Solve [(3/6-1/3)*(4/6+frac{1/3)^-1}{(frac{3}{4}+frac{1}{3}-frac{1}{6}+frac{1}{3})^-1}]=

$$[ \frac { ( \frac { 3 } { 6 } - \frac { 1 } { 3 } ) \cdot ( \frac { 4 } { 6 } + \frac { 1 } { 3 } ) ^ { - 1 } } { ( \frac { 3 } { 4 } + \frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 3 } ) ^ { - 1 } } ] =$$

Evaluate

$$\frac{5}{24}\approx 0.208333333$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{4}{6}+\frac{1}{3}\right)^{-1}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

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

$$\frac{\frac{1}{6}\left(\frac{4}{6}+\frac{1}{3}\right)^{-1}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{6}\left(\frac{2}{3}+\frac{1}{3}\right)^{-1}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

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

$$\frac{\frac{1}{6}\times 1^{-1}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Calculate 1 to the power of -1 and get 1.

$$\frac{\frac{1}{6}\times 1}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Multiply \frac{1}{6} and 1 to get \frac{1}{6}.

$$\frac{\frac{1}{6}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Add \frac{3}{4} and \frac{1}{3} to get \frac{13}{12}.

$$\frac{\frac{1}{6}}{\left(\frac{13}{12}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Subtract \frac{1}{6} from \frac{13}{12} to get \frac{11}{12}.

$$\frac{\frac{1}{6}}{\left(\frac{11}{12}+\frac{1}{3}\right)^{-1}}$$

Add \frac{11}{12} and \frac{1}{3} to get \frac{5}{4}.

$$\frac{\frac{1}{6}}{\left(\frac{5}{4}\right)^{-1}}$$

Calculate \frac{5}{4} to the power of -1 and get \frac{4}{5}.

$$\frac{\frac{1}{6}}{\frac{4}{5}}$$

Divide \frac{1}{6} by \frac{4}{5} by multiplying \frac{1}{6} by the reciprocal of \frac{4}{5}.

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

Multiply \frac{1}{6} and \frac{5}{4} to get \frac{5}{24}.

$$\frac{5}{24}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 3} = 0.20833333333333334$$