Solve 5/-6*22/3div(-7/8)

$$\frac { 5 } { - 6 } \times 2 \frac { 2 } { 3 } \div ( \frac { - 7 } { 8 } )$$

Evaluate

$$\frac{160}{63}\approx 2.53968254$$

Solution Steps

Fraction \frac{5}{-6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{-\frac{5}{6}\times \frac{2\times 3+2}{3}}{\frac{-7}{8}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{5}{6}\times \frac{6+2}{3}}{\frac{-7}{8}}$$

Add 6 and 2 to get 8.

$$\frac{-\frac{5}{6}\times \frac{8}{3}}{\frac{-7}{8}}$$

Multiply -\frac{5}{6} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-5\times 8}{6\times 3}}{\frac{-7}{8}}$$

Do the multiplications in the fraction \frac{-5\times 8}{6\times 3}.

$$\frac{\frac{-40}{18}}{\frac{-7}{8}}$$

Reduce the fraction \frac{-40}{18} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{20}{9}}{\frac{-7}{8}}$$

Fraction \frac{-7}{8} can be rewritten as -\frac{7}{8} by extracting the negative sign.

$$\frac{-\frac{20}{9}}{-\frac{7}{8}}$$

Divide -\frac{20}{9} by -\frac{7}{8} by multiplying -\frac{20}{9} by the reciprocal of -\frac{7}{8}.

$$-\frac{20}{9}\left(-\frac{8}{7}\right)$$

Multiply -\frac{20}{9} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-20\left(-8\right)}{9\times 7}$$

Do the multiplications in the fraction \frac{-20\left(-8\right)}{9\times 7}.

$$\frac{160}{63}$$

Factor

$$\frac{2 ^ {5} \cdot 5}{3 ^ {2} \cdot 7} = 2\frac{34}{63} = 2.5396825396825395$$