Nine-Nine Algorithms Twenty-One?

To reduce a value by seven-tenths: multiply by fourteen and divide by twenty. In the previous page, the author established a system of "doubling" the ratio for ease of use on a counting board. Here, $\frac{14}{20}$ is used to represent $\frac{7}{10}$.
To reduce by eight-tenths: multiply by sixteen and divide by twenty.
To reduce by nine-tenths: multiply by eighteen and divide by twenty.

To reduce by one-ninth|original: 九分減一; jiǔ fēn jiǎn yī: multiply by two and divide by eighteen. The text shifts from tenths to specific unit fractions. Multiplying by $\frac{2}{18}$ is mathematically equivalent to $\frac{1}{9}$.
To reduce by one-eighth: multiply by two and divide by sixteen.
To reduce by one-seventh: multiply by two and divide by fourteen.
To reduce by one-sixth: multiply by two and divide by twelve.
To reduce by one-fifth: multiply by two and divide by ten.

Nine times nine is eighty-one. What is the result if this number is multiplied by itself|original: 自相乘; zì xiāng chéng? This asks for the square of 81 ($81^2$).

The answer is: Six thousand five hundred and sixty-one.