Vedic maths · trick 31 of 36 · free

Vinculum (bar) numbers — Vedic maths trick

A bar over a digit means that digit is taken away. Writing 9s and 8s as bars (19 = 21̅) turns big digits into small ones, and turning bar numbers back into ordinary numbers is a quick “all from 9 and the last from 10”.

The trick

Nikhilam Navatashcaramam Dashatah — “all from 9 and the last from 10”

  1. A barred digit is subtracted: 324 = 300 − 20 + 4.
  2. To change to an ordinary number: the barred digits become “all from 9 and the last from 10”.
  3. The digit just before the bars goes down by 1. Digits after the bars stay the same.

Use it for: Reading bar numbers, and making multiplication easier: 98 = 102 (100 − 2), so 98 × 7 = 700 − 14 = 686.

Worked example: 5321 = 4681

  1. The bars mean 5000 − 300 − 20 + 1.
  2. Barred digits 3 2: 9 − 3 = 6, 10 − 2 = 8 → 68.
  3. The digit before them, 5, goes down to 4.
  4. Answer: 4681.

Check: 5000 − 300 − 20 + 1 = 4681 ✓

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