Transpose and adjust

Paravartya Yojayet

This sutra means 'transpose and adjust' and provides shortcuts for division using the complement of the divisor. The simplest case is dividing by 9, where a running digit-sum gives the quotient and remainder instantly. The method generalizes to divisors like 8, 11, 99, etc.

How It Works

1.Write out the digits of the dividend (e.g. 1234 → 1, 2, 3, 4).
2.Bring down the first digit as-is. This starts the quotient.
3.Add the running total to the next digit to get the next quotient digit.
4.Continue until you reach the last digit — the final sum gives the remainder.
5.If any intermediate sum is 9 or more, carry over to the previous digit.

Examples

1234 ÷ 9

Step 1 / 7

Divide 1234 by 9. Write out the digits of 1234.

Digit 11

Digit 22

Digit 33

Digit 44

Try It Yourself

2345 ÷ 9

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