### **VEDIC MATHS SUTRAS**

Vedic maths is a system of ma**t**hematics that was rediscovered by **Swami Bharati Krishna Tirthaji **in the early 20th century. He claimed that he found **16 sutras (formulas) and 13 sub-sutras** (sub-formulas) in the Vedas that can be used to solve any mathematical problem. Vedic maths is not only about arithmetic, but also covers algebra, geometry, trigonometry, calculus, and more. Vedic maths is based on the principle of unity, which means that everything is connected and can be simplified to a single entity.

#### **Vedic Maths Main Sutras**

Vedic Maths there are sixteen main sutras .These Vedic Maths Sutras are discussed below in the tabular form.

**Ekadhikena Purvena—Meaning –**By one more than the one before This Sutra simplifies squaring numbers close to base values**Nikhilam Navatashcaramam Dashatah****Meaning –**All from 9 and the last from 10.A powerful technique for subtraction, especially useful when dealing with numbers close to multiples of 10.**Urdhva Tiryak Meaning –**Vertically and Crosswise.This Sutra streamlines multiplication, especially useful for multiplying large numbers.**Paraavartya Yojayet Meaning-**Transpose and adjustThis technique aids in simplifying complex mathematical problems involving equations and variables.**Shunyam Saamyasamuccaye Meaning –**When the sum is the same, that sum is zero.An effective approach for solving algebraic equations with equal sums on both sides.**Anurupye Shunyamanyat Meaning-**If one is in ratio, the other is zeroThis Sutra is indispensable for solving proportionality problems.**Yavadunam Tavadunikritya Varga Samam Meaning-**Whatever the extent of its deficiency, lessen that deficiency to form a squareSimplifies division and finding square roots.**Vilokanam Meaning –**By mere observationA technique that encourages quick, intuitive solutions based on patterns and observations.**Sankalana-vyavakalanabhyam Meaning –**By addition and by subtractionThis Sutra offers techniques for both addition and subtraction, enabling quick calculations**Puranapuranabhyam Meaning –**By the completion or non-completion.This Sutra aids in finding fractions and complements, simplifying various mathematical operations.**Chalana-kalanabyham Meaning –**Differences and Similarities Useful for problems involving ratios and proportions**Yaavadunam Meaning-**Partial ProductsThis Sutra facilitates the multiplication of large numbers by breaking them down into smaller, more manageable parts**Vestanam Meaning-**Specific and GeneralThis Sutra helps in solving problems where a specific value is derived from a general one**Yavadvividham Vyashtih Meaning-**Separately the particular from the generalThis Sutra is handy for finding individual components from a group**Samuccaye Meaning-**Collective addition.Useful for quick summations, especially when dealing with a series of numbers**Ekanyunena Purvena****Meaning –**By one less than the previous one This Sutra provides a technique for division and helps in finding quotients efficiently

### VEDIC MATHS SUB-SUTRAS

Vedic maths tricks are also known as sub-sutras or corollaries. They are derived from the main sutras and provide additional methods or shortcuts to solve problems faster and easier. There are 13 sub sutras. These sub sutras are discussed below in the table.

**Antyayordashakepi Meaning – t**he last digit remains the sameThis sub-Sutra aids in quickly determining the last digit of a product.**Sopantyadvayamantyam Meaning –**The last two of the lastUseful for solving problems where the last two digits are required.**Ekaadhikena Purvena Meaning –**One more than the previousThis sub-Sutra extends the “Ekadhikena Purvena” technique for squaring numbers closer to the base**Paravartya Sutra Meaning –**Transposition and adjustmentHelps in solving linear equations and balance problems**Calana-Kalanabhyam Meaning –**Differences and SimilaritiesOffers additional methods for solving ratio and proportion problems.**Gunakasamuccayah Meaning –**The product of the sumUseful for solving problems involving the product of two sums.**Gunita Samuccayah Meaning –**The product of the sum is the sum of productsAids in simplifying algebraic expressions.**Yavadunam Tavatirekena Varga Yojayet Meaning –**By one less than the one so much is the squareProvides an alternative approach for finding squares.**Antyayordasake’pi Meaning –**The last digit is as it isUseful for quick calculations involving the last digit of numbers**Antyayorekadhikaduhitayor Meaning –**On the last two digitsEnables efficient calculations when focusing on the last two digits.**Ardhasamuccayah Samuccayoh Meaning –**The sum of the half-sums is the sumA technique for adding fractions with common denominators**Ekanyunena Sesena Meaning –**One less than the one followed by the lastFacilitates quick division.**Sesanyankena Caramena**The last by the last, and the ultimate by one less than the last A technique for division, especially when dealing with recurring decimals

These Sutras and sub-Sutras together constitute the comprehensive system of Vedic Mathematics, offering a multitude of strategies and techniques for mental calculations and problem-solving. Mastery of these principles can significantly enhance one’s mathematical prowess and efficiency.