Mathematical sutras


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Sutra 1Ekadhikena PurnvenaBy one more than the previous one.
  • Squaring numbers ending in 5
  • Calculating the value of vulgar fractions whose denominators end in 9
Sutra 2Nikhilam Navatashcaramam DashatahAll from 9 and the last from 10
  • Multiplication of numbers close to 10, 100, 1000...etc.
  • Division by 9
Sutra 3Urdhva TiryagbyhamVertically and Crosswise
  • Multiplication and division of large numbers
Sutra 4Paraavartya YojayetTranspose and Apply
  • Division of numbers when divisors is slightly greater than 10, 100, 1000... etc.
Sutra 5Sunyam Saamya SamuccayeEquated to Zero
  • Used in several different places where some of the identities are equated to 0
Sutra 6Anurupye - SunyamanyatIf one is in ratio, the other one is zero.
  • Solving simultaneous linear equations
  • Finding out the product of two numbers when both close to the same base
Sutra 7Sankalana - VyavakalanabhyamBy addition and by subtraction.
  • Solving simultaneous equations where x and y coefficients are interchanged.
Sutra 8PuranapuranabhyamBy completion or by non-completion.
  • Finding the roots of quadratic equations.
Sutra 9Chalana - KalanabhyamSequential motion.
  • Factorising 3rd, 4th and 5th-degree expressions.
Sutra 10Ekanyunena PurvenaOne less than the previous one.
  • Multiplications of numbers such as 9/ 99/ 999... etc.
Sutra 11YavadunamThe deficiency.These all Sutras have various applications in different contexts and are often also applied along with the above-mentioned Sutras.
Sutra 12VyastisamashtihWhole as one and one as whole.
Sutra 13Sesanyan Kena CaramenaRemainder by the last digit.
Sutra 14SopantyadvayamantyamUltimate and twice the penultimate.
Sutra 15GunitasamuccayahThe whole product is the same.
Sutra 16Gunaka SamuccayahCollectivity of multipliers.

No.NameParent SutraMeaningApplication
Sub-Sutra 1AnurupyenaEkadhikina PurvenaProportionality
  • Finding the product of two numbers that are close to powers of 10 (10 / 100/ 1000..etc.)
Sub-Sutra 2Adyamadyenantya-MantyenaUrdhva-TiryagbyhamThe first by the first and the last by the last.
  • Factorization of quadratic equations
  • Multiplying terms containing two different units (eg. ft. and in)
Sub-Sutra 3Yavadunam Tavadunikrtya Varganca YojayetSankalana-VyavakalanabhyamWhatever the deficiency, subtract that deficit from the number and write alongside the square of that deficit
  • Finding squares/cubes of numbers close to 10, 100, 1000...etc.
Sub-Sutra 4Antyayor DasakepiPuranapuranabyhamSum of last digits is 10.
  • Multiplication of numbers whose last digits add up to 10, 100. 1000... etc. if the remaining digits are the same. (eg. 64x66, 783x717 etc.)
Sub-Sutra 5AntyayorevaChalana - KalanabhyamOnly the last terms.
  • Solving special types of algebraic equations.
Sub-Sutra 6Lopana SthapanabhyamVyashtisamanstihBy alternate elimination and retention.
  • Solving 2nd-degree homogenous equations with 3 variables.
  • Finding HCF of algebraic equations.
Sub-Sutra 7VilokanamSesanyan Kena CaramenaObservation.
  • Solving problems by making simple observations. Can be applied in:
    • Partial Fractions
    • Simultaneous Linear Equations
    • Simultaneous Quadratic Equations
Sub-Sutra 8Gunita Samuccayah-Samuccaya GunitahSopantyadvayamantyamThe product of the sum of coefficients is equal to the sum of coefficients in the product.
  • Factorization and solving of algebraic equations.
Sub-Sutra 9Sisyate SesasamjnahNikhilam Navatashcaramam DashatahAll from 9 and last from 10.
  • A corollary of Nikhilam Navatashcaramam Dashatah.
Sub-Sutra 10Kevalaih Saptakam GunyatParaavartya YojayetIn case of 7 multiplicands should be 143.
  • Division based on 1/7 = 0.142857 (approx. 0.143)
Sub-Sutra 11VestanamSunyam Saamya SamuccayeBy osculation.
  • Perform divisibility checks for numbers.
Sub-Sutra 12Yavadunam TavadunamAnurupye - SunyamanyatLessen by the deficiency.
  • Finding the cube of a number that is close to the powers of 10 such as 10, 100, 1000...etc.
Sub-Sutra 13SamuccayagunitahYavadunamBy the deficiency.
  • Used in special cases.


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