Solve T-(2/10)(1/10)+(1/10)^2/(frac{2{10})^2-(frac{1}{10})}

$$T - \frac { ( \frac { 2 } { 10 } ) ( \frac { 1 } { 10 } ) + ( \frac { 1 } { 10 } ) ^ { 2 } } { ( \frac { 2 } { 10 } ) ^ { 2 } - ( \frac { 1 } { 10 } ) }$$

Evaluate

$$T = \frac{1}{2} = 0.5$$

Solution Steps

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$T-\frac{\frac{1}{5}\times \frac{1}{10}+\left(\frac{1}{10}\right)^{2}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Multiply \frac{1}{5} and \frac{1}{10} to get \frac{1}{50}.

$$T-\frac{\frac{1}{50}+\left(\frac{1}{10}\right)^{2}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Calculate \frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$T-\frac{\frac{1}{50}+\frac{1}{100}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Add \frac{1}{50} and \frac{1}{100} to get \frac{3}{100}.

$$T-\frac{\frac{3}{100}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$T-\frac{\frac{3}{100}}{\left(\frac{1}{5}\right)^{2}-\frac{1}{10}}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$T-\frac{\frac{3}{100}}{\frac{1}{25}-\frac{1}{10}}$$

Subtract \frac{1}{10} from \frac{1}{25} to get -\frac{3}{50}.

$$T-\frac{\frac{3}{100}}{-\frac{3}{50}}$$

Divide \frac{3}{100} by -\frac{3}{50} by multiplying \frac{3}{100} by the reciprocal of -\frac{3}{50}.

$$T-\frac{3}{100}\left(-\frac{50}{3}\right)$$

Multiply \frac{3}{100} and -\frac{50}{3} to get -\frac{1}{2}.

$$T-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$T+\frac{1}{2}$$

Expand

$$T = \frac{1}{2} = 0.5$$

Solution Steps

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$T-\frac{\frac{1}{5}\times \frac{1}{10}+\left(\frac{1}{10}\right)^{2}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Multiply \frac{1}{5} and \frac{1}{10} to get \frac{1}{50}.

$$T-\frac{\frac{1}{50}+\left(\frac{1}{10}\right)^{2}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Calculate \frac{1}{10} to the power of 2 and get \frac{1}{100}.

$$T-\frac{\frac{1}{50}+\frac{1}{100}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Add \frac{1}{50} and \frac{1}{100} to get \frac{3}{100}.

$$T-\frac{\frac{3}{100}}{\left(\frac{2}{10}\right)^{2}-\frac{1}{10}}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$T-\frac{\frac{3}{100}}{\left(\frac{1}{5}\right)^{2}-\frac{1}{10}}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$T-\frac{\frac{3}{100}}{\frac{1}{25}-\frac{1}{10}}$$

Subtract \frac{1}{10} from \frac{1}{25} to get -\frac{3}{50}.

$$T-\frac{\frac{3}{100}}{-\frac{3}{50}}$$

Divide \frac{3}{100} by -\frac{3}{50} by multiplying \frac{3}{100} by the reciprocal of -\frac{3}{50}.

$$T-\frac{3}{100}\left(-\frac{50}{3}\right)$$

Multiply \frac{3}{100} and -\frac{50}{3} to get -\frac{1}{2}.

$$T-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$T+\frac{1}{2}$$