Vedic Maths Sutra 11 : Vyaṣṭi-samaṣṭiḥ

Sūtra 11 of 16
व्यष्टि-समष्टिः
Vyaṣṭi-samaṣṭiḥ
“Part and Whole” (Specific and General)

Meaning & Essence

This Sūtra means “Part and Whole” or “Specific and General”.

It teaches us to look at a problem both from the point of view of the individual parts and from the point of view of the whole (or the average). A very practical application is multiplying two numbers that are equidistant from a convenient mean.

Mathematical Principle

If two numbers are equally distant from a convenient average \( m \):

\[ (m - d)(m + d) = m^2 - d^2 \]

So the product is simply the square of the mean minus the square of the deviation.

Worked Examples

Example 1 → \( 58 \times 62 \)
  • Mean (average) = 60
  • Deviation \( d = 2 \)
  • \( 60^2 = 3600 \)
  • \( 2^2 = 4 \)
  • \( 3600 - 4 = 3596 \)
Answer: 3596
Example 2 → \( 25 \times 31 \)
  • Mean = 28
  • Deviation \( d = 3 \)
  • \( 28^2 = 784 \)
  • \( 3^2 = 9 \)
  • \( 784 - 9 = 775 \)
Answer: 775
Example 3 → \( 47 \times 53 \)
  • Mean = 50
  • Deviation \( d = 3 \)
  • \( 50^2 = 2500 \)
  • \( 3^2 = 9 \)
  • \( 2500 - 9 = 2491 \)
Answer: 2491
Interactive Demo – Multiply two numbers via the mean

Enter two numbers that are roughly the same distance from a convenient average.

Please enter two valid numbers

    When to Use This Sūtra

    • Multiplying two numbers that are equidistant from a convenient average
    • Relating a specific case to the general (mean) case
    • Mental calculation when the numbers are symmetrically placed around a round figure
    • Situations involving “part versus whole” thinking

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