Solve (2/3)^-1+2/5-(3/4)^-1*(8/9)^-1

$$( \frac { 2 } { 3 } ) ^ { - 1 } + \frac { 2 } { 5 } - ( \frac { 3 } { 4 } ) ^ { - 1 } \cdot ( \frac { 8 } { 9 } ) ^ { - 1 }$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Calculate \frac{2}{3} to the power of -1 and get \frac{3}{2}.

$$\frac{3}{2}+\frac{2}{5}-\left(\frac{3}{4}\right)^{-1}\times \left(\frac{8}{9}\right)^{-1}$$

Add \frac{3}{2} and \frac{2}{5} to get \frac{19}{10}.

$$\frac{19}{10}-\left(\frac{3}{4}\right)^{-1}\times \left(\frac{8}{9}\right)^{-1}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{19}{10}-\frac{4}{3}\times \left(\frac{8}{9}\right)^{-1}$$

Calculate \frac{8}{9} to the power of -1 and get \frac{9}{8}.

$$\frac{19}{10}-\frac{4}{3}\times \frac{9}{8}$$

Multiply \frac{4}{3} and \frac{9}{8} to get \frac{3}{2}.

$$\frac{19}{10}-\frac{3}{2}$$

Subtract \frac{3}{2} from \frac{19}{10} to get \frac{2}{5}.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$