Solve {left(2/5right)}^2-52/5-1/2-3{left(-1/2right)}^2

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

Evaluate

$$\frac{211}{100}=2.11$$

Solution Steps

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}-\frac{5\times 5+2}{5}\times \frac{-1}{2}-3\times \left(\frac{-1}{2}\right)^{2}$$

Multiply 5 and 5 to get 25.

$$\frac{4}{25}-\frac{25+2}{5}\times \frac{-1}{2}-3\times \left(\frac{-1}{2}\right)^{2}$$

Add 25 and 2 to get 27.

$$\frac{4}{25}-\frac{27}{5}\times \frac{-1}{2}-3\times \left(\frac{-1}{2}\right)^{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{4}{25}-\frac{27}{5}\left(-\frac{1}{2}\right)-3\times \left(\frac{-1}{2}\right)^{2}$$

Multiply \frac{27}{5} and -\frac{1}{2} to get -\frac{27}{10}.

$$\frac{4}{25}-\left(-\frac{27}{10}\right)-3\times \left(\frac{-1}{2}\right)^{2}$$

The opposite of -\frac{27}{10} is \frac{27}{10}.

$$\frac{4}{25}+\frac{27}{10}-3\times \left(\frac{-1}{2}\right)^{2}$$

Add \frac{4}{25} and \frac{27}{10} to get \frac{143}{50}.

$$\frac{143}{50}-3\times \left(\frac{-1}{2}\right)^{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{143}{50}-3\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{143}{50}-3\times \frac{1}{4}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{143}{50}-\frac{3}{4}$$

Subtract \frac{3}{4} from \frac{143}{50} to get \frac{211}{100}.

$$\frac{211}{100}$$

Factor

$$\frac{211}{2 ^ {2} \cdot 5 ^ {2}} = 2\frac{11}{100} = 2.11$$