Solve [(2/3-1/9)*13(2/3-1)^2]:[(1/2-1)*2frac{1}{2}]=

$$[ ( \frac { 2 } { 3 } - \frac { 1 } { 9 } ) \cdot 13 ( \frac { 2 } { 3 } - 1 ) ^ { 2 } ] : [ ( \frac { 1 } { 2 } - 1 ) \cdot 2 \frac { 1 } { 2 } ] =$$

Evaluate

$$-\frac{52}{81}\approx -0.641975309$$

Solution Steps

Subtract \frac{1}{9} from \frac{2}{3} to get \frac{5}{9}.

$$\frac{\frac{5}{9}\times 13\left(\frac{2}{3}-1\right)^{2}}{\left(\frac{1}{2}-1\right)\times \frac{2\times 2+1}{2}}$$

Multiply \frac{5}{9} and 13 to get \frac{65}{9}.

$$\frac{\frac{65}{9}\left(\frac{2}{3}-1\right)^{2}}{\left(\frac{1}{2}-1\right)\times \frac{2\times 2+1}{2}}$$

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

$$\frac{\frac{65}{9}\left(-\frac{1}{3}\right)^{2}}{\left(\frac{1}{2}-1\right)\times \frac{2\times 2+1}{2}}$$

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

$$\frac{\frac{65}{9}\times \frac{1}{9}}{\left(\frac{1}{2}-1\right)\times \frac{2\times 2+1}{2}}$$

Multiply \frac{65}{9} and \frac{1}{9} to get \frac{65}{81}.

$$\frac{\frac{65}{81}}{\left(\frac{1}{2}-1\right)\times \frac{2\times 2+1}{2}}$$

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

$$\frac{\frac{65}{81}}{-\frac{1}{2}\times \frac{2\times 2+1}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{65}{81}}{-\frac{1}{2}\times \frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{65}{81}}{-\frac{1}{2}\times \frac{5}{2}}$$

Multiply -\frac{1}{2} and \frac{5}{2} to get -\frac{5}{4}.

$$\frac{\frac{65}{81}}{-\frac{5}{4}}$$

Divide \frac{65}{81} by -\frac{5}{4} by multiplying \frac{65}{81} by the reciprocal of -\frac{5}{4}.

$$\frac{65}{81}\left(-\frac{4}{5}\right)$$

Multiply \frac{65}{81} and -\frac{4}{5} to get -\frac{52}{81}.

$$-\frac{52}{81}$$

Factor

$$-\frac{52}{81} = -0.6419753086419753$$