Solve 5/6div[4/5div(-1-1/3)]

$$\frac { 5 } { 6 } \div [ \frac { 4 } { 5 } \div ( - 1 - \frac { 1 } { 3 } ) ]$$

Evaluate

$$-\frac{25}{18}\approx -1.388888889$$

Solution Steps

Divide \frac{5}{6} by \frac{\frac{4}{5}}{-1-\frac{1}{3}} by multiplying \frac{5}{6} by the reciprocal of \frac{\frac{4}{5}}{-1-\frac{1}{3}}.

$$\frac{5\left(-1-\frac{1}{3}\right)}{6\times \frac{4}{5}}$$

Convert -1 to fraction -\frac{3}{3}.

$$\frac{5\left(-\frac{3}{3}-\frac{1}{3}\right)}{6\times \frac{4}{5}}$$

Since -\frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times \frac{-3-1}{3}}{6\times \frac{4}{5}}$$

Subtract 1 from -3 to get -4.

$$\frac{5\left(-\frac{4}{3}\right)}{6\times \frac{4}{5}}$$

Express 5\left(-\frac{4}{3}\right) as a single fraction.

$$\frac{\frac{5\left(-4\right)}{3}}{6\times \frac{4}{5}}$$

Multiply 5 and -4 to get -20.

$$\frac{\frac{-20}{3}}{6\times \frac{4}{5}}$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$\frac{-\frac{20}{3}}{6\times \frac{4}{5}}$$

Express 6\times \frac{4}{5} as a single fraction.

$$\frac{-\frac{20}{3}}{\frac{6\times 4}{5}}$$

Multiply 6 and 4 to get 24.

$$\frac{-\frac{20}{3}}{\frac{24}{5}}$$

Divide -\frac{20}{3} by \frac{24}{5} by multiplying -\frac{20}{3} by the reciprocal of \frac{24}{5}.

$$-\frac{20}{3}\times \frac{5}{24}$$

Multiply -\frac{20}{3} times \frac{5}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-20\times 5}{3\times 24}$$

Do the multiplications in the fraction \frac{-20\times 5}{3\times 24}.

$$\frac{-100}{72}$$

Reduce the fraction \frac{-100}{72} to lowest terms by extracting and canceling out 4.

$$-\frac{25}{18}$$

Factor

$$-\frac{25}{18} = -1\frac{7}{18} = -1.3888888888888888$$