Solve 21-1/81*1/3/1-frac{1{3}}

$$\frac { 21 - \frac { 1 } { 81 } \cdot \frac { 1 } { 3 } } { 1 - \frac { 1 } { 3 } }$$

Evaluate

$$\frac{2551}{81}\approx 31.49382716$$

Solution Steps

Multiply \frac{1}{81} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21-\frac{1\times 1}{81\times 3}}{1-\frac{1}{3}}$$

Do the multiplications in the fraction \frac{1\times 1}{81\times 3}.

$$\frac{21-\frac{1}{243}}{1-\frac{1}{3}}$$

Convert 21 to fraction \frac{5103}{243}.

$$\frac{\frac{5103}{243}-\frac{1}{243}}{1-\frac{1}{3}}$$

Since \frac{5103}{243} and \frac{1}{243} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5103-1}{243}}{1-\frac{1}{3}}$$

Subtract 1 from 5103 to get 5102.

$$\frac{\frac{5102}{243}}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{5102}{243}}{\frac{3}{3}-\frac{1}{3}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5102}{243}}{\frac{3-1}{3}}$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{5102}{243}}{\frac{2}{3}}$$

Divide \frac{5102}{243} by \frac{2}{3} by multiplying \frac{5102}{243} by the reciprocal of \frac{2}{3}.

$$\frac{5102}{243}\times \frac{3}{2}$$

Multiply \frac{5102}{243} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5102\times 3}{243\times 2}$$

Do the multiplications in the fraction \frac{5102\times 3}{243\times 2}.

$$\frac{15306}{486}$$

Reduce the fraction \frac{15306}{486} to lowest terms by extracting and canceling out 6.

$$\frac{2551}{81}$$

Factor

$$\frac{2551}{3 ^ {4}} = 31\frac{40}{81} = 31.493827160493826$$