---|
| 1 | Anurupyena | This sub-sutra is for Proportionately. |
| 2 | Sisyate Sesasamjnah | Remainder remains constant. |
| 3 | Adyamdyenantya-mantye-na | First by first and last by last. |
| 4 | Kevalaih Saptakam Gunyat | For 7 the Multiplicand is 143. |
| 5 | Vestanam | By osculation. |
| 6 | Yavadunam Tavadunam | Lessen by the difference. |
| 7 | Yavadunam Tavadunam Varganca Yojayet | Whatever the difference lessens by that amount and set up the square of the difference. |
| 8 | Antyayordasake | Last totaling 10. |
| 9 | Antyayoreva | Only the last terms. |
| 10 | Samuccayagunitah | The sum of the coefficients in the product. |
| 11 | Lopanasthapanabhyam | By alternate elimination and retention. |
| 12 | Vilokanam | By observation. |
| 13 | Gunitasmuccayah Samuccayagunitah | The product of the sum is the sum of the products. |
What Are the 3 Rules of Vedic Mathematics?
There are many rules in Vedic mathematics. All these rules can help you increase your speed of calculation and get results in a short time. With the thorough practice of Vedic mathematics, you can solve complex calculations in seconds. This gives you an advantage over others in examinations where time is always a constraint.
These methods are also extremely helpful for your children. They help them develop their intelligence and improve their problem-solving skills.
For your understanding, we have listed three simple rules of Vedic mathematics.
Vedic Maths Rule for Addition:
1. Square of a 2-Digit Number Ending with 5
Let us find the square of 75.
- The last two digits will always end with 25.
- Now, add 1 to the first digit and then multiply this with the first digit.
- Here, the first digit is 7, and if we add 1 to 7, the result is 8.
- Again, multiply this result by the first digit.
- (7+1)*7= 8* 7= 56
- Therefore, the answer is 5625.
With the same formula, try to find out the square of 65.
2. To Multiply Any Number by 5
We have to consider two cases for this. But you should identify if the number is odd or even.
1. If the Number Is Even:
Let’s multiply 1258*5.
- Divide 1258 by 2, 1258/2=629
- Add a 0 as the last digit of the number, this will be your answer.
- In this case, the answer is 6290.
Try this for 5882*5.
2. If the Number Is Odd:
Let’s multiply 6573*5
- Subtract 1 from the number and then divide by 2. In this case, 6573-1= 6572/2=3286.
- Now, with 5 as the last digit, your answer will be 32865.
Try this for 7773*5.
3. To Multiply a 2-Digit by 11
Let’s multiply, 69*11.
- Place it like this, the first digit of the first number (first digit of the first number+second digit of the first number) and the second digit of the first number.
- In this case, 6(6+9)9, place 9 in the unit’s place, add 6+9=15, and then carry the 1 and add with
- The result is 759.
Similarly, try for 49*11.
FAQ: Vedic Math Sutras
- How many formulas are in Vedic Math?
Vedic mathematics consists of 16 sutras and thirteen sub-sutras. With the help of these formulae or techniques, one can solve complex calculations in arithmetic, algebra, trigonometry, and calculus.
- What are the four levels of Vedic Maths?
Most courses in Vedic mathematics have two levels: junior and senior. These levels are again divided into two parts. The complexity of the levels may vary according to the age group. Some courses may also have three levels. The classification of courses into different levels is determined by the institution’s curriculum. In any case, the content of the course is the same.
- What are the concepts of Vedic Maths?
The two most important concepts in Vedic mathematics are bases and complements. A base is a number that begins with 1 and ends with 0. 10, 100, and 1000 are bases, while 20, 200, and 2000 are not considered.
When the addition of two numbers produces a number that is closest to a base, it is called a complement. If we consider the number 82, the nearest base to 82 is 100. If we add 18 to 82, we get 100. Therefore, 82 and 18 are complements of each other.
- How many sutras are there in Vedic Math?
There are sixteen sutras in Vedic mathematics. All the sutras of Vedic mathematics are extremely useful and can be applied to addition, subtraction, multiplication, division, square and cube roots, linear equations, quadratic equations, trigonometry, and infinitesimal calculus.
- What are the most important sutras?
All the sutras of Vedic mathematics are important. A person who has mastered this subject can use these techniques to solve numerical problems or everyday calculations in the best possible way.
Wrapping Up
Vedic mathematics is a collection of the simplest tricks for solving numerical problems or other mathematical calculations that occur in daily life. Mastering Vedic math sutras will reduce your dependence on calculators.
Students can perform better in school and take competitive examinations. It opens up another dimension of mathematics, which makes this subject interesting. It improves logical thinking and visualization skills and increases the l intelligence of a person.
So, to achieve the desired results, it is important to have a thorough knowledge of the Vedic math sutras. These sutras or formulae will take your mathematical knowledge to the next level. We hope that this blog can help in understanding the various sutras and sub-sutras.
Do share your favourite Vedic maths sutra or sub-sutra in the comments below.
