Solve 5^-1+(1/2+1/3):13/2+3^-1-(1-2/3)

$$5 ^ { - 1 } + ( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) : \frac { 13 } { 2 } + 3 ^ { - 1 } - ( 1 - \frac { 2 } { 3 } )$$

Evaluate

$$\frac{64}{195}\approx 0.328205128$$

Solution Steps

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

$$\frac{1}{5}+\frac{\frac{1}{2}+\frac{1}{3}}{\frac{13}{2}}+3^{-1}-\left(1-\frac{2}{3}\right)$$

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

$$\frac{1}{5}+\frac{\frac{5}{6}}{\frac{13}{2}}+3^{-1}-\left(1-\frac{2}{3}\right)$$

Divide \frac{5}{6} by \frac{13}{2} by multiplying \frac{5}{6} by the reciprocal of \frac{13}{2}.

$$\frac{1}{5}+\frac{5}{6}\times \frac{2}{13}+3^{-1}-\left(1-\frac{2}{3}\right)$$

Multiply \frac{5}{6} and \frac{2}{13} to get \frac{5}{39}.

$$\frac{1}{5}+\frac{5}{39}+3^{-1}-\left(1-\frac{2}{3}\right)$$

Add \frac{1}{5} and \frac{5}{39} to get \frac{64}{195}.

$$\frac{64}{195}+3^{-1}-\left(1-\frac{2}{3}\right)$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{64}{195}+\frac{1}{3}-\left(1-\frac{2}{3}\right)$$

Add \frac{64}{195} and \frac{1}{3} to get \frac{43}{65}.

$$\frac{43}{65}-\left(1-\frac{2}{3}\right)$$

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

$$\frac{43}{65}-\frac{1}{3}$$

Subtract \frac{1}{3} from \frac{43}{65} to get \frac{64}{195}.

$$\frac{64}{195}$$

Factor

$$\frac{2 ^ {6}}{3 \cdot 5 \cdot 13} = 0.3282051282051282$$