Vedic maths · trick 3 of 36 · free

Multiplying numbers near 10, 100 and 1000 — Vedic maths trick

When both numbers are close to 10 or 100, multiply their small differences from that base instead of the big numbers.

The trick

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

  1. Write how far each number is from the base (− if below, + if above).
  2. Left part: cross-add — one number plus the other’s difference.
  3. Right part: multiply the two differences; it must have as many digits as the base has zeros (carry the extra).
  4. One above and one below? The right part is negative: take 1 from the left part and write base − that amount.

Use it for: Both numbers near 10 (7 × 8, 12 × 13), 100 (97 × 96, 104 × 107) or 1000 (996 × 989) — also one above and one below: 103 × 98 → 101 | −06 → 100 | 94 = 10094.

Worked example: 97 × 96 = 9312

  1. Base 100: 97 is −3, 96 is −4.
  2. Left part: 97 − 4 = 93.
  3. Right part: (−3) × (−4) = 12 → two digits: 12.
  4. Answer: 9312.

Check: 97 × 96 = 97 × 100 − 97 × 4 = 9700 − 388 = 9312 ✓

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