Solve 4/5*frac{sqrt{2}}{2}-3/5*frac{sqrt{2}}{2}

$$\frac{ 4 }{ 5 } \times \frac{ \sqrt{ 2 } }{ 2 } - \frac{ 3 }{ 5 } \times \frac{ \sqrt{ 2 } }{ 2 }$$

Evaluate

$$\frac{\sqrt{2}}{10}\approx 0.141421356$$

Solution Steps

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

$$\frac{4\sqrt{2}}{5\times 2}-\frac{3}{5}\times \frac{\sqrt{2}}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\sqrt{2}}{5}-\frac{3}{5}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{3}{5} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\sqrt{2}}{5}-\frac{3\sqrt{2}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{2\sqrt{2}}{5}-\frac{3\sqrt{2}}{10}$$

Combine \frac{2\sqrt{2}}{5} and -\frac{3\sqrt{2}}{10} to get \frac{1}{10}\sqrt{2}.

$$\frac{1}{10}\sqrt{2}$$