Solve [(1/2+3/4-1/10)*4/3-1]^-1

$$[ ( \frac { 1 } { 2 } + \frac { 3 } { 4 } - \frac { 1 } { 10 } ) \times \frac { 4 } { 3 } - 1 ] ^ { - 1 }$$

Evaluate

$$\frac{15}{8}=1.875$$

Solution Steps

Add \frac{1}{2} and \frac{3}{4} to get \frac{5}{4}.

$$\left(\left(\frac{5}{4}-\frac{1}{10}\right)\times \frac{4}{3}-1\right)^{-1}$$

Subtract \frac{1}{10} from \frac{5}{4} to get \frac{23}{20}.

$$\left(\frac{23}{20}\times \frac{4}{3}-1\right)^{-1}$$

Multiply \frac{23}{20} and \frac{4}{3} to get \frac{23}{15}.

$$\left(\frac{23}{15}-1\right)^{-1}$$

Subtract 1 from \frac{23}{15} to get \frac{8}{15}.

$$\left(\frac{8}{15}\right)^{-1}$$

Calculate \frac{8}{15} to the power of -1 and get \frac{15}{8}.

$$\frac{15}{8}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1.875$$