Vedic Maths Sutras

1

Ekadhikena Purvena

By one more than the one before

This Sutra simplifies squaring numbers close to base values

2

Nikhilam Navatashcaramam Dashatah

All from 9 and the last from 10.

A powerful technique for subtraction, especially useful when dealing with numbers close to multiples of 10.

3

Urdhva Tiryak

Vertically and Crosswise.

This Sutra streamlines multiplication, especially useful for multiplying large numbers.

4

Paraavartya Yojayet

Transpose and adjust

This technique aids in simplifying complex mathematical problems involving equations and variables.

5

Shunyam Saamyasamuccaye

When the sum is the same, that sum is zero.

An effective approach for solving algebraic equations with equal sums on both sides.

6

Anurupye Shunyamanyat

If one is in ratio, the other is zero

This Sutra is indispensable for solving proportionality problems.

7

Yavadunam Tavadunikritya Varga Samam

Whatever the extent of its deficiency, lessen that deficiency to form a square

Simplifies division and finding square roots.

8

Vilokanam

By mere observation

A technique that encourages quick, intuitive solutions based on patterns and observations.

9

Sankalana-vyavakalanabhyam

By addition and by subtraction

This Sutra offers techniques for both addition and subtraction, enabling quick calculations

10

Puranapuranabhyam

By the completion or non-completion.

This Sutra aids in finding fractions and complements, simplifying various mathematical operations.

11

Chalana-kalanabyham

Differences and Similarities

Useful for problems involving ratios and proportions

12

Yaavadunam

Partial Products

This Sutra facilitates the multiplication of large numbers by breaking them down into smaller, more manageable parts

13

Vestanam

Specific and General

This Sutra helps in solving problems where a specific value is derived from a general one

14

Yavadvividham Vyashtih

Separately the particular from the general

This Sutra is handy for finding individual components from a group

15

Samuccaye

Collective addition.

Useful for quick summations, especially when dealing with a series of numbers

16

Ekanyunena Purvena

By one less than the previous one

This Sutra provides a technique for division and helps in finding quotients efficiently

1

Antyayordashakepi

The last digit remains the same

This sub-Sutra aids in quickly determining the last digit of a product.

2

Sopantyadvayamantyam

The last two of the last

Useful for solving problems where the last two digits are required.

3

Ekaadhikena Purvena

One more than the previous

This sub-Sutra extends the “Ekadhikena Purvena” technique for squaring numbers closer to the base

4

Paravartya Sutra

Transposition and adjustment

Helps in solving linear equations and balance problems

5

Calana-Kalanabhyam

Differences and Similarities

Offers additional methods for solving ratio and proportion problems.

6

Gunakasamuccayah

The product of the sum

Useful for solving problems involving the product of two sums.

7

Gunita Samuccayah

The product of the sum is the sum of products

Aids in simplifying algebraic expressions.

8

Yavadunam Tavatirekena Varga Yojayet

By one less than the one so much is the square

Provides an alternative approach for finding squares.

9

Antyayordasake’pi

The last digit is as it is

Useful for quick calculations involving the last digit of numbers

10

Antyayorekadhikaduhitayor

On the last two digits

Enables efficient calculations when focusing on the last two digits.

11

Ardhasamuccayah Samuccayoh

The sum of the half-sums is the sum

A technique for adding fractions with common denominators

12

Ekanyunena Sesena

One less than the one followed by the last

Facilitates quick division.

13

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.