What Are the 16 Sutras of Vedic Maths? A Beginner's Guide
The sixteen sutras of Vedic mathematics are the major formulae in word form for the system proposed by Bharati Krishna Tirthaji. These range through various methods that can be used in arithmetical and algebraic operations.
To the new learner of Vedic mathematics, the Sutras have more than just names to remember. It is important to know the concept behind each and its application too.
16 Sutras of Vedic Mathematics
Below is a basic introduction to the Vedic Mathematics 16 Sutras and their popular English interpretations.
- 1
Ekadhikena Purvena
By one more than the previous one.
This Sutra is founded upon the idea of adding one to the number that precedes another. This particular Sutra is especially famous for its calculation related to numbers ending in 5 and other repetitive sequences.
- 2
Nikhilam Navatashcaramam Dashatah
All from 9 and the last from 10.
This is one of the most popular Sutras of Vedic Math. It is extremely useful in computations involving numbers close to a base such as 10, 100, or 1,000.
- 3
Urdhva-Tiryagbhyam
Vertically and crosswise.
This Sutra gives a general way to multiply numbers. Unlike the regular method of multiplying numbers, this Sutra allows numbers to be multiplied vertically and crosswise.
It can be used for various multiplications and usually taught as one of the key approaches in mental math.
- 4
Paravartya Yojayet
Transpose and adjust.
- 5
Shunyam Saamyasamuccaye
The sum that is equal, should be taken as zero.
- 6
Anurupye Shunyamanyat
If there is any relationship between the terms of an equation, then their product will be equal to zero.
- 7
Sankalana-Vyavakalanabhyam
By addition and by subtraction.
This Sutra utilizes addition and subtraction to solve mathematical problems.
It can be used for solving some algebraic equations and numeric relationships where adding or subtracting something would help.
- 8
Puranapuranabhyam
By the completion or non-completion.
This Sutra relates to dealing with complete or incomplete numbers and may prove helpful when the number or expression is near a convenient number.
- 9
Chalana-Kalanabhyam
Differences and Similarities.
This Sutra deals with finding relationships, differences, and similarities between mathematical expressions.
This Sutra can find application in advanced mathematical workings. However, at the beginner level, it teaches an important concept of Vedic Maths,
- 10
Yavadunam
Whatever the extent of its deficiency.
This Sutra is particularly helpful when the number is near a convenient number but is little less than the convenient number.
For instance, in the case of working with numbers that are near 100, the deficiency from 100 of the number can help in the process.
- 11
Vyashtisamanstih
Part and whole.
This sutra talks about getting an idea about a whole quantity through its individual parts.
Sometimes, a difficult mathematical calculation can be easier when broken into pieces. Understanding individual parts, one can combine them and find out the answer to the whole.
- 12
Shesanyankena Charamena
The remainders by the last digit.
This sutra talks about remainders and the last digits of numbers.
It can be used while making calculations that involve division. Sometimes, it can be useful while dealing with some numerical patterns as well.
- 13
Sopantyadvayamantyam
The ultimate and twice the penultimate.
This sutra has something to do with the last digit of a mathematical pattern or series and the number immediately preceding it.
- 14
Ekanyunena Purvena
By one less than the previous one.
This Sutra makes use of the principle of taking one less than the preceding number or quantity.
It becomes particularly helpful while dealing with numbers near to powers of 10 like 9, 99 or 999.
- 15
Gunitasamuccayah
The product of the sum is equal to the sum of the products.
This Sutra deals with relationships that occur between products and sums.
It can be used to solve some algebraic calculations and will help learners to identify mathematical relations and identities without having to expand them all the time.
- 16
Gunakasamuchyah
The factors of the sum are equal to the sum of the factors.
This last Sutra deals with relationships between factors and sums.
It has mostly been used for algebraic relations and factorization. For starters, the basic idea should be understood first and the applications learned later.
What are Vedic Maths Sutras?
The Vedic Maths Sutras are short mathematical rules or formulas utilized in Vedic mathematics to perform various calculations easily. In total, there are 16 primary Sutras providing a specific way to solve mathematical problems that include arithmetic, multiplication, division, algebra, and number sequence.
Sutra means a short formula or rule. Unlike the usual long methods, the Vedic Maths Sutras teach students to discover relationships and patterns among the numbers and apply the right method to solve problems.
Who Developed the 16 Sutras
It is widely thought that the 16 Sutras of Vedic Mathematics were formulated, organised, and publicised by Swami Bharati Krishna Tirthaji (1884-1960), an Indian scholar and guru who became the Shankaracharya of Puri This man introduced these mathematical formulae in the context of Vedic mathematics.
According to the traditional viewpoint, the 16 Sutras were invented and arranged by Tirthaji based on his understanding of certain mathematical principles contained in ancient Indian literature. This scholar published his book, Vedic Mathematics posthumously in 1965, and it remains the primary source of knowledge about these formulae.
