Solve 1/6/[1/(3/5-3/10)]

$$\frac { 1 } { 6 } / [ 1 / ( \frac { 3 } { 5 } - \frac { 3 } { 10 } ) ]$$

Evaluate

$$\frac{1}{20}=0.05$$

Solution Steps

Divide \frac{1}{6} by \frac{1}{\frac{3}{5}-\frac{3}{10}} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{\frac{3}{5}-\frac{3}{10}}.

$$\frac{\frac{3}{5}-\frac{3}{10}}{6}$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{6}{10}-\frac{3}{10}}{6}$$

Since \frac{6}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-3}{10}}{6}$$

Subtract 3 from 6 to get 3.

$$\frac{\frac{3}{10}}{6}$$

Express \frac{\frac{3}{10}}{6} as a single fraction.

$$\frac{3}{10\times 6}$$

Multiply 10 and 6 to get 60.

$$\frac{3}{60}$$

Reduce the fraction \frac{3}{60} to lowest terms by extracting and canceling out 3.

$$\frac{1}{20}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5} = 0.05$$