Solve 1/2-3/5:3/frac{1{6}-2/3}:frac{-1+frac{1}{3}}{(2-frac{1}{3})^3}

$$\frac { \frac { 1 } { 2 } - \frac { 3 } { 5 } : 3 } { \frac { 1 } { 6 } - \frac { 2 } { 3 } } : \frac { - 1 + \frac { 1 } { 3 } } { ( 2 - \frac { 1 } { 3 } ) ^ { 3 } }$$

Evaluate

$$\frac{25}{6}\approx 4.166666667$$

Solution Steps

Divide \frac{\frac{1}{2}-\frac{\frac{3}{5}}{3}}{\frac{1}{6}-\frac{2}{3}} by \frac{-1+\frac{1}{3}}{\left(2-\frac{1}{3}\right)^{3}} by multiplying \frac{\frac{1}{2}-\frac{\frac{3}{5}}{3}}{\frac{1}{6}-\frac{2}{3}} by the reciprocal of \frac{-1+\frac{1}{3}}{\left(2-\frac{1}{3}\right)^{3}}.

$$\frac{\left(\frac{1}{2}-\frac{\frac{3}{5}}{3}\right)\left(2-\frac{1}{3}\right)^{3}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

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

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

Cancel out 3 in both numerator and denominator.

$$\frac{\left(\frac{1}{2}-\frac{1}{5}\right)\left(2-\frac{1}{3}\right)^{3}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

Subtract \frac{1}{5} from \frac{1}{2} to get \frac{3}{10}.

$$\frac{\frac{3}{10}\left(2-\frac{1}{3}\right)^{3}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

$$\frac{\frac{3}{10}\times \left(\frac{5}{3}\right)^{3}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

Calculate \frac{5}{3} to the power of 3 and get \frac{125}{27}.

$$\frac{\frac{3}{10}\times \frac{125}{27}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

Multiply \frac{3}{10} and \frac{125}{27} to get \frac{25}{18}.

$$\frac{\frac{25}{18}}{\left(\frac{1}{6}-\frac{2}{3}\right)\left(-1+\frac{1}{3}\right)}$$

Subtract \frac{2}{3} from \frac{1}{6} to get -\frac{1}{2}.

$$\frac{\frac{25}{18}}{-\frac{1}{2}\left(-1+\frac{1}{3}\right)}$$

Add -1 and \frac{1}{3} to get -\frac{2}{3}.

$$\frac{\frac{25}{18}}{-\frac{1}{2}\left(-\frac{2}{3}\right)}$$

Multiply -\frac{1}{2} and -\frac{2}{3} to get \frac{1}{3}.

$$\frac{\frac{25}{18}}{\frac{1}{3}}$$

Divide \frac{25}{18} by \frac{1}{3} by multiplying \frac{25}{18} by the reciprocal of \frac{1}{3}.

$$\frac{25}{18}\times 3$$

Multiply \frac{25}{18} and 3 to get \frac{25}{6}.

$$\frac{25}{6}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$$