Solve 1/2+3/2div(1-2/3)^2-1

$$\frac { 1 } { 2 } + \frac { 3 } { 2 } \div ( 1 - \frac { 2 } { 3 } ) ^ { 2 } - 1$$

Evaluate

$$13$$

Solution Steps

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

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

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{2}+\frac{\frac{3}{2}}{\frac{1}{9}}-1$$

Divide \frac{3}{2} by \frac{1}{9} by multiplying \frac{3}{2} by the reciprocal of \frac{1}{9}.

$$\frac{1}{2}+\frac{3}{2}\times 9-1$$

Multiply \frac{3}{2} and 9 to get \frac{27}{2}.

$$\frac{1}{2}+\frac{27}{2}-1$$

Add \frac{1}{2} and \frac{27}{2} to get 14.

$$14-1$$

Subtract 1 from 14 to get 13.

$$13$$

Factor

$$13$$