- Vedic Maths uses 16 sutras to complete its complicated calculations through fast methods.
- These sutras are used in Vedic Mathematics tricks to enhance speed, accuracy, and mental calculations.
- Every sutra has its specific usage through applications like multiplication and algebra.
- Practical examples enable students to learn through intuitive methods, which make learning easier.
- Widely used in exams and taught by institutes like Winwinx Academy
Overview
Vedic Mathematics represents an ancient Indian calculation method that mathematicians consider both easy to use and effective to use. The essence of Mathematics is not to make simple things complicated but to make complicated things simple. It is true to the ideal subject, Vedic Maths.
This system was discovered and its rules developed by Jagadguru Bharati Krishna Tirthaji, and allowed users to do mathematical calculations more quickly and efficiently. The Sutras of Vedic Mathematics offer formulas that can help the user to do basic arithmetic functions, more complicated algebra, and sophisticated mathematical functions using only simple mental calculation techniques. Vedic Mathematics has a remarkable coherence and simplicity, making it accessible and truly ‘brain-friendly’ math.
What are the 16 Sutras of Vedic Mathematics?
The Sutras of Vedic Mathematics are 16 terse Sanskrit phrases that indicate particular mathematical strategies. Every sutra is a guiding principle to solving specific kinds of problems, including multiplication, division, algebraic equations, and factorization.
These sutras are also versatile and can be used in various situations, hence they are potent in solving problems. Besides the main sutras, sub-sutras also exist, which expand their uses.
Also, these are easy to apply, and they cover each and every part of Mathematics making it more efficient, flexible, and fast, as you can solve most of the questions mentally.
List of 16 Sutras of Vedic Mathematics with Examples
1. Ekadhikena Purvena (By one more than the previous)
What does Ekadhikena Purvena mean?
Ekadhikena Purvena is a Vedic Mathematics Sutra that means “By one more than the previous one.” It is commonly used to simplify certain calculations, especially for quickly finding the square of numbers that end in 5.
What is Ekadhikena Purvena used for?
This Sutra is particularly useful for squaring numbers ending in 5. It allows you to calculate the answer mentally with fewer steps instead of using the traditional multiplication method.
Example:
To find 65²
Multiply the first digit by one more than itself 6 × (6 + 1) = 6 × 7 = 42
Whenever a number ends in 5, its square will always end in 25.
So:
Multiply 6 × 7 = 42 and append 25 → 4225
2. Nikhilam Navatashcaramam Dashatah (All from 9 and last from 10)
What does Nikhilam Navatashcaramam Dashatah mean?
Nikhilam Navatashcaramam Dashatah means “All from 9 and the last from 10.” This Sutra is commonly used to simplify calculations involving numbers that are close to a convenient base, such as 10, 100, 1000, and so on.
What is it used for?
This is one of the most powerful Vedic Mathematics tricks, used for multiplying.
- Multiplication of numbers close to a base
- Faster mental calculations
- Numbers near 10/100/1000
Example:
95 x 93
Base = 100
(100 – 5 ) 95 → (100 – 7) 93
Cross subtract → (100 – (5+7)) = 88
Multiply (-5 × – 7) = 35 → 35
Answer = 8835
3. Urdhva-Tiryagbhyam (Vertically and Crosswise)
What does it mean?
Urdhva-Tiryagbhyam means “Vertically and Crosswise.” This Sutra provides a systematic method for performing multiplication by working with numbers vertically and diagonally.
What is it used for?
A general multiplication method applicable to all numbers.
- 2-digit multiplication
- Larger-number multiplication
- Mental calculation practice
Example:
23 × 14
(2×1), (2×4 + 3×1), (3×4)
→ 2 | 11 | 12 → 322 (after carrying adjustments → 322)
4. Paravartya Yojayet (Transpose and Adjust)
What does it mean?
Paravartya Yojayet means “Transpose and Adjust.” This Sutra is based on rearranging or transposing terms and then making the necessary adjustments to solve a calculation.
What is it used for?
Used for solving division problems and algebraic equations. It simplifies complex expressions by rearranging terms.
Example (Division):
Solve: 1 ÷ 19
Using this sutra, we transpose and adjust to get a recurring decimal:
1 ÷ 19 = 0.052631…
It helps simplify long division into a pattern-based approach.
5. Shunyam Saamyasamuccaye (When the sum is the same, it is zero)
What does Shunyam Saamyasamuccaye mean?
Shunyam Saamyasamuccaye can be understood as “When the sum is the same, it is zero.” This Sutra is used in certain algebraic equations where matching sums can help identify a solution quickly.
What is it used for?
This sutra helps solve equations quickly when certain terms are equal.
- Solving certain algebraic equations
- Identifying zero-value expressions
- Simplifying equations with repeated or matching combinations
- Recognizing patterns that can reduce calculation steps
Example:
Solve:
(x + 3)/(x + 5) = (x + 7)/(x + 9)
Check sums:
3 + 9 = 12
5 + 7 = 12
Since sums are equal → x = 0
6. Anurupyena Shunyamanyat (If one is zero, the other is zero)
What does Anurupyena Shunyamanyat mean?
