Solve -(3/5*1/6+5/6)+frac{1/2}{frac{-13}{6}}

$$\frac { - ( \frac { 3 } { 5 } \cdot \frac { 1 } { 6 } + \frac { 5 } { 6 } ) + \frac { 1 } { 2 } } { \frac { - 13 } { 6 } }$$

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

Multiply \frac{3}{5} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(\frac{3\times 1}{5\times 6}+\frac{5}{6}\right)+\frac{1}{2}}{\frac{-13}{6}}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 6}.

$$\frac{-\left(\frac{3}{30}+\frac{5}{6}\right)+\frac{1}{2}}{\frac{-13}{6}}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{-\left(\frac{1}{10}+\frac{5}{6}\right)+\frac{1}{2}}{\frac{-13}{6}}$$

Least common multiple of 10 and 6 is 30. Convert \frac{1}{10} and \frac{5}{6} to fractions with denominator 30.

$$\frac{-\left(\frac{3}{30}+\frac{25}{30}\right)+\frac{1}{2}}{\frac{-13}{6}}$$

Since \frac{3}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{3+25}{30}+\frac{1}{2}}{\frac{-13}{6}}$$

Add 3 and 25 to get 28.

$$\frac{-\frac{28}{30}+\frac{1}{2}}{\frac{-13}{6}}$$

Reduce the fraction \frac{28}{30} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{14}{15}+\frac{1}{2}}{\frac{-13}{6}}$$

Least common multiple of 15 and 2 is 30. Convert -\frac{14}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{-\frac{28}{30}+\frac{15}{30}}{\frac{-13}{6}}$$

Since -\frac{28}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-28+15}{30}}{\frac{-13}{6}}$$

Add -28 and 15 to get -13.

$$\frac{-\frac{13}{30}}{\frac{-13}{6}}$$

Fraction \frac{-13}{6} can be rewritten as -\frac{13}{6} by extracting the negative sign.

$$\frac{-\frac{13}{30}}{-\frac{13}{6}}$$

Divide -\frac{13}{30} by -\frac{13}{6} by multiplying -\frac{13}{30} by the reciprocal of -\frac{13}{6}.

$$-\frac{13}{30}\left(-\frac{6}{13}\right)$$

Multiply -\frac{13}{30} times -\frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\left(-6\right)}{30\times 13}$$

Do the multiplications in the fraction \frac{-13\left(-6\right)}{30\times 13}.

$$\frac{78}{390}$$

Reduce the fraction \frac{78}{390} to lowest terms by extracting and canceling out 78.

$$\frac{1}{5}$$

Factor

$$\frac{1}{5} = 0.2$$