Solve frac{1/sqrt{2}}{2}+2/1-5/2

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

Evaluate

$$\frac{\sqrt{2}-2}{4}\approx -0.146446609$$

Solution Steps

Express \frac{\frac{1}{\sqrt{2}}}{2} as a single fraction.

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

Rationalize the denominator of \frac{1}{\sqrt{2}\times 2} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

Anything divided by one gives itself.

$$\frac{\sqrt{2}}{4}+2-\frac{5}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\sqrt{2}}{4}+\frac{4}{2}-\frac{5}{2}$$

Since \frac{4}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}}{4}+\frac{4-5}{2}$$

Subtract 5 from 4 to get -1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$\frac{\sqrt{2}}{4}-\frac{2}{4}$$

Since \frac{\sqrt{2}}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{2}-2}{4}$$

Factor

$$\frac{\sqrt{2} - 2}{4} = -0.1464466094067262$$