Anurupyena Shunyamanyat is commonly interpreted as “If one is zero, the other is zero.” It is associated with recognizing proportional relationships and special algebraic patterns that can simplify calculations.
What is it used for?
This Sutra can be applied to:
- Certain algebraic equations
- Proportional relationships
- Simplifying calculations
- Recognizing relationships between related expressions
Example:
If:
(x − 2)/(x − 3) = 4/5
Cross multiply:
5(x − 2) = 4(x − 3)
5x − 10 = 4x − 12
5x – 4x = -12 +10
x = -2
If one side becomes zero, the corresponding term also becomes zero.
7. Sankalana-Vyavakalanabhyam (By addition and subtraction)
What does Sankalana-Vyavakalanabhyam mean?
Sankalana-Vyavakalanabhyam means “By addition and subtraction.” This Sutra uses addition and subtraction together to simplify certain mathematical problems, especially simultaneous equations.
What is it used for?
It is particularly useful for:
- Solving simultaneous equations
- Finding unknown variables
- Eliminating one variable quickly
- Simplifying algebraic calculations
Example:
x + y = 10
x − y = 2
Add → 2x = 12 → x = 6, y = 4
8. Puranapuranabhyam (By completion or non-completion)
What does Puranapuranabhyam mean?
Puranapuranabhyam means “By completion or non-completion.” The idea is to complete a number to a convenient value, such as 10, 100, or 1000, and then adjust the remaining amount.
What is it used for?
This approach can make calculations easier when working with numbers that are close to convenient bases.
It can be useful for:
- Mental addition
- Completing numbers to 10, 100 or 1000
- Simplifying calculations
- Faster arithmetic
Example:
Adding 98 + 7
To make 98 into 100, we need:
98 + 2 = 100
So, we take 2 from 7.
Original: 7
After giving 2 → 7 − 2 = 5
Now the problem becomes:
100 + 5 → result = 105
9. Chalana-Kalanabhyam (Differences and similarities)
What does Chalana-Kalanabhyam mean?
Chalana-Kalanabhyam can be understood as “Differences and similarities.” The Sutra is associated with recognizing relationships between expressions by examining their differences and similarities.
It can help simplify certain mathematical and algebraic problems by identifying useful patterns.
What is it used for?
It can be useful in:
- Algebraic manipulation
- Recognizing mathematical patterns
- Factorization
- Certain higher-level mathematical calculations
Example:
Solve:
x² − 9 = 0
Using difference:
x² − 3² = (x − 3)(x + 3)
So,
x = 3 or x = -3
10. Yavadunam (Whatever the deficiency)
What does Yavadunam mean?
Yavadunam means “Whatever the deficiency.” This Sutra is particularly useful for squaring numbers that are close to a convenient base such as 10, 100, or 1000.
Instead of performing a traditional multiplication, we use the number’s deficiency from the base.
What is it used for?
Yavadunam is useful for:
- Squaring numbers below a base
- Fast mental calculations
- Squaring numbers close to 10, 100 or 1000
- Reducing multiplication steps
Example:
97²
Base = 100 → deficiency = 3
(100 – 3 = 97)
97 − 3 = 94
3² = 09
Answer = 9409
11. Vyashtisamanstih (Part and whole)
What does Vyashtisamanstih mean?
Vyashtisamanstih refers to the relationship between parts and the whole. The idea is to break a larger calculation into smaller, manageable parts and then combine those parts to obtain the final result.
What is it used for?
This approach can help with:
- Breaking complex calculations into smaller parts
- Mental arithmetic
- Addition and calculation using place values
- Simplifying larger numerical expressions
Example:
Find: 123 + 456
Break into parts:
(100 + 400) + (20 + 50) + (3 + 6)
= 500 + 70 + 9
= 579
12. Shesanyankena Charamena (Remainder by the last digit)
What does Shesanyankena Charamena mean?
Shesanyankena Charamena is associated with using the remainder and the final part of a number to simplify certain calculations. It can be useful when working with divisibility and remainders.
What is it used for?
- Finding remainders
- Divisibility calculations
- Number patterns
- Simplifying certain division problems
Example:
Find the remainder when 123 ÷ 9
Add digits:
1 + 2 + 3 = 6
Remainder = 6
13. Sopaantyadvayamantyam (The ultimate and twice the penultimate)
What does Sopaantyadvayamantyam mean?
Sopaantyadvayamantyam is traditionally associated with using the last term and twice the penultimate term in certain algebraic calculations. It can help identify useful relationships between the coefficients of an expression.
What is it used for?
- Certain quadratic equations
- Algebraic factorization
- Working with polynomial expressions
- Recognizing relationships between coefficients
Example:
Solve:
x² + 7x + 10
Break middle term:
x² + 5x + 2x + 10
= x(x + 5) + 2(x + 5)
= (x + 5)(x + 2)
14. Ekanyunena Purvena (By one less than the previous)
What does Ekanyunena Purvena mean?
