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Divide by 9 with running sums

From the sutra Nikhilaṃ, All from 9: dividing by 9 with running sums, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sutra

Try it with your numbers

When to use it

Dividing any number by 9.

The idea

The quotient digits are running totals of the digits. The remainder is the total of all the digits. Fix up if the remainder is 9 or more.

Worked example: 2301 ÷ 9

  1. 2 5 5Digits: 2, 3, 0, 1. Running totals, leaving out the last digit: 2, 5, 5.
  2. 2 5 5 r 6Remainder start: total of all digits = 6.
  3. 255 r 6Carry the tens of each running total to the left and take out any 9s from the remainder. Final: 255 remainder 6.

Practice this trick

All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.