Vedic Maths Tricks Formulas and Solved Examples for Competitive Exams
The concept of Vedic Maths is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Using special techniques and mental calculation tricks based on ancient Indian sutras, Vedic Maths helps students boost their calculation speed, reduce errors, and increase their confidence for school and competitive exams.
Understanding Vedic Maths
Vedic Maths is an ancient Indian calculation method that uses a set of 16 main sutras (formulas) and 13 sub-sutras to make mathematical operations much faster and easier. This system covers arithmetic, algebra, geometry, calculus, and more, but it is mainly known for its powerful mental maths shortcuts. Concepts like mental maths, rapid multiplication, and calculation techniques are all related to Vedic Maths. Students often use these tricks to solve complex sums quickly, finish worksheets faster, and excel in exams.
Origin and History of Vedic Maths
The term "Vedic Mathematics" comes from the Sanskrit word "Veda," meaning knowledge. The system was popularized in the early 20th century by Swami Bharati Krishna Tirtha, who is considered the "Father of Vedic Maths." He studied ancient Indian texts and distilled various mathematical formulas into easy-to-remember sutras. Today, these teachings are widely respected and used in many schools and coaching centers in India and around the world.
Quick facts about Vedic Maths origin:
- Developed from ancient Indian scriptures ("Vedas")
- Formalized by Swami Bharati Krishna Tirtha (1884–1960)
- Consists of 16 main sutras and 13 sub-sutras
- Helps in mental calculation, speed maths, and competitive exams
Key Principles: The 16 Sutras of Vedic Maths
Vedic Maths is based on 16 main rules called "sutras." Each sutra is a general formula that can be used for solving various types of problems. Here’s a table to give you a clearer idea:
Vedic Maths Sutras Table
| Sutra Name | Meaning / Use |
|---|---|
| Ekadhikena Purvena | By one more than the previous one |
| Nikhilam Navatashcaramam Dashatah | All from 9 and the last from 10 |
| Urdhva-Tiryagbhyam | Vertically and crosswise (multiplication) |
| Paravartya Yojayet | Transpose and adjust (division) |
| Anurupyena | Proportionately |
Each sutra offers a shortcut for mathematical calculations, making it easier for students to answer questions quickly in exams and daily life.
Vedic Maths Tricks: Examples
Vedic Maths tricks can be applied to addition, subtraction, multiplication, division, squares, square roots, and more. Here are step-by-step examples using some of the most popular sutras:
Example 1: Fast Addition Using Ekadhikena Purvena
Add 98765 + 63217 + 89522 + 60543.
1. Write the numbers in columns, digit by digit.2. Add column-wise from right to left.
3. Whenever the sum in a place value exceeds 10, use the "Ekadhika" dot above the next digit to carry over efficiently.
4. Repeat for all columns to get the final answer.
Example 2: Multiplication Shortcut (Unit Digits Add to 10)
Multiply 63 × 67.
1. The unit digits (3 + 7) sum to 102. Tens digit: 6
3. Multiply tens digit by next number: 6 × 7 = 42
4. Multiply unit digits: 3 × 7 = 21
5. Write the results together: Answer is 4221
You can learn more multiplication tricks at Multiplication Tricks and build your skills further.
Vedic Maths vs. Traditional Methods and Abacus
It’s common for students and parents to wonder how Vedic Maths compares with other calculation tools like the abacus or regular classroom methods. Here’s a clear comparison:
| Feature | Vedic Maths | Abacus | Traditional Maths |
|---|---|---|---|
| Speed | Very Fast (mental calculation) | Fast (with practice) | Standard |
| Tools Needed | None / Paper | Abacus instrument | Paper, pen |
| Best For | All ages, exam prep | Young children (basics) | All students |
| Application | Competitive exams, day-to-day | Early mathematics | School syllabus |
If you want more on abacus basics, see Abacus (if live in your dump).
Books, Resources & Practice PDFs
Many students request Vedic Maths books, worksheets, and PDFs for practice. Here are some trusted resources:
- Vedic Maths PDF (download for methods and examples)
- Multiplication Tables 2–20 for practising multiplication and division using Vedic tricks
- Fractions Worksheet for applying Vedic Maths to fractions
- Maths Tricks for more exam-oriented strategies and mental maths hacks
Practice Worksheets and Sample Problems
Use these exercises to get comfortable with Vedic Maths tricks before your school or competitive exams:
- Apply Nikhilam Sutra to calculate 98 × 97 without long multiplication.
- Use Urdhva-Tiryagbhyam to solve 23 × 31 stepwise.
- Try the Ekadhikena Purvena trick for adding three-digit numbers orally.
- Download a worksheet to practice Vedic methods on fractions.
Benefits of Vedic Maths
Vedic Maths offers many advantages for students:
- Reduces calculation time and cuts down on mistakes
- Increases confidence in mental maths and school exams
- Supports preparation for competitive tests (like Olympiads, NTSE, and more)
- Works across all topics in arithmetic, algebra, and geometry
- Improves memory and concentration naturally
Vedic Maths has become very popular in early grade maths too, encouraging kids to find maths fun and easy from the start.
Frequently Asked Questions about Vedic Maths
What is Vedic Maths?
