Solve 1/2*20/25-1/2*frac{2sqrt{5}}{5}-1

$$\frac { 1 } { 2 } \times \frac { 20 } { 25 } - \frac { 1 } { 2 } \times \frac { 2 \sqrt { 5 } } { 5 } - 1$$

Evaluate

$$\frac{-\sqrt{5}-3}{5}\approx -1.047213595$$

Short Solution Steps

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}\times \frac{4}{5}-\frac{1}{2}\times \frac{2\sqrt{5}}{5}-1$$

Multiply \frac{1}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 5}-\frac{1}{2}\times \frac{2\sqrt{5}}{5}-1$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 5}.

$$\frac{4}{10}-\frac{1}{2}\times \frac{2\sqrt{5}}{5}-1$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}-\frac{1}{2}\times \frac{2\sqrt{5}}{5}-1$$

Multiply \frac{1}{2} times \frac{2\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{2\sqrt{5}}{2\times 5}-1$$

Cancel out 2 in both numerator and denominator.

$$\frac{2}{5}-\frac{\sqrt{5}}{5}-1$$

Since \frac{2}{5} and \frac{\sqrt{5}}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+\sqrt{5}}{5}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{5}{5}.

$$\frac{2+\sqrt{5}}{5}-\frac{5}{5}$$

Since \frac{2+\sqrt{5}}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2+\sqrt{5}-5}{5}$$

Do the calculations in 2+\sqrt{5}-5.

$$\frac{-3+\sqrt{5}}{5}$$

Factor

$$\frac{-\sqrt{5} - 3}{5} = -1.047213595499958$$