Solve 1/9*3/2/1-frac{1{10}}

$$\frac{ \frac{ 1 }{ 9 } \times \frac{ 3 }{ 2 } }{ 1- \frac{ 1 }{ 10 } }$$

Evaluate

$$\frac{5}{27}\approx 0.185185185$$

Solution Steps

Multiply \frac{1}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 3}{9\times 2}}{1-\frac{1}{10}}$$

Do the multiplications in the fraction \frac{1\times 3}{9\times 2}.

$$\frac{\frac{3}{18}}{1-\frac{1}{10}}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{6}}{1-\frac{1}{10}}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{1}{6}}{\frac{10}{10}-\frac{1}{10}}$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{6}}{\frac{10-1}{10}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{1}{6}}{\frac{9}{10}}$$

Divide \frac{1}{6} by \frac{9}{10} by multiplying \frac{1}{6} by the reciprocal of \frac{9}{10}.

$$\frac{1}{6}\times \frac{10}{9}$$

Multiply \frac{1}{6} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 10}{6\times 9}$$

Do the multiplications in the fraction \frac{1\times 10}{6\times 9}.

$$\frac{10}{54}$$

Reduce the fraction \frac{10}{54} to lowest terms by extracting and canceling out 2.

$$\frac{5}{27}$$

Factor

$$\frac{5}{3 ^ {3}} = 0.18518518518518517$$