Vedic Maths Sutras & Sub-Sutras (Beginner-Friendly Guide)
Vedic Mathematics is one of the fastest and most interesting ways to do calculations. It is based on a set of 16 Sutras (main formulas) and 13 Sub-Sutras (sub-formulas) that make solving maths problems easy and enjoyable.
This beginner-friendly guide will explain each Sutra and Sub-Sutra in simple, easy-to-understand language, along with examples so you can start practicing right away.
What are Sutras in Vedic Maths?
The word "Sutra" means "formula" or "thread of knowledge" in Sanskrit. In Vedic Maths, a Sutra is like a quick trick or shortcut that helps you solve problems faster and with fewer steps.
The 16 Main Sutras of Vedic Maths
- Ekadhikena Purvena – "By one more than the previous one".
Example: To square 25 → Take the previous digit (2), add one (2+1=3), multiply (2×3=6), and then add 25 → 625. - Nikhilam Navatashcaramam Dashatah – "All from 9 and the last from 10".
Example: 1000 – 746 → Subtract each from 9 (except last from 10) → 254. - Urdhva Tiryagbhyam – "Vertically and crosswise".
Example: Multiply 12 × 13 using vertical and cross multiplications instead of the long method. - Paravartya Yojayet – "Transpose and adjust".
Example: Useful in solving linear equations quickly. - Shunyam Samyasamuccaye – "If the sum is the same, it is zero".
Example: Helps in simplifying algebraic equations with repeated terms. - Anurupyena – "Proportionally".
Example: Helps when multiplying numbers with proportional values. - Sankalana Vyavakalanabhyam – "By addition and subtraction".
Example: Used for solving simultaneous equations. - Puranapuranabhyam – "By completion and non-completion".
Example: Helpful in completing complex sums by filling missing values. - Chalana Kalanabhyam – "Differences and similarities".
Example: Useful for calculus and advanced problem-solving. - Yavadunam – "Whatever the extent of its deficiency".
Example: For 98², take deficiency (2), square it (4), subtract from 10000 to get 9604. - Vyasti Samasti – "Part and Whole".
Example: Break numbers into parts for simpler calculations. - Shesanyankena Charamena – "The remainders by the last digit".
Example: Helps in divisibility checks and remainder calculations. - Sopaantyadvayamantyam – "The ultimate and twice the penultimate".
Example: For quick division and polynomial solutions. - Ekanyunena Purvena – "One less than the previous".
Example: Shortcut for multiplying numbers near bases. - Gunitasamuchyah – "The product of the sum is equal to the sum of the product".
Example: Handy in algebraic simplifications. - Gunakasamuchyah – "The factors of the sum are equal to the sum of the factors".
Example: Solving factorization problems quickly.
The 13 Sub-Sutras of Vedic Maths
- Anurupyena – Proportionally.
- Sisyate Sesasamjnah – Remainder remains constant.
- Adyamadyenantyamantyena – First by first and last by last.
- Kevalaih Saptakam Gunyat – Multiply by 7 simply.
- Vestanam – Apply excess or deficiency methods.
- Yavadunam Tavadunam – Apply deficiency equally.
- Yavadunam Tavadunikritya Varganca Yojayet – Square of deficiency rule.
- Antyayoreva – Focus only on the last terms.
- Samuccayagunitah – Multiply the sum.
- Lopanasthapanabhyam – Elimination and substitution.
- Vilokanam – Use observation.
- Gunitasamuccayah Samuccayagunitah – Relation of factors and sums.
- Dhvajanka – Flag method for division.
How to Start Learning Vedic Maths
- Begin with simple and common sutras like Nikhilam and Urdhva Tiryagbhyam.
- Practice 5–10 problems every day to build speed.
- Apply these tricks while solving school homework or exam problems.
- Watch tutorials or take an online class for step-by-step learning.
- Teach these methods to a friend — teaching helps you learn faster.
Conclusion
Vedic Maths is a powerful tool for students and anyone who wants to make mathematics simple, fast, and fun. By practicing these 16 Sutras and 13 Sub-Sutras, you will notice a huge improvement in your calculation speed and confidence.
Start small, practice daily, and enjoy the beauty of quick mathematics!
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