Ekanyunena Purvena means “By one less than the previous one.” This Sutra can be useful for performing certain calculations involving numbers close to a convenient base, particularly numbers such as 99, 999 and similar values.
What is it used for?
- Multiplication involving numbers close to a base
- Calculations with numbers ending in 9
- Fast mental calculations
- Working with powers or products near convenient bases
Example:
99 × 97
Base = 100
Subtract each number from 100:
- 99 → 100 − 99 = 1 → so deviation is −1
- 97 → 100 − 97 = 3 → so deviation is −3
Now subtract diagonally:
- 99 − 3 = 96
(or 97 − 1 = 96 — both give same result)
Multiply deviations
- (−1) × (−3) = 3
Since base is 100 (2 zeros), write it as 03 – 99 × 97 = 9603
15. Gunitasamuccayah (The product of the sum is equal to the sum of the product)
What does Gunitasamuccayah mean?
Gunitasamuccayah expresses a relationship between a product of sums and a sum of products. It is associated with algebraic identities and can be useful when checking or simplifying certain expressions.
What is it used for?
- Algebraic simplification
- Checking mathematical identities
- Working with polynomial expressions
- Understanding relationships between sums and products
Example:
Check:
(2 + 3)(4 + 5)
LHS:
5 × 9 = 45
RHS:
(2×4) + (2×5) + (3×4) + (3×5)
= 8 + 10 + 12 + 15 = 45
Both sides equal → Verified
16. Gunakasamuccayah (The factors of the sum are equal to the sum of the factors)
What does Gunakasamuccayah mean?
Gunakasamuccayah is associated with relationships between factors and sums. It can be used as a principle for recognizing and checking certain algebraic relationships.
What is it used for?
- Algebraic expressions
- Factorization
- Checking relationships between factors
- Simplifying certain polynomial expressions
Example:
Factor:
6x + 9
Take the common factor:
3(2x + 3)
Here, the sum and factors balance in structure.
Importance of Sutras of Vedic Mathematics
Vedic Mathematics sutras are valuable instruments in enhancing problem-solving abilities. They help students to approach Mathematics with competence and confidence.
These sutras not only induce creativity in intelligent students but can also help slow learners in understanding Mathematics.
Some key advantages include:
- Speed: Problems are solved much faster than traditional methods
- Accuracy: Reduces chances of calculation errors
- Mental ability: Encourages solving without pen and paper
- Confidence: Builds a strong foundation in Mathematics
Because of these benefits, Vedic Mathematics tricks are widely used in competitive exams such as banking, SSC, and entrance tests.
Applications of Vedic Mathematics Tricks in Real Life
- Competitive Exams
Vedic Mathematics tricks will enable students to save time, which will provide them with an advantage over others.
- Daily Calculations
These techniques make the daily calculations simple, both in shopping and in budgeting.
- Academic Excellence
This makes it easier to understand concepts, thus resulting in improved academic performance.
Tips to Master Vedic Mathematics
- Practice regularly with simple problems
- Understand the logic behind each sutra
- Apply techniques in daily calculations
- Start with basic sutras and gradually move to advanced ones
Everyone is looking for new ways of solving mathematical problems, and that is the main reason behind the interest in Vedic Mathematics.
Final Thought
To conclude, the 16 Sutras of Vedic Mathematics provide a strong mathematical solution method that enables efficient problem resolution in Mathematics. The students who learn these techniques will experience better performance in speed and accuracy while building their self-assurance.
Over the last few years, there have been various organizations in India and abroad that are promoting Vedic Mathematics. Today, Vedic Maths has been taught in engineering and management colleges, and even students of IIT’s are said to be using the ancient techniques for quick calculations.
Through dedicated practice and support from educational institutions like Winwinx Academy, learners can achieve mathematical excellence while developing a lifelong love for the subject.
FAQ’S
What are the 16 Sutras of Vedic Mathematics?
The 16 Sutras are mathematical principles traditionally associated with Vedic Mathematics. Each Sutra provides a particular approach that can be applied to suitable mathematical calculations.
Who introduced the 16 Sutras of Vedic Mathematics?
The 16 Sutras are associated with the Vedic Mathematics system popularized in the modern era by Bharati Krishna Tirtha.
What is the easiest Vedic Maths Sutra?
For beginners, Ekadhikena Purvena is often easy to demonstrate with numbers ending in 5, although the best starting Sutra depends on the learner and the type of calculation.
Can children learn Vedic Mathematics?
Yes. Age-appropriate Vedic Mathematics techniques can be introduced progressively, starting with simple calculations and examples.
Are Vedic Mathematics techniques useful for mental maths?
Many Vedic Mathematics techniques are designed to simplify suitable calculations and can be useful for mental calculation practice.
How many Sutras are there in Vedic Mathematics?
The commonly presented system contains 16 Sutras, along with associated sub-formulas or Upa-Sutras.
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