Vedic Maths Sutras

S.No

Sutras or Formulae

Sub-Sutras or Corollaries

1

Ekadhikena Purvena
(One more than the previous)
Division eg. 1/17

Anurupyena
(Proportionately) Multiplications

2

Nikhilam Navatascaram Dashtah
(All from 9 last from 10)
Multiplication eg 9998 X 9999

Sishyate Seshasanjnah

3

Urdhva-tiryaghyam
(Vertically and cross-wise)

Adhyam-adhyena antyam-antyena
(First by the first and last by the last)

4

Paravartya Yojayet
(Transpose and apply)

Kevalaih Saptakam Gunyat

5

Sunyam Samya samuccaye
(when Samuccaya is the same, that Samuccaya is zero)

Veshtanam

6

(Anurupye) Sunyamanyat

Yavadunam Tavadunam

7

Sankalana-vyavakalana

Yavadunam Tavadunikrtya Vargamca Yojayet

8

Purna purnabhyam

Antyayor Dasakepi (also for two numbers whose last digits together total is TEN)

9

Calana-Kalanabhyam

Antyayoreva

10

Yavadunam

Samuccayagunitah

11

Vyashti samashti

Lopana Sthapanabhyam
"by (alternate) Elimination and Retention"

12

Seshanyankena caramena

Vikolanam

13

Sopantya dvayamantyam

Gunita samuccayah Samucchaya gunitah

14

Ekanyunena purvena
(one less than the previous)
one of the multiplier-digits is all 9

15

Gunita Samuccayah

16.

Gunaka Samuccayah

SUTRAS

TRANSLATION

By one more than the one before

All from 9 and the last from 10

Vertically and Cross-wise

Transpose and Apply

If the Samuccaya is the Same it is Zero

If One is in Ratio the Other is Zero

By Addition and by Subtraction

By the Completion or Non-Completion

Differential Calculus

By the Deficiency

Specific and General

The Remainders by the Last Digit

The Ultimate and Twice the Penultimate

By One Less than the One Before

The Product of the Sums

All the Multipliers

SUB SUTRAS

TRANSLATION

Proportionately

The Remainder Remains Constant

The First by the First and the Last by the Last

For 7 the Multiplicand is 143

By Osculation

Lessen by the Deficiency

Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency

Last Totalling 10

Only the Last Terms

The Sum of the Products

By Alternative Elimination and Retention

By Mere Observation

The Product of the Sums is the Sum of the Products