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

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

Evaluate

$$\frac{7\sqrt{2}}{10}\approx 0.989949494$$

Short Solution Steps

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

$$\frac{3\sqrt{2}}{5\times 2}-\left(-\frac{4}{5}\times \frac{\sqrt{2}}{2}\right)$$

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

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

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\times 2 and 5 is 2\times 5. Multiply \frac{-2\sqrt{2}}{5} times \frac{2}{2}.

$$\frac{3\sqrt{2}}{2\times 5}-\frac{2\left(-2\right)\sqrt{2}}{2\times 5}$$

Since \frac{3\sqrt{2}}{2\times 5} and \frac{2\left(-2\right)\sqrt{2}}{2\times 5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\sqrt{2}-2\left(-2\right)\sqrt{2}}{2\times 5}$$

Do the multiplications in 3\sqrt{2}-2\left(-2\right)\sqrt{2}.

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

Do the calculations in 3\sqrt{2}+4\sqrt{2}.

$$\frac{7\sqrt{2}}{2\times 5}$$

Expand 2\times 5.

$$\frac{7\sqrt{2}}{10}$$