What is Nikhilam Navatashcaramam Dashatah ?

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The sutra “Nikhilam Navatashcaramam Dashatah” translates to “All from 9 and the Last from 10” in English. This sutra is particularly useful for subtraction, especially when dealing with numbers close to multiples of 10. Here’s how it works:

  1. Find the complement to 10: Look at the digit you want to subtract from 10 and find its complement to 10. For example, if you want to subtract 7 from 10, the complement to 10 of 7 is 3.
  2. Subtract the complements: Subtract the complements of each digit from 9. For example, if you want to subtract 784 from 1000:
    • The complement of 7 to 10 is 3, so subtract 3 from 9, which equals 6.
    • The complement of 8 to 10 is 2, so subtract 2 from 9, which equals 7.
    • The complement of 4 to 10 is 6, so subtract 6 from 9, which equals 3.
    • Therefore, the result is 631.

This sutra simplifies the process of subtraction by breaking it down into steps that involve finding complements to 10 and subtracting them from 9. It’s a useful mental technique for quick calculations and is one of the many efficient methods taught in Vedic Mathematics.