Vedic Maths is an ancient Indian system using special sutras for fast calculation in arithmetic, algebra, and geometry, making maths simpler and quicker.
Who is the father of Vedic Maths?
Swami Bharati Krishna Tirtha, who discovered and compiled the 16 Vedic sutras.
Is Vedic Maths difficult to learn?
No. With step-by-step practice and examples, anyone can master Vedic Maths. Resources like Maths Tricks make learning easier.
How is Vedic Maths different from abacus and traditional maths?
Vedic Maths is faster, requires no physical tools, and uses logical shortcuts, while abacus relies on a frame/beads mainly for young kids, and regular maths uses standard school methods.
Common Doubts and Confusion Busters
- Some students think Vedic Maths is "magic" — actually, every shortcut has a logical explanation using the sutras.
- Consistent practice is key. Try a Maths Tricks worksheet regularly to improve.
- Not all exams include Vedic Maths, but its methods help with speed tests and MCQs everywhere.
- Many students notice less anxiety in maths once they master Vedic calculation tricks.
Summary
We explored Vedic Maths, the logic of sutra-based calculation, key tricks and examples, and the practical benefits for all students. Practice with Vedantu and your calculation speed, memory, and confidence will keep improving, making exams and daily maths fun and stress-free!
Further Learning & Related Maths Topics
- Prime Numbers
- Addition of Fractions
- Number System
- Algebraic Expression
- Area and Perimeter
- Multiplication Tricks
- Class 2 Maths
- Fractions Worksheet
- Worksheet on Multiplying Fractions
- Maths Tricks
Keep exploring these links to supercharge your maths preparation and get the most out of learning with Vedantu.
FAQs on Vedic Maths Techniques for Faster Mental Calculation
1. What is Vedic Maths?
Vedic Maths is a system of fast calculation techniques based on 16 Sutras (formulas) and 13 sub-sutras derived from ancient Indian mathematics. It simplifies arithmetic, algebra, multiplication, division, and mental maths using short methods. Vedic Maths focuses on:
- Quick mental calculation
- Pattern-based problem solving
- Reducing lengthy traditional steps
- Improving speed and accuracy in exams
2. What are the 16 Sutras in Vedic Maths?
The 16 Sutras of Vedic Maths are word-formulas that guide different types of calculations. Some of the most important Sutras include:
- Ekadhikena Purvena (By one more than the previous one)
- Nikhilam Navatashcaramam Dashatah (All from 9 and last from 10)
- Urdhva Tiryagbhyam (Vertically and crosswise)
- Paravartya Yojayet (Transpose and adjust)
3. How do you multiply numbers using Vedic Maths?
You can multiply numbers in Vedic Maths using the Urdhva Tiryagbhyam Sutra, which means "vertically and crosswise." For example, to multiply 23 × 14:
- Step 1: Multiply units → 3 × 4 = 12 (write 2, carry 1)
- Step 2: Cross multiply → (2 × 4) + (3 × 1) = 8 + 3 = 11; add carry = 12 (write 2, carry 1)
- Step 3: Multiply tens → 2 × 1 = 2; add carry = 3
4. How does the Nikhilam Sutra work in Vedic Maths?
The Nikhilam Sutra is used to multiply numbers close to a base like 10, 100, or 1000 by subtracting from the base. For example, multiply 98 × 97:
- Base = 100
- 98 is 2 less than 100; 97 is 3 less than 100
- Cross subtract → 98 − 3 or 97 − 2 = 95
- Multiply deficits → 2 × 3 = 6
5. How do you square a number ending in 5 using Vedic Maths?
To square a number ending in 5, use the Sutra Ekadhikena Purvena, meaning "one more than the previous digit." For example, find 25²:
- Take the digit before 5 → 2
- Multiply by one more → 2 × 3 = 6
- Write 25 at the end
6. Is Vedic Maths useful for competitive exams?
Yes, Vedic Maths is highly useful for competitive exams because it improves calculation speed and mental accuracy. It helps in exams like:
- Banking exams
- SSC and government exams
- CAT, MBA entrance tests
- School Olympiads
7. What is the difference between Vedic Maths and traditional maths methods?
The main difference is that Vedic Maths uses shortcut Sutras, while traditional maths uses step-by-step standard algorithms. Key differences include:
- Vedic Maths emphasizes mental calculation
- Traditional methods rely more on written steps
- Vedic methods are faster for large numbers
- Traditional methods are more universally taught in schools
8. Can Vedic Maths be used for division?
Yes, Vedic Maths provides fast division methods using the Paravartya Yojayet Sutra, meaning "transpose and adjust." For example, dividing 123 ÷ 9:
- 9 × 13 = 117
- Subtract: 123 − 117 = 6
9. What are the benefits of learning Vedic Maths for students?
The main benefits of learning Vedic Maths are improved mental agility, faster calculations, and better number sense. Students gain:
- Increased confidence in maths
- Better performance in timed tests
- Stronger understanding of number patterns
- Reduced calculation errors
10. Is Vedic Maths difficult to learn?
No, Vedic Maths is not difficult to learn because it is based on simple patterns and logical shortcuts. Beginners can start with:
- Squaring numbers ending in 5
- Multiplication near base 10 or 100
- Simple cross-multiplication methods
