Solve (1/2+1/3-1/6)^3+2/3*frac{4}{5}

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 6 } ) ^ { 3 } + \frac { 2 } { 3 } \times \frac { 4 } { 5 }$$

Evaluate

$$\frac{112}{135}\approx 0.82962963$$

Solution Steps

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$\left(\frac{5}{6}-\frac{1}{6}\right)^{3}+\frac{2}{3}\times \frac{4}{5}$$

Subtract \frac{1}{6} from \frac{5}{6} to get \frac{2}{3}.

$$\left(\frac{2}{3}\right)^{3}+\frac{2}{3}\times \frac{4}{5}$$

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{8}{27}+\frac{2}{3}\times \frac{4}{5}$$

Multiply \frac{2}{3} and \frac{4}{5} to get \frac{8}{15}.

$$\frac{8}{27}+\frac{8}{15}$$

Add \frac{8}{27} and \frac{8}{15} to get \frac{112}{135}.

$$\frac{112}{135}$$

Factor

$$\frac{2 ^ {4} \cdot 7}{3 ^ {3} \cdot 5} = 0.8296296296296296$$