Solve 8/3:2/frac{1{2}:3/2}:(9*15/2):frac{1}{3}

$$\frac { \frac { 8 } { 3 } : 2 } { \frac { 1 } { 2 } : \frac { 3 } { 2 } } : ( 9 \cdot \frac { 15 } { 2 } ) : \frac { 1 } { 3 }$$

Evaluate

$$\frac{8}{45}\approx 0.177777778$$

Solution Steps

Divide \frac{\frac{\frac{\frac{8}{3}}{2}}{\frac{\frac{1}{2}}{\frac{3}{2}}}}{9\times \frac{15}{2}} by \frac{1}{3} by multiplying \frac{\frac{\frac{\frac{8}{3}}{2}}{\frac{\frac{1}{2}}{\frac{3}{2}}}}{9\times \frac{15}{2}} by the reciprocal of \frac{1}{3}.

$$\frac{\frac{\frac{\frac{8}{3}}{2}}{\frac{\frac{1}{2}}{\frac{3}{2}}}\times 3}{9\times \frac{15}{2}}$$

Divide \frac{\frac{8}{3}}{2} by \frac{\frac{1}{2}}{\frac{3}{2}} by multiplying \frac{\frac{8}{3}}{2} by the reciprocal of \frac{\frac{1}{2}}{\frac{3}{2}}.

$$\frac{\frac{\frac{8}{3}\times \frac{3}{2}}{2\times \frac{1}{2}}\times 3}{9\times \frac{15}{2}}$$

Multiply \frac{8}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{8\times 3}{3\times 2}}{2\times \frac{1}{2}}\times 3}{9\times \frac{15}{2}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{\frac{8}{2}}{2\times \frac{1}{2}}\times 3}{9\times \frac{15}{2}}$$

Divide 8 by 2 to get 4.

$$\frac{\frac{4}{2\times \frac{1}{2}}\times 3}{9\times \frac{15}{2}}$$

Cancel out 2 and 2.

$$\frac{\frac{4}{1}\times 3}{9\times \frac{15}{2}}$$

Anything divided by one gives itself.

$$\frac{4\times 3}{9\times \frac{15}{2}}$$

Multiply 4 and 3 to get 12.

$$\frac{12}{9\times \frac{15}{2}}$$

Express 9\times \frac{15}{2} as a single fraction.

$$\frac{12}{\frac{9\times 15}{2}}$$

Multiply 9 and 15 to get 135.

$$\frac{12}{\frac{135}{2}}$$

Divide 12 by \frac{135}{2} by multiplying 12 by the reciprocal of \frac{135}{2}.

$$12\times \frac{2}{135}$$

Express 12\times \frac{2}{135} as a single fraction.

$$\frac{12\times 2}{135}$$

Multiply 12 and 2 to get 24.

$$\frac{24}{135}$$

Reduce the fraction \frac{24}{135} to lowest terms by extracting and canceling out 3.

$$\frac{8}{45}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2} \cdot 5} = 0.17777777777777778$$