Solve (2/3div3/2)/(frac{5{3}*1/2)}

$$\frac { ( \frac { 2 } { 3 } \div \frac { 3 } { 2 } ) } { ( \frac { 5 } { 3 } \times \frac { 1 } { 2 } ) }$$

Evaluate

$$\frac{8}{15}\approx 0.533333333$$

Solution Steps

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

$$\frac{\frac{2}{3}\times \frac{2}{3}}{\frac{5}{3}\times \frac{1}{2}}$$

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

$$\frac{\frac{2\times 2}{3\times 3}}{\frac{5}{3}\times \frac{1}{2}}$$

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

$$\frac{\frac{4}{9}}{\frac{5}{3}\times \frac{1}{2}}$$

Multiply \frac{5}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{9}}{\frac{5\times 1}{3\times 2}}$$

Do the multiplications in the fraction \frac{5\times 1}{3\times 2}.

$$\frac{\frac{4}{9}}{\frac{5}{6}}$$

Divide \frac{4}{9} by \frac{5}{6} by multiplying \frac{4}{9} by the reciprocal of \frac{5}{6}.

$$\frac{4}{9}\times \frac{6}{5}$$

Multiply \frac{4}{9} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 6}{9\times 5}$$

Do the multiplications in the fraction \frac{4\times 6}{9\times 5}.

$$\frac{24}{45}$$

Reduce the fraction \frac{24}{45} to lowest terms by extracting and canceling out 3.

$$\frac{8}{15}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 5} = 0.5333333333333333$$