(Corollary: Anurupyena)

Meaning: By one more than the previous one

Ekadhikena Purvena (One More than the Previous) is a sutra useful in finding squares of numbers (like 25×25, 95×95, 105×105, 992×992, etc) and special divisions like 1 divided by 19, 29, 39, …. 199, etc. just in one step.

(Corollary: Sisyate Sesasamjnah)

Meaning: All from 9 and the last from 10

The method is used while multiplication through Base Multiplication.

(Corollary: Adyamadyenantyamantyena)

Meaning: Vertically and crosswise

It is the general formula applicable to all cases of multiplication and also in the division of a large number by another.

Cross Multiplication of Numbers for 3,4,5 Digits.

(Corollary: Kevalaih Saptakam Gunyat)

Meaning: Transpose and adjust

Paravartya in solving simple equations: Recall that ‘paravartya yojayet’ means ‘transpose and apply’

This method is used while dividing numbers in Vedic Maths.

(Corollary: Vestanam)

Meaning: When the sum is the same that sum is zero

Shunyam shutra explains various methods for getting our answer for the value of “x” in a linear equation.

Solving Linear Equations through Vedic Maths.

(Corollary: Yavadunam Tavadunam)

Meaning: If one is in ratio, the other is zero

The Sutra Anurupye Sunyamanyat says : ‘If one is in ratio, the other one is zero’. We use this Sutra in solving a special type of simultaneous simple equations.

“Example 1: 3x + 7y = 2 4x + 21y = 6

Observe that the y-coefficients are in the ratio 7 : 21 i.e., 1 : 3, which is same as the ratio of independent terms i.e., 2 : 6 i.e., 1 : 3.
Hence the other variable x = 0 and 7y = 2 or 21y = 6 gives y = 2 / 7.”

(Corollary: Yavadunam Tavadunikritya Varga Yojayet)

Meaning: By addition and by subtraction

This Sutra means ‘by addition and by subtraction’. It can be applied in solving a special type of simultaneous equations where the x – coefficients and the y – coefficients are found interchanged.

i.e., ( 45x – 23y ) + ( 23x – 45y ) = 113 + 91 i.e., 68x – 68y = 204 x – y = 3 subtract one from other, i.e., ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91 i.e., 22x + 22y = 22 x + y = 1 and repeat the same sutra, we get x = 2 and y = – 1 Very simple addition and subtraction are enough, however big the coefficients may be.

(Corollary: Antyayordashake’pi)

Meaning: By the completion or non-completion

The Sūtra: pūraṇāpūraṇābhyāṃ (By completion, or non-completion) is a technique used to factorize and solve quadratic, cubic and bi-quadratic equations.

(Corollary: Antyayoreva)

Meaning: Differences and Similarities

(Corollary: Vilokanam)

Meaning:The remainders by the last digit

(Corollary: Lopanasthapanabhyam)

Meaning: Part and Whole

(Corollary: Vilokanam)

Meaning: The remainders by the last digit

(Corollary: Gunitasamuccayah Samuccayagunitah)

Meaning: The ultimate and twice the penultimate

(Corollary: Dhvajanka)

Meaning: By one less than the previous one

The Sutra Ekanyunena Purvena comes as a sub-Sutra to Nikhilam which gives the meaning ‘One less than the previous’ or ‘One less than the one before’. … This Ekanyuna Sutra can be utilized for the purpose of postulating mental one-line answers to the question.

12*99= 1188

(Corollary: Dwandwa Yoga)

Meaning: The product of the sum is equal to the sum of the product

“It means the product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product”

(Corollary: Adyam Antyam Madhyam)

Meaning: The factors of the sum is equal to the sum of the factors