Technique explanation

Teaching Explanation

Sometimes a number isn't near 10, 100, or 1000, but it is near a multiple like 50 (which is 100 ÷ 2) or 20 (which is 10 × 2). We call this a Working Base.

You can use the same near-base steps, but you must add one "Scaling Step." If your working base is 50, you treat it like 100, but at the very end, you must divide your left-hand result by 2 to account for the fact that 50 is half of 100.

Method Condition

Useful for numbers near 20, 50, 200, 500, etc.

Standard Fallback

Standard multiplication or Lesson 08 crosswise.

Misconception & Correction

  • Misconception: Scaling both the left and right parts of the answer.
  • Correction: Only the left-hand part (the sum/difference part) is scaled. The right-hand part (the product of differences) remains as calculated.
Module
Vedic Math — Strategy Builder
Worked examples

Worked Examples

Example: 48 × 46 (Working Base 50, which is 100 ÷ 2)

  1. Differences from 50: -2 and -4.
  2. Left Part: 48 - 4 = 44.
  3. Scaling Step: Since 50 = 100/2, divide the left part by 2: 44 ÷ 2 = 22.
  4. Right Part: (-2) × (-4) = 08 (Use 2 digits because we related it to 100).
  • Result: 2208.
  • Independent Check: 48 × 40 = 1920; 48 × 6 = 288; 1920 + 288 = 2208. (Matches)

Example: 21 × 23 (Working Base 20, which is 10 × 2)

  1. Differences from 20: +1 and +3.
  2. Left Part: 21 + 3 = 24.
  3. Scaling Step: Since 20 = 10 × 2, multiply the left part by 2: 24 × 2 = 48.
  4. Right Part: 1 × 3 = 3 (Use 1 digit because we related it to 10).
  • Result: 483.
  • Independent Check: 21 × 20 = 420; 21 × 3 = 63; 420 + 63 = 483. (Matches)
Academy Course
Vedic Math: Foundations to Reference Applications