Solve (27)5/3div(125)-4/3*(9)-3/2

$$(27) \frac{ 5 }{ 3 } \div (125) \frac{ -4 }{ 3 } \times (9) \frac{ -3 }{ 2 }$$

Evaluate

$$\frac{162}{25}=6.48$$

Solution Steps

Express 27\times \frac{5}{3} as a single fraction.

$$\frac{\frac{27\times 5}{3}}{125}\times \frac{-4}{3}\times 9\times \frac{-3}{2}$$

Multiply 27 and 5 to get 135.

$$\frac{\frac{135}{3}}{125}\times \frac{-4}{3}\times 9\times \frac{-3}{2}$$

Divide 135 by 3 to get 45.

$$\frac{45}{125}\times \frac{-4}{3}\times 9\times \frac{-3}{2}$$

Reduce the fraction \frac{45}{125} to lowest terms by extracting and canceling out 5.

$$\frac{9}{25}\times \frac{-4}{3}\times 9\times \frac{-3}{2}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{9}{25}\left(-\frac{4}{3}\right)\times 9\times \frac{-3}{2}$$

Multiply \frac{9}{25} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-4\right)}{25\times 3}\times 9\times \frac{-3}{2}$$

Do the multiplications in the fraction \frac{9\left(-4\right)}{25\times 3}.

$$\frac{-36}{75}\times 9\times \frac{-3}{2}$$

Reduce the fraction \frac{-36}{75} to lowest terms by extracting and canceling out 3.

$$-\frac{12}{25}\times 9\times \frac{-3}{2}$$

Express -\frac{12}{25}\times 9 as a single fraction.

$$\frac{-12\times 9}{25}\times \frac{-3}{2}$$

Multiply -12 and 9 to get -108.

$$\frac{-108}{25}\times \frac{-3}{2}$$

Fraction \frac{-108}{25} can be rewritten as -\frac{108}{25} by extracting the negative sign.

$$-\frac{108}{25}\times \frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$-\frac{108}{25}\left(-\frac{3}{2}\right)$$

Multiply -\frac{108}{25} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-108\left(-3\right)}{25\times 2}$$

Do the multiplications in the fraction \frac{-108\left(-3\right)}{25\times 2}.

$$\frac{324}{50}$$

Reduce the fraction \frac{324}{50} to lowest terms by extracting and canceling out 2.

$$\frac{162}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {4}}{5 ^ {2}} = 6\frac{12}{25} = 6.48$$