Solve 2/31/4left(-5/4div-3/2right)frac{4}{5}frac{1}{2}frac{8}{5}

$$\frac{ 2 }{ 3 } \frac{ 1 }{ 4 } \left( - \frac{ 5 }{ 4 } \div \frac{ -3 }{ 2 } \right) \frac{ 4 }{ 5 } \frac{ 1 }{ 2 } \frac{ 8 }{ 5 }$$

Evaluate

$$\frac{4}{45}\approx 0.088888889$$

Solution Steps

Multiply \frac{2}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{3\times 4}\times \frac{-\frac{5}{4}}{\frac{-3}{2}}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 4}.

$$\frac{2}{12}\times \frac{-\frac{5}{4}}{\frac{-3}{2}}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}\times \frac{-\frac{5}{4}}{\frac{-3}{2}}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

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

$$\frac{1}{6}\times \frac{-5\times 2}{4\left(-3\right)}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{6}\times \frac{-5}{-3\times 2}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Multiply -3 and 2 to get -6.

$$\frac{1}{6}\times \frac{-5}{-6}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.

$$\frac{1}{6}\times \frac{5}{6}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

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

$$\frac{1\times 5}{6\times 6}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

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

$$\frac{5}{36}\times \frac{4}{5}\times \frac{1}{2}\times \frac{8}{5}$$

Multiply \frac{5}{36} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{36\times 5}\times \frac{1}{2}\times \frac{8}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{36}\times \frac{1}{2}\times \frac{8}{5}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{1}{9}\times \frac{1}{2}\times \frac{8}{5}$$

Multiply \frac{1}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{9\times 2}\times \frac{8}{5}$$

Do the multiplications in the fraction \frac{1\times 1}{9\times 2}.

$$\frac{1}{18}\times \frac{8}{5}$$

Multiply \frac{1}{18} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{18\times 5}$$

Do the multiplications in the fraction \frac{1\times 8}{18\times 5}.

$$\frac{8}{90}$$

Reduce the fraction \frac{8}{90} to lowest terms by extracting and canceling out 2.

$$\frac{4}{45}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2} \cdot 5} = 0.08888888888888889$$