Solve 3/10-11/2*1/6/frac{2{5}:(-1frac{1}{3})}

$$\frac { \frac { 3 } { 10 } - 1 \frac { 1 } { 2 } \cdot \frac { 1 } { 6 } } { \frac { 2 } { 5 } : ( - 1 \frac { 1 } { 3 } ) }$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{\frac{3}{10}-\frac{2+1}{2}\times \frac{1}{6}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{10}-\frac{3}{2}\times \frac{1}{6}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Multiply \frac{3}{2} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{10}-\frac{3\times 1}{2\times 6}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 6}.

$$\frac{\frac{3}{10}-\frac{3}{12}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{10}-\frac{1}{4}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Least common multiple of 10 and 4 is 20. Convert \frac{3}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{6}{20}-\frac{5}{20}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Since \frac{6}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6-5}{20}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{1}{20}}{\frac{\frac{2}{5}}{-\frac{1\times 3+1}{3}}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{1}{20}}{\frac{\frac{2}{5}}{-\frac{3+1}{3}}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{1}{20}}{\frac{\frac{2}{5}}{-\frac{4}{3}}}$$

Divide \frac{2}{5} by -\frac{4}{3} by multiplying \frac{2}{5} by the reciprocal of -\frac{4}{3}.

$$\frac{\frac{1}{20}}{\frac{2}{5}\left(-\frac{3}{4}\right)}$$

Multiply \frac{2}{5} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{20}}{\frac{2\left(-3\right)}{5\times 4}}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 4}.

$$\frac{\frac{1}{20}}{\frac{-6}{20}}$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{20}}{-\frac{3}{10}}$$

Divide \frac{1}{20} by -\frac{3}{10} by multiplying \frac{1}{20} by the reciprocal of -\frac{3}{10}.

$$\frac{1}{20}\left(-\frac{10}{3}\right)$$

Multiply \frac{1}{20} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-10\right)}{20\times 3}$$

Do the multiplications in the fraction \frac{1\left(-10\right)}{20\times 3}.

$$\frac{-10}{60}$$

Reduce the fraction \frac{-10}{60} to lowest terms by extracting and canceling out 10.

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

Factor

$$-\frac{1}{6} = -0.16666666666666666$$