Vedic Maths Sutra 04 : Parāvartya Yojayet

Sūtra 4 of 16

परावर्त्य योजयेत्

Parāvartya Yojayet

“Transpose and Apply”

Meaning & Essence

This Sūtra means “Transpose and Apply”. It is primarily used for division, especially when the divisor is slightly greater than a power of 10 (such as 11, 12, 13, 14… or 101, 112, etc.).

The key idea is to transpose (change the sign of the excess digits of the divisor) and then apply them in a simple multiplication-and-addition process. This turns ordinary long division into a much faster and more elegant procedure.

Mathematical Principle

When the divisor is of the form \( 10 + d \) (slightly above 10), we transpose the excess \( d \) to \( -d \) and work from left to right.

\[ \text{Divisor } = 10 + d \quad \Rightarrow \quad \text{Use } -d \text{ (transposed)} \]

Steps in simple language:

• Write the divisor and put the transposed (negative) excess below the remaining digits
• Bring down the first digit(s) of the dividend as the first digit of the quotient
• Multiply that quotient digit by the transposed number and add it to the next digit of the dividend
• Continue until the remainder portion is reached
• The digits before the remainder line form the Quotient; the last part is the Remainder

Worked Examples

Example 1 → Divide \( 1225 \div 12 \)

• Divisor 12 → transpose the excess → use −2
• Separate last digit for remainder: 122 | 5
• Bring down 1 → multiply by −2 → add to next digit: 2 + (−2) = 0
• Bring down 0 → multiply by −2 → add to next: 2 + (−0) = 2, then 5 + (−4) = 1
• Quotient = 102, Remainder = 1

Answer: 102 R 1

Visual step-by-step walkthrough of Example 1 (1225 ÷ 12)

Example 2 → Divide \( 1697 \div 14 \)

• Divisor 14 → transpose → use −4
• Separate last digit: 169 | 7
• 1 × (−4) = −4 → 6 + (−4) = 2
• 2 × (−4) = −8 → 9 + (−8) = 1
• 1 × (−4) = −4 → 7 + (−4) = 3

Answer: 121 R 3

Example 3 → Divide \( 432 \div 11 \)

• Divisor 11 → transpose → use −1
• Separate last digit: 43 | 2
• 4 × (−1) = −4 → 3 + (−4) = −1
• −1 × (−1) = +1 → 2 + 1 = 3
• Quotient has a negative digit → convert: 4̄1 becomes 39

Answer: 39 R 3

Interactive Demo – Divide by numbers near 10 (11–19)

Please enter a valid dividend and a divisor between 11 and 19

When to Use This Sūtra

• Division when the divisor is slightly greater than a power of 10 (11–19, 101–199, etc.)
• Algebraic division of polynomials
• Solving simple linear and quadratic equations by transposition
• Complements the Nikhilam method (which is better when the divisor is slightly less than a power of 10)

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