Solve 1/5*[1/3div(1/2+5/6)]

$$\frac { 1 } { 5 } \times [ \frac { 1 } { 3 } \div ( \frac { 1 } { 2 } + \frac { 5 } { 6 } ) ]$$

Evaluate

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

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{1}{5}\times \frac{\frac{1}{3}}{\frac{3}{6}+\frac{5}{6}}$$

Since \frac{3}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}\times \frac{\frac{1}{3}}{\frac{3+5}{6}}$$

Add 3 and 5 to get 8.

$$\frac{1}{5}\times \frac{\frac{1}{3}}{\frac{8}{6}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}\times \frac{\frac{1}{3}}{\frac{4}{3}}$$

Divide \frac{1}{3} by \frac{4}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{4}{3}.

$$\frac{1}{5}\times \frac{1}{3}\times \frac{3}{4}$$

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}\times \frac{1\times 3}{3\times 4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{5}\times \frac{1}{4}$$

Multiply \frac{1}{5} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{5\times 4}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 4}.

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

Factor

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