## Ekadhikina Purvena (By one more than the previous one):

This sutra suggests adding one more than the previous number. It is often utilized for rapid multiplication by nine. For instance, to multiply a number by nine, you add the number to itself and subtract one.

## Nikhilam Navatascaramam Dasatah (All from 9 and the last from 10):

This sutra suggests adding one more than the previous number. It is often utilized for rapid multiplication by nine. For instance, to multiply a number by nine, you add the number to itself and subtract one.

## Urdhva-Tiryagbyham (Vertically and Crosswise):

This sutra is used for the rapid multiplication of numbers. It involves multiplying the vertical and cross products of digits and summing them up to obtain the final result.

## Paravartya Yojayet (Transpose and adjust):

This sutra focuses on division. It suggests transposing the divisor and adjusting the quotient to simplify division calculations. By using this technique, divisions involving numbers close to powers of ten become easier.

## Shunyam Saamyasamuccaye (If the Samuccaya (remainder) is the same it is zero):

This sutra states that if the remainders obtained after division are the same, then the difference between the two numbers being divided is divisible by their common divisor. It helps simplify division problems by utilizing common remainders.

## Sankalana-vyavakalana (Addition and subtraction):

This sutra emphasizes the use of addition and subtraction to simplify calculations. It is applied when dealing with numbers having a common component, where you can perform operations based on their relationship to each other.

## Ekanyunena Purvena (By one less than the previous one):

This sutra suggests subtracting one from the previous number. It is commonly used in pattern-based calculations or when working with consecutive numbers.

## Sankalana-Kalana-Vyavakalana (Addition-multiplication-subtraction):

This sutra combines addition, multiplication, and subtraction. It provides a sequence of operations to simplify complex calculations.

## Gunakasamuccaya (Factors of the sum and the difference):

This sutra explores the relationship between the sum and difference of two numbers and their product. It allows for efficient calculation of the product by considering its sum and difference.

## Dashasutra (The rule of ten):

This sutra focuses on multiplication and division by powers of ten. It provides techniques for easily shifting decimal places and adjusting numbers accordingly.

## Dvandvamukha (The product of the sum and the difference):

This sutra states that the product of the sum and difference of two numbers is equal to the difference of their squares. It enables efficient calculation of squares by using the sum and difference of two numbers.

## Kalanadhikena (By the deficiency):

This sutra suggests adding the deficiency. It is useful when dealing with numbers close to a reference or base number.

## Samuccayagunitah (The sum is obtained by multiplication):

This sutra states that the sum can be obtained by multiplication. It provides a method for finding the sum of a series of numbers by multiplying the average by the count of terms.

## Antyayoreapi (After the last):

This sutra suggests carrying out calculations after the last digit or term. It is used when numbers have been rounded or truncated.

## Puranapuranabyham (By the completion or non-completion):

This sutra deals with fractions and provides techniques for adding or subtracting fractions by adjusting their numerators and denominators to achieve common terms.

## Sopaantyadvayamantyam (The ultimate and twice the penultimate):

This sutra states that the sum of the squares of the ultimate and twice the penultimate terms is equal to the sum of squares of the given series. It facilitates quick calculation of the sum of squares of consecutive terms.

These sutras, with their unique approaches and techniques, form the basis of Vedic mathematics. They offer efficient methods for calculations, enhance mental math skills, and provide insights into mathematical relationships and patterns. By mastering these sutras, one can perform calculations with speed, accuracy, and a deeper understanding of mathematical concepts.