Use of 16 Sutras in Calculations
Multiplication – Urdhva-Tiryagbhyam
The meaning of Urdhva-Tiryagbhyam is "vertically and crosswise" which provides a systematic procedure to multiply numbers by considering the vertical and crosswise products.
- 2 x 3 = 6
- Crosswise: (1 x 3) + (2 x 1) = 5
- 1 x 1 = 1
Division – Paravartya Yojayet
The meaning of Paravartya Yojayet is "transpose and apply" which can be applied to some division problems by rearranging the problem to get an appropriate formula. For example, while doing division with respect to the divisor close to a convenient base, then the method considers the difference or adjustment of the divisor from the base.
3. Squaring Numbers – Ekadhikena Purvena
"Ekadhikena Purvena" translates into "one more than the previous one." There is a common use of this sutra, which is squaring numbers ending in 5.
- Get the number preceding 5: 3
- Add 1 to it: 3 + 1 = 4
- Multiply: 3 × 4 = 12
- Append 25.
Such tricks make some squaring problems simple and convenient.
4. Subtraction – Nikhilam Navatashcaramam Dashatah
"Nikhilam Navatashcaramam Dashatah" means "all from 9 and the last from 10." This method is helpful when subtracting numbers close to some base numbers like 10, 100, or 1,000.
5. Algebra – Sankalana-Vyavakalanabhyam
Sankalana-Vyavakalanabhyam implies "by addition and by subtraction." This technique is applicable in some cases where an equation may be solved using addition and subtraction of equations.
- By adding both the equations: 2x = 12
- Hence, x = 6
- Substitute the value of x: 6 + y = 10
- Thus, y = 4
This is an example of how addition and subtraction can make an algebraic calculation easy.
Is It Possible to Learn All 16 Sutras as a Beginner?
The answer is yes, it is possible to learn all 16 sutras of Vedic mathematics as a beginner. However, one need not necessarily learn them all at once because each has a distinct application and importance.
One can start by learning some of the commonly used sutras, comprehend the basic concepts, and apply them to solve a few examples. Gradually, as a beginner gets used to those, they can learn some other advanced sutras and use them accordingly.
How Long Does It Take to Learn the 16 Sutras?
The amount of time needed to master Vedic Mathematics depends on your speed of learning and comprehension of the techniques used. If you're a beginner, you may be able to grasp the basics of Vedic mathematics in a few weeks through regular practiceWith regular practice, you will be able to identify when a particular Vedic mathematics technique should be used to solve certain problems. Beginners who are keen on exploring the techniques and Vedic mathematics formulae can do so gradually.
Why Understanding Matters More Than Memorizing .
Just learning the names of the 16 Sutras of Vedic Maths will not be enough to help anyone get comfortable using Vedic Maths methods. The logic of understanding the meanings, applications, and usage of the Sutras allows one to know when and how to use a particular method. Once one understands the logic behind the method, he can easily use it on various problems without having to rely on memory of specific steps. This way, Vedic Maths for beginners will become more meaningful, and confidence in practice will improve. Thus, the learners should concentrate on understanding the concepts and practicing.
How to Learn the 16 Sutras Systematically
Learning the 16 Sutras of Vedic Math in a systematic manner will help learners make the whole process much easier. Start by getting acquainted with the meaning of the Sutra and the concept it carries rather than trying to learn all 16 Sutras at one go.. It is possible to explore the formulas and of Vedic Maths tricks with the help of practice. Practice is extremely important in gaining familiarity with the process. Learning about the works of Bharati Krishna Tirthaji will also give some historical perspective on Vedic Mathematics.
FAQ
What are the 16 Sutras of Vedic Maths?
16 Sutras of Vedic Mathematics are a list of mathematical formulae that can be used to work on various calculations and problems in a systematic way. These formulas make some mathematical processes easy. Students can learn about these formulae by applying them in Vedic Mathematics.
Who discovered the 16 Sutras?
The 16 sutras are linked to Bharati Krishna Tirthaji, who is an Indian mathematician and formerly a Shankaracharya of Puri. These rules are found in his book, Vedic Mathematics. His method includes different ways of solving mathematical questions which learners can learn from.
Can beginners learn all 16 Sutras?
Yes, Vedic Maths for beginners could also include learning the 16 Sutras in a step-by-step manner. Beginners do not have to learn all the rules in one go. They need to start with simpler concepts, learn each technique, and practice on a regular basis to simplify the whole learning process.
Are Vedic Maths Sutras formulas?
Vedic Maths Sutras should be interpreted as principles or methods as opposed to formulas. Each Sutra has its own way of solving which can be applied to varied mathematical problems. The principles can be easily grasped by learners and Vedic maths formulas applied after proper practice.
Which Vedic Maths Sutra is used for multiplication?
Meaning Vertically and Cross-wise Urdhva-Tiryagbhyam is one of the famous Vedic Mathematics techniques applied in multiplication. The method allows for systematic multiplication using both vertical and cross-wise computations. Other Sutras like Nikhilam may be applied in special cases of multiplication of numbers near